Research Article Multifeatures Fusion and Nonlinear Dimension …downloads.hindawi.com/journals/sv/2016/4632562.pdf · 2019-07-30 · Research Article Multifeatures Fusion and Nonlinear

Research ArticleMultifeatures Fusion and Nonlinear Dimension Reduction forIntelligent Bearing Condition Monitoring

Liang Guo Hongli Gao Haifeng Huang Xiang He and ShiChao Li

School of Mechanical Engineering Southwest Jiaotong University Chengdu 610031 China

Correspondence should be addressed to Hongli Gao hongli gaohomeswjtueducn

Received 17 October 2015 Revised 7 January 2016 Accepted 17 January 2016

Academic Editor Peng Chen

Copyright copy 2016 Liang Guo et al This 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

Condition-based maintenance is critical to reduce the costs of maintenance and improve the production efficiency Data-drivenmethod based on neural network (NN) is one of the most used models for mechanical components condition recognitionIn this paper we introduce a new bearing condition recognition method based on multifeatures extraction and deep neuralnetwork (DNN) First the method calculates time domain frequency domain and time-frequency domain features to representcharacteristic of vibration signalsThen the nonlinear dimension reduction algorithm based on deep learning is proposed to reducethe redundancy information Finally the top-layer classifier of deep neural network outputs the bearing condition The proposedmethod is validated using experiment test-bed bearing vibration data Meanwhile some comparative studies are performed theresults show the advantage of the proposed method in adaptive features selection and superior accuracy in bearing conditionrecognition

1 Introduction

Bearing degradation is one of themost common fault sourcesin rotating machinery system Unexpected bearing failurecan lead to large costs of maintenance and loss of revenueTraditionally the maintenance activity is selected from pre-ventive and corrective maintenance However preventivemaintenance may typically involve the high maintenancecosts and corrective maintenance may reduce the productiveefficiency [1 2] So condition-based maintenance based oncondition monitoring is critical to assure safe and efficientoperation of rotating machinery system [3]

Generally among the various approaches of bearingcondition monitoring it can be classified into two categoriessignal processing-based approaches and pattern recognition-based approaches In signal processing-based approachessome mathematical or statistical operations are performedon the measurement signal and then the bearing conditionis judged through the prior knowledge of human beingsThe kurtosis coefficient is a major indicator of bearingperformance degradation detection [4] The other statisticalparameters such as the first-order moment (eg mean 119909) thesecond-order moment (eg variance 1205902) and Crest Factor

are utilized in the study of bearing condition monitoringusually The statistical analysis method is widely used forits simplicity and computation [5] Spectrum analysis is alsoeffective in tracking fault of bearing [6] Spectral kurtosisin frequency domain is an effective tool to enhance themachinery fault features [7] For bearing condition mon-itoring and fault diagnosis envelope spectrum analysis isused for diagnostics bearing where faults signal has anamplitudemodulating effect on the characteristic frequencies[8] However the spectral analysis method has no timescale information In order to overcome that shortcomingsome new approaches based on time-frequency analysis areproposed for bearing faults detecting and localizing Shi et al[9] proposed a wavelet-based envelop spectrum method todetect the defect in rolling element bearings

Meanwhile pattern recognition-based condition moni-toring is composed of two parts feature extraction and pat-tern recognition The signal processing-based feature extrac-tion approach is a basic step in conditionmonitoring Patternrecognition is another critical issue Classification-basedmachine learning algorithms are commonly used in industryand academic fields for condition recognition [10] Support

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 4632562 10 pageshttpdxdoiorg10115520164632562

2 Shock and Vibration

vector machines (SVMs) map the input data into high-dimension space with different kernel functions to efficientlyperform a nonlinear classification Abbasion et al [11] presenta new method based on wavelet analysis (WP) and supportvector machine (SVM) to diagnosis of multifault of bearingArtificial neural networks (ANN) are able to learn expertknowledge through a representative set of data So ANNis commonly adopted in automated detection of machineconditions [12] Bin et al [13] extract the fault characteristicscombined empiricalmode decomposition andwavelet packetdecomposition Then BP neural network is taken to identifythemodel of bearing In addition to BP neural network fuzzyneural network [14] conditional random field [15] recurrentneural network [16] and radial basis function neural network[17] are also applied in bearing intelligent condition moni-toring Deep neural network (DNN) is a new kind of neuralnetwork architectures that attempts to abstract the high-levelfeatures from the raw signal through multilayer nonlineartransformation [18] Hinton and Salakhutdinov [19] point outthat deep learning can convert high-dimensional data to low-dimension nonlinearly by training a multilayer neural net-work Since then deep neural network has widely been usedin speech recognition [20] image recognition [21] naturallanguage processing [22] and some other classification andrecognition applications But recently the bearing conditionmonitoring based on deep neural network almost cannot befound in academic and industrial

In this paper we propose a new method based on mul-tifeatures fusion and DNN nonlinear dimension reductionto recognize bearing condition The time domain featuresfrequency domain features and time-frequency features arefused for integrating the bearing condition features Thosefeatures are input into the deep neural network (DNN) asthe input vector Then the DNN model will extract the high-level abstraction of input data and recognize the bearingcondition The remainder of this paper is organized asfollows The proposed method is presented in Section 2Section 3 discusses the case study where the proposedmethod is validated through real-world bearing vibrationsignal Section 4 presents the conclusion and future work

2 Condition Recognition Usingthe Proposed Method

The proposed method for bearing condition monitor-ing mainly includes three steps feature extraction fea-ture dimension reduction and condition recognition Thedetailed process is as follows

21 Feature Extraction The presence of defect of machinerycomponents can barely be determined from the raw accelera-tion signal To get a better understanding of the raw vibrationsignal we tried to extract the time domain frequency domainand time-frequency domain features

211 Time Domain Features Time domain features of vibra-tion signals have proved to be useful to present themachinerycondition FromTable 1 we apply those classical time domain

