Research ArticleA Fuzzy-Based Analytic Hierarchy Process for Mechanical NoiseSource Identification of a Diesel Engine

Junhong Zhang12 Qidi Zhou 1 Jiewei Lin 1 Weidong Li1 Zhoujie Tang1

and Chaoyang Duan1

1State Key Laboratory of Engines Tianjin University Tianjin 300072 China2Renai College Tianjin University Tianjin 301636 China

Correspondence should be addressed to Jiewei Lin linjieweitjueducn

Received 23 June 2018 Revised 19 November 2018 Accepted 14 January 2019 Published 10 February 2019

Academic Editor Andrea Spaggiari

Copyright copy 2019 Junhong Zhang et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper a novel fuzzy-based analytic hierarchy process (FAHP) is proposed for identifying noise sources of diesel engine andsorting their contributions+e hierarchy tree consists of 5 levels including the component level the frequency band level the testpoint level the operating condition level and the overall noise level +e variational mode decomposition (VMD) is employed todecompose the overall noise into several frequency bands +e factor weights between levels are determined by the partialcoherence analysis (PCA) to consider the correlation of component vibration and radiated noise in different frequency bands Afuzzy consistency matrix is then constructed to order the corresponding factors level by level that can avoid the consistenceproblem of the traditional AHP Based on the rig test of a diesel engine the proposed approach is implemented to weight the noisesources identified It is shown the overall weighting order of the six major noise sources is (in descending order) the oil pan the leftblock the valve cover the flywheel housing and the right block

1 Introduction

NVH problems are increasingly important in nowadays au-tomobile industry and reduction in engine noise is one of themost concerns A precise recognition of the noise sources andtheir contribution is the first step in interior noise control [1ndash3]

In the noise source identification of the engine signalprocessing-based approach is quite popular these days be-cause of its comprehensive performance in accuracy [4 5]flexibility and cost-saving [6 7] Lots of method have beenproposed such as the cyclic Wiener filtering [8 9] the time-frequency analysis [10ndash12] the blind source separation[13 14] and the coherent spectrum analysis (CSA) [15] Butit is still very difficult for only using one signal processingmethod to perfectly handle the complex noise problem Forthis reason the analytic hierarchy process (AHP) [16 17] hasbeen proved suitable for decision-making of complex sys-tems It has been widely used in social political economicand technological problems with multiple choices In thenoise identification of the diesel engine a great amount offactors should be considered such as frequency engine

speed load and component Besides correlations betweenfactors (eg frequency band and component vibration andvibration between component and radiated noise) haveinfluence on the weighting coefficients of the noise source Inthis situation the AHP could be an effective solution inweighting noise sources of a diesel engine Liang [18] utilizedthe cepstrum analysis and the AHP in weighting the noisecontribution from engine components+e overall noise wasdecomposed into five frequency bands and one operatingspeed was considered Zhang et al [19] proposed a combinedAHP approach to analyse the contribution of differentengine parts to the overall radiated noise in different enginespeeds +e decomposition by ensemble empirical modedecomposition (EEMD) was affected by the modal aliasingproblem in intrinsic mode functions (IMFs) And the co-herent spectrum analysis (CSA) is limited in the case thatmultiple inputs are not independent from each other

On the contrary some limits have been found for thetraditional AHP approach [20 21] (1) the consistency of thejudgment matrix is very costly to achieve (2) preferencesmismatch the objective priority and (3) the uncertainty of

HindawiShock and VibrationVolume 2019 Article ID 2854836 14 pageshttpsdoiorg10115520192854836

subjective evaluation reduces the accuracy To overcome theabove shortages the fuzzy-based AHP (FAHP) [22 23] isdeveloped to take into account the uncertainty in decision-making A fuzzy scale is used to express the preference orrelative importance of the target property instead of adoptingan exact value from pairwise comparison In addition thefuzzy consistency matrix [24ndash27] used in the FAHP can bedetermined by membership functions (MFs) so the consis-tency of the judgment matrix is met automatically [28 29] Itcan be seen that the FAHP is able to improve the traditionalnoise source weighting approach as long as reasonablestructures and components of the hierarchy tree is built

In this paper a novel approach based on the FAHP isproposed to weight the noise sources of the diesel engineBased on a rig test the overall noise is decomposed intoseveral frequency bands using the variational mode de-composition (VMD) +en the correlation between thevibration of engine component and the overall radiatednoise is analysed through partial coherence analysis (PCA)A FAHP is constructed to determine the weights of thecomponent to the overall noise Finally the identificationresults are verified by the near-field noise measurement

2 Methods

21 Variational Mode Decomposition +e VMD algorithm[30] is a self-adaptive signal processing method which candecompose a mixed signal into a number of IMFs +ediscrete subsignals have finite orders of mode with specificsparsity properties for being reconstructed back to theoriginal signal [31] +e constrained variational problem isgiven as follows

minμk wk

1113944k

zt z(t) +j

πt1113874 1113875μk(t)1113876 1113877e

minusjwkt

2

2

⎧⎨

⎩

⎫⎬

⎭

st 1113944k

μk f

(1)

where μk1113864 1113865 μ1 μk1113864 1113865 and ωk1113864 1113865 ω1 ωk1113864 1113865 are themodal components and the corresponding centre fre-quencies 1113936k 1113936

Kk1 is the summation of modes k is the

number of modes and f is the input signal To make theproblem unconstraint it is necessary to bring in the qua-dratic penalty factor α and the Lagrange multiplier λ +equadratic penalty factor is used to improve the high re-construction accuracy in dealing with the Gaussian noise+e Lagrange multiplier can enforce constraints effectivelywhich can be obtained as follows

L μk1113864 1113865 ωk1113864 1113865 λ( 1113857 α1113944k

zt δ(t) +j

πt1113874 1113875μk(t)1113876 1113877e

minusjωkt

2

2

+ x(t)minus 1113944k

μk(t)

2

2

+langλ(t) f(t)minus 1113944k

μk(t)rang

(2)

Using the alternate direction method of multipliersfor the extended Lagrange expression through alternatingoptimization of μk ωk and λ the optimal solution of the

equation can be obtained +e VMD method can beimplemented by the following steps

Step 1 Initialize μ1k1113864 1113865 ω1k1113864 1113865 and λ1 and set n 0

Step 2 Count n n+ 1

Step 3 For k 1 1 k obtain

μn+1k argmin

μk

L μn+1iltk1113966 1113967 μn

igek1113864 1113865 ωni1113864 1113865 λn

1113872 1113873

ωn+1k argmin

ωk

L μn+1i1113966 1113967 μn+1

iltk1113966 1113967 ωnigek1113864 1113865 λn

1113872 1113873

λn+1 λn

+ τ fminus 1113944k

μn+1k

⎛⎝ ⎞⎠

(3)

Step 4 Judge the convergence

1113944k

μn+1k minus μ

nk

22

μnk

22

lt c (4)

where c is the convergence judgment condition +e pro-gram stops if the convergence is met at Step 4 otherwise theiteration circulates from Steps 2 to 4

A simulation signal S S1+ S2+ S3+ S4 is given by thefollowing equation

S1 05 cos(2π middot 6t)

S2 cos(2π middot 20t)

S3 cos(2π middot 50t)

S4 03 cos(2π middot 400 middot t)eminus104times(tminus02)2

+ 04 cos(2π middot 400t)eminus104times(tminus05)2

+ 03 cos(2π middot 400t)eminus104times(tminus08)2

(5)

Figure 1 shows the original components of S1 to S4 andthe decomposed IMFs by VMD It can be seen clearly thatthe simulation signal S is accurately decomposed into fourIMFs and the IMFs represent the characters of originalcomponents exactly

22 Partial Coherence Analysis For a multi-input single-output system with independent inputs CSA is capable toestimate the relationship between input and output effi-ciently [32] while it is not the case in this paper For enginenoise acoustic sources are correlated It is not very ap-propriate to use CSA because wrong correlation between theradiated noise and the component vibration may be broughtin To avoid this the PCA is applied because it can removethe coherence of other inputs from the target So thecorrelations between inputs and outputs can be found outproperly as shown in Figure 2 and six input channelsrepresent the main acoustic sources of mechanical noiseincluding the oil pan (X1) the left block (X2) the right block(X3) the gear cover (X4) the flywheel housing (X5) and thevalve cover (X6) L1 to L6 are the conditioned transfer

2 Shock and Vibration

functions of corresponding acoustic source whereN(t) is thesensor noise Y(t) is the IMFs of the measured acousticsignal

+e PCA can be adopted by the following steps [33]

Step 1 Transform signals from time domain into frequencydomain X(t) Y(t)⟶ X(f) Y(f)

Step 2 Calculate the self-power spectra and the cross-powerspectra of the transformed signals

Sxx 1

MNFFT1113944

M

i1Xi(f)X

lowasti (f)

Syy 1

MNFFT1113944

M

i1Yi(f)Y

lowasti (f)

Sxy 1

MNFFT1113944

M

i1Xi(f)Y

lowasti (f)

(6)

where Sxx and Syy represent the self-power spectra of theinput and the output respectively Sxy represents the cross-power spectrum of the input and output and Xlowasti (f) andXlowasti (f) are conjugate complex numbers of Xi(f ) and Yi(f )

Step 3 Calculate the conditioned transfer functions and theconditioned power spectra

Lij Sijmiddot(iminus1)

Siimiddot(iminus1)

Sijmiddotr Sijmiddot(rminus1) minusLrjSirmiddot(rminus1)

Sjjmiddotr Sjjmiddot(rminus1) minusLrjSjrmiddot(rminus1)

(7)

where Lij is the conditioned transfer function Sijmiddotr is theconditioned cross-power spectrum between the input andoutput without coherent effects from X1 X2 Xr and Sjjmiddotris the conditioned self-power spectrum without coherenteffects from other signals

Step 4 Calculate the input partial coherent power spectrum

c2iymiddotr

Siymiddotr

11138681113868111386811138681113868

111386811138681113868111386811138682

SiimiddotrSyymiddotr

Syxiprime c

2iymiddotrSiimiddotr

(8)

where c2iymiddotr is the partial coherent function describing the

correlation between Xi(t) and Y(t) in the whole frequencyrange Siimiddotr is the conditioned self-power spectrum and Syxi

primeis the input partial coherent power spectrum (PCPS) thatshows the relationship between component vibration andradiated noise

23 Fuzzy AHP +e detailed process of the FAHP can bedescribed as follows

Step 1 Establish the fuzzy judgment matrix A from pairwisecomparisons Determine the fuzzy judgment matrix A

[aij]ntimesn according to the relative importance of factors in thesame layer +e elements in matrix A are in the range of 01 to09 where 05 represents the two factors are equally important

S 11

00 02 04 06

t (s)

08 10

00 02 04 06 08 10

00 02 04 06 08 10

00 02 04 06 08 10

0ndash1

10

ndash1

10

ndash1

10

ndash1

S 2S 3

S 4

(a)

IMF1

1

00 02 04 06

t (s)

08 10

00 02 04 06 08 10

00 02 04 06 08 10

00 02 04 06 08 10

0ndash1

10

ndash1

10

ndash1

10

ndash1

IMF2

IMF3

IMF4

(b)

Figure 1 Components from (a) original signal and (b) decomposition of VMD

Oil pan

Le block

Right block

Gear cover

Flywheel housing

Valve cover

L1 ( f)

L2 ( f)

L4 ( f)

L5 ( f)

L6 ( f)

Enginesum

N (t)

L3 ( f)

X1 (t)

X2 (t)

X3 (t)

X4 (t)

X5 (t)

X6 (t)

Y (t)

Figure 2 +e PCA diagram in engine noise identification

Shock and Vibration 3

Step 2 Calculate the fuzzy consistency matrix R and thereciprocal matrixM Transform A [aij]ntimesn into R [rij]ntimesn+e calculation can be done by the following equation

rij 12n

1113944

n

k1aik minus 1113944

n

k1ajk

⎛⎝ ⎞⎠ + 05 (9)

+en the matrix R can be converted into the reciprocalfuzzy consistency matrix M through mij rijrji

Step 3 Calculate the initial weighting vector ω0 +e initialweighting vector ω0 ω1 ω2 middot middot middot ωn1113858 1113859 can be obtained bythe least-squares method

ω0 1nminus

12 z

+1

n z1113944

n

j1rij

z nminus 12

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

Step 4 Calculate the final weighting vector V

(1) Initialize V0 v01 v02 middot middot middot v0n1113858 1113859 by ω0

(2) For k 1 2 3 n

Vk+1 MVk (11)

(3) Check the convergence by the following equation

Vk+1

infinminus Vk

infinle ε (12)

(4) If the convergence is met output the final weightingvector as follows

Vk+1 Vk+11

1113936ni1Vk+1i

Vk+12

1113936ni1Vk+1i

Vk+13

1113936ni1Vk+1i

middot middot middotVk+1n

1113936ni1Vk+1i

1113890 1113891

(13)

Otherwise jump back to Step 2

24 Flow Chart +e overall framework is given in Figure 3and the process can be divided into six steps

Step 1 Decompose the noise signal into a series of IMFs inconsecutive frequency bands by VMD

Step 2 Analyse the relationship between component vi-bration and radiated noise through PCA to obtain theweighting order of components in each frequency band

Step 3 Construct the hierarchy tree and establish the fuzzyconsistency matrices Obtain the contributions of noisesources to the decomposed noise in different frequency bands

Step 4 Calculate the contributions of noise in differentfrequency bands to different test points according to theA-weighted SPL and construct the combined weight matrixof the test point level

Step 5 Obtain the contributions of noise at different testpoints to different engine speeds and construct the com-bined weight matrix of the operating speed level

Step 6 Construct the fuzzy consistency matrix of theobjective level according to the A-weighted SPL and theusage rate of engine speeds and obtain the overall weightsof noise sources

3 Measurements

+e noise and vibration experiment is carried out on a testrig in a semianechoic chamber with less than 18 dB back-ground SPL as shown in Figure 4 Acoustic signals arecollected using five MA231 acoustic sensors (BSWA Tech-nology Co Ltd China) 1m away from the front the rear theleft the right and the top surfaces of engine +e near-fieldnoise (001m away from the measuring surface) as well asthe vibration of some highly concerned components ismeasured including the oil pan the block the flywheelhousing and the valve cover In the vibration measurementthe triaxial accelerometers (PCB Piezotronics Inc US) arearranged at different regions for large component and themean acceleration is employed In order to reduce un-certainty error during the test all the microphones andaccelerometers are calibrated before the measurementaccording to the instructions in the test environment and allthe test cases are recorded for three times separately

+e experiment is carried out at four typical enginespeeds of 700 rmin (idle) 1400 rmin (maximum torque)1800 rmin (most commonly used operating condition ofconstruction machinery with 80 load) and 2200 rmin(rated) +e combustion settings of the four typical oper-ating conditions are listed in Table 1 +e sampling fre-quency is 10240Hz and the intake noise the exhaust noiseand the fan noise are removed from the measurement

4 Results and Discussion

In this section only the 1800 rmin case is used as an ex-ample to show the results due to the huge amount of dataand the analysis procedure of other operating conditions isin the same way as the showcase

41 Noise Decomposition In order to improve signal de-composition accuracy the trend term and cumulative errorare eliminated from the raw data before the formal analysis+e central frequency of IMF is used as the criteria forchoosing the best modal number K Overdecompositionoccurs when the difference of the central frequencies of twoadjacent IMFs is smaller than 10 of the whole frequencyrange Four K values are employed in this study including 45 6 and 7 +e central frequencies of the correspondingIMFs are listed in Table 2 For K 7 the central frequencydifference of IMF4 and IMF5 is 147Hzlt 10timeswhole fre-quency range (2707ndash240) 2467Hz As a result the K 7case is considered as overdecomposition so that K 6 is