Table 1 Time domain features extraction

Name Formula

RMS 1198751199051= radic

1

119873

119873

sum

119899=1

119909 (119899)2

Skewness 1199011199052=

1

119873

119873

sum

119899=1

(119909 (119899) minus 119909)3

1205903

Kurtosis 1199011199053=

1

119873

119873

sum

119899=1

(119909 (119899) minus 119909)4

1205904

minus 2

Peak to Peak 1199011199054= 119909max minus 119909min

Crest Factor 1199011199055=

|119909 (119899)|maxRMS

Shape Factor 1199011199056=

RMS(1119873)sum

119873

119899=1|119909 (119899)|

Impulse Factor 1199011199057=

|119909 (119899)|max

(1119873)sum119873

119899=1|119909 (119899)|

Margin Factor 1199011199058=

|119909 (119899)|maxRMS

statistical features to represent the bearing condition ThePeak to Peak value calculates the difference between themaximum and minimum value in the signal The RootMean Square (RMS)measures the power content of vibrationsignal Those are the first moment and second moment ofprobability distribution Skewness an asymmetrymeasure isdefined as the third moment Kurtosis a descriptor of signalshape is based on a scaled calculation of the fourth momentof the data The Crest Factor Shape Factor Impulse Factorand Margin Factor are some dimensionless quantities thatgovern the bearing degeneration behavior

212 Frequency Domain Features The signal spectrum con-tains rich condition information The spectral kurtosis indi-cating the presence of short transients and their frequencylocations is obtained by calculating the kurtosis from eachfrequency band For a number 119872 of 119873-point realization atthe frequency index119898 the spectral kurtosis is given as [23]

119866SK (119898) =sum119872

119894=1

10038161003816100381610038161003816119883119894

119873(119898)

10038161003816100381610038161003816

4

(sum119872

119894=1

1003816100381610038161003816119883119894

119873(119898)

1003816100381610038161003816

2

)

2minus 2 (1)

where 119872 is the realization of the process that contains 119873points And 119883

119894 is the data from frequency transform Inpractice the categories of failures are not known Similar tothe rolling bearing the inner outer races and the cage faultshave the chance to appear So the frequency signatures aredifficult to obtain due to the fact that the fault may concernall the components of the test bearing at the same timeWe proposed a new condition indicator which is obtained

Shock and Vibration 3

by calculating the correlation coefficient between the twovibration signals

CO119883119884=

sum119873

119894=1(119909119894minus 119909) (119910

119894minus 119909)

radicsum119873

119894=1(119909119894minus 119909)2radicsum119873

119894=1(119910119894minus 119909)2

(2)

where 119909119894and 119910

119894are two spectral kurtosis vectors of size119873 119909

119894

is the standard spectral kurtosis frequency distribution 119910119894is

the spectral kurtosis of current signal And 119909 and 119910 are theircorresponding means

213 Time-Frequency Domain Features Wavelet transfer(WT) decomposes signal into time-frequency space and hasthe excellent performance to present the signal characteristicHowever WT just subdivides signal into low-frequencybands To get more detailed signal frequency representationthe wavelet package transform (WPT) is performedThroughthe WPT a signal can be divided into high-frequency andlow-frequency bands with the binary tree form At eachdecomposition levels the signal is divided into two mutualorthogonal subspaces

119880119895119896= 119880119895+12119896

oplus 119880119895+12119896+1

(3)

where 119895 indicates the tree level and 119896 is the node index inlevel 119895 The dividing is operating until decomposition level119869 then the process will produce 2119869 subspaces which aremutual orthogonal subspaces The WP function 119882119899

119895119896(119905) is

mathematically expressed as below [24]

119882119899

119895119896(119905) = 2

1198952119882119899(2119895119905 minus 119896) (4)

where 119895 and 119896 are the scale and translation parametersrespectively 119899 is the oscillation parameter So the WP coef-ficients 119878119899

119895119896are obtained by the inner product between the

signal 119909(119905) and the WP functions119882119899119895119896 as below

119878119899

119895119896= ⟨119909119882

119899

119895119896⟩ = int

infin

minusinfin

119909 (119905)119882119899

119895119896(119905) 119889119905 (5)

22 Deep Neural Network Feature vector selection anddimension reduction facilitate the pattern classificationDeepneural network (DNN) attempts to abstract the high-leveldata structure by using multiple nonlinear transformationFrom Figure 1 the main processing step includes layeredpretraining and fine-tuning In this paper the AutoencoderDNN structure is applied to process the multidimensionalfeature data

221 Pretraining During the pretraining stage an Autoen-coder network consists of three layers the input layer thehidden layer and the output layer Firstly the input layer 119909is mapped into the hidden layer 119910 with the equation

119910 = 119904 (W119909 + 119887) (6)

where W is the weight matrix 119887 is the bias value and 119904 is atransfer function usually it is nonlinear such as the sigmoid

Original feature

Reconstruction

Hidden layer 1 Original feature

Hidden layer 1

H layer 2

Output

Fine-tuning

Hidden layer 1

Reconstruction

Hidden layer 2

Pretraining

Figure 1 The framework for deep learning

function This processing is called encoder Secondly thedecoder processing maps the hidden layer 119910 into the outputlayer 119911 with the equation

119911 = 119904 (W1015840119910 + 1198871015840) (7)

where the weight matrix W1015840 is constrained to the transposeof the encoder mapping W1015840 = W119879 The output value 119911 isseen as the prediction of input 119909with the code value 119910 So thenetwork is optimized by minimizing the error between thevalues 119911 and 119909 such as 119871(119909119911) = 119909 minus 1199112 So the loss functioncan be described as

119871119867(119909 119911) = minus

119889

sum

119896=1

[119909119896log 119911119896+ (1 minus 119909

119896) log (1 minus 119911

119896)] (8)

The code layer (hidden layer) 119910 has fewer nodes thanthe input and output layer It can be seen as the compressedrepresentation of the input layer This is similar to the PCAdata dimensionality reduction But the Autoencoder is thenonlinear method

222 Fine-Tuning The multihidden layers of the Autoen-coder are unsupervised pretrainingThen those hidden layersare combined with the Softmax classifier to construct thedeep neural networkThe fine-tuning trains the whole neuralnetwork with the supervised learning method to improve theperformance During the fine-tuning all layers are stackedinto a single model so all of the model parameters canbe optimized Backpropagation algorithm for fine-tuningAutoencoder is used And the detailed equations and deriva-tion process can be found in [25]

23 Structure of the Proposed Method To estimate the oper-ation condition of rolling bearing a new feature extractionand process scheme is proposed in this paper The goal of themethod is to extract the bearing conditionrsquos indicator featuresand fuse those features to the recognition model to indicatethe bearing operation condition Then the deep neuralnetwork reduces the features matrix dimension nonlinearly


Data preprocess

Data preprocess

Multifeaturesextraction

Model pretraining Model fine-turning

Feature dimensionreduction

Bearing condition

DNN

DNN

Model training

Bearing condition recognition

Softmaxclassification


Figure 2 The framework for bearing condition estimation

and recognizes the bearing condition As shown in Figure 2the proposed method is described as follows

Step 1 Preprocess the raw signal with normalization

Step 2 Extract features of the input signal with time domainfrequency domain and time-frequency domain

Step 3 Smooth the features bymoving average filter and thennormalize the filtered features

Step 4 Pretrain the Autoencoder neural network with thefeatures of training and testing set by unsupervised learning

Step 5 Fine-tune the stacked Autoencoder neural networkwith the label training set

Step 6 Estimate the bearing operation condition under thetrained model

3 Experiments Analysis and Discussion

31 Description of the Platform PRONOSTIA The exper-imentation platform is PRONOSTIA (Figure 3) which isdesigned to validate bearing performance degradation andcondition monitoring assessment In the present experimen-tal test-bed a series of experiments about bearing degradationprocess is performed All kinds of failure inner race faultouter race fault ball fault and so on will have the chance tooccur in the experiment

The platform is mainly consisting of drive part and loadpart In the driven part the asynchronous motor (250W)with a gearbox drives the shaft rotating The testing bearing

Bearing tested Accelerometers

CouplingTorquemeterSpeed sensor

AC motor

Figure 3 The experimental platform PRONOSTIA

inner race is fixed through the shaft The load part isproduced by a force actuator (119901119899119890119906119898119886119905119894119888119895119886119888119896) which exertsan exceeding force of the bearingrsquos maximum dynamic loadon the testing bearing to reduce the bearingrsquos life cycle Twoaccelerometers (1198631198841198791198771198601198733035119861) are mounted horizontallyand vertically on the housing of the test roller bearing topick up the horizontal and the vertical accelerations as shownin Figure 3 The sampling frequency of the data acquisitionis 25600Hz and the vibration data provided by the twoaccelerometers are collected every 1 second [26 27]

The bearing degradation data consists of three categoriesthe first operating condition (1800 rpm and 4000N) thesecond operating condition (1650 rpm and 4200N) and thethird operating condition (1500 rpm and 5000N) Empir-ically the bearing full life cycle can be divided into four


0 500 1000 1500 2000 2500 3000minus60minus40minus20

0204060

Normal Early fault

Training set

Time (s)

0 500 1000 1500 2000 2500minus60minus40minus20

0204060

Testing set

Time (s)

Degradation Fault

Normal Early fault Degradation Fault

Vibr

atio

n m

agni

tude

(mmiddots2

)Vi

brat

ion

mag

nitu

de(m

middots2)

Figure 4 The run-to-fail vibration signal of bearing1 1 andbearing1 3

failure levels normal early fault degradation and failure asshown in Figure 4There are six run-to-fail datasets And thenumber of different testing bearings are 2830 871 911 797515 and 1637 So the total samples are 7534 Half of them(3767) are chosen randomly as the training samples Theother half are used as the testing samples

32 Feature Extraction The raw vibration signals are non-stationary and nontrendable which makes it difficult toobtain the condition estimation According to Section 2the time domain frequency domain and time-frequencydomain feature extractionmethods are applied to indicate thecharacteristics of bearing vibration signal

As Table 1 the eight classical time domain features areshown in Figures 5(a)ndash5(h) From those figures the featuresare almost trend but also with some impulse noise Movingaverage filter is performed to smooth those features with anaverage size 15 determined empirically The red curve is thefiltered feature which is more smooth especially eliminatingthe influence of impulse Normalization of features areconducted to transfer the features within the same scale

For the spectrum kurtosis (SK) in frequency domainWelchrsquos estimate of the SK is employed to indicate thelocations in the frequency domain of the raw signal [28 29]Set window length119882

119899= 28 overlap length 119874

119899= 119882119899lowast 34

and FFT length 119865119899= 2 lowast 119882

119899 The length of raw signal is

2560 through (1) we can get the spectrum kurtosis 119866SKSelect mean of the first five 119866SK as the standard templateof each vibration dataset and the correlation coefficient canbe calculated by (2) Hence Figure 5(i) is regarded as thebearing monitoring index from the frequency domain fea-ture As visual inspection the correlation coefficient curves ofspectrum kurtosis are of significant tendency and noiselessTime-frequency domain features based on wavelet packetdecomposition provide arbitrary time-frequency resolutionof specified signal From Figure 6(a) at the bearing initialoperation stage the frequency component is mainly focusedon 400sim600Hz But with the increase of running timethere are certain changes that come out for the concentrated

frequency band At the end of bearing service it moves downto 0sim200Hz as shown in Figure 6(b)

Based on these observations we quantify the spreadof energy in the time-frequency plane using the sum ofabsolute amplitude Over time the different time-frequencydistributions have different curve trends From Figure 6(c)we separate the six frequency bands 0sim150Hz 151sim300Hz301sim450Hz 451sim600Hz and 601sim800Hz For the severeoscillation of frequency band curve the length of movingaverage filter is set to 21 Figure 6(d) is the filtered andnormalized curves Thus eight time domain features onefrequency domain feature and five time-frequency domainfeatures for individual horizontal and vertical vibration signalare detectedThey are smoothed by the average moving filterAnd for improving the convergence speed of the regressionalgorithm all the features are normalized