4 Shock and Vibration

employed in the VMD decomposition +e IMFs obtainedfrom the acoustic signal recorded at the left-side test point at1800 rmin are given in Figure 5

+e lower and upper limits of the frequency bandare determined by time-frequency analysis using wavelettransform As shown in Figure 6 the six frequency bandsare 0ndash500Hz 500ndash800Hz 800ndash1200Hz 1200ndash1800Hz1800ndash2500Hz and 2500ndash4000Hz In lower frequencyranges eg 0ndash500Hz and 500ndash800Hz obvious periodicitycan be found for the radiated noise +is periodic charactercorresponds to the ignitions of cylinder +e six consec-utive highlight parts along the time correlate to the ig-nitions of the six cylinders in a working cycle (720degCAin 04 s at 1800 rmin) Most engine parts contributeto the low frequency radiated noise because their lower

vibration modes fall in these frequency bands For higherfrequency the energy distribution still shows periodiccharacters but more details within every single stroke canbe found From this point of view each IMF has its ownphysical meaning and it can improve the reliability of thefollowing PCA

Component vibration

1m radiated noise

Near-field noise

Engine test

PCAInput conditioned

coherent power spectra

Fuzzy consistency matrices

Contributions of lower levels to

higher levels

Coherence analysis

Component level

Frequency level

Test point level

Speed level

Target level

Fuzzy AHP

Validation

IMFnfrequency band n

VMDIMF1frequency band 1IMF2frequency band 2

Signal processing

Figure 3 +e overall framework of the noise source weighting process

Fan isremoved

Sound-absorbing cotton

Exhaust noise is led outto the outside

Sound-absorbing cotton

Intake noise is led outto the outside

Figure 4 Arrangement of the noise and vibration test

Table 1 +e combustion settings of the four typical operating conditions

Operating conditions Intakepressure (MPa)

Intaketemperature (degC)

Fuel injectiontiming (degCA)

Maximum in-cylinderpressure (MPa)

Fuel injectionpressure (MPa)

Idle condition 00027 26 69 131 433701400 rmin + 100 load 02497 51 41 184 1544781800 rmin + 80 load 01879 484 108 181 178243Rated condition 01749 483 112 179 179441

Table 2 Decomposition results with different modal numbers

Modalnumber K

Central frequencies (Hz)IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7

4 276 766 1442 2596 mdash mdash mdash5 274 762 1384 1780 2675 mdash mdash6 251 577 823 1409 1924 2702 mdash7 240 561 810 1245 1392 1922 2707

Shock and Vibration 5

42 Partial Coherence Analysis +e radiated noise of theengine contains the vibration information of the enginecomponent so the contributions of various components tothe measured noise can be identified according to the cor-relation between noise and vibration Many of the accessories

are rigidly connected to the engine block so the vibrationbetween different noise sources is coupled It is why the PCAis chosen to recognize the correlation of component vibrationand radiated noise +e input partial coherent power spectra(PCPS) of the 1800 rmin case are shown in Figure 7

Amplitu

de 50

ndash500 01 02 03 04

IMF1 2

0ndash200 01 02 03 04

IMF2 2

0ndash200 01 02 03 04

IMF3 2

0ndash200 01 02 03 04

IMF4 2

0ndash200 01 02 03 04

IMF5 2

0ndash200 01 02 03 04

IMF6 2

0ndash200 01 02

t (s)03 04

Figure 5 +e measured and VMD decomposed signals from the left-side test point at 1800 rmin

04030201

2

0

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(a)

t (s)

Freq

uenc

y (H

z)

04030201

2

0

1

0

4000

2000

0

(b)

04030201

2

05

15

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(c)

t (s)

Freq

uenc

y (H

z)

04030201

1

0

05

0

4000

2000

0

(d)

040302t (s)

01

04

0

02

0

Freq

uenc

y (H

z)

4000

2000

0

(e)

t (s)

Freq

uenc

y (H

z)

04030201

04

0

02

0

4000

2000

0

(f )

Figure 6 Time-frequency results of IMFs

6 Shock and Vibration

6

Am

plitu

de 543210

050403020100

06

04

02

000 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Oil panLe block Right block

8

Am

plitu

de 6420

04

02

03

02

01

00000 100 200 300

Frequency (Hz)400 500 0 100 200 300 400 500 0 100 200 300 400 500

Gear cover

Flyweel housingValue cover

(a)

20

Am

plitu

de 1510

50

012

008

004

000

09

06

03

00500 600 700 800 500 600 700 800 500 600 700 800

Oil pan

Le blockRight block

15

Am

plitu

de 10

05

00

10

05

00

43210

Frequency (Hz)500 600 700 800 500 600 700 800 500 600 700 800

Gear coverFlyweel housing

Value cover

(b)

40302010

0

6

4

2

0

0403020100

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Oil pan Le block Right block

4

2

0

0806040200

12

08

04

00

Frequency (Hz)

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Value coverFlywheel housingGear cover

(c)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

450

300

150

0

86420

04

02

00

Oil pan Le block Right block

Frequency (Hz)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

60

40

20

0

43210

1612

840

Value coverFlywheel housing

Gear cover

(d)

Figure 7 Continued

Shock and Vibration 7

+e coherences of the component to the noise are (1) for0ndash500Hz gear covergt oil pangt right blockgt left block-gtflywheel housinggt valve cover (2) for 500ndash800Hz oilpangt valve covergt gear covergtflywheel housinggt rightblockgt left block (3) for 800ndash1200Hz oil pangt left block-gt gear covergt valve covergtflywheel housinggt right block(4) for 1200ndash1800Hz oil pangt gear covergt valve covergt leftblockgtflywheel housinggt right block (5) for 1800ndash2500Hzgear covergt oil pangt left blockgt valve covergt right block-gtflywheel housing and (6) for 2500ndash4000Hz gear cover-gt left blockgtflywheel housinggt oil pangt valve covergt rightblock

It can be seen that the input PCPS of the oil pan is thelargest between a wide frequency band of 500ndash1800Hz It isbecause the lower vibration modes of such a thin-walledcomponent are easy to excite due to the excitation of thebody skirt In other frequency bands the gear cover showsthe largest input PCPS below 500Hz and above 1800Hz+emain reasons are the resonances of the component in thelow-frequency range and the dynamic meshing force be-tween gear teeth at high frequency So the above twocomponents are the top 2 contributors in most cases For theleft block the amplitude of input PCPS in 1800ndash4000Hz isconsiderable because the fuel injection pump and the aircompressor radiate great portion of noise in this high-frequency range

43 Weighting Analysis of Noise Sources

431 Analytic Hierarchy Tree As analysed above for aspecific component (noise source) its contribution to thenoise varies in different aspects such as the frequency bandthe testing point and the engine speed On this basis thehierarchy tree (Figure 8) for weighting the noise sourcesconsists of five levels from top to bottom (1) objective level(2) operating speed level (3) testing point level (4) fre-quency band level and (5) noise sources level

432 Fuzzy Consistency Matrix +e fuzzy consistencymatrices for the frequency level are constructed according tothe condition coherent power spectra and listed in Table 3Based on the one-third octave SPL the fuzzy consistencymatrices for the test point level and the operating speed levelcan be calculated in the same way Table 4 shows the fuzzyconsistency matrix for the left testing point (C1) Table 5presents the fuzzy consistency matrix for the engine speed of1800 rmin (B3) For the top level the fuzzy consistencymatrix can be obtained based on the usage proportion of theengine speed and the A-weighted SPL as shown in Table 6

433 Weighting Order of Noise Sources Based on theconsistency matrices of adjacent levels the combined weight

Am

plitu

de

400

200

0

120

80

40

0

9

6

3

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Oil pan Le blockRight block

Frequency (Hz)

Am

plitu

de

450

300

150

0

6

4

2

0

120906030

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Value coverFlywheel housing

Gear cover

(e)

60453015

02500 3000 3500 4000

Am

plitu

de

Oil pan

300

200

100

02500 3000 3500 4000

Am

plitu

de

Gear cover

60

40

20

02500 3000 3500

Frequency (Hz)4000

Flywheel housing

12

8

4

02500 3000 3500 4000

Value cover

160120

8040

02500 3000 3500 4000

Le block

864202500 3000 3500 4000

Right block

(f )

Figure 7 +e input partial coherent power spectra of (a) 0ndash500Hz (b) 500ndash800Hz (c) 800ndash1200Hz (d) 1200ndash1800Hz (e) 1800ndash2500Hzand (f) 2500ndash4000Hz

8 Shock and Vibration

matrices can be obtained Table 7 gives the combined weightcoefficients for the left testing point (C1) and Table 8 is thecombined weight coefficients for 1800 rmin (B3) +econtributions of the noise source to the radiated noise atdifferent engine speeds are calculated and shown in Figure 9

+e contribution of the component to the overall noisechanges with the engine speed But some patterns still can be

(A)Weight order

(B1)Idle speed

(B2)1400rmin

(B3)1800rmin

(B4)2200rmin

(C1)Left

(C2)Right

(C3)Front

(C5)Top

(D1)0ndash500Hz

(D2)500ndash800Hz

(D3)800ndash1200Hz

(D4)1200ndash1800Hz

(E3)Right block

(E1)Oil pan

(E2)Left block

(E4)Gear cover

(E5)Flywheel housing

(E6)Valve cover

(D5)1800ndash2500Hz

(D6)2500ndash4000Hz

(C4)Rear

Figure 8 +e hierarchy tree conducted for noise source weighting analysis

Table 3 +e fuzzy consistency matrices for the frequency level

E1 E2 E3 E4 E5 E6 Weight

D10ndash500Hz

E1 0500 0630 0638 0466 0647 0659 0229E2 0370 0500 0508 0336 0517 0529 0134E3 0362 0492 0500 0328 0508 0521 0129E4 0534 0664 0672 0500 0681 0693 0265E5 0363 0483 0492 0319 0500 0512 0125E6 0341 0471 0479 0307 0488 0500 0118

D2 500ndash800Hz

E1 0500 0728 0695 0662 0676 0587 0286E2 0272 0500 0467 0433 0447 0359 0110E3 0305 0533 0500 0467 0481 0393 0126E4 0338 0567 0533 0500 0514 0426 0145E5 0324 0553 0519 0486 0500 0412 0137E6 0413 0641 0607 0574 0588 0500 0197

D3 800ndash1200Hz

E1 0500 0804 0631 0669 0783 0738 0286E2 0196 0500 0327 0365 0479 0433 0187E3 0369 0673 0500 0538 0653 0607 0111E4 0331 0635 0462 0500 0614 0568 0163E5 0217 0521 0348 0386 0500 0454 0117E6 0263 0567 0393 0432 0546 0500 0136

D4 1200ndash1800Hz

E1 0500 0741 0840 0628 0792 0698 0360E2 0259 0500 0599 0387 0552 0458 0122E3 0160 0401 0500 0288 0452 0358 0078E4 0372 0613 0712 0500 0664 0570 0197E5 0208 0448 0548 0336 0500 0406 0097E6 0302 0542 0642 0430 0594 0500 0146

D5 1800ndash2500Hz

E1 0500 0596 0754 0483 0763 0629 0252E2 0404 0500 0658 0388 0667 0533 0166E3 0246 0342 0500 0229 0508 0375 0084E4 0517 0613 0771 0500 0779 0646 0272E5 0238 0333 0492 0221 0500 0367 0082E6 0371 0467 0625 0354 0633 0500 0144

D6 2500ndash4000Hz

E1 0500 0376 0627 0317 0482 0613 0138E2 0624 0500 0751 0441 0607 0738 0236E3 0373 0249 0500 0190 0356 0487 0080E4 0683 0559 0810 0500 0666 0797 0313E5 0518 0393 0644 0334 0500 0631 0149E6 0387 0262 0513 0203 0369 0500 0084

Table 4 +e fuzzy consistency matrix for left testing point (C1) at1800 rmin

C1 D1 D2 D3 D4 D5 D6 WeightD1 0500 0423 0373 0345 0388 0450 0114D2 0577 0500 0450 0422 0464 0527 0157D3 0627 0550 0500 0472 0514 0577 0192D4 0655 0578 0528 0500 0543 0605 0215D5 0613 0536 0486 0458 0500 0563 0181D6 0550 0473 0423 0395 0438 0500 0141

Table 5 +e fuzzy consistency matrix for engine speed of 1800 rmin (B3)

B3 C1 C2 C3 C4 C5 WeightC1 0500 0624 0577 0638 0661 0293C2 0376 0500 0453 0514 0537 0176C3 0423 0547 0500 0561 0584 0213C4 0362 0486 0439 0500 0523 0166C5 0339 0463 0416 0477 0500 0152

Table 6 +e fuzzy consistency matrix for target level (A)

A B1 B2 B3 B4 WeightB1 0500 0412 0312 0350 0155B2 0588 0500 0400 0437 0222B3 0688 0600 0500 0537 0336B4 0650 0563 0463 0500 0287

Shock and Vibration 9

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

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functions of corresponding acoustic source whereN(t) is thesensor noise Y(t) is the IMFs of the measured acousticsignal

+e PCA can be adopted by the following steps [33]

Step 1 Transform signals from time domain into frequencydomain X(t) Y(t)⟶ X(f) Y(f)

Step 2 Calculate the self-power spectra and the cross-powerspectra of the transformed signals

Sxx 1

MNFFT1113944

M

i1Xi(f)X

lowasti (f)

Syy 1

MNFFT1113944

M

i1Yi(f)Y

lowasti (f)

Sxy 1

MNFFT1113944

M

i1Xi(f)Y

lowasti (f)

(6)

where Sxx and Syy represent the self-power spectra of theinput and the output respectively Sxy represents the cross-power spectrum of the input and output and Xlowasti (f) andXlowasti (f) are conjugate complex numbers of Xi(f ) and Yi(f )

Step 3 Calculate the conditioned transfer functions and theconditioned power spectra

Lij Sijmiddot(iminus1)

Siimiddot(iminus1)

Sijmiddotr Sijmiddot(rminus1) minusLrjSirmiddot(rminus1)

Sjjmiddotr Sjjmiddot(rminus1) minusLrjSjrmiddot(rminus1)

(7)

where Lij is the conditioned transfer function Sijmiddotr is theconditioned cross-power spectrum between the input andoutput without coherent effects from X1 X2 Xr and Sjjmiddotris the conditioned self-power spectrum without coherenteffects from other signals

Step 4 Calculate the input partial coherent power spectrum

c2iymiddotr

Siymiddotr

11138681113868111386811138681113868

111386811138681113868111386811138682

SiimiddotrSyymiddotr

Syxiprime c

2iymiddotrSiimiddotr

(8)

where c2iymiddotr is the partial coherent function describing the

correlation between Xi(t) and Y(t) in the whole frequencyrange Siimiddotr is the conditioned self-power spectrum and Syxi

primeis the input partial coherent power spectrum (PCPS) thatshows the relationship between component vibration andradiated noise

23 Fuzzy AHP +e detailed process of the FAHP can bedescribed as follows

Step 1 Establish the fuzzy judgment matrix A from pairwisecomparisons Determine the fuzzy judgment matrix A

[aij]ntimesn according to the relative importance of factors in thesame layer +e elements in matrix A are in the range of 01 to09 where 05 represents the two factors are equally important

S 11

00 02 04 06

t (s)

08 10

00 02 04 06 08 10

00 02 04 06 08 10

00 02 04 06 08 10

0ndash1

10

ndash1

10

ndash1

10

ndash1

S 2S 3

S 4

(a)

IMF1

1

00 02 04 06

t (s)

08 10

00 02 04 06 08 10

00 02 04 06 08 10

00 02 04 06 08 10

0ndash1

10

ndash1

10

ndash1

10

ndash1

IMF2

IMF3

IMF4

(b)

Figure 1 Components from (a) original signal and (b) decomposition of VMD

Oil pan

Le block

Right block

Gear cover

Flywheel housing

Valve cover

L1 ( f)

L2 ( f)

L4 ( f)

L5 ( f)

L6 ( f)

Enginesum

N (t)

L3 ( f)

X1 (t)

X2 (t)

X3 (t)

X4 (t)

X5 (t)

X6 (t)

Y (t)

Figure 2 +e PCA diagram in engine noise identification

Shock and Vibration 3

Step 2 Calculate the fuzzy consistency matrix R and thereciprocal matrixM Transform A [aij]ntimesn into R [rij]ntimesn+e calculation can be done by the following equation

rij 12n

1113944

n

k1aik minus 1113944

n

k1ajk

⎛⎝ ⎞⎠ + 05 (9)

+en the matrix R can be converted into the reciprocalfuzzy consistency matrix M through mij rijrji

Step 3 Calculate the initial weighting vector ω0 +e initialweighting vector ω0 ω1 ω2 middot middot middot ωn1113858 1113859 can be obtained bythe least-squares method

ω0 1nminus

12 z

+1

n z1113944

n

j1rij

z nminus 12

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

Step 4 Calculate the final weighting vector V

(1) Initialize V0 v01 v02 middot middot middot v0n1113858 1113859 by ω0

(2) For k 1 2 3 n

Vk+1 MVk (11)

(3) Check the convergence by the following equation

Vk+1

infinminus Vk

infinle ε (12)

(4) If the convergence is met output the final weightingvector as follows

Vk+1 Vk+11

1113936ni1Vk+1i

Vk+12

1113936ni1Vk+1i

Vk+13

1113936ni1Vk+1i

middot middot middotVk+1n

1113936ni1Vk+1i

1113890 1113891

(13)

Otherwise jump back to Step 2

24 Flow Chart +e overall framework is given in Figure 3and the process can be divided into six steps

Step 1 Decompose the noise signal into a series of IMFs inconsecutive frequency bands by VMD

Step 2 Analyse the relationship between component vi-bration and radiated noise through PCA to obtain theweighting order of components in each frequency band

Step 3 Construct the hierarchy tree and establish the fuzzyconsistency matrices Obtain the contributions of noisesources to the decomposed noise in different frequency bands

Step 4 Calculate the contributions of noise in differentfrequency bands to different test points according to theA-weighted SPL and construct the combined weight matrixof the test point level

Step 5 Obtain the contributions of noise at different testpoints to different engine speeds and construct the com-bined weight matrix of the operating speed level

Step 6 Construct the fuzzy consistency matrix of theobjective level according to the A-weighted SPL and theusage rate of engine speeds and obtain the overall weightsof noise sources

3 Measurements

+e noise and vibration experiment is carried out on a testrig in a semianechoic chamber with less than 18 dB back-ground SPL as shown in Figure 4 Acoustic signals arecollected using five MA231 acoustic sensors (BSWA Tech-nology Co Ltd China) 1m away from the front the rear theleft the right and the top surfaces of engine +e near-fieldnoise (001m away from the measuring surface) as well asthe vibration of some highly concerned components ismeasured including the oil pan the block the flywheelhousing and the valve cover In the vibration measurementthe triaxial accelerometers (PCB Piezotronics Inc US) arearranged at different regions for large component and themean acceleration is employed In order to reduce un-certainty error during the test all the microphones andaccelerometers are calibrated before the measurementaccording to the instructions in the test environment and allthe test cases are recorded for three times separately

+e experiment is carried out at four typical enginespeeds of 700 rmin (idle) 1400 rmin (maximum torque)1800 rmin (most commonly used operating condition ofconstruction machinery with 80 load) and 2200 rmin(rated) +e combustion settings of the four typical oper-ating conditions are listed in Table 1 +e sampling fre-quency is 10240Hz and the intake noise the exhaust noiseand the fan noise are removed from the measurement

4 Results and Discussion

In this section only the 1800 rmin case is used as an ex-ample to show the results due to the huge amount of dataand the analysis procedure of other operating conditions isin the same way as the showcase

41 Noise Decomposition In order to improve signal de-composition accuracy the trend term and cumulative errorare eliminated from the raw data before the formal analysis+e central frequency of IMF is used as the criteria forchoosing the best modal number K Overdecompositionoccurs when the difference of the central frequencies of twoadjacent IMFs is smaller than 10 of the whole frequencyrange Four K values are employed in this study including 45 6 and 7 +e central frequencies of the correspondingIMFs are listed in Table 2 For K 7 the central frequencydifference of IMF4 and IMF5 is 147Hzlt 10timeswhole fre-quency range (2707ndash240) 2467Hz As a result the K 7case is considered as overdecomposition so that K 6 is

4 Shock and Vibration

employed in the VMD decomposition +e IMFs obtainedfrom the acoustic signal recorded at the left-side test point at1800 rmin are given in Figure 5

+e lower and upper limits of the frequency bandare determined by time-frequency analysis using wavelettransform As shown in Figure 6 the six frequency bandsare 0ndash500Hz 500ndash800Hz 800ndash1200Hz 1200ndash1800Hz1800ndash2500Hz and 2500ndash4000Hz In lower frequencyranges eg 0ndash500Hz and 500ndash800Hz obvious periodicitycan be found for the radiated noise +is periodic charactercorresponds to the ignitions of cylinder +e six consec-utive highlight parts along the time correlate to the ig-nitions of the six cylinders in a working cycle (720degCAin 04 s at 1800 rmin) Most engine parts contributeto the low frequency radiated noise because their lower

vibration modes fall in these frequency bands For higherfrequency the energy distribution still shows periodiccharacters but more details within every single stroke canbe found From this point of view each IMF has its ownphysical meaning and it can improve the reliability of thefollowing PCA

Component vibration

1m radiated noise

Near-field noise

Engine test

PCAInput conditioned

coherent power spectra

Fuzzy consistency matrices

Contributions of lower levels to

higher levels

Coherence analysis

Component level

Frequency level

Test point level

Speed level

Target level

Fuzzy AHP

Validation

IMFnfrequency band n

VMDIMF1frequency band 1IMF2frequency band 2

Signal processing

Figure 3 +e overall framework of the noise source weighting process

Fan isremoved

Sound-absorbing cotton

Exhaust noise is led outto the outside

Sound-absorbing cotton

Intake noise is led outto the outside

Figure 4 Arrangement of the noise and vibration test

Table 1 +e combustion settings of the four typical operating conditions

Operating conditions Intakepressure (MPa)

Intaketemperature (degC)

Fuel injectiontiming (degCA)

Maximum in-cylinderpressure (MPa)

Fuel injectionpressure (MPa)

Idle condition 00027 26 69 131 433701400 rmin + 100 load 02497 51 41 184 1544781800 rmin + 80 load 01879 484 108 181 178243Rated condition 01749 483 112 179 179441

Table 2 Decomposition results with different modal numbers

Modalnumber K

Central frequencies (Hz)IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7

4 276 766 1442 2596 mdash mdash mdash5 274 762 1384 1780 2675 mdash mdash6 251 577 823 1409 1924 2702 mdash7 240 561 810 1245 1392 1922 2707

Shock and Vibration 5

42 Partial Coherence Analysis +e radiated noise of theengine contains the vibration information of the enginecomponent so the contributions of various components tothe measured noise can be identified according to the cor-relation between noise and vibration Many of the accessories

are rigidly connected to the engine block so the vibrationbetween different noise sources is coupled It is why the PCAis chosen to recognize the correlation of component vibrationand radiated noise +e input partial coherent power spectra(PCPS) of the 1800 rmin case are shown in Figure 7

Amplitu

de 50

ndash500 01 02 03 04

IMF1 2

0ndash200 01 02 03 04

IMF2 2

0ndash200 01 02 03 04

IMF3 2

0ndash200 01 02 03 04

IMF4 2

0ndash200 01 02 03 04

IMF5 2

0ndash200 01 02 03 04

IMF6 2

0ndash200 01 02

t (s)03 04

Figure 5 +e measured and VMD decomposed signals from the left-side test point at 1800 rmin

04030201

2

0

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(a)

t (s)

Freq

uenc

y (H

z)

04030201

2

0

1

0

4000

2000

0

(b)

04030201

2

05

15

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(c)

t (s)

Freq

uenc

y (H

z)

04030201

1

0

05

0

4000

2000

0

(d)

040302t (s)

01

04

0

02

0

Freq

uenc

y (H

z)

4000

2000

0

(e)

t (s)

Freq

uenc

y (H

z)

04030201

04

0

02

0

4000

2000

0

(f )

Figure 6 Time-frequency results of IMFs

6 Shock and Vibration

6

Am

plitu

de 543210

050403020100

06

04

02

000 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Oil panLe block Right block

8

Am

plitu

de 6420

04

02

03

02

01

00000 100 200 300

Frequency (Hz)400 500 0 100 200 300 400 500 0 100 200 300 400 500

Gear cover

Flyweel housingValue cover

(a)

20

Am

plitu

de 1510

50

012

008

004

000

09

06

03

00500 600 700 800 500 600 700 800 500 600 700 800

Oil pan

Le blockRight block

15

Am

plitu

de 10

05

00

10

05

00

43210

Frequency (Hz)500 600 700 800 500 600 700 800 500 600 700 800

Gear coverFlyweel housing

Value cover

(b)

40302010

0

6

4

2

0

0403020100

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Oil pan Le block Right block

4

2

0

0806040200

12

08

04

00

Frequency (Hz)

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Value coverFlywheel housingGear cover

(c)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

450

300

150

0

86420

04

02

00

Oil pan Le block Right block

Frequency (Hz)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

60

40

20

0

43210

1612

840

Value coverFlywheel housing

Gear cover

(d)

Figure 7 Continued

Shock and Vibration 7

+e coherences of the component to the noise are (1) for0ndash500Hz gear covergt oil pangt right blockgt left block-gtflywheel housinggt valve cover (2) for 500ndash800Hz oilpangt valve covergt gear covergtflywheel housinggt rightblockgt left block (3) for 800ndash1200Hz oil pangt left block-gt gear covergt valve covergtflywheel housinggt right block(4) for 1200ndash1800Hz oil pangt gear covergt valve covergt leftblockgtflywheel housinggt right block (5) for 1800ndash2500Hzgear covergt oil pangt left blockgt valve covergt right block-gtflywheel housing and (6) for 2500ndash4000Hz gear cover-gt left blockgtflywheel housinggt oil pangt valve covergt rightblock

It can be seen that the input PCPS of the oil pan is thelargest between a wide frequency band of 500ndash1800Hz It isbecause the lower vibration modes of such a thin-walledcomponent are easy to excite due to the excitation of thebody skirt In other frequency bands the gear cover showsthe largest input PCPS below 500Hz and above 1800Hz+emain reasons are the resonances of the component in thelow-frequency range and the dynamic meshing force be-tween gear teeth at high frequency So the above twocomponents are the top 2 contributors in most cases For theleft block the amplitude of input PCPS in 1800ndash4000Hz isconsiderable because the fuel injection pump and the aircompressor radiate great portion of noise in this high-frequency range

43 Weighting Analysis of Noise Sources

431 Analytic Hierarchy Tree As analysed above for aspecific component (noise source) its contribution to thenoise varies in different aspects such as the frequency bandthe testing point and the engine speed On this basis thehierarchy tree (Figure 8) for weighting the noise sourcesconsists of five levels from top to bottom (1) objective level(2) operating speed level (3) testing point level (4) fre-quency band level and (5) noise sources level

432 Fuzzy Consistency Matrix +e fuzzy consistencymatrices for the frequency level are constructed according tothe condition coherent power spectra and listed in Table 3Based on the one-third octave SPL the fuzzy consistencymatrices for the test point level and the operating speed levelcan be calculated in the same way Table 4 shows the fuzzyconsistency matrix for the left testing point (C1) Table 5presents the fuzzy consistency matrix for the engine speed of1800 rmin (B3) For the top level the fuzzy consistencymatrix can be obtained based on the usage proportion of theengine speed and the A-weighted SPL as shown in Table 6

433 Weighting Order of Noise Sources Based on theconsistency matrices of adjacent levels the combined weight

Am

plitu

de

400

200

0

120

80

40

0

9

6

3

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Oil pan Le blockRight block

Frequency (Hz)

Am

plitu

de

450

300

150

0

6

4

2

0

120906030

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Value coverFlywheel housing

Gear cover

(e)

60453015

02500 3000 3500 4000

Am

plitu

de

Oil pan

300

200

100

02500 3000 3500 4000

Am

plitu

de

Gear cover

60

40

20

02500 3000 3500

Frequency (Hz)4000

Flywheel housing

12

8

4

02500 3000 3500 4000

Value cover

160120

8040

02500 3000 3500 4000

Le block

864202500 3000 3500 4000

Right block

(f )

Figure 7 +e input partial coherent power spectra of (a) 0ndash500Hz (b) 500ndash800Hz (c) 800ndash1200Hz (d) 1200ndash1800Hz (e) 1800ndash2500Hzand (f) 2500ndash4000Hz

8 Shock and Vibration

matrices can be obtained Table 7 gives the combined weightcoefficients for the left testing point (C1) and Table 8 is thecombined weight coefficients for 1800 rmin (B3) +econtributions of the noise source to the radiated noise atdifferent engine speeds are calculated and shown in Figure 9

+e contribution of the component to the overall noisechanges with the engine speed But some patterns still can be

(A)Weight order

(B1)Idle speed

(B2)1400rmin

(B3)1800rmin

(B4)2200rmin

(C1)Left

(C2)Right

(C3)Front

(C5)Top

(D1)0ndash500Hz

(D2)500ndash800Hz

(D3)800ndash1200Hz

(D4)1200ndash1800Hz

(E3)Right block

(E1)Oil pan

(E2)Left block

(E4)Gear cover

(E5)Flywheel housing

(E6)Valve cover

(D5)1800ndash2500Hz

(D6)2500ndash4000Hz

(C4)Rear

Figure 8 +e hierarchy tree conducted for noise source weighting analysis

Table 3 +e fuzzy consistency matrices for the frequency level

E1 E2 E3 E4 E5 E6 Weight

D10ndash500Hz

E1 0500 0630 0638 0466 0647 0659 0229E2 0370 0500 0508 0336 0517 0529 0134E3 0362 0492 0500 0328 0508 0521 0129E4 0534 0664 0672 0500 0681 0693 0265E5 0363 0483 0492 0319 0500 0512 0125E6 0341 0471 0479 0307 0488 0500 0118

D2 500ndash800Hz

E1 0500 0728 0695 0662 0676 0587 0286E2 0272 0500 0467 0433 0447 0359 0110E3 0305 0533 0500 0467 0481 0393 0126E4 0338 0567 0533 0500 0514 0426 0145E5 0324 0553 0519 0486 0500 0412 0137E6 0413 0641 0607 0574 0588 0500 0197

D3 800ndash1200Hz

E1 0500 0804 0631 0669 0783 0738 0286E2 0196 0500 0327 0365 0479 0433 0187E3 0369 0673 0500 0538 0653 0607 0111E4 0331 0635 0462 0500 0614 0568 0163E5 0217 0521 0348 0386 0500 0454 0117E6 0263 0567 0393 0432 0546 0500 0136

D4 1200ndash1800Hz

E1 0500 0741 0840 0628 0792 0698 0360E2 0259 0500 0599 0387 0552 0458 0122E3 0160 0401 0500 0288 0452 0358 0078E4 0372 0613 0712 0500 0664 0570 0197E5 0208 0448 0548 0336 0500 0406 0097E6 0302 0542 0642 0430 0594 0500 0146

D5 1800ndash2500Hz

E1 0500 0596 0754 0483 0763 0629 0252E2 0404 0500 0658 0388 0667 0533 0166E3 0246 0342 0500 0229 0508 0375 0084E4 0517 0613 0771 0500 0779 0646 0272E5 0238 0333 0492 0221 0500 0367 0082E6 0371 0467 0625 0354 0633 0500 0144