33 Results andDiscussion Through all above feature figuresnot all of them have the same important degrees to identifythe bearing condition So before those features are fedinto the classifier we reduce their dimension through deepAutoencoder neural network And it includes two stagespretraining stage and fine-turning stage The pretraining isan unsupervised learning process So in this case we usethe feature data from training and testing set to train theAutoencoder networksThus in the first operation conditionthere are 7534 samples from the six run-to-fail sets withdifferent operation condition In our experiment the neuronrsquosnumber of input layer is 28 the first hidden layer is 20 thesecond hidden layer is 5 and the output layer is 4 Duringthe first hidden layer training the input layerrsquos neurons are28 the hidden layerrsquos neurons are 20 and the output layerrsquosneurons are 28 Through (6)sim(8) the BP algorithm is used totrain the Autoencoder network When the training networkarrives at the stop condition the first hidden layer 119871

1can be

gotThen the first hidden layer1198711is assigned to input layer for

the second hidden layer training The hidden layerrsquos neuronsare 5 Each layer is trained as a denoising Autoencoder byminimizing the reconstruction of its input Once all layersare pretrained the network goes through the second stage oftraining (fine-tuning) Fine-tuning is a supervised learningprocess where we want to minimize prediction error on asupervised task A Softmax classifier layer is added to thetop of the network We then train the whole neural networkto get the optimal parameters And the transfer function ofthe last layer is tanh The results are shown in Table 2 Thedegeneration stage works out the most accuracy rate with982 For comparison PCA dimension reduction SVMclassification and unpretraining method is applied to thedataset to test the classification rate

331 PCA Dimension Reduction Method Principle compo-nent analysis (PCA) is an effective linear data dimensionreduction method [30] and is often used for bearing faultdiagnosis and classification PCA has ability to extract themost significant representation features In the experiment28 features are extracted in every sample PCA is applied tothe training feature sets and just five most distinct principle


Corresponding

500 1000 1500 2000 2500 30000Times (s)

0

1

2

3

4

5

6

7A

mpl

itude

(a) RMS

Corresponding

0

20

40

60

80

100

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(b) Peak to Peak

Corresponding

500 1000 1500 2000 2500 30000Times (s)

minus4

minus3

minus2

minus1

0

1

2

Am

plitu

de

(c) Skewness

Corresponding

0

10

20

30

40

50

60A

mpl

itude

500 1000 1500 2000 2500 30000Times (s)

(d) Kurtosis

Corresponding

08

1

12

14

16

18

2

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(e) Crest Factor

Corresponding

1

2

3

4

5

6

7

8

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(f) Shape Factor

Figure 5 Continued


Corresponding

500 1000 1500 2000 2500 30000Times (s)

2

4

6

8

10

12A

mpl

itude

(g) Impulse Factor

Corresponding

0

5

10

15

20

25

30

35

40

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(h) Margin Factor

Corresponding

minus02

0

02

04

06

08

Mag

nitu

de

500 1000 1500 2000 2500 30000Times (s)

(i) Corresponding coefficient

Figure 5 (a)sim(h) are the time domain features and (i) is the frequency domain feature of bearing1 1

components are accounted Then the transformation matrixbased on the training set is applied to the test signal At last thecompressed features are used for classification by BP neuralnetwork with three layersThe results can be found in Table 2

332 SVM Classification Method Support vector machine(SVM) is a classical supervised learningmodel with the rigor-ous statistical learning theoryThekernel of SVMmodel is theconstruction of kernel function implicitly mapping the inputdata into the high-dimensional spaces And SVMs have beenfound to be remarkably effective in many machinery faultdiagnoses [31] In many bearing fault diagnosis applications[32] the RBF kernel obtains the significant classificationaccuracy rate In the experiment we mainly consider theRBF kernel And the raw features input directly into SVMclassification the result is shown in Table 2

333 The Influence of Unsupervised Prelearning An impor-tant improvement of deep learning is the unsupervisedlearning which does not need the label data to train theneural network [33] And the unsupervised learning canfind the appropriate initial weights values which are helpfulfor optimizing the weights in nonlinear deep learning Forvalidating the significant of pretraining the deep learningmodel is built without unsupervised prelearning its result isshown in Table 2 The result indicates that the unsupervisedprelearning can improve the recognition accurate rate ofbearing condition

334 The Influence of Different Features To investigate theinfluence of different features different feature combinationis analyzed First the features are divided into three cate-gories traditional features (Feature 1) traditional features and


12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006 008

Time (s)

09

08

07

06

05

04

03

02

01

(a) Initial vibration signal

008

12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006

Time (s)

02

04

06

08

1

12

14

16

(b) Final vibration signal

0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

Time (s)

Mag

nitu

de

601sim800Hz451sim600Hz

301sim450Hz151sim300Hz0sim150Hz

(c) Frequency energy

0 500 1000 1500 2000 2500 3000minus1

minus05

0

05

1

15

2

Time (s)

Mag

nitu

de



(d) Smooth and normalization of frequency energy

Figure 6 The time-frequency domain features of bearing1 1

Table 2 The results of different algorithms

Proposed method Proposed PCA SVM UnpretrainingNormal Early fault Degeneration Fault

Normal 0965 0035 0 0 0965 0915 0940 0915Early 0132 0783 0085 0 0783 0788 0774 0777Degeneration 0 0004 0982 0014 0982 0950 0935 0960Fault 0 0 0048 0952 0952 0922 0933 0922Success rate 0965 0783 0982 0952 0935 0898 0909 0897

spectrum kurtosis (Feature 2) traditional features spectrumkurtosis and WPT (Feature 3) Then those featuresrsquo com-bination is reduced dimension and distinguished conditionclassification by deep learningmodelThe result can be found

in Table 3 As you can see the proposed feature extractionmethod can improve the bearing condition recognitionaccuracy And the spectrum kurtosis and WPT features arealso helpful