D6 2500ndash4000Hz

E1 0500 0376 0627 0317 0482 0613 0138E2 0624 0500 0751 0441 0607 0738 0236E3 0373 0249 0500 0190 0356 0487 0080E4 0683 0559 0810 0500 0666 0797 0313E5 0518 0393 0644 0334 0500 0631 0149E6 0387 0262 0513 0203 0369 0500 0084

Table 4 +e fuzzy consistency matrix for left testing point (C1) at1800 rmin

C1 D1 D2 D3 D4 D5 D6 WeightD1 0500 0423 0373 0345 0388 0450 0114D2 0577 0500 0450 0422 0464 0527 0157D3 0627 0550 0500 0472 0514 0577 0192D4 0655 0578 0528 0500 0543 0605 0215D5 0613 0536 0486 0458 0500 0563 0181D6 0550 0473 0423 0395 0438 0500 0141

Table 5 +e fuzzy consistency matrix for engine speed of 1800 rmin (B3)

B3 C1 C2 C3 C4 C5 WeightC1 0500 0624 0577 0638 0661 0293C2 0376 0500 0453 0514 0537 0176C3 0423 0547 0500 0561 0584 0213C4 0362 0486 0439 0500 0523 0166C5 0339 0463 0416 0477 0500 0152

Table 6 +e fuzzy consistency matrix for target level (A)

A B1 B2 B3 B4 WeightB1 0500 0412 0312 0350 0155B2 0588 0500 0400 0437 0222B3 0688 0600 0500 0537 0336B4 0650 0563 0463 0500 0287

Shock and Vibration 9

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

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Step 2 Calculate the fuzzy consistency matrix R and thereciprocal matrixM Transform A [aij]ntimesn into R [rij]ntimesn+e calculation can be done by the following equation

rij 12n

1113944

n

k1aik minus 1113944

n

k1ajk

⎛⎝ ⎞⎠ + 05 (9)

+en the matrix R can be converted into the reciprocalfuzzy consistency matrix M through mij rijrji

Step 3 Calculate the initial weighting vector ω0 +e initialweighting vector ω0 ω1 ω2 middot middot middot ωn1113858 1113859 can be obtained bythe least-squares method

ω0 1nminus

12 z

+1

n z1113944

n

j1rij

z nminus 12

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

Step 4 Calculate the final weighting vector V

(1) Initialize V0 v01 v02 middot middot middot v0n1113858 1113859 by ω0

(2) For k 1 2 3 n

Vk+1 MVk (11)

(3) Check the convergence by the following equation

Vk+1

infinminus Vk

infinle ε (12)

(4) If the convergence is met output the final weightingvector as follows

Vk+1 Vk+11

1113936ni1Vk+1i

Vk+12

1113936ni1Vk+1i

Vk+13

1113936ni1Vk+1i

middot middot middotVk+1n

1113936ni1Vk+1i

1113890 1113891

(13)

Otherwise jump back to Step 2

24 Flow Chart +e overall framework is given in Figure 3and the process can be divided into six steps

Step 1 Decompose the noise signal into a series of IMFs inconsecutive frequency bands by VMD

Step 2 Analyse the relationship between component vi-bration and radiated noise through PCA to obtain theweighting order of components in each frequency band

Step 3 Construct the hierarchy tree and establish the fuzzyconsistency matrices Obtain the contributions of noisesources to the decomposed noise in different frequency bands

Step 4 Calculate the contributions of noise in differentfrequency bands to different test points according to theA-weighted SPL and construct the combined weight matrixof the test point level

Step 5 Obtain the contributions of noise at different testpoints to different engine speeds and construct the com-bined weight matrix of the operating speed level

Step 6 Construct the fuzzy consistency matrix of theobjective level according to the A-weighted SPL and theusage rate of engine speeds and obtain the overall weightsof noise sources

3 Measurements

+e noise and vibration experiment is carried out on a testrig in a semianechoic chamber with less than 18 dB back-ground SPL as shown in Figure 4 Acoustic signals arecollected using five MA231 acoustic sensors (BSWA Tech-nology Co Ltd China) 1m away from the front the rear theleft the right and the top surfaces of engine +e near-fieldnoise (001m away from the measuring surface) as well asthe vibration of some highly concerned components ismeasured including the oil pan the block the flywheelhousing and the valve cover In the vibration measurementthe triaxial accelerometers (PCB Piezotronics Inc US) arearranged at different regions for large component and themean acceleration is employed In order to reduce un-certainty error during the test all the microphones andaccelerometers are calibrated before the measurementaccording to the instructions in the test environment and allthe test cases are recorded for three times separately

+e experiment is carried out at four typical enginespeeds of 700 rmin (idle) 1400 rmin (maximum torque)1800 rmin (most commonly used operating condition ofconstruction machinery with 80 load) and 2200 rmin(rated) +e combustion settings of the four typical oper-ating conditions are listed in Table 1 +e sampling fre-quency is 10240Hz and the intake noise the exhaust noiseand the fan noise are removed from the measurement

4 Results and Discussion

In this section only the 1800 rmin case is used as an ex-ample to show the results due to the huge amount of dataand the analysis procedure of other operating conditions isin the same way as the showcase

41 Noise Decomposition In order to improve signal de-composition accuracy the trend term and cumulative errorare eliminated from the raw data before the formal analysis+e central frequency of IMF is used as the criteria forchoosing the best modal number K Overdecompositionoccurs when the difference of the central frequencies of twoadjacent IMFs is smaller than 10 of the whole frequencyrange Four K values are employed in this study including 45 6 and 7 +e central frequencies of the correspondingIMFs are listed in Table 2 For K 7 the central frequencydifference of IMF4 and IMF5 is 147Hzlt 10timeswhole fre-quency range (2707ndash240) 2467Hz As a result the K 7case is considered as overdecomposition so that K 6 is

4 Shock and Vibration

employed in the VMD decomposition +e IMFs obtainedfrom the acoustic signal recorded at the left-side test point at1800 rmin are given in Figure 5

+e lower and upper limits of the frequency bandare determined by time-frequency analysis using wavelettransform As shown in Figure 6 the six frequency bandsare 0ndash500Hz 500ndash800Hz 800ndash1200Hz 1200ndash1800Hz1800ndash2500Hz and 2500ndash4000Hz In lower frequencyranges eg 0ndash500Hz and 500ndash800Hz obvious periodicitycan be found for the radiated noise +is periodic charactercorresponds to the ignitions of cylinder +e six consec-utive highlight parts along the time correlate to the ig-nitions of the six cylinders in a working cycle (720degCAin 04 s at 1800 rmin) Most engine parts contributeto the low frequency radiated noise because their lower

vibration modes fall in these frequency bands For higherfrequency the energy distribution still shows periodiccharacters but more details within every single stroke canbe found From this point of view each IMF has its ownphysical meaning and it can improve the reliability of thefollowing PCA

Component vibration

1m radiated noise

Near-field noise

Engine test

PCAInput conditioned

coherent power spectra

Fuzzy consistency matrices

Contributions of lower levels to

higher levels

Coherence analysis

Component level

Frequency level

Test point level

Speed level

Target level

Fuzzy AHP

Validation

IMFnfrequency band n

VMDIMF1frequency band 1IMF2frequency band 2

Signal processing

Figure 3 +e overall framework of the noise source weighting process

Fan isremoved

Sound-absorbing cotton

Exhaust noise is led outto the outside

Sound-absorbing cotton

Intake noise is led outto the outside

Figure 4 Arrangement of the noise and vibration test

Table 1 +e combustion settings of the four typical operating conditions

Operating conditions Intakepressure (MPa)

Intaketemperature (degC)

Fuel injectiontiming (degCA)

Maximum in-cylinderpressure (MPa)

Fuel injectionpressure (MPa)

Idle condition 00027 26 69 131 433701400 rmin + 100 load 02497 51 41 184 1544781800 rmin + 80 load 01879 484 108 181 178243Rated condition 01749 483 112 179 179441

Table 2 Decomposition results with different modal numbers

Modalnumber K

Central frequencies (Hz)IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7

4 276 766 1442 2596 mdash mdash mdash5 274 762 1384 1780 2675 mdash mdash6 251 577 823 1409 1924 2702 mdash7 240 561 810 1245 1392 1922 2707

Shock and Vibration 5

42 Partial Coherence Analysis +e radiated noise of theengine contains the vibration information of the enginecomponent so the contributions of various components tothe measured noise can be identified according to the cor-relation between noise and vibration Many of the accessories

are rigidly connected to the engine block so the vibrationbetween different noise sources is coupled It is why the PCAis chosen to recognize the correlation of component vibrationand radiated noise +e input partial coherent power spectra(PCPS) of the 1800 rmin case are shown in Figure 7

Amplitu

de 50

ndash500 01 02 03 04

IMF1 2

0ndash200 01 02 03 04

IMF2 2

0ndash200 01 02 03 04

IMF3 2

0ndash200 01 02 03 04

IMF4 2

0ndash200 01 02 03 04

IMF5 2

0ndash200 01 02 03 04

IMF6 2

0ndash200 01 02

t (s)03 04

Figure 5 +e measured and VMD decomposed signals from the left-side test point at 1800 rmin

04030201

2

0

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(a)

t (s)

Freq

uenc

y (H

z)

04030201

2

0

1

0

4000

2000

0

(b)

04030201

2

05

15

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(c)

t (s)

Freq

uenc

y (H

z)

04030201

1

0

05

0

4000

2000

0

(d)

040302t (s)

01

04

0

02

0

Freq

uenc

y (H

z)

4000

2000

0

(e)

t (s)

Freq

uenc

y (H

z)

04030201

04

0

02

0

4000

2000

0

(f )

Figure 6 Time-frequency results of IMFs

6 Shock and Vibration

6

Am

plitu

de 543210

050403020100

06

04

02

000 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Oil panLe block Right block

8

Am

plitu

de 6420

04

02

03

02

01

00000 100 200 300

Frequency (Hz)400 500 0 100 200 300 400 500 0 100 200 300 400 500

Gear cover

Flyweel housingValue cover

(a)

20

Am

plitu

de 1510

50

012

008

004

000

09

06

03

00500 600 700 800 500 600 700 800 500 600 700 800

Oil pan

Le blockRight block

15

Am

plitu

de 10

05

00

10

05

00

43210

Frequency (Hz)500 600 700 800 500 600 700 800 500 600 700 800

Gear coverFlyweel housing

Value cover

(b)

40302010

0

6

4

2

0

0403020100

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Oil pan Le block Right block

4

2

0

0806040200

12

08

04

00

Frequency (Hz)

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Value coverFlywheel housingGear cover

(c)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

450

300

150

0

86420

04

02

00

Oil pan Le block Right block

Frequency (Hz)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

60

40

20

0

43210

1612

840

Value coverFlywheel housing

Gear cover

(d)

Figure 7 Continued

Shock and Vibration 7

+e coherences of the component to the noise are (1) for0ndash500Hz gear covergt oil pangt right blockgt left block-gtflywheel housinggt valve cover (2) for 500ndash800Hz oilpangt valve covergt gear covergtflywheel housinggt rightblockgt left block (3) for 800ndash1200Hz oil pangt left block-gt gear covergt valve covergtflywheel housinggt right block(4) for 1200ndash1800Hz oil pangt gear covergt valve covergt leftblockgtflywheel housinggt right block (5) for 1800ndash2500Hzgear covergt oil pangt left blockgt valve covergt right block-gtflywheel housing and (6) for 2500ndash4000Hz gear cover-gt left blockgtflywheel housinggt oil pangt valve covergt rightblock

It can be seen that the input PCPS of the oil pan is thelargest between a wide frequency band of 500ndash1800Hz It isbecause the lower vibration modes of such a thin-walledcomponent are easy to excite due to the excitation of thebody skirt In other frequency bands the gear cover showsthe largest input PCPS below 500Hz and above 1800Hz+emain reasons are the resonances of the component in thelow-frequency range and the dynamic meshing force be-tween gear teeth at high frequency So the above twocomponents are the top 2 contributors in most cases For theleft block the amplitude of input PCPS in 1800ndash4000Hz isconsiderable because the fuel injection pump and the aircompressor radiate great portion of noise in this high-frequency range

43 Weighting Analysis of Noise Sources

431 Analytic Hierarchy Tree As analysed above for aspecific component (noise source) its contribution to thenoise varies in different aspects such as the frequency bandthe testing point and the engine speed On this basis thehierarchy tree (Figure 8) for weighting the noise sourcesconsists of five levels from top to bottom (1) objective level(2) operating speed level (3) testing point level (4) fre-quency band level and (5) noise sources level

432 Fuzzy Consistency Matrix +e fuzzy consistencymatrices for the frequency level are constructed according tothe condition coherent power spectra and listed in Table 3Based on the one-third octave SPL the fuzzy consistencymatrices for the test point level and the operating speed levelcan be calculated in the same way Table 4 shows the fuzzyconsistency matrix for the left testing point (C1) Table 5presents the fuzzy consistency matrix for the engine speed of1800 rmin (B3) For the top level the fuzzy consistencymatrix can be obtained based on the usage proportion of theengine speed and the A-weighted SPL as shown in Table 6

433 Weighting Order of Noise Sources Based on theconsistency matrices of adjacent levels the combined weight

Am

plitu

de

400

200

0

120

80

40

0

9

6

3

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Oil pan Le blockRight block

Frequency (Hz)

Am

plitu

de

450

300

150

0

6

4

2

0

120906030

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Value coverFlywheel housing

Gear cover

(e)

60453015

02500 3000 3500 4000

Am

plitu

de

Oil pan

300

200

100

02500 3000 3500 4000

Am

plitu

de

Gear cover

60

40

20

02500 3000 3500

Frequency (Hz)4000

Flywheel housing

12

8

4

02500 3000 3500 4000

Value cover

160120

8040

02500 3000 3500 4000

Le block

864202500 3000 3500 4000

Right block

(f )

Figure 7 +e input partial coherent power spectra of (a) 0ndash500Hz (b) 500ndash800Hz (c) 800ndash1200Hz (d) 1200ndash1800Hz (e) 1800ndash2500Hzand (f) 2500ndash4000Hz

8 Shock and Vibration

matrices can be obtained Table 7 gives the combined weightcoefficients for the left testing point (C1) and Table 8 is thecombined weight coefficients for 1800 rmin (B3) +econtributions of the noise source to the radiated noise atdifferent engine speeds are calculated and shown in Figure 9

+e contribution of the component to the overall noisechanges with the engine speed But some patterns still can be

(A)Weight order

(B1)Idle speed

(B2)1400rmin

(B3)1800rmin

(B4)2200rmin

(C1)Left

(C2)Right

(C3)Front

(C5)Top

(D1)0ndash500Hz

(D2)500ndash800Hz

(D3)800ndash1200Hz

(D4)1200ndash1800Hz

(E3)Right block

(E1)Oil pan

(E2)Left block

(E4)Gear cover

(E5)Flywheel housing

(E6)Valve cover

(D5)1800ndash2500Hz

(D6)2500ndash4000Hz

(C4)Rear

Figure 8 +e hierarchy tree conducted for noise source weighting analysis

Table 3 +e fuzzy consistency matrices for the frequency level

E1 E2 E3 E4 E5 E6 Weight

D10ndash500Hz

E1 0500 0630 0638 0466 0647 0659 0229E2 0370 0500 0508 0336 0517 0529 0134E3 0362 0492 0500 0328 0508 0521 0129E4 0534 0664 0672 0500 0681 0693 0265E5 0363 0483 0492 0319 0500 0512 0125E6 0341 0471 0479 0307 0488 0500 0118

D2 500ndash800Hz

E1 0500 0728 0695 0662 0676 0587 0286E2 0272 0500 0467 0433 0447 0359 0110E3 0305 0533 0500 0467 0481 0393 0126E4 0338 0567 0533 0500 0514 0426 0145E5 0324 0553 0519 0486 0500 0412 0137E6 0413 0641 0607 0574 0588 0500 0197

D3 800ndash1200Hz

E1 0500 0804 0631 0669 0783 0738 0286E2 0196 0500 0327 0365 0479 0433 0187E3 0369 0673 0500 0538 0653 0607 0111E4 0331 0635 0462 0500 0614 0568 0163E5 0217 0521 0348 0386 0500 0454 0117E6 0263 0567 0393 0432 0546 0500 0136

D4 1200ndash1800Hz

E1 0500 0741 0840 0628 0792 0698 0360E2 0259 0500 0599 0387 0552 0458 0122E3 0160 0401 0500 0288 0452 0358 0078E4 0372 0613 0712 0500 0664 0570 0197E5 0208 0448 0548 0336 0500 0406 0097E6 0302 0542 0642 0430 0594 0500 0146

D5 1800ndash2500Hz

E1 0500 0596 0754 0483 0763 0629 0252E2 0404 0500 0658 0388 0667 0533 0166E3 0246 0342 0500 0229 0508 0375 0084E4 0517 0613 0771 0500 0779 0646 0272E5 0238 0333 0492 0221 0500 0367 0082E6 0371 0467 0625 0354 0633 0500 0144

D6 2500ndash4000Hz

E1 0500 0376 0627 0317 0482 0613 0138E2 0624 0500 0751 0441 0607 0738 0236E3 0373 0249 0500 0190 0356 0487 0080E4 0683 0559 0810 0500 0666 0797 0313E5 0518 0393 0644 0334 0500 0631 0149E6 0387 0262 0513 0203 0369 0500 0084

Table 4 +e fuzzy consistency matrix for left testing point (C1) at1800 rmin

C1 D1 D2 D3 D4 D5 D6 WeightD1 0500 0423 0373 0345 0388 0450 0114D2 0577 0500 0450 0422 0464 0527 0157D3 0627 0550 0500 0472 0514 0577 0192D4 0655 0578 0528 0500 0543 0605 0215D5 0613 0536 0486 0458 0500 0563 0181D6 0550 0473 0423 0395 0438 0500 0141

Table 5 +e fuzzy consistency matrix for engine speed of 1800 rmin (B3)

B3 C1 C2 C3 C4 C5 WeightC1 0500 0624 0577 0638 0661 0293C2 0376 0500 0453 0514 0537 0176C3 0423 0547 0500 0561 0584 0213C4 0362 0486 0439 0500 0523 0166C5 0339 0463 0416 0477 0500 0152

Table 6 +e fuzzy consistency matrix for target level (A)

A B1 B2 B3 B4 WeightB1 0500 0412 0312 0350 0155B2 0588 0500 0400 0437 0222B3 0688 0600 0500 0537 0336B4 0650 0563 0463 0500 0287

Shock and Vibration 9

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

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employed in the VMD decomposition +e IMFs obtainedfrom the acoustic signal recorded at the left-side test point at1800 rmin are given in Figure 5

+e lower and upper limits of the frequency bandare determined by time-frequency analysis using wavelettransform As shown in Figure 6 the six frequency bandsare 0ndash500Hz 500ndash800Hz 800ndash1200Hz 1200ndash1800Hz1800ndash2500Hz and 2500ndash4000Hz In lower frequencyranges eg 0ndash500Hz and 500ndash800Hz obvious periodicitycan be found for the radiated noise +is periodic charactercorresponds to the ignitions of cylinder +e six consec-utive highlight parts along the time correlate to the ig-nitions of the six cylinders in a working cycle (720degCAin 04 s at 1800 rmin) Most engine parts contributeto the low frequency radiated noise because their lower

vibration modes fall in these frequency bands For higherfrequency the energy distribution still shows periodiccharacters but more details within every single stroke canbe found From this point of view each IMF has its ownphysical meaning and it can improve the reliability of thefollowing PCA

Component vibration

1m radiated noise

Near-field noise

Engine test

PCAInput conditioned

coherent power spectra

Fuzzy consistency matrices

Contributions of lower levels to

higher levels

Coherence analysis

Component level

Frequency level

Test point level

Speed level

Target level

Fuzzy AHP

Validation

IMFnfrequency band n

VMDIMF1frequency band 1IMF2frequency band 2

Signal processing

Figure 3 +e overall framework of the noise source weighting process

Fan isremoved

Sound-absorbing cotton

Exhaust noise is led outto the outside

Sound-absorbing cotton

Intake noise is led outto the outside

Figure 4 Arrangement of the noise and vibration test

Table 1 +e combustion settings of the four typical operating conditions

Operating conditions Intakepressure (MPa)

Intaketemperature (degC)

Fuel injectiontiming (degCA)

Maximum in-cylinderpressure (MPa)

Fuel injectionpressure (MPa)

Idle condition 00027 26 69 131 433701400 rmin + 100 load 02497 51 41 184 1544781800 rmin + 80 load 01879 484 108 181 178243Rated condition 01749 483 112 179 179441

Table 2 Decomposition results with different modal numbers

Modalnumber K

Central frequencies (Hz)IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7

4 276 766 1442 2596 mdash mdash mdash5 274 762 1384 1780 2675 mdash mdash6 251 577 823 1409 1924 2702 mdash7 240 561 810 1245 1392 1922 2707

Shock and Vibration 5

42 Partial Coherence Analysis +e radiated noise of theengine contains the vibration information of the enginecomponent so the contributions of various components tothe measured noise can be identified according to the cor-relation between noise and vibration Many of the accessories

are rigidly connected to the engine block so the vibrationbetween different noise sources is coupled It is why the PCAis chosen to recognize the correlation of component vibrationand radiated noise +e input partial coherent power spectra(PCPS) of the 1800 rmin case are shown in Figure 7

Amplitu

de 50

ndash500 01 02 03 04

IMF1 2

0ndash200 01 02 03 04

IMF2 2

0ndash200 01 02 03 04

IMF3 2

0ndash200 01 02 03 04

IMF4 2

0ndash200 01 02 03 04

IMF5 2

0ndash200 01 02 03 04

IMF6 2

0ndash200 01 02

t (s)03 04

Figure 5 +e measured and VMD decomposed signals from the left-side test point at 1800 rmin

04030201

2

0

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(a)

t (s)

Freq

uenc

y (H

z)

04030201

2

0

1

0

4000

2000

0

(b)

04030201

2

05

15

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(c)

t (s)

Freq

uenc

y (H

z)

04030201

1

0

05

0

4000

2000

0

(d)

040302t (s)

01

04

0

02

0

Freq

uenc

y (H

z)

4000

2000

0

(e)

t (s)

Freq

uenc

y (H

z)

04030201

04

0

02

0

4000

2000

0

(f )

Figure 6 Time-frequency results of IMFs

6 Shock and Vibration

6

Am

plitu

de 543210

050403020100

06

04

02

000 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Oil panLe block Right block

8

Am

plitu

de 6420

04

02

03

02

01

00000 100 200 300

Frequency (Hz)400 500 0 100 200 300 400 500 0 100 200 300 400 500

Gear cover

Flyweel housingValue cover

(a)

20

Am

plitu

de 1510

50

012

008

004

000

09

06

03

00500 600 700 800 500 600 700 800 500 600 700 800

Oil pan

Le blockRight block

15

Am

plitu

de 10

05

00

10

05

00

43210

Frequency (Hz)500 600 700 800 500 600 700 800 500 600 700 800

Gear coverFlyweel housing

Value cover

(b)

40302010

0

6

4

2

0

0403020100

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Oil pan Le block Right block

4

2

0

0806040200

12

08

04

00

Frequency (Hz)

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Value coverFlywheel housingGear cover

(c)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

450

300

150

0

86420

04

02

00

Oil pan Le block Right block

Frequency (Hz)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

60

40

20

0

43210

1612

840

Value coverFlywheel housing

Gear cover

(d)

Figure 7 Continued

Shock and Vibration 7

+e coherences of the component to the noise are (1) for0ndash500Hz gear covergt oil pangt right blockgt left block-gtflywheel housinggt valve cover (2) for 500ndash800Hz oilpangt valve covergt gear covergtflywheel housinggt rightblockgt left block (3) for 800ndash1200Hz oil pangt left block-gt gear covergt valve covergtflywheel housinggt right block(4) for 1200ndash1800Hz oil pangt gear covergt valve covergt leftblockgtflywheel housinggt right block (5) for 1800ndash2500Hzgear covergt oil pangt left blockgt valve covergt right block-gtflywheel housing and (6) for 2500ndash4000Hz gear cover-gt left blockgtflywheel housinggt oil pangt valve covergt rightblock

It can be seen that the input PCPS of the oil pan is thelargest between a wide frequency band of 500ndash1800Hz It isbecause the lower vibration modes of such a thin-walledcomponent are easy to excite due to the excitation of thebody skirt In other frequency bands the gear cover showsthe largest input PCPS below 500Hz and above 1800Hz+emain reasons are the resonances of the component in thelow-frequency range and the dynamic meshing force be-tween gear teeth at high frequency So the above twocomponents are the top 2 contributors in most cases For theleft block the amplitude of input PCPS in 1800ndash4000Hz isconsiderable because the fuel injection pump and the aircompressor radiate great portion of noise in this high-frequency range

43 Weighting Analysis of Noise Sources

431 Analytic Hierarchy Tree As analysed above for aspecific component (noise source) its contribution to thenoise varies in different aspects such as the frequency bandthe testing point and the engine speed On this basis thehierarchy tree (Figure 8) for weighting the noise sourcesconsists of five levels from top to bottom (1) objective level(2) operating speed level (3) testing point level (4) fre-quency band level and (5) noise sources level

432 Fuzzy Consistency Matrix +e fuzzy consistencymatrices for the frequency level are constructed according tothe condition coherent power spectra and listed in Table 3Based on the one-third octave SPL the fuzzy consistencymatrices for the test point level and the operating speed levelcan be calculated in the same way Table 4 shows the fuzzyconsistency matrix for the left testing point (C1) Table 5presents the fuzzy consistency matrix for the engine speed of1800 rmin (B3) For the top level the fuzzy consistencymatrix can be obtained based on the usage proportion of theengine speed and the A-weighted SPL as shown in Table 6

433 Weighting Order of Noise Sources Based on theconsistency matrices of adjacent levels the combined weight

Am

plitu

de

400

200

0

120

80

40

0

9

6

3

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Oil pan Le blockRight block

Frequency (Hz)

Am

plitu

de

450

300

150

0

6

4

2

0

120906030

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Value coverFlywheel housing

Gear cover

(e)

60453015

02500 3000 3500 4000

Am

plitu

de

Oil pan

300

200

100

02500 3000 3500 4000

Am

plitu

de

Gear cover

60

40

20

02500 3000 3500

Frequency (Hz)4000

Flywheel housing

12

8

4

02500 3000 3500 4000

Value cover

160120

8040

02500 3000 3500 4000

Le block

864202500 3000 3500 4000

Right block

(f )

Figure 7 +e input partial coherent power spectra of (a) 0ndash500Hz (b) 500ndash800Hz (c) 800ndash1200Hz (d) 1200ndash1800Hz (e) 1800ndash2500Hzand (f) 2500ndash4000Hz

8 Shock and Vibration

matrices can be obtained Table 7 gives the combined weightcoefficients for the left testing point (C1) and Table 8 is thecombined weight coefficients for 1800 rmin (B3) +econtributions of the noise source to the radiated noise atdifferent engine speeds are calculated and shown in Figure 9

+e contribution of the component to the overall noisechanges with the engine speed But some patterns still can be

(A)Weight order

(B1)Idle speed

(B2)1400rmin

(B3)1800rmin

(B4)2200rmin

(C1)Left

(C2)Right

(C3)Front

(C5)Top

(D1)0ndash500Hz

(D2)500ndash800Hz

(D3)800ndash1200Hz

(D4)1200ndash1800Hz

(E3)Right block

(E1)Oil pan

(E2)Left block

(E4)Gear cover

(E5)Flywheel housing

(E6)Valve cover

(D5)1800ndash2500Hz

(D6)2500ndash4000Hz

(C4)Rear

Figure 8 +e hierarchy tree conducted for noise source weighting analysis

Table 3 +e fuzzy consistency matrices for the frequency level

E1 E2 E3 E4 E5 E6 Weight

D10ndash500Hz

E1 0500 0630 0638 0466 0647 0659 0229E2 0370 0500 0508 0336 0517 0529 0134E3 0362 0492 0500 0328 0508 0521 0129E4 0534 0664 0672 0500 0681 0693 0265E5 0363 0483 0492 0319 0500 0512 0125E6 0341 0471 0479 0307 0488 0500 0118

D2 500ndash800Hz

E1 0500 0728 0695 0662 0676 0587 0286E2 0272 0500 0467 0433 0447 0359 0110E3 0305 0533 0500 0467 0481 0393 0126E4 0338 0567 0533 0500 0514 0426 0145E5 0324 0553 0519 0486 0500 0412 0137E6 0413 0641 0607 0574 0588 0500 0197

D3 800ndash1200Hz

E1 0500 0804 0631 0669 0783 0738 0286E2 0196 0500 0327 0365 0479 0433 0187E3 0369 0673 0500 0538 0653 0607 0111E4 0331 0635 0462 0500 0614 0568 0163E5 0217 0521 0348 0386 0500 0454 0117E6 0263 0567 0393 0432 0546 0500 0136

D4 1200ndash1800Hz

E1 0500 0741 0840 0628 0792 0698 0360E2 0259 0500 0599 0387 0552 0458 0122E3 0160 0401 0500 0288 0452 0358 0078E4 0372 0613 0712 0500 0664 0570 0197E5 0208 0448 0548 0336 0500 0406 0097E6 0302 0542 0642 0430 0594 0500 0146

D5 1800ndash2500Hz

E1 0500 0596 0754 0483 0763 0629 0252E2 0404 0500 0658 0388 0667 0533 0166E3 0246 0342 0500 0229 0508 0375 0084E4 0517 0613 0771 0500 0779 0646 0272E5 0238 0333 0492 0221 0500 0367 0082E6 0371 0467 0625 0354 0633 0500 0144

D6 2500ndash4000Hz

E1 0500 0376 0627 0317 0482 0613 0138E2 0624 0500 0751 0441 0607 0738 0236E3 0373 0249 0500 0190 0356 0487 0080E4 0683 0559 0810 0500 0666 0797 0313E5 0518 0393 0644 0334 0500 0631 0149E6 0387 0262 0513 0203 0369 0500 0084

Table 4 +e fuzzy consistency matrix for left testing point (C1) at1800 rmin

C1 D1 D2 D3 D4 D5 D6 WeightD1 0500 0423 0373 0345 0388 0450 0114D2 0577 0500 0450 0422 0464 0527 0157D3 0627 0550 0500 0472 0514 0577 0192D4 0655 0578 0528 0500 0543 0605 0215D5 0613 0536 0486 0458 0500 0563 0181D6 0550 0473 0423 0395 0438 0500 0141

Table 5 +e fuzzy consistency matrix for engine speed of 1800 rmin (B3)

B3 C1 C2 C3 C4 C5 WeightC1 0500 0624 0577 0638 0661 0293C2 0376 0500 0453 0514 0537 0176C3 0423 0547 0500 0561 0584 0213C4 0362 0486 0439 0500 0523 0166C5 0339 0463 0416 0477 0500 0152

Table 6 +e fuzzy consistency matrix for target level (A)

A B1 B2 B3 B4 WeightB1 0500 0412 0312 0350 0155B2 0588 0500 0400 0437 0222B3 0688 0600 0500 0537 0336B4 0650 0563 0463 0500 0287