Table 3 The results of different features combination

Features AccuracyFeature 1 0892Feature 2 0913Feature 3 0935

4 Conclusion and Future Works

Condition-based maintenance based on condition moni-toring is critical to reduce the cost of maintenance andimprove production efficiency of industry In this papera novel method based on multifeatures extraction deepneural network features dimensional reduction and condi-tion recognition is proposed Time frequency and time-frequency domain features are fused to represent the char-acteristic of bearing operation conditionThen the nonlineardimension reduction method based on deep learning isproposed to highlight the hidden patterns and to compressthe information At last a classification in which the differentbearing operation stage is identified is added to the top levelof deep neural network This condition monitoring system isvalidated with real-world vibrationmonitoring data collectedfrom bearing A comparative study is performed between theproposed method and PCA dimension reduction methodSVM classificationmethod unpretrainingmethod and threedifferent featuresrsquo combination Those results demonstratethe advantage of the proposed method in achieving moreaccurate condition estimation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by the National Natural ScienceFoundation of China (no 51275426) and Innovation Fundsof Southwest Jiaotong University

References

[1] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[2] P-L Zhang B Li S-S Mi Y-T Zhang and D-S Liu ldquoBearingfault detection using multi-scale fractal dimensions based onmorphological coversrdquo Shock and Vibration vol 19 no 6 pp1373ndash1383 2012

[3] H Liao E A Elsayed and L-Y Chan ldquoMaintenance ofcontinuously monitored degrading systemsrdquo European Journalof Operational Research vol 175 no 2 pp 821ndash835 2006

[4] S AMcInerny andYDai ldquoBasic vibration signal processing forbearing fault detectionrdquo IEEE Transactions on Education vol46 no 1 pp 149ndash156 2003

[5] R B W Heng and M J M Nor ldquoStatistical analysis of soundand vibration signals for monitoring rolling element bearingconditionrdquo Applied Acoustics vol 53 no 1 pp 211ndash226 1998

[6] L C K Reuben and D Mba ldquoBearing time-to-failure estima-tion using spectral analysis featuresrdquo Structural HealthMonitor-ing vol 13 no 2 pp 219ndash230 2014

[7] C Ruiz-Carcel E Hernani-Ros Y Cao and D Mba ldquoUse ofspectral kurtosis for improving signal to noise ratio of acousticemission signal from defective bearingsrdquo Journal of FailureAnalysis and Prevention vol 14 no 3 pp 363ndash371 2014

[8] P Borghesani R Ricci S Chatterton and P Pennacchi ldquoA newprocedure for using envelope analysis for rolling element bear-ing diagnostics in variable operating conditionsrdquo MechanicalSystems and Signal Processing vol 38 no 1 pp 23ndash35 2013

[9] D F Shi W J Wang and L S Qu ldquoDefect detection forbearings using envelope spectra of wavelet transformrdquo Journalof Vibration and AcousticsmdashTransactions of the ASME vol 126no 4 pp 567ndash573 2004

[10] A Moosavian H Ahmadi A Tabatabaeefar and M Khaz-aee ldquoComparison of two classifiers K-nearest neighbor andartificial neural network for fault diagnosis on a main enginejournal-bearingrdquo Shock and Vibration vol 20 no 2 pp 263ndash272 2013

[11] S Abbasion A Rafsanjani A Farshidianfar and N IranildquoRolling element bearings multi-fault classification based onthe wavelet denoising and support vector machinerdquoMechanicalSystems and Signal Processing vol 21 no 7 pp 2933ndash2945 2007

[12] B Samanta and K R Al-Balushi ldquoArtificial neural networkbased fault diagnostics of rolling element bearings using time-domain featuresrdquoMechanical Systems and Signal Processing vol17 no 2 pp 317ndash328 2003

[13] G F Bin J J Gao X J Li and B S Dhillon ldquoEarly faultdiagnosis of rotating machinery based on wavelet packetsmdashempirical mode decomposition feature extraction and neuralnetworkrdquoMechanical Systems and Signal Processing vol 27 no1 pp 696ndash711 2012

[14] C Chen and G Vachtsevanos ldquoBearing condition predictionconsidering uncertainty an interval type-2 fuzzy neural net-work approachrdquoRobotics andComputer-IntegratedManufactur-ing vol 28 no 4 pp 509ndash516 2012

[15] GWang X Feng and C Liu ldquoBearing fault classification basedon conditional random fieldrdquo Shock and Vibration vol 20 no4 pp 591ndash600 2013

[16] S Seker E Ayaz and E Turkcan ldquoElmanrsquos recurrent neuralnetwork applications to condition monitoring in nuclear powerplant and rotating machineryrdquo Engineering Applications ofArtificial Intelligence vol 16 no 7-8 pp 647ndash656 2003

[17] G S Vijay S P Pai N S Sriram and R B K N Rao ldquoRadialbasis function neural network based comparison of dimen-sionality reduction techniques for effective bearing diagnosticsrdquoProceedings of the Institution of Mechanical Engineers Part JJournal of Engineering Tribology vol 227 no 6 pp 640ndash6532013

[18] Y Bengio ldquoLearning deep architectures for AIrdquo Foundationsand Trends in Machine Learning vol 2 no 1 pp 1ndash27 2009

[19] G E Hinton and R R Salakhutdinov ldquoReducing the dimen-sionality of data with neural networksrdquo Science vol 313 no5786 pp 504ndash507 2006

[20] L Deng G Hinton and B Kingsbury ldquoNew types of deepneural network learning for speech recognition and relatedapplications an overviewrdquo in Proceedings of the 38th IEEE Inter-national Conference on Acoustics Speech and Signal Processing


(ICASSP rsquo13) pp 8599ndash8603 IEEE Vancouver Canada May2013

[21] D Ciregan U Meier and J Schmidhuber ldquoMulti-column deepneural networks for image classificationrdquo in Proceedings of theIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 3642ndash3649 IEEE Providence RI USA June2012

[22] Y Goldberg and O Levy ldquoword2vecexplained derivingMikolov et alrsquos negative-sampling word-embedding methodrdquohttparxivorgabs14023722

[23] J J G de la Rosa and A Moreno Munoz ldquoHigher-order cumu-lants and spectral kurtosis for early detection of subterraneantermitesrdquoMechanical Systems and Signal Processing vol 22 no2 pp 279ndash294 2008

[24] G G Yen and K-C Lin ldquoWavelet packet feature extractionfor vibration monitoringrdquo IEEE Transactions on IndustrialElectronics vol 47 no 3 pp 650ndash667 2000

[25] A Ng Sparse Autoencoder vol 72 of CS294A Lecture Notes2011

[26] P Nectoux R Gouriveau K Medjaher et al ldquoPronostia anexperimental platform for bearings accelerated degradationtestsrdquo in Proceedings of the Conference on Prognostics andHealthManagement pp 1ndash8 Minneapolis Minn USA September2012

[27] E Sutrisno H Oh A S S Vasan and M Pecht ldquoEstimationof remaining useful life of ball bearings using data drivenmethodologiesrdquo in Proceedings of the IEEE Conference onPrognostics and HealthManagement (PHM rsquo12) pp 1ndash7 DenverColo USA June 2012

[28] J Antoni ldquoThe spectral kurtosis a useful tool for characterisingnon-stationary signalsrdquoMechanical Systems and Signal Process-ing vol 20 no 2 pp 282ndash307 2006

[29] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[30] M D Farrell Jr and R M Mersereau ldquoOn the impact of PCAdimension reduction for hyperspectral detection of difficulttargetsrdquo IEEE Geoscience and Remote Sensing Letters vol 2 no2 pp 192ndash195 2005

[31] Q Hu Z He Z Zhang and Y Zi ldquoFault diagnosis of rotatingmachinery based on improved wavelet package transform andSVMs ensemblerdquoMechanical Systems and Signal Processing vol21 no 2 pp 688ndash705 2007

[32] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[33] Q V Le ldquoBuilding high-level features using large scale unsu-pervised learningrdquo in Proceedings of the 38th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo13) pp 8595ndash8598 IEEE Vancouver Canada May 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



vector machines (SVMs) map the input data into high-dimension space with different kernel functions to efficientlyperform a nonlinear classification Abbasion et al [11] presenta new method based on wavelet analysis (WP) and supportvector machine (SVM) to diagnosis of multifault of bearingArtificial neural networks (ANN) are able to learn expertknowledge through a representative set of data So ANNis commonly adopted in automated detection of machineconditions [12] Bin et al [13] extract the fault characteristicscombined empiricalmode decomposition andwavelet packetdecomposition Then BP neural network is taken to identifythemodel of bearing In addition to BP neural network fuzzyneural network [14] conditional random field [15] recurrentneural network [16] and radial basis function neural network[17] are also applied in bearing intelligent condition moni-toring Deep neural network (DNN) is a new kind of neuralnetwork architectures that attempts to abstract the high-levelfeatures from the raw signal through multilayer nonlineartransformation [18] Hinton and Salakhutdinov [19] point outthat deep learning can convert high-dimensional data to low-dimension nonlinearly by training a multilayer neural net-work Since then deep neural network has widely been usedin speech recognition [20] image recognition [21] naturallanguage processing [22] and some other classification andrecognition applications But recently the bearing conditionmonitoring based on deep neural network almost cannot befound in academic and industrial

In this paper we propose a new method based on mul-tifeatures fusion and DNN nonlinear dimension reductionto recognize bearing condition The time domain featuresfrequency domain features and time-frequency features arefused for integrating the bearing condition features Thosefeatures are input into the deep neural network (DNN) asthe input vector Then the DNN model will extract the high-level abstraction of input data and recognize the bearingcondition The remainder of this paper is organized asfollows The proposed method is presented in Section 2Section 3 discusses the case study where the proposedmethod is validated through real-world bearing vibrationsignal Section 4 presents the conclusion and future work

2 Condition Recognition Usingthe Proposed Method

The proposed method for bearing condition monitor-ing mainly includes three steps feature extraction fea-ture dimension reduction and condition recognition Thedetailed process is as follows

21 Feature Extraction The presence of defect of machinerycomponents can barely be determined from the raw accelera-tion signal To get a better understanding of the raw vibrationsignal we tried to extract the time domain frequency domainand time-frequency domain features

211 Time Domain Features Time domain features of vibra-tion signals have proved to be useful to present themachinerycondition FromTable 1 we apply those classical time domain

Table 1 Time domain features extraction

Name Formula

RMS 1198751199051= radic

1

119873

119873

sum

119899=1

119909 (119899)2

Skewness 1199011199052=

1

119873

119873

sum

119899=1

(119909 (119899) minus 119909)3

1205903

Kurtosis 1199011199053=

1

119873

119873

sum

119899=1

(119909 (119899) minus 119909)4

1205904

minus 2

Peak to Peak 1199011199054= 119909max minus 119909min

Crest Factor 1199011199055=

|119909 (119899)|maxRMS

Shape Factor 1199011199056=

RMS(1119873)sum

119873

119899=1|119909 (119899)|

Impulse Factor 1199011199057=

|119909 (119899)|max

(1119873)sum119873

119899=1|119909 (119899)|

Margin Factor 1199011199058=

|119909 (119899)|maxRMS

statistical features to represent the bearing condition ThePeak to Peak value calculates the difference between themaximum and minimum value in the signal The RootMean Square (RMS)measures the power content of vibrationsignal Those are the first moment and second moment ofprobability distribution Skewness an asymmetrymeasure isdefined as the third moment Kurtosis a descriptor of signalshape is based on a scaled calculation of the fourth momentof the data The Crest Factor Shape Factor Impulse Factorand Margin Factor are some dimensionless quantities thatgovern the bearing degeneration behavior

212 Frequency Domain Features The signal spectrum con-tains rich condition information The spectral kurtosis indi-cating the presence of short transients and their frequencylocations is obtained by calculating the kurtosis from eachfrequency band For a number 119872 of 119873-point realization atthe frequency index119898 the spectral kurtosis is given as [23]

119866SK (119898) =sum119872

119894=1

10038161003816100381610038161003816119883119894

119873(119898)

10038161003816100381610038161003816

4

(sum119872

119894=1

1003816100381610038161003816119883119894

119873(119898)

1003816100381610038161003816

2

)

2minus 2 (1)

where 119872 is the realization of the process that contains 119873points And 119883

119894 is the data from frequency transform Inpractice the categories of failures are not known Similar tothe rolling bearing the inner outer races and the cage faultshave the chance to appear So the frequency signatures aredifficult to obtain due to the fact that the fault may concernall the components of the test bearing at the same timeWe proposed a new condition indicator which is obtained



CO119883119884=

sum119873

119894=1(119909119894minus 119909) (119910

119894minus 119909)

radicsum119873

119894=1(119909119894minus 119909)2radicsum119873

119894=1(119910119894minus 119909)2

(2)

where 119909119894and 119910


119894




119880119895119896= 119880119895+12119896

oplus 119880119895+12119896+1

(3)


119895119896(119905) is


119882119899

119895119896(119905) = 2

1198952119882119899(2119895119905 minus 119896) (4)




119878119899

119895119896= ⟨119909119882

119899

119895119896⟩ = int

infin

minusinfin

119909 (119905)119882119899

119895119896(119905) 119889119905 (5)



119910 = 119904 (W119909 + 119887) (6)


Original feature

Reconstruction


Hidden layer 1

H layer 2

Output

Fine-tuning

Hidden layer 1

Reconstruction

Hidden layer 2

Pretraining



119911 = 119904 (W1015840119910 + 1198871015840) (7)


119871119867(119909 119911) = minus

119889

sum

119896=1

[119909119896log 119911119896+ (1 minus 119909

119896) log (1 minus 119911

119896)] (8)





Data preprocess

Data preprocess




Bearing condition

DNN

DNN

Model training

















AC motor






0204060

Normal Early fault

Training set

Time (s)


0204060

Testing set

Time (s)

Degradation Fault


Vibr

atio

n m

agni

tude

(mmiddots2

)Vi

brat

ion

mag

nitu

de(m

middots2)







119899= 119882119899lowast 34







1can be





Corresponding

500 1000 1500 2000 2500 30000Times (s)

0

1

2

3

4

5

6

7A

mpl

itude

(a) RMS

Corresponding

0

20

40

60

80

100

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(b) Peak to Peak

Corresponding

500 1000 1500 2000 2500 30000Times (s)

minus4

minus3

minus2

minus1

0

1

2

Am

plitu

de

(c) Skewness

Corresponding

0

10

20

30

40

50

60A

mpl

itude

500 1000 1500 2000 2500 30000Times (s)

(d) Kurtosis

Corresponding

08

1

12

14

16

18

2

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(e) Crest Factor

Corresponding

1

2

3

4

5

6

7

8

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(f) Shape Factor

Figure 5 Continued


Corresponding

500 1000 1500 2000 2500 30000Times (s)

2

4

6

8

10

12A

mpl

itude

(g) Impulse Factor

Corresponding

0

5

10

15

20

25

30

35

40

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(h) Margin Factor

Corresponding

minus02

0

02

04

06

08

Mag

nitu

de

500 1000 1500 2000 2500 30000Times (s)








12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006 008

Time (s)

09

08

07

06

05

04

03

02

01


008

12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006

Time (s)

02

04

06

08

1

12

14

16


0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

Time (s)

Mag

nitu

de




0 500 1000 1500 2000 2500 3000minus1

minus05

0

05

1

15

2

Time (s)

Mag

nitu

de

















Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











CO119883119884=

sum119873

119894=1(119909119894minus 119909) (119910

119894minus 119909)

radicsum119873

119894=1(119909119894minus 119909)2radicsum119873

119894=1(119910119894minus 119909)2

(2)

where 119909119894and 119910


119894




119880119895119896= 119880119895+12119896

oplus 119880119895+12119896+1

(3)


119895119896(119905) is


119882119899

119895119896(119905) = 2

1198952119882119899(2119895119905 minus 119896) (4)




119878119899

119895119896= ⟨119909119882

119899

119895119896⟩ = int

infin

minusinfin

119909 (119905)119882119899

119895119896(119905) 119889119905 (5)



119910 = 119904 (W119909 + 119887) (6)


Original feature

Reconstruction


Hidden layer 1

H layer 2

Output

Fine-tuning

Hidden layer 1

Reconstruction

Hidden layer 2

Pretraining



119911 = 119904 (W1015840119910 + 1198871015840) (7)


119871119867(119909 119911) = minus

119889

sum

119896=1

[119909119896log 119911119896+ (1 minus 119909

119896) log (1 minus 119911

119896)] (8)





Data preprocess

Data preprocess




Bearing condition

DNN

DNN

Model training

















AC motor






0204060

Normal Early fault

Training set

Time (s)


0204060

Testing set

Time (s)

Degradation Fault


Vibr

atio

n m

agni

tude

(mmiddots2

)Vi

brat

ion

mag

nitu

de(m

middots2)







119899= 119882119899lowast 34







1can be





Corresponding

500 1000 1500 2000 2500 30000Times (s)

0

1

2

3

4

5

6

7A

mpl

itude

(a) RMS

Corresponding

0

20

40

60

80

100

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(b) Peak to Peak

Corresponding

500 1000 1500 2000 2500 30000Times (s)

minus4

minus3

minus2

minus1

0

1

2

Am

plitu

de

(c) Skewness

Corresponding

0

10

20

30

40

50

60A

mpl

itude

500 1000 1500 2000 2500 30000Times (s)

(d) Kurtosis

Corresponding

08

1

12

14

16

18

2

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(e) Crest Factor

Corresponding

1

2

3

4

5

6

7

8

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(f) Shape Factor

Figure 5 Continued


Corresponding

500 1000 1500 2000 2500 30000Times (s)

2

4

6

8

10

12A

mpl

itude

(g) Impulse Factor

Corresponding

0

5

10

15

20

25

30

35

40

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(h) Margin Factor

Corresponding

minus02

0

02

04

06

08

Mag

nitu

de

500 1000 1500 2000 2500 30000Times (s)








12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006 008

Time (s)

09

08

07

06

05

04

03

02

01


008

12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006

Time (s)

02

04

06

08

1

12

14

16


0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

Time (s)

Mag

nitu

de




0 500 1000 1500 2000 2500 3000minus1

minus05

0

05

1

15

2

Time (s)

Mag

nitu

de

















Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Data preprocess

Data preprocess




Bearing condition

DNN

DNN

Model training

















AC motor






0204060

Normal Early fault

Training set

Time (s)


0204060

Testing set

Time (s)

Degradation Fault


Vibr

atio

n m

agni

tude

(mmiddots2

)Vi

brat

ion

mag

nitu

de(m

middots2)







119899= 119882119899lowast 34







1can be





Corresponding

500 1000 1500 2000 2500 30000Times (s)

0

1

2

3

4

5

6

7A

mpl

itude

(a) RMS

Corresponding

0

20

40

60

80

100

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(b) Peak to Peak

Corresponding

500 1000 1500 2000 2500 30000Times (s)

minus4

minus3

minus2

minus1

0

1

2

Am

plitu

de

(c) Skewness

Corresponding

0

10

20

30

40

50

60A

mpl

itude

500 1000 1500 2000 2500 30000Times (s)

(d) Kurtosis

Corresponding

08

1

12

14

16

18

2

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(e) Crest Factor

Corresponding

1

2

3

4

5

6

7

8

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(f) Shape Factor

Figure 5 Continued


Corresponding

500 1000 1500 2000 2500 30000Times (s)

2

4

6

8

10

12A

mpl

itude

(g) Impulse Factor

Corresponding

0

5

10

15

20

25

30

35

40

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(h) Margin Factor

Corresponding

minus02

0

02

04

06

08

Mag

nitu

de

500 1000 1500 2000 2500 30000Times (s)








12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006 008

Time (s)

09

08

07

06

05

04

03

02

01


008

12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006

Time (s)

02

04

06

08

1

12

14

16


0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

Time (s)

Mag

nitu

de




0 500 1000 1500 2000 2500 3000minus1

minus05

0

05

1

15

2

Time (s)

Mag

nitu

de

















Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0204060

Normal Early fault

Training set

Time (s)


0204060

Testing set

Time (s)

Degradation Fault


Vibr

atio

n m

agni

tude

(mmiddots2

)Vi

brat

ion

mag

nitu

de(m

middots2)







119899= 119882119899lowast 34







1can be





Corresponding

500 1000 1500 2000 2500 30000Times (s)

0

1

2

3

4

5

6

7A

mpl

itude

(a) RMS

Corresponding

0

20

40

60

80

100

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(b) Peak to Peak

Corresponding

500 1000 1500 2000 2500 30000Times (s)

minus4

minus3

minus2

minus1

0

1

2

Am

plitu

de

(c) Skewness

Corresponding

0

10

20

30

40

50

60A

mpl

itude

500 1000 1500 2000 2500 30000Times (s)

(d) Kurtosis

Corresponding

08

1

12

14

16

18

2

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(e) Crest Factor

Corresponding

1

2

3

4

5

6

7

8

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(f) Shape Factor

Figure 5 Continued


Corresponding

500 1000 1500 2000 2500 30000Times (s)

2

4

6

8

10

12A

mpl

itude

(g) Impulse Factor

Corresponding

0

5

10

15

20

25

30

35

40

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(h) Margin Factor

Corresponding

minus02

0

02

04

06

08

Mag

nitu

de

500 1000 1500 2000 2500 30000Times (s)








12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006 008

Time (s)

09

08

07

06

05

04

03

02

01


008

12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006

Time (s)

02

04

06

08

1

12

14

16


0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

Time (s)

Mag

nitu

de




0 500 1000 1500 2000 2500 3000minus1

minus05

0

05

1

15

2

Time (s)

Mag

nitu

de

















Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Corresponding

500 1000 1500 2000 2500 30000Times (s)

0

1

2

3

4

5

6

7A

mpl

itude

(a) RMS

Corresponding

0

20

40

60

80

100

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(b) Peak to Peak

Corresponding

500 1000 1500 2000 2500 30000Times (s)

minus4

minus3

minus2

minus1

0

1

2

Am

plitu

de

(c) Skewness

Corresponding

0

10

20

30

40

50

60A

mpl

itude

500 1000 1500 2000 2500 30000Times (s)

(d) Kurtosis

Corresponding

08

1

12

14

16

18

2

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(e) Crest Factor

Corresponding

1

2

3

4

5

6

7

8

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(f) Shape Factor

Figure 5 Continued


Corresponding

500 1000 1500 2000 2500 30000Times (s)

2

4

6

8

10

12A

mpl

itude

(g) Impulse Factor

Corresponding

0

5

10

15

20

25

30

35

40

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(h) Margin Factor

Corresponding

minus02

0

02

04

06

08

Mag

nitu

de

500 1000 1500 2000 2500 30000Times (s)








12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006 008

Time (s)

09

08

07

06

05

04

03

02

01


008

12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006

Time (s)

02

04

06

08

1

12

14

16


0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

Time (s)

Mag

nitu

de




0 500 1000 1500 2000 2500 3000minus1

minus05

0

05

1

15

2

Time (s)

Mag

nitu

de

















Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Corresponding

500 1000 1500 2000 2500 30000Times (s)

2

4

6

8

10

12A

mpl

itude

(g) Impulse Factor

Corresponding

0

5

10

15

20

25

30

35

40

Am

plitu

de

500 1000 1500 2000 2500 30000Times (s)

(h) Margin Factor

Corresponding

minus02

0

02

04

06

08

Mag

nitu

de

500 1000 1500 2000 2500 30000Times (s)








12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006 008

Time (s)

09

08

07

06

05

04

03

02

01


008

12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006

Time (s)

02

04

06

08

1

12

14

16


0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

Time (s)

Mag

nitu

de




0 500 1000 1500 2000 2500 3000minus1

minus05

0

05

1

15

2

Time (s)

Mag

nitu

de

















Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006 008

Time (s)

09

08

07

06

05

04

03

02

01


008

12000

10000

8000

6000

4000

2000

Freq

uenc

y (H

z)

0 002 004 006

Time (s)

02

04

06

08

1

12

14

16


0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

Time (s)

Mag

nitu

de




0 500 1000 1500 2000 2500 3000minus1

minus05

0

05

1

15

2

Time (s)

Mag

nitu

de

















Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Multifeatures Fusion and Nonlinear Dimension …downloads.hindawi.com/journals/sv/2016/4632562.pdf · 2019-07-30 · Research Article Multifeatures Fusion and Nonlinear