Shock and Vibration 9

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

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42 Partial Coherence Analysis +e radiated noise of theengine contains the vibration information of the enginecomponent so the contributions of various components tothe measured noise can be identified according to the cor-relation between noise and vibration Many of the accessories

are rigidly connected to the engine block so the vibrationbetween different noise sources is coupled It is why the PCAis chosen to recognize the correlation of component vibrationand radiated noise +e input partial coherent power spectra(PCPS) of the 1800 rmin case are shown in Figure 7

Amplitu

de 50

ndash500 01 02 03 04

IMF1 2

0ndash200 01 02 03 04

IMF2 2

0ndash200 01 02 03 04

IMF3 2

0ndash200 01 02 03 04

IMF4 2

0ndash200 01 02 03 04

IMF5 2

0ndash200 01 02 03 04

IMF6 2

0ndash200 01 02

t (s)03 04

Figure 5 +e measured and VMD decomposed signals from the left-side test point at 1800 rmin

04030201

2

0

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(a)

t (s)

Freq

uenc

y (H

z)

04030201

2

0

1

0

4000

2000

0

(b)

04030201

2

05

15

1

0

Freq

uenc

y (H

z)

4000

2000

0

t (s)

(c)

t (s)

Freq

uenc

y (H

z)

04030201

1

0

05

0

4000

2000

0

(d)

040302t (s)

01

04

0

02

0

Freq

uenc

y (H

z)

4000

2000

0

(e)

t (s)

Freq

uenc

y (H

z)

04030201

04

0

02

0

4000

2000

0

(f )

Figure 6 Time-frequency results of IMFs

6 Shock and Vibration

6

Am

plitu

de 543210

050403020100

06

04

02

000 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Oil panLe block Right block

8

Am

plitu

de 6420

04

02

03

02

01

00000 100 200 300

Frequency (Hz)400 500 0 100 200 300 400 500 0 100 200 300 400 500

Gear cover

Flyweel housingValue cover

(a)

20

Am

plitu

de 1510

50

012

008

004

000

09

06

03

00500 600 700 800 500 600 700 800 500 600 700 800

Oil pan

Le blockRight block

15

Am

plitu

de 10

05

00

10

05

00

43210

Frequency (Hz)500 600 700 800 500 600 700 800 500 600 700 800

Gear coverFlyweel housing

Value cover

(b)

40302010

0

6

4

2

0

0403020100

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Oil pan Le block Right block

4

2

0

0806040200

12

08

04

00

Frequency (Hz)

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Value coverFlywheel housingGear cover

(c)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

450

300

150

0

86420

04

02

00

Oil pan Le block Right block

Frequency (Hz)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

60

40

20

0

43210

1612

840

Value coverFlywheel housing

Gear cover

(d)

Figure 7 Continued

Shock and Vibration 7

+e coherences of the component to the noise are (1) for0ndash500Hz gear covergt oil pangt right blockgt left block-gtflywheel housinggt valve cover (2) for 500ndash800Hz oilpangt valve covergt gear covergtflywheel housinggt rightblockgt left block (3) for 800ndash1200Hz oil pangt left block-gt gear covergt valve covergtflywheel housinggt right block(4) for 1200ndash1800Hz oil pangt gear covergt valve covergt leftblockgtflywheel housinggt right block (5) for 1800ndash2500Hzgear covergt oil pangt left blockgt valve covergt right block-gtflywheel housing and (6) for 2500ndash4000Hz gear cover-gt left blockgtflywheel housinggt oil pangt valve covergt rightblock

It can be seen that the input PCPS of the oil pan is thelargest between a wide frequency band of 500ndash1800Hz It isbecause the lower vibration modes of such a thin-walledcomponent are easy to excite due to the excitation of thebody skirt In other frequency bands the gear cover showsthe largest input PCPS below 500Hz and above 1800Hz+emain reasons are the resonances of the component in thelow-frequency range and the dynamic meshing force be-tween gear teeth at high frequency So the above twocomponents are the top 2 contributors in most cases For theleft block the amplitude of input PCPS in 1800ndash4000Hz isconsiderable because the fuel injection pump and the aircompressor radiate great portion of noise in this high-frequency range

43 Weighting Analysis of Noise Sources

431 Analytic Hierarchy Tree As analysed above for aspecific component (noise source) its contribution to thenoise varies in different aspects such as the frequency bandthe testing point and the engine speed On this basis thehierarchy tree (Figure 8) for weighting the noise sourcesconsists of five levels from top to bottom (1) objective level(2) operating speed level (3) testing point level (4) fre-quency band level and (5) noise sources level

432 Fuzzy Consistency Matrix +e fuzzy consistencymatrices for the frequency level are constructed according tothe condition coherent power spectra and listed in Table 3Based on the one-third octave SPL the fuzzy consistencymatrices for the test point level and the operating speed levelcan be calculated in the same way Table 4 shows the fuzzyconsistency matrix for the left testing point (C1) Table 5presents the fuzzy consistency matrix for the engine speed of1800 rmin (B3) For the top level the fuzzy consistencymatrix can be obtained based on the usage proportion of theengine speed and the A-weighted SPL as shown in Table 6

433 Weighting Order of Noise Sources Based on theconsistency matrices of adjacent levels the combined weight

Am

plitu

de

400

200

0

120

80

40

0

9

6

3

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Oil pan Le blockRight block

Frequency (Hz)

Am

plitu

de

450

300

150

0

6

4

2

0

120906030

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Value coverFlywheel housing

Gear cover

(e)

60453015

02500 3000 3500 4000

Am

plitu

de

Oil pan

300

200

100

02500 3000 3500 4000

Am

plitu

de

Gear cover

60

40

20

02500 3000 3500

Frequency (Hz)4000

Flywheel housing

12

8

4

02500 3000 3500 4000

Value cover

160120

8040

02500 3000 3500 4000

Le block

864202500 3000 3500 4000

Right block

(f )

Figure 7 +e input partial coherent power spectra of (a) 0ndash500Hz (b) 500ndash800Hz (c) 800ndash1200Hz (d) 1200ndash1800Hz (e) 1800ndash2500Hzand (f) 2500ndash4000Hz

8 Shock and Vibration

matrices can be obtained Table 7 gives the combined weightcoefficients for the left testing point (C1) and Table 8 is thecombined weight coefficients for 1800 rmin (B3) +econtributions of the noise source to the radiated noise atdifferent engine speeds are calculated and shown in Figure 9

+e contribution of the component to the overall noisechanges with the engine speed But some patterns still can be

(A)Weight order

(B1)Idle speed

(B2)1400rmin

(B3)1800rmin

(B4)2200rmin

(C1)Left

(C2)Right

(C3)Front

(C5)Top

(D1)0ndash500Hz

(D2)500ndash800Hz

(D3)800ndash1200Hz

(D4)1200ndash1800Hz

(E3)Right block

(E1)Oil pan

(E2)Left block

(E4)Gear cover

(E5)Flywheel housing

(E6)Valve cover

(D5)1800ndash2500Hz

(D6)2500ndash4000Hz

(C4)Rear

Figure 8 +e hierarchy tree conducted for noise source weighting analysis

Table 3 +e fuzzy consistency matrices for the frequency level

E1 E2 E3 E4 E5 E6 Weight

D10ndash500Hz

E1 0500 0630 0638 0466 0647 0659 0229E2 0370 0500 0508 0336 0517 0529 0134E3 0362 0492 0500 0328 0508 0521 0129E4 0534 0664 0672 0500 0681 0693 0265E5 0363 0483 0492 0319 0500 0512 0125E6 0341 0471 0479 0307 0488 0500 0118

D2 500ndash800Hz

E1 0500 0728 0695 0662 0676 0587 0286E2 0272 0500 0467 0433 0447 0359 0110E3 0305 0533 0500 0467 0481 0393 0126E4 0338 0567 0533 0500 0514 0426 0145E5 0324 0553 0519 0486 0500 0412 0137E6 0413 0641 0607 0574 0588 0500 0197

D3 800ndash1200Hz

E1 0500 0804 0631 0669 0783 0738 0286E2 0196 0500 0327 0365 0479 0433 0187E3 0369 0673 0500 0538 0653 0607 0111E4 0331 0635 0462 0500 0614 0568 0163E5 0217 0521 0348 0386 0500 0454 0117E6 0263 0567 0393 0432 0546 0500 0136

D4 1200ndash1800Hz

E1 0500 0741 0840 0628 0792 0698 0360E2 0259 0500 0599 0387 0552 0458 0122E3 0160 0401 0500 0288 0452 0358 0078E4 0372 0613 0712 0500 0664 0570 0197E5 0208 0448 0548 0336 0500 0406 0097E6 0302 0542 0642 0430 0594 0500 0146

D5 1800ndash2500Hz

E1 0500 0596 0754 0483 0763 0629 0252E2 0404 0500 0658 0388 0667 0533 0166E3 0246 0342 0500 0229 0508 0375 0084E4 0517 0613 0771 0500 0779 0646 0272E5 0238 0333 0492 0221 0500 0367 0082E6 0371 0467 0625 0354 0633 0500 0144

D6 2500ndash4000Hz

E1 0500 0376 0627 0317 0482 0613 0138E2 0624 0500 0751 0441 0607 0738 0236E3 0373 0249 0500 0190 0356 0487 0080E4 0683 0559 0810 0500 0666 0797 0313E5 0518 0393 0644 0334 0500 0631 0149E6 0387 0262 0513 0203 0369 0500 0084

Table 4 +e fuzzy consistency matrix for left testing point (C1) at1800 rmin

C1 D1 D2 D3 D4 D5 D6 WeightD1 0500 0423 0373 0345 0388 0450 0114D2 0577 0500 0450 0422 0464 0527 0157D3 0627 0550 0500 0472 0514 0577 0192D4 0655 0578 0528 0500 0543 0605 0215D5 0613 0536 0486 0458 0500 0563 0181D6 0550 0473 0423 0395 0438 0500 0141

Table 5 +e fuzzy consistency matrix for engine speed of 1800 rmin (B3)

B3 C1 C2 C3 C4 C5 WeightC1 0500 0624 0577 0638 0661 0293C2 0376 0500 0453 0514 0537 0176C3 0423 0547 0500 0561 0584 0213C4 0362 0486 0439 0500 0523 0166C5 0339 0463 0416 0477 0500 0152

Table 6 +e fuzzy consistency matrix for target level (A)

A B1 B2 B3 B4 WeightB1 0500 0412 0312 0350 0155B2 0588 0500 0400 0437 0222B3 0688 0600 0500 0537 0336B4 0650 0563 0463 0500 0287

Shock and Vibration 9

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

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Submit your manuscripts atwwwhindawicom

6

Am

plitu

de 543210

050403020100

06

04

02

000 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Oil panLe block Right block

8

Am

plitu

de 6420

04

02

03

02

01

00000 100 200 300

Frequency (Hz)400 500 0 100 200 300 400 500 0 100 200 300 400 500

Gear cover

Flyweel housingValue cover

(a)

20

Am

plitu

de 1510

50

012

008

004

000

09

06

03

00500 600 700 800 500 600 700 800 500 600 700 800

Oil pan

Le blockRight block

15

Am

plitu

de 10

05

00

10

05

00

43210

Frequency (Hz)500 600 700 800 500 600 700 800 500 600 700 800

Gear coverFlyweel housing

Value cover

(b)

40302010

0

6

4

2

0

0403020100

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Oil pan Le block Right block

4

2

0

0806040200

12

08

04

00

Frequency (Hz)

Am

plitu

de

800 1000 1200 800 1000 1200 800 1000 1200

Value coverFlywheel housingGear cover

(c)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

450

300

150

0

86420

04

02

00

Oil pan Le block Right block

Frequency (Hz)

Am

plitu

de

1200 1400 1600 1800 1200 1400 1600 1800 1200 1400 1600 1800

60

40

20

0

43210

1612

840

Value coverFlywheel housing

Gear cover

(d)

Figure 7 Continued

Shock and Vibration 7

+e coherences of the component to the noise are (1) for0ndash500Hz gear covergt oil pangt right blockgt left block-gtflywheel housinggt valve cover (2) for 500ndash800Hz oilpangt valve covergt gear covergtflywheel housinggt rightblockgt left block (3) for 800ndash1200Hz oil pangt left block-gt gear covergt valve covergtflywheel housinggt right block(4) for 1200ndash1800Hz oil pangt gear covergt valve covergt leftblockgtflywheel housinggt right block (5) for 1800ndash2500Hzgear covergt oil pangt left blockgt valve covergt right block-gtflywheel housing and (6) for 2500ndash4000Hz gear cover-gt left blockgtflywheel housinggt oil pangt valve covergt rightblock

It can be seen that the input PCPS of the oil pan is thelargest between a wide frequency band of 500ndash1800Hz It isbecause the lower vibration modes of such a thin-walledcomponent are easy to excite due to the excitation of thebody skirt In other frequency bands the gear cover showsthe largest input PCPS below 500Hz and above 1800Hz+emain reasons are the resonances of the component in thelow-frequency range and the dynamic meshing force be-tween gear teeth at high frequency So the above twocomponents are the top 2 contributors in most cases For theleft block the amplitude of input PCPS in 1800ndash4000Hz isconsiderable because the fuel injection pump and the aircompressor radiate great portion of noise in this high-frequency range

43 Weighting Analysis of Noise Sources

431 Analytic Hierarchy Tree As analysed above for aspecific component (noise source) its contribution to thenoise varies in different aspects such as the frequency bandthe testing point and the engine speed On this basis thehierarchy tree (Figure 8) for weighting the noise sourcesconsists of five levels from top to bottom (1) objective level(2) operating speed level (3) testing point level (4) fre-quency band level and (5) noise sources level

432 Fuzzy Consistency Matrix +e fuzzy consistencymatrices for the frequency level are constructed according tothe condition coherent power spectra and listed in Table 3Based on the one-third octave SPL the fuzzy consistencymatrices for the test point level and the operating speed levelcan be calculated in the same way Table 4 shows the fuzzyconsistency matrix for the left testing point (C1) Table 5presents the fuzzy consistency matrix for the engine speed of1800 rmin (B3) For the top level the fuzzy consistencymatrix can be obtained based on the usage proportion of theengine speed and the A-weighted SPL as shown in Table 6

433 Weighting Order of Noise Sources Based on theconsistency matrices of adjacent levels the combined weight

Am

plitu

de

400

200

0

120

80

40

0

9

6

3

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Oil pan Le blockRight block

Frequency (Hz)

Am

plitu

de

450

300

150

0

6

4

2

0

120906030

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Value coverFlywheel housing

Gear cover

(e)

60453015

02500 3000 3500 4000

Am

plitu

de

Oil pan

300

200

100

02500 3000 3500 4000

Am

plitu

de

Gear cover

60

40

20

02500 3000 3500

Frequency (Hz)4000

Flywheel housing

12

8

4

02500 3000 3500 4000

Value cover

160120

8040

02500 3000 3500 4000

Le block

864202500 3000 3500 4000

Right block

(f )

Figure 7 +e input partial coherent power spectra of (a) 0ndash500Hz (b) 500ndash800Hz (c) 800ndash1200Hz (d) 1200ndash1800Hz (e) 1800ndash2500Hzand (f) 2500ndash4000Hz

8 Shock and Vibration

matrices can be obtained Table 7 gives the combined weightcoefficients for the left testing point (C1) and Table 8 is thecombined weight coefficients for 1800 rmin (B3) +econtributions of the noise source to the radiated noise atdifferent engine speeds are calculated and shown in Figure 9

+e contribution of the component to the overall noisechanges with the engine speed But some patterns still can be

(A)Weight order

(B1)Idle speed

(B2)1400rmin

(B3)1800rmin

(B4)2200rmin

(C1)Left

(C2)Right

(C3)Front

(C5)Top

(D1)0ndash500Hz

(D2)500ndash800Hz

(D3)800ndash1200Hz

(D4)1200ndash1800Hz

(E3)Right block

(E1)Oil pan

(E2)Left block

(E4)Gear cover

(E5)Flywheel housing

(E6)Valve cover

(D5)1800ndash2500Hz

(D6)2500ndash4000Hz

(C4)Rear

Figure 8 +e hierarchy tree conducted for noise source weighting analysis

Table 3 +e fuzzy consistency matrices for the frequency level

E1 E2 E3 E4 E5 E6 Weight

D10ndash500Hz

E1 0500 0630 0638 0466 0647 0659 0229E2 0370 0500 0508 0336 0517 0529 0134E3 0362 0492 0500 0328 0508 0521 0129E4 0534 0664 0672 0500 0681 0693 0265E5 0363 0483 0492 0319 0500 0512 0125E6 0341 0471 0479 0307 0488 0500 0118

D2 500ndash800Hz

E1 0500 0728 0695 0662 0676 0587 0286E2 0272 0500 0467 0433 0447 0359 0110E3 0305 0533 0500 0467 0481 0393 0126E4 0338 0567 0533 0500 0514 0426 0145E5 0324 0553 0519 0486 0500 0412 0137E6 0413 0641 0607 0574 0588 0500 0197

D3 800ndash1200Hz

E1 0500 0804 0631 0669 0783 0738 0286E2 0196 0500 0327 0365 0479 0433 0187E3 0369 0673 0500 0538 0653 0607 0111E4 0331 0635 0462 0500 0614 0568 0163E5 0217 0521 0348 0386 0500 0454 0117E6 0263 0567 0393 0432 0546 0500 0136

D4 1200ndash1800Hz

E1 0500 0741 0840 0628 0792 0698 0360E2 0259 0500 0599 0387 0552 0458 0122E3 0160 0401 0500 0288 0452 0358 0078E4 0372 0613 0712 0500 0664 0570 0197E5 0208 0448 0548 0336 0500 0406 0097E6 0302 0542 0642 0430 0594 0500 0146

D5 1800ndash2500Hz

E1 0500 0596 0754 0483 0763 0629 0252E2 0404 0500 0658 0388 0667 0533 0166E3 0246 0342 0500 0229 0508 0375 0084E4 0517 0613 0771 0500 0779 0646 0272E5 0238 0333 0492 0221 0500 0367 0082E6 0371 0467 0625 0354 0633 0500 0144

D6 2500ndash4000Hz

E1 0500 0376 0627 0317 0482 0613 0138E2 0624 0500 0751 0441 0607 0738 0236E3 0373 0249 0500 0190 0356 0487 0080E4 0683 0559 0810 0500 0666 0797 0313E5 0518 0393 0644 0334 0500 0631 0149E6 0387 0262 0513 0203 0369 0500 0084

Table 4 +e fuzzy consistency matrix for left testing point (C1) at1800 rmin

C1 D1 D2 D3 D4 D5 D6 WeightD1 0500 0423 0373 0345 0388 0450 0114D2 0577 0500 0450 0422 0464 0527 0157D3 0627 0550 0500 0472 0514 0577 0192D4 0655 0578 0528 0500 0543 0605 0215D5 0613 0536 0486 0458 0500 0563 0181D6 0550 0473 0423 0395 0438 0500 0141

Table 5 +e fuzzy consistency matrix for engine speed of 1800 rmin (B3)

B3 C1 C2 C3 C4 C5 WeightC1 0500 0624 0577 0638 0661 0293C2 0376 0500 0453 0514 0537 0176C3 0423 0547 0500 0561 0584 0213C4 0362 0486 0439 0500 0523 0166C5 0339 0463 0416 0477 0500 0152

Table 6 +e fuzzy consistency matrix for target level (A)

A B1 B2 B3 B4 WeightB1 0500 0412 0312 0350 0155B2 0588 0500 0400 0437 0222B3 0688 0600 0500 0537 0336B4 0650 0563 0463 0500 0287

Shock and Vibration 9

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

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Active and Passive Electronic Components

VLSI Design

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Hindawiwwwhindawicom Volume 2018

Shock and Vibration

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Submit your manuscripts atwwwhindawicom

+e coherences of the component to the noise are (1) for0ndash500Hz gear covergt oil pangt right blockgt left block-gtflywheel housinggt valve cover (2) for 500ndash800Hz oilpangt valve covergt gear covergtflywheel housinggt rightblockgt left block (3) for 800ndash1200Hz oil pangt left block-gt gear covergt valve covergtflywheel housinggt right block(4) for 1200ndash1800Hz oil pangt gear covergt valve covergt leftblockgtflywheel housinggt right block (5) for 1800ndash2500Hzgear covergt oil pangt left blockgt valve covergt right block-gtflywheel housing and (6) for 2500ndash4000Hz gear cover-gt left blockgtflywheel housinggt oil pangt valve covergt rightblock

It can be seen that the input PCPS of the oil pan is thelargest between a wide frequency band of 500ndash1800Hz It isbecause the lower vibration modes of such a thin-walledcomponent are easy to excite due to the excitation of thebody skirt In other frequency bands the gear cover showsthe largest input PCPS below 500Hz and above 1800Hz+emain reasons are the resonances of the component in thelow-frequency range and the dynamic meshing force be-tween gear teeth at high frequency So the above twocomponents are the top 2 contributors in most cases For theleft block the amplitude of input PCPS in 1800ndash4000Hz isconsiderable because the fuel injection pump and the aircompressor radiate great portion of noise in this high-frequency range

43 Weighting Analysis of Noise Sources

431 Analytic Hierarchy Tree As analysed above for aspecific component (noise source) its contribution to thenoise varies in different aspects such as the frequency bandthe testing point and the engine speed On this basis thehierarchy tree (Figure 8) for weighting the noise sourcesconsists of five levels from top to bottom (1) objective level(2) operating speed level (3) testing point level (4) fre-quency band level and (5) noise sources level

432 Fuzzy Consistency Matrix +e fuzzy consistencymatrices for the frequency level are constructed according tothe condition coherent power spectra and listed in Table 3Based on the one-third octave SPL the fuzzy consistencymatrices for the test point level and the operating speed levelcan be calculated in the same way Table 4 shows the fuzzyconsistency matrix for the left testing point (C1) Table 5presents the fuzzy consistency matrix for the engine speed of1800 rmin (B3) For the top level the fuzzy consistencymatrix can be obtained based on the usage proportion of theengine speed and the A-weighted SPL as shown in Table 6

433 Weighting Order of Noise Sources Based on theconsistency matrices of adjacent levels the combined weight

Am

plitu

de

400

200

0

120

80

40

0

9

6

3

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Oil pan Le blockRight block

Frequency (Hz)

Am

plitu

de

450

300

150

0

6

4

2

0

120906030

01800 2000 2200 2400 1800 2000 2200 2400 1800 2000 2200 2400

Value coverFlywheel housing

Gear cover

(e)

60453015

02500 3000 3500 4000

Am

plitu

de

Oil pan

300

200

100

02500 3000 3500 4000

Am

plitu

de

Gear cover

60

40

20

02500 3000 3500

Frequency (Hz)4000

Flywheel housing

12

8

4

02500 3000 3500 4000

Value cover

160120

8040

02500 3000 3500 4000

Le block

864202500 3000 3500 4000

Right block

(f )

Figure 7 +e input partial coherent power spectra of (a) 0ndash500Hz (b) 500ndash800Hz (c) 800ndash1200Hz (d) 1200ndash1800Hz (e) 1800ndash2500Hzand (f) 2500ndash4000Hz

8 Shock and Vibration

matrices can be obtained Table 7 gives the combined weightcoefficients for the left testing point (C1) and Table 8 is thecombined weight coefficients for 1800 rmin (B3) +econtributions of the noise source to the radiated noise atdifferent engine speeds are calculated and shown in Figure 9

+e contribution of the component to the overall noisechanges with the engine speed But some patterns still can be

(A)Weight order

(B1)Idle speed

(B2)1400rmin

(B3)1800rmin

(B4)2200rmin

(C1)Left

(C2)Right

(C3)Front

(C5)Top

(D1)0ndash500Hz

(D2)500ndash800Hz

(D3)800ndash1200Hz

(D4)1200ndash1800Hz

(E3)Right block

(E1)Oil pan

(E2)Left block

(E4)Gear cover

(E5)Flywheel housing

(E6)Valve cover

(D5)1800ndash2500Hz

(D6)2500ndash4000Hz

(C4)Rear

Figure 8 +e hierarchy tree conducted for noise source weighting analysis

Table 3 +e fuzzy consistency matrices for the frequency level

E1 E2 E3 E4 E5 E6 Weight

D10ndash500Hz

E1 0500 0630 0638 0466 0647 0659 0229E2 0370 0500 0508 0336 0517 0529 0134E3 0362 0492 0500 0328 0508 0521 0129E4 0534 0664 0672 0500 0681 0693 0265E5 0363 0483 0492 0319 0500 0512 0125E6 0341 0471 0479 0307 0488 0500 0118

D2 500ndash800Hz

E1 0500 0728 0695 0662 0676 0587 0286E2 0272 0500 0467 0433 0447 0359 0110E3 0305 0533 0500 0467 0481 0393 0126E4 0338 0567 0533 0500 0514 0426 0145E5 0324 0553 0519 0486 0500 0412 0137E6 0413 0641 0607 0574 0588 0500 0197

D3 800ndash1200Hz

E1 0500 0804 0631 0669 0783 0738 0286E2 0196 0500 0327 0365 0479 0433 0187E3 0369 0673 0500 0538 0653 0607 0111E4 0331 0635 0462 0500 0614 0568 0163E5 0217 0521 0348 0386 0500 0454 0117E6 0263 0567 0393 0432 0546 0500 0136

D4 1200ndash1800Hz

E1 0500 0741 0840 0628 0792 0698 0360E2 0259 0500 0599 0387 0552 0458 0122E3 0160 0401 0500 0288 0452 0358 0078E4 0372 0613 0712 0500 0664 0570 0197E5 0208 0448 0548 0336 0500 0406 0097E6 0302 0542 0642 0430 0594 0500 0146

D5 1800ndash2500Hz

E1 0500 0596 0754 0483 0763 0629 0252E2 0404 0500 0658 0388 0667 0533 0166E3 0246 0342 0500 0229 0508 0375 0084E4 0517 0613 0771 0500 0779 0646 0272E5 0238 0333 0492 0221 0500 0367 0082E6 0371 0467 0625 0354 0633 0500 0144

D6 2500ndash4000Hz

E1 0500 0376 0627 0317 0482 0613 0138E2 0624 0500 0751 0441 0607 0738 0236E3 0373 0249 0500 0190 0356 0487 0080E4 0683 0559 0810 0500 0666 0797 0313E5 0518 0393 0644 0334 0500 0631 0149E6 0387 0262 0513 0203 0369 0500 0084

Table 4 +e fuzzy consistency matrix for left testing point (C1) at1800 rmin

C1 D1 D2 D3 D4 D5 D6 WeightD1 0500 0423 0373 0345 0388 0450 0114D2 0577 0500 0450 0422 0464 0527 0157D3 0627 0550 0500 0472 0514 0577 0192D4 0655 0578 0528 0500 0543 0605 0215D5 0613 0536 0486 0458 0500 0563 0181D6 0550 0473 0423 0395 0438 0500 0141

Table 5 +e fuzzy consistency matrix for engine speed of 1800 rmin (B3)

B3 C1 C2 C3 C4 C5 WeightC1 0500 0624 0577 0638 0661 0293C2 0376 0500 0453 0514 0537 0176C3 0423 0547 0500 0561 0584 0213C4 0362 0486 0439 0500 0523 0166C5 0339 0463 0416 0477 0500 0152

Table 6 +e fuzzy consistency matrix for target level (A)

A B1 B2 B3 B4 WeightB1 0500 0412 0312 0350 0155B2 0588 0500 0400 0437 0222B3 0688 0600 0500 0537 0336B4 0650 0563 0463 0500 0287

Shock and Vibration 9

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

matrices can be obtained Table 7 gives the combined weightcoefficients for the left testing point (C1) and Table 8 is thecombined weight coefficients for 1800 rmin (B3) +econtributions of the noise source to the radiated noise atdifferent engine speeds are calculated and shown in Figure 9

+e contribution of the component to the overall noisechanges with the engine speed But some patterns still can be

(A)Weight order

(B1)Idle speed

(B2)1400rmin

(B3)1800rmin

(B4)2200rmin

(C1)Left

(C2)Right

(C3)Front

(C5)Top

(D1)0ndash500Hz

(D2)500ndash800Hz

(D3)800ndash1200Hz

(D4)1200ndash1800Hz

(E3)Right block

(E1)Oil pan

(E2)Left block

(E4)Gear cover

(E5)Flywheel housing

(E6)Valve cover

(D5)1800ndash2500Hz

(D6)2500ndash4000Hz

(C4)Rear

Figure 8 +e hierarchy tree conducted for noise source weighting analysis

Table 3 +e fuzzy consistency matrices for the frequency level

E1 E2 E3 E4 E5 E6 Weight

D10ndash500Hz

E1 0500 0630 0638 0466 0647 0659 0229E2 0370 0500 0508 0336 0517 0529 0134E3 0362 0492 0500 0328 0508 0521 0129E4 0534 0664 0672 0500 0681 0693 0265E5 0363 0483 0492 0319 0500 0512 0125E6 0341 0471 0479 0307 0488 0500 0118

D2 500ndash800Hz

E1 0500 0728 0695 0662 0676 0587 0286E2 0272 0500 0467 0433 0447 0359 0110E3 0305 0533 0500 0467 0481 0393 0126E4 0338 0567 0533 0500 0514 0426 0145E5 0324 0553 0519 0486 0500 0412 0137E6 0413 0641 0607 0574 0588 0500 0197

D3 800ndash1200Hz

E1 0500 0804 0631 0669 0783 0738 0286E2 0196 0500 0327 0365 0479 0433 0187E3 0369 0673 0500 0538 0653 0607 0111E4 0331 0635 0462 0500 0614 0568 0163E5 0217 0521 0348 0386 0500 0454 0117E6 0263 0567 0393 0432 0546 0500 0136

D4 1200ndash1800Hz

E1 0500 0741 0840 0628 0792 0698 0360E2 0259 0500 0599 0387 0552 0458 0122E3 0160 0401 0500 0288 0452 0358 0078E4 0372 0613 0712 0500 0664 0570 0197E5 0208 0448 0548 0336 0500 0406 0097E6 0302 0542 0642 0430 0594 0500 0146

D5 1800ndash2500Hz

E1 0500 0596 0754 0483 0763 0629 0252E2 0404 0500 0658 0388 0667 0533 0166E3 0246 0342 0500 0229 0508 0375 0084E4 0517 0613 0771 0500 0779 0646 0272E5 0238 0333 0492 0221 0500 0367 0082E6 0371 0467 0625 0354 0633 0500 0144

D6 2500ndash4000Hz

E1 0500 0376 0627 0317 0482 0613 0138E2 0624 0500 0751 0441 0607 0738 0236E3 0373 0249 0500 0190 0356 0487 0080E4 0683 0559 0810 0500 0666 0797 0313E5 0518 0393 0644 0334 0500 0631 0149E6 0387 0262 0513 0203 0369 0500 0084

Table 4 +e fuzzy consistency matrix for left testing point (C1) at1800 rmin

C1 D1 D2 D3 D4 D5 D6 WeightD1 0500 0423 0373 0345 0388 0450 0114D2 0577 0500 0450 0422 0464 0527 0157D3 0627 0550 0500 0472 0514 0577 0192D4 0655 0578 0528 0500 0543 0605 0215D5 0613 0536 0486 0458 0500 0563 0181D6 0550 0473 0423 0395 0438 0500 0141

Table 5 +e fuzzy consistency matrix for engine speed of 1800 rmin (B3)

B3 C1 C2 C3 C4 C5 WeightC1 0500 0624 0577 0638 0661 0293C2 0376 0500 0453 0514 0537 0176C3 0423 0547 0500 0561 0584 0213C4 0362 0486 0439 0500 0523 0166C5 0339 0463 0416 0477 0500 0152

Table 6 +e fuzzy consistency matrix for target level (A)

A B1 B2 B3 B4 WeightB1 0500 0412 0312 0350 0155B2 0588 0500 0400 0437 0222B3 0688 0600 0500 0537 0336B4 0650 0563 0463 0500 0287

Shock and Vibration 9

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

found +e oil pan is the most significant contributor re-gardless of engine speed followed by the gear cover and theleft block At lower engine speeds idle and 1400 rmin thecontributions from gear cover and left block are quite closewhile the gear cover contributes more at higher enginespeeds (1800 rmin and 2200 rmin) +e contributions ofthe right block the flywheel and the valve cover are similarand less important in this case

434 Result Validation and Discussion +e overallweighting coefficients of the components to the radiatednoise (Table 9) are calculated on the basis of the combinedweight matrices considering the surface area effect +esurface area effect here relates to the outer surface of thecomponent and acts by means of area factor A componentwith the large outer surface is supposed to make greatercontribution to the noise radiation comparing with a smallerone Without considering the surface area effect theweighting order of components is oil pangt gear covergt left

blockgt valve covergt flywheel housinggt right block Whenthe surface area is taken into account the weighting orderslightly changes into oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

+e calculated weighting order of the components tothe overall noise is verified using the near-field noise indifferent operating conditions +e measured near-fieldnoise of components and the computed weighting orderunder 700 rmin are given in Table 10 as an example It canbe seen from the comparison that the calculated weightingorder of components are consistent with the near-field noisemeasurement +is clearly proves the validity of the pro-posed approach for noise source weighting of the dieselengine

According to the overall weighting order the mainobjective of the noise control of this diesel engine can bedetermined But the detailed strategy still depends on thecontributions from different aspects engine speed andfrequency band Table 11 gives the weight coefficients of theengine component regarding the frequency range of 0ndash500Hz at the engine speed of 1800 rmin +e calculatedweighting orders of noise sources to the noise in differentfrequency bands at different speeds are given in Figure 10

Table 7+e combined weight matrix for the left testing point (C1)

C1-D-E D10114

D20157

D30192

D40215

D50181

D60141 Weight

E1 0229 0286 0286 0360 0252 0138 0268E2 0134 0110 0187 0122 0166 0236 0158E3 0129 0126 0111 0078 0084 0080 0099E4 0265 0145 0163 0197 0272 0313 0220E5 0125 0137 0117 0097 0082 0149 0115E6 0118 0197 0136 0146 0144 0084 0140

Table 8 +e combined weight matrix for the engine speed of1800 rmin (B3)

B3-C-D-E C10293

C20176

C30213

C40166

C50152 Weight

E1 0268 0259 0259 0263 0266 0263E2 0158 0163 0162 0162 0161 0161E3 0099 0104 0105 0103 0102 0102E4 0220 0215 0212 0213 0212 0215E5 0115 0119 0120 0118 0117 0118E6 0140 0140 0142 0141 0142 0141

03

02

01

00

Wei

ght

Oil pan Le block Right block Gear cover Flywheelhousing

Valve cover

Idle speed

1400rmin

1800rmin

2200rmin

Figure 9 +e weight of components at different speeds

Table 9+e final weight matrix of components to the overall noise

AndashEB1 B2 B3 B4 Area

factor

Overall weight

0155 0222 0336 0287 Withoutarea effect

Witharea effect

E1 0255 0261 0263 0256 0405 0259 0421E2 0195 019 0161 017 0196 0176 0138E3 0136 0107 0102 0105 0213 0109 0094E4 0162 0179 0215 0217 0162 0199 0129E5 0134 0115 0118 0116 0202 0120 0097E6 0118 0148 0141 0136 0221 0137 0121

Table 10 +e tested near-field noise and the weighting order ofcomponents at 700 rmin

Components Near-fieldnoise (dB)

Calculatedweighting order

Oil pan left block 1011 1Left block 989 2Right block 986 3Gear cover 956 5Flywheel housing 979 4Valve cover 946 6

Table 11 +e combined weight matrix of components for 0ndash500Hz at 1800 rmin

B3-D1-E C1-D10224

C2-D10171

C3-D10244

C4-D10163

C5-D10198 Weight

E1 0229 0247 0243 0246 0238 0240E2 0134 0139 0141 0148 0136 0139E3 0129 0124 0121 0115 0126 0123E4 0265 0239 0248 0247 0251 0251E5 0125 0127 0119 0115 0128 0123E6 0118 0124 0128 0129 0121 0124

10 Shock and Vibration

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)

Wei

ght

500 800 1200 1800 2500 4000

05

04

03

02

01

00

Oil pan Gear coverLe block Flywheel housingRight block Valve cover

One-third octave

(a)

80

40

0

Am

plitu

de (d

B)

Frequency (Hz)W

eigh

t500 800 1200 1800 2500 4000

05

04

03

02

01

00

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(b)

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(c)

Figure 10 Continued

Shock and Vibration 11

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

As discussed above the contribution of components tothe overall noise depends on the frequency band and theengine speed For the radiated noise below 1800Hz the oilpan is almost the greatest contribution for all engine speedsconsidered +e oil pan even dominates over other com-ponents for some frequency bands at some speedseg 500ndash800Hz at 700 rmin 0ndash1800Hz at 1400 rminand 500ndash1800Hz at 1800 rmin In the case of higher fre-quency noise the left block contributes most at 700 rminand 1400 rmin and the gear cover takes the first placeat higher speeds except for the case of 2500ndash4000Hz at2200 rmin

+e 1800 rmin case is the only exception that the gearcover breaks the dominance of the oil pan in the frequencyrange below 1800Hz At this speed the weight of the gearcover is a little bit higher than the oil pan It may be becausethe low-order vibration modes of the gear cover are excitedup due to the rigid connection with the engine block For thesame reason the flywheel housing also contributes con-siderably at idle speed (700 rmin)

+e left block plays an important role in the frequencyrange higher than 1800Hz Since the right side of the engineblock does not show a similar performance as the left sidethe combustion excitation can be excluded from the reasonsbehind It is noted that fuel injection pump and air com-pressor are rigidly mounted on the left block which canradiate high-frequency noise

Apart from the left block the gear cover is even morenoticeable in the frequency range of 1800 to 4000Hz at1800 rmin and 2200 rmin At high speeds the dynamicmeshing force of gears becomes significant and it can di-rectly transmit to the gear cover through the transmissionshaft +erefore a considerable radiated noise from thiscomponent can be found in the high-frequency rangeeg 1800ndash2500Hz and 2500ndash4000Hz

+e radiated noise from the valve cover mainly relates tothe combustion process and the valve movements At lowerspeed it is known the combustion excitation is more sig-nificant than the mechanical excitation Although the noisedue to valve movements is low at low speed the valve coverstill has important effect on the overall noise at 700 rminand 1400 rmin As the engine speed increases the contri-bution of the valve cover decreases first and then rises againIt is because the high-speed movement of the valve partsstarts to take the place

5 Conclusions

An integrated approach of VMD-PCA-FAHP is proposedfor noise source weighting of the diesel engine Based on thenoise and vibration measurement the approach is imple-mented on the weighting analysis and the result is validatedusing the near-field noise Conclusions can be drawn asfollows

(1) +e integrated VMD-PCA-FAHP approach is ap-plicable in noise source identification and weightinganalysis of the diesel engine It can provide reliableweighting results in terms of contribution of enginecomponent to noise

(2) +e VMD decomposes the noise signal into severalmeaningful IMFs and the frequency bands can bedetermined by the time-frequency analysis +ecorrelations between component vibration and noisecan be dig out by the PCA without coupled effectfrom other components

(3) +e FAHP eliminates the subjective influence of juryevaluation on the conduction of the consistencymatrix It also simplifies the process in searching theweighting matrix of high consistency

80

40

0

Am

plitu

de (d

B)

Wei

ght

05

04

03

02

01

00

Frequency (Hz)500 800 1200 1800 2500 4000

Gear coverFlywheel housing

Oil panLe blockRight block Valve cover

One-third octave

(d)

Figure 10 Contributions of the noise source to the noise in different frequency bands at (a) 700 rmin (b) 1400 rmin (c) 1800 rmin and(d) 2200 rmin

12 Shock and Vibration

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

(4) Considering the surface area effect the overallweighting order of engine components to the radi-ated noise is oil pangt left blockgt gear covergt valvecovergt flywheel housinggt right block

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors gratefully acknowledge the National Key RampDProgram of China (2017YFC0211301)

References

[1] S drsquoAmbrosio and A Ferrari ldquoDiesel engines equipped withpiezoelectric and solenoid injectors hydraulic performance ofthe injectors and comparison of the emissions noise and fuelconsumptionrdquo Applied Energy vol 211 pp 1324ndash1342 2018

[2] A J Torregrosa A Broatch R Novella et al ldquoImpact ofgasoline and diesel blends on combustion noise and pollutantemissions in premixed charge compression ignition enginesrdquoEnergy vol 137 pp 58ndash68 2017

[3] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSoundquality prediction for engine-radiated noiserdquo MechanicalSystems and Signal Processing vol 56-57 pp 277ndash287 2015

[4] C Serviere J L Lacoume and ME Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine Part IIseparation of combustion noise and piston-slap using blindsource separationrdquo Mechanical Systems amp Signal Processingvol 19 no 6 pp 1218ndash1229 2005

[5] M-H Lu and M U Jen ldquoSource identification and reductionof engine noiserdquo Noise Control Engineering Journal vol 58no 3 pp 251ndash258 2010

[6] S Bruhl and A Roder ldquoAcoustic noise source modellingbased on microphone array measurementsrdquo Journal of Soundand Vibration vol 231 pp 611ndash617 2000

[7] R D Sante and G L Rossi ldquoA new approach to the mea-surement of transverse vibration and acoustic radiation ofautomotive belts using laser Doppler vibrometry and acousticintensity techniquesrdquo Measurement Science and Technologyvol 12 pp 525ndash533 2001

[8] M E Badaoui J Daniere F Guillet and C Serviere ldquoSep-aration of combustion noise and piston-slap in diesel engine-part I separation of combustion noise and piston-slap indiesel engine by cyclic Wiener filteringrdquo Mechanical Systemsand Signal Processing vol 19 no 6 pp 1209ndash1217 2005

[9] M Akil and C Serviere ldquoSeparability of convolutive mixturesapplication to the separation of combustion noise and piston-slap in diesel enginerdquo in Independent Component Analysisand Blind Signal Separation pp 319ndash326 Springer BerlinHeidelberg 2006

[10] J Wang L Tang Y Luo et al ldquoA weighted EMD-basedprediction model based on TOPSIS and feed forward neuralnetwork for noised time seriesrdquo Knowledge-Based Systemsvol 132 pp 167ndash178 2017

[11] Y Zhang J Lian and F Liu ldquoAn improved filtering methodbased on EEMD and wavelet-threshold for modal parameteridentification of hydraulic structurerdquoMechanical Systems andSignal Processing vol 68-69 pp 316ndash329 2016

[12] M Buzzoni E Mucchi and G Dalpiaz ldquoA CWT-basedmethodology for piston slap experimental characterizationrdquoMechanical Systems and Signal Processing vol 86 pp 16ndash282017

[13] X Liu and R B Randall ldquoBlind source separation of internalcombustion engine piston slap from other measured vibrationsignalsrdquo Mechanical Systems and Signal Processing vol 19no 6 pp 1196ndash1208 2005

[14] A Albarbar F Gu and A D Ball ldquoDiesel engine fuel in-jection monitoring using acoustic measurements and in-dependent component analysisrdquoMeasurement vol 43 no 10pp 1376ndash1386 2010

[15] W Tao T Schuller M Huet and F Richecoeur ldquoCoherententropy induced and acoustic noise separation in compactnozzlesrdquo Journal of Sound and Vibration vol 394 pp 237ndash255 2017

[16] T L Saaty ldquo+e analytic hierarchy process planning prioritysetting resource allocationrdquo in Fe Analytic Hierarchy Pro-cess Planning Priority Setting Resource Allocation McGraw-Hill New York NY USA 1980

[17] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo Interfaces vol 24 no 6 pp 19ndash43 1994

[18] X Liang ldquoNon-harmonic radiation noise source identifica-tion of engines based on the cepstrum analysis and analytichierarchy processrdquo in Proceedings of SAE Technical PapersSeries p 4 Washington DC USA May 2013

[19] J Zhang J Wang J Lin et al ldquoDiesel engine noise sourceidentification based on EEMD coherent power spectrumanalysis and improved AHPrdquo Measurement Science ampTechnology vol 26 no 9 article 095010 2015

[20] H Nezarat F Sereshki and M Ataei ldquoRanking of geologicalrisks in mechanized tunneling by using fuzzy analytical hi-erarchy process (FAHP)rdquo Tunnelling and Underground SpaceTechnology vol 50 pp 358ndash364 2015

[21] J Ooi M A B Promentilla R R Tan et al ldquoIntegration offuzzy analytic hierarchy process into multi-objective com-puter aided molecular designrdquo Computers amp Chemical En-gineering vol 109 2018

[22] H J Zimmermann Fuzzy Set Feory-and Its ApplicationsKluwer-Nijhoff Pub Leiden Netherlands 1985

[23] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8no 3 pp 338ndash353 1965

[24] Y Min and S Zhang ldquoFuzzy consistent matrix and its ap-plicationrdquo Journal of Systems Engineering amp Electronics vol 8no 1 pp 57ndash64 2012

[25] L W Lee Group Decision Making with Incomplete FuzzyPreference Relations Based on the Additive Consistency andthe Order Consistency Pergamon Press Inc Oxford UK2012

[26] S-M Chen T-E Lin and L-W Lee ldquoGroup decisionmaking using incomplete fuzzy preference relations based onthe additive consistency and the order consistencyrdquo In-formation Sciences vol 259 no 14 pp 1ndash15 2014

[27] J Krej On Additive Consistency of Interval Fuzzy PreferenceRelations Pergamon Press Inc Oxford UK 2017

[28] H Zhou M Jia Y Feng et al ldquoEvaluation system for au-tomatic fare gate capacity based on delphi and improvedFAHPrdquo in Proceedings of Data Driven Control and LearningSystems Conference pp 754ndash759 Chongqing China May2017

Shock and Vibration 13

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[29] J-P Gao Z-S Xu D-L Liu and H-H Cao ldquoApplication ofthe model based on fuzzy consistent matrix and AHP in theassessment of fire risk of subway tunnelrdquo Procedia Engi-neering vol 71 no 16 pp 591ndash596 2014

[30] K Dragomiretskiy and D Zosso ldquoVariational mode de-compositionrdquo IEEE Transactions on Signal Processing vol 62no 3 pp 531ndash544 2014

[31] P Dey U Satija and B Ramkumar ldquoSingle channel blindsource separation based on variational mode decompositionand PCArdquo in Proceedings of 2015 Annual IEEE India Con-ference (INDICON) pp 1ndash5 New Delhi India December2015

[32] G Shu and X Liang ldquoIdentification of complex diesel enginenoise sources based on coherent power spectrum analysisrdquoMechanical Systems and Signal Processing vol 21 no 1pp 405ndash416 2007

[33] H B Huang X R Huang M L Yang T C Lim andW P Ding ldquoIdentification of vehicle interior noise sourcesbased on wavelet transform and partial coherence analysisrdquoMechanical Systems and Signal Processing vol 109 pp 247ndash267 2018

14 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom