Vibration Analysis for Machine Monitoring and Diagnosis: A

Review ArticleVibration Analysis for Machine Monitoring and Diagnosis ASystematic Review

Mohamad Hazwan Mohd Ghazali 1 and Wan Rahiman 12

1School of Electrical and Electronic Engineering Universiti Sains Malaysia Engineering Campus Nibong Tebal 14300Penang Malaysia2Cluster of Smart Port and Logistic Technology (COSPALT) Universiti SainsMalaysia Engineering Campus Nibong Tebal 14300Penang Malaysia

Correspondence should be addressed to Wan Rahiman wanrahimanusmmy

Received 4 July 2021 Revised 3 August 2021 Accepted 25 August 2021 Published 11 September 2021

Academic Editor Gang Tang

Copyright copy 2021 Mohamad Hazwan Mohd Ghazali and Wan Rahiman +is is an open access article distributed under theCreative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium providedthe original work is properly cited

Untimely machinery breakdown will incur significant losses especially to the manufacturing company as it affects the productionrates During operation machines generate vibrations and there are unwanted vibrations that will disrupt the machine systemwhich results in faults such as imbalance wear and misalignment +us vibration analysis has become an effective method tomonitor the health and performance of the machine +e vibration signatures of the machines contain important informationregarding the machine condition such as the source of failure and its severity Operators are also provided with an early warningfor scheduled maintenance Numerous approaches for analyzing the vibration data of machinery have been proposed over theyears and each approach has its characteristics advantages and disadvantages +is manuscript presents a systematic review ofup-to-date vibration analysis for machine monitoring and diagnosis It involves data acquisition (instrument applied such asanalyzer and sensors) feature extraction and fault recognition techniques using artificial intelligence (AI) Several researchquestions (RQs) are aimed to be answered in this manuscript A combination of time domain statistical features and deep learningapproaches is expected to be widely applied in the future where fault features can be automatically extracted from the rawvibration signals +e presence of various sensors and communication devices in the emerging smart machines will present a newand huge challenge in vibration monitoring and diagnosing

1 Introduction

Machines are widely used in todayrsquos industries and areparamount for factory operation Careful monitoring of themachines must be done and when the machines dobreakdown unexpectedly it will cause massive loss to thecompany +is can be prevented by diagnosing the machineto determine the fault or potential fault such as imbalancewear misalignment defective bearing friction whirl andcracking teeth in gearing [1 2] Several available diagnosismethods have been applied over the years including oilanalysis vibration signal analysis particle analysis corro-sion monitoring acoustic signal analysis and wear debrisanalysis [3 4] Among these analyses acoustic and vibrationsignal analysis emerge as popular choices because many

faults can be identified without stopping the machine ortearing themachine down+e changes of these signals oftenindicate the presence of a fault Acoustic analysis has theadvantages of short analysis time high recognition effi-ciency and nondestructive testing However it is verychallenging to properly capture the acoustic signals due toseveral factors such as environmental conditions differentparameter of recording software and reflected acousticsignals [5] Vibration signals analysis also has some ad-vantages and disadvantages Real-time machine monitoringcan be achieved using vibration analysis and there are manywell-developed signal processing techniques that can beapplied +e limitations of vibration analysis are noisecontamination and proper mounting position of the vi-bration sensors [6] Another technique that can be used for

HindawiShock and VibrationVolume 2021 Article ID 9469318 25 pageshttpsdoiorg10115520219469318

machine monitoring and diagnosis is thermal imaginganalysis In this analysis an infrared camera is usually usedto detect many electrical faults in the machine based on thethermal anomalies +e thermal images obtained are usefulin detecting and locating the machinersquos faults However thistechnique is expensive and requires a longer time to processthe thermal images compared to processing the acoustic andvibration signals Vibration analysis is considered as the bestmethod in determining the machine condition [7]According to Saucedo-Dorantes et al [8] the percentage offault diagnosis techniques conducted with the means ofvibration analysis exceeds 82 Machines are mostly madeup of moving parts that generate unwanted vibration andwith vibration analysis and a decision on whether themachine can continue to operate or needs to be shut downand repaired can be made [3]

+e machinersquos condition can be determined by the vi-bration amplitude and frequency as both can reveal theseverity and source of the machine problem respectively [9]At first without the help of vibration equipment machineconditions can still be diagnosed with a human brain oftrained personnel coupled with the senses of touch andhearing which acts as a vibration analyzer However humanperception is somewhat limited and it is impossible to detectproblems that are beyond the capability of human senses oftouch and hearing +en vibration analysis was based on areal-time spectral analyzer and now it can be categorizedinto time frequency and time-frequency domain [10] Timeand frequency domain analysis analyses the time series ofdata with respect to time and frequency respectively Time-frequency domain analysis used both time and frequencydomains at the same time [3] Vibration analysis for mostmachine monitoring and diagnosis can be divided into low-speed and high-speed machines Because currently there isno universally accepted speed range to differentiate bothtypes of machines machines with rotating speeds up to600 rpm such as wind turbines and paper mills are con-sidered low-speed machines According to Kim et al [11]low-speed machines can be very time-consuming and moredifficult to monitor compared to high-speed machines as therotating elements and the fault is typically low unless thefault has reached above the background noise level Vi-bration monitoring of low-speed machines is highly asso-ciated with low-speed bearing in ensuring the reliability ofthe machine

+e vibration analysis for machine monitoring anddiagnosis typically consists of three main steps which aredata acquisition signal processing and fault recognitionTo date there are lots of techniques and instruments usedin each of the aforementioned steps and choosing the rightones might be quite challenging +is is because eachmethod and instrument have its characteristics advan-tages and disadvantages +ese methods can be dividedinto two main groups which are model-based and data-driven methods Model-based methods require an ana-lytical model of the system whereas data-driven methodsdo not need any assumption about the systemrsquos model Indata-driven methods advanced signal processing tech-niques are applied Because it is very difficult to model a

faulty system data-driven methods are widely applied inmachine diagnosis and monitoring compared to model-based methods +us the main contribution of this articleis the review of various data-driven vibration analysistechniques and instruments used for monitoring and di-agnosing the machines However due to a wide range oftechniques only the widely used ones are discussed in thisarticle +ere are several review articles regarding this areaand Table 1 discusses each of the review articles Based onTable 1 we aimed to fill the research gap in reviewing thevibration analysis for machine monitoring and diagnosiswhere the data acquisition system and comparison be-tween different vibration analysis techniques including thelatest deep learning approach are not discussed We alsoaimed to answer the following research questions de-scribed in Table 2

+is manuscript is organized as follows In the nextsection the research approach for this review article isdiscussed +en Sections 3ndash5 will follow the vibrationanalysis steps as shown in Figure 1 Firstly in Section 3the data acquisition stage is discussed +is stage involvesthe types of vibration sensors used to obtain the vibrationdata and analyzers for analyzing the acquired data +edata acquisition stage is not discussed in most of thepublished review articles Besides different sensormounting techniques are also discussed in this sectionSection 4 is about the signal processing or feature ex-traction methods performed by researchers over the yearsbased on the time frequency and time-frequency do-mains +e final stage in vibration analysis which is thefault recognition stage is discussed in Section 5 In thissection different AI-based methods such as supportvector machine (SVM) neural network (NN) includingdeep learning fuzzy logic and genetic algorithm (GA) inthe fault recognition step are discussed +e discussionsand findings of our review are explained in Section 6 andwe conclude our studies in Section 7

2 Research Approach

A comprehensive literature study was conducted to an-swer the five research questions A Systematic LiteratureReview (SLR) approach was employed to collect the rel-evant primary studies regarding the vibration analysis formachine monitoring and diagnosis [17] Firstly weclassified the articles and the selected papers were thenanalyzed and differentiated through the content analysismethod +e results can be classified into four maincategories

(1) Survey where review articles made by other re-searchers on vibration analysis for machine moni-toring and diagnosis are discussed

(2) Simulation where the performance of the proposedtechnique is evaluated through simulation methods

(3) Experimentreal-time deployments where themethods developed are applied experimentally or inreal environments

2 Shock and Vibration

(4) Performance comparison where the proposedtechnique is utilized and compared with othermethods in terms of accuracy or robustness

+e databases used for the electronic search wereMultidisciplinary Digital Publishing Institute (MDPI) In-stitute of Electrical and Electronics Engineers (IEEE) XploreAssociation for Computing Machinery (ACM) Digital Li-brary ScienceDirect Web of Science Wiley Online LibraryResearchgate Springer Scopus and Google Scholar Torefine the search results a set of inclusion and exclusioncriteria is used in determining the relevant articles whichcan be observed in Table 3

+e article searching process starts by selecting themain search term ldquomachine monitoringrdquo or ldquomachinediagnosisrdquo +e second search term was ldquovibration analy-sisrdquo So the search sentence was as follows ldquomachinemonitoringrdquo OR ldquomachine diagnosisrdquo AND ldquovibrationanalysisrdquo +e reason why we decided to use these simplekeywords is to get good coverage of potential studies Nextwe refine the search terms by adding the ldquoartificial intel-ligencerdquo term such as SVM NN deep learning fuzzy logicand GA as the third term+e first and second search termsare retained +e aim is to obtain the missing articles aftersearching with the ldquomachine monitoringrdquo or ldquomachinediagnosisrdquo and ldquovibration analysisrdquo terms 100 relatedstudies were targeted to provide enough information forcategorization and research trends Next we classified allthe selected articles into the aforementioned categories+e total number of suitable articles collected was 105 andsome of the articles could be classified into more than onecategory

3 Data Acquisition Methods (RQ 1)

According to Elango et al [10] a trained worker withoutacademic qualifications can carry out the data collectionwork but data processing work in determining the conditionof the machine requires an engineer Referring to Figure 2there are two instruments that are crucial in the data col-lecting stage which are analyzer and sensor Vibration

analyzer can be divided into standalone and computer-basedanalyzer whereas vibration sensor consists of accelerometervelocity transducer displacement sensor and laser Dopplervibrometer (LDV)+e accelerometer can be further dividedinto piezoelectric and microelectromechanical system(MEMS) accelerometer

4 Analyzer

Analyzer is an instrument used to analyze the vibration dataproduced by machinery It is composed of a sensor (which ispresented in the later section of this paper) amplifier filterand AD converter +e signal from the vibration sensorpasses through the amplifier to increase the resolution andsignal-to-noise ratio +e amplified signal then passesthrough a filter so that aliasing would not be encountered inthe digitization stage +e signal is digitized in AD con-verter and then it goes through the processing unit where itcan be portrayed as a time waveform or can be furtherprocessed to acquire frequency spectrum [10 18] +e vi-bration analyzer can be divided into conventional andcomputer-based vibration analyzer A conventional vibra-tion analyzer is a standalone instrument that is specificallybuilt for vibration It is a complex and expensive instrumentusually used by vibration experts +is instrument can helpthe user to determine the presence of a problem as well as itsroot cause and time for the machine to fail +ere are singledual and four-channel analyzers available in the market Asingle channel analyzer can only receive an input from oneaccelerometer at a time whereas a dual-channel analyzer canreceive inputs from two differently placed accelerometers atthe same time [19] A four-channel analyzer can accept inputfrom multiple sensors and capable of measuring horizontalvertical axial and early bearing detection simultaneously Itis usually used with a triaxial accelerometer +e key ad-vantage of a four-channel analyzer is the ability to observethe operating deflection shape (ODS) of a machine Nuawiet al [20] used a four-channel vibration analyzer in themonitoring process of bearing condition and the applicationof a dual-channel analyzer for machine monitoring can beseen in [21 22] Another cheaper alternative is a handheldvibration meter +is battery-powered device is equipped

Table 1 List of review articles or survey regarding vibration analysis for machine monitoring and diagnosis

Authors Scope CommentsVishwakarma et al[12]

Presented a review of some vibration feature extractionmethods applied to different types of rotating machines

No discussion on the data acquisition system and AI-based fault recognition techniques

Kumar et al [3]Reviewed various techniques including the AI methodsused for fault diagnosis based on vibration analysis

methods

No discussion on the data acquisition system and thecomparison between different feature extraction and

fault recognition methods are not presented

Boudiaf et al [13]Presented the vibration analysis techniques in terms oftheir capabilities advantages and disadvantages in

monitoring rolling element bearings

Only discussed four types of vibration analysistechniques

Aherwar [14]Discussed a variety of vibration analysis approaches indiagnosing the rotating machinery including the AI

methods

No discussion on the data acquisition system and thereview was conducted in 2012 thus it lacks the latest AI

methods such as deep learningSait and Sharaf-Eldeen [15]

Presented a review of vibration-based analysis damagedetection techniques to monitor gearbox condition

No discussion on the data acquisition system frequencydomain methods and AI techniques

Sadeghi et al [16] Discussed on the fault diagnosis in large electricalmachines using vibration signals

Most of the vibration analysis techniques are notdiscussed in this article

Shock and Vibration 3

with an accelerometer and provides a display of vibrationlevels when in contact with machinery [19] It requires verylittle skill to use but its measurement capability is somewhatlimited and lacking in data storage performance

A computer-based vibration analyzer is an emerginginstrument where vibration data can be processed virtuallywith the help of specific software and a personal computer+is method has gained popularity because it is simpleinexpensive and easy to repair and can perform most of thefunctions available in the conventional vibration analyzersuch as oscilloscope multimeter and waveform generatorLabVIEW is a widely used programming language in thismethod due to numerous arrays of data acquisition cardsand measurement systems supported by it [23ndash25] Ansariand Baig [23] used the computer-based vibration analyzer tomonitor the condition of the machine and they found that a

conventional vibration analyzer is faster and more accurateTo overcome these limitations dedicated hardware such asDigital Signal Processor (DSP) or Field Programmable GateArray (FPGA) was used alongside a personal computer andsensor for user control and result display [18] +e computerprocessor usually has to handle the whole operating systemin addition to the virtual analyzer whereas the DSP onlyperforms one task+is makes the vibration analysis faster ina computer equipped with DSP In [26] vibration analysison the rotating machine has been conducted by employingtwo DSPs Rangel-Magdaleno et al [27] has conducted avibration analysis on the CNC machine using an FPGAdevice FPGA played a role in processing the vibration dataand the computer screen portrayed the results obtained forfurther analysis Rodriguez-Donate et al [28] developed anonline monitoring system for the induction motor with the

Start

Analyzer

Sensor

Time Domain

Frequency Domain

Time-FrequencyDomain

AI-Based

Data Acquisition

Feature ExtractionSignal Processing

Fault Recognition

End

Figure 1 +e framework of the article where data acquisition stage is discussed first followed by feature extraction techniques and faultrecognition approaches based on AI

Table 2 +e research questions aimed to be answered in this study

RQ MotivationRQ 1 what are the current and future instruments used for themachinersquos vibration data acquisition process

+e answer to this question helps to determine the best instrumentto be applied for respective vibration analysis

RQ 2 what are the most used vibration signal processing techniquesand the comparison between them including the advantages andlimitations of each method

Answering this question can help to determine the most appliedtechniques and identifying the benefits and drawbacks of each

vibrationrsquos signal processing methodsRQ 3 what are the latest AI techniques used in machine vibrationmonitoring and diagnosis and how does it perform compared toother widely used AI methods

By answering this question the latest AI method applied in machinevibration monitoring and diagnosis can be identified and the

performance can be compared with the widely used AI methodsRQ 4 what are the future directions regarding vibration analysis formachine monitoring and diagnosis

+e answer to this question can help new researchers fill the researchgap regarding this area

RQ 5 what are the most influential articles for each method Answering this question can help the readers identify the articles thatcan be used as references for their research


implementation of FPGA and they found that the FPGA-based system has better processing speed compared to DSPand all the peripheral digital structures and processing unitcan be included in a single chip Compared to DSP acomputer-based vibration analyzer using FPGA is betterbecause it can achieve true parallelism Both devices actuallyprovide better performances than using only a computer-based vibration analyzer [18] More information regardingDSP and FPGA analyzers can be found in [29ndash31]

5 Sensor

A sensor or transducer is a device that converts mechanicalsignals to electrical signals [32] +e type of sensors used isusually based on the frequency range sensitivity design andoperational limitations No matter what type of sensors isused the stiffer the mounting of the sensor the higher thefrequency range and its reading accuracy [33] In vibrationanalysis there are three widely used sensors for acquiring thevibration signal +ese sensors are accelerometer velocityand displacement sensor+e noncontact LDV sensor is alsodiscussed in this section +e advantages and disadvantagesof each vibration sensor can be seen in Table 4

51 Sensor Mounting Method Choosing a mounting methodas well as implementing it correctly is an important factor invibration data collection For continuous or online monitoringof machine condition vibration sensors are usually mountedpermanently at a specific location in the machine Mountingcan be divided into fourmainmethods namely stud-mountedadhesive-mounted magnet-mounted and nonmounted Studmounting is usually preferable for permanent mounting ap-plications +e sensor is screwed in a stud and secured to themachine Apart from highly reliable and secure this mountingtechnique has the widest frequency response compared toother methods Make sure that the location where the sensor isgoing to be mounted is clean and paint free because any ir-regularities in the mounting surface will produce impropermeasurements or worst damage to the sensor itself [19] Foradhesive mounting no extensive machining is required asepoxy glue or wax will be applied If the machine cannot bedrilled for stud mounting adhesive mounting is generally thebest alternative Although this mounting technique is easy toapply the accuracy of the measurement is reduced because ofthe presence of damping in the adhesive [19] In addition tothat it is also more difficult to remove the sensor compared toother mounting methods +e magnetic mounting method is

Table 3 +e inclusion and exclusion criteria used for articles searching in this study

Inclusion criteria Exclusioncriteria

Articles should fall into one of the four categories mentioned in this studyArticles that arenot written in

English

Articles should meet both the search terms

Articles that arenot related tothe vibrationanalysis formachine

monitoring anddiagnosis

Articles are published or accepted during the period between 1996 and 2021 (covering 25 years period) Duplicatedarticles

Articles should be listed at least in one of the research databasesArticles should be published or accepted at a conference journal magazines or theses

Data Acquisition

SensorAnalyzer

LDVDisplacementSensor

VelocityTransducer

MEMSPiezoelectric

AccelerometerComputer-BasedAnalyzer

ConventionalStandalone Analyzer

Figure 2 +e data acquisition stage of the proposed review article


usually limited to temporary applications with a portableanalyzer and not preferable for permanent monitoring becausethe high-frequency signals might be disrupted +e non-mounting method is typically applied by a probe tip wherethere is no external mechanism between the transducer and thetarget surface It is usually used in areas that are difficult toreach +e length of the probe tip however will affect themeasurement with longer probes lead to more inaccuracies

52 Accelerometer An accelerometer is a device used tomeasure the vibration or acceleration of a structure in the SIunit of g (m) +e working mechanism is that when thepiezoelectric material in the accelerometer is subjected to aforce it produces a charge corresponding to the force ap-plied Because force is directly proportional to the accel-eration any change to this factor will produce a change inthe charge produced which is then amplified [33] Uniaxialaccelerometer can only detect movement in one planewhereas triaxial accelerometer covers all the three dimen-sions Compared to the uniaxial accelerometer triaxial ac-celerometer has a higher memory capacity but much moreexpensive [34] Accelerometer is a widely used sensor due toits reliability simplicity and robustness It can be furtherdivided into a piezoelectric and MEMS accelerometer Pi-ezoelectric accelerometer relies on the piezoelectric effect ofquartz or ceramic crystals which are usually preloaded togenerate an electrical output that is proportional to theapplied acceleration Changes in the charge produced de-pend on this acceleration [35 36] Piezoelectric acceler-ometer possesses several advantages such as better frequencyand dynamic range lightweight and high sensitivityHowever it is vulnerable to interference from the externalenvironment [37] It also requires electronic integration inorder to obtain velocity and displacement data because it isAC coupled [37] Salami et al [38] demostrated the appli-cation of LabVIEW in monitoring and analyzing the vi-bration signals where piezoelectric accelerometer was usedin their study Igba et al [39] installed the piezoelectricaccelerometer sensor on the operational turbines to obtainthe vibration data for time domain analysis Khadersab andShivakumar [40] used the piezoelectric accelerometer toobtain vibration data from rotating machinery to analyze thebearing faults Figure 3(a) shows the vibration measurementpiezoelectric accelerometer

MEMS accelerometer usually consists of movable proofmass with plates supported by a mechanical suspensionsystem to the frame [41] When it is subjected to acceler-ation the proof mass tends to resist motion due to its owninertia and therefore the spring is stretched or compressedAs a result force corresponds to the applied acceleration iscreated MEMS accelerometer is DC coupled and verysuitable for measuring low-frequency vibration and accel-eration It requires low processing power and providessuperior sensitivity [41] Modern MEMS accelerometerprovides quite good data quality up to several tens of kHz+e drawback is that it suffers from a poor signal-to-noiseratio Contreras-Medina et al [42] used a low-cost MEMSaccelerometer in detecting machinery failures Chaudhury

et al [41] used the MEMS accelerometer in different rotatingmachines for vibration monitoring A performance com-parison between conventional piezoelectric accelerometerand MEMS accelerometer can be seen in [43 44] It wasfound that MEMS accelerometerrsquos sensitivity is more stablecompared with the piezoelectric accelerometers and thislow-cost MEMS accelerometer can be a good alternative tothe high-cost piezoelectric accelerometer +is sensor hasalso been applied in [26 39]

53 Velocity Transducer A velocity transducer measures thevoltage produced by the relative movement of the objectusually in the ms or cms unit It works based on theconcept of electromagnetic induction and it can operatewithout any external device [45] As the surface where thesensor is mounted vibrates the movement of the magnet inthe coil will produce a voltage proportional to the velocity ofthe vibration [46] +is voltage signal represents the vi-bration produced and is then feeds a meter or analyzer [33]Velocity sensors are not recommended when diagnosing thehigh-speed machinery because the operational frequencyrange is limited from 10Hz to 2 kHz [10] Generally velocitytransducer costs less than other sensors and coupled with itseasy installation feature it is favorable in monitoring thevibration of rotating machinery However it is big heavyand most velocity transducers are prone to reliabilityproblems at operational temperatures that exceed 121degC[37 47] A velocity transducer was applied by Rossi [48] tomeasure the frame vibration of compressor which usuallycomprises of frequencies below 10Hz Figure 3(b) shows thevibration measurement using velocity transducer

54 Displacement Sensor A displacement sensor which issometimes called eddy current or proximity sensor measuresboth relative vibration and position of the shaft +e dis-placement unit can be in m cm or mm It is usually used inmeasuring low-frequency vibration of less than 10Hz but itcan also measure vibration up to 300Hz [45] However theydo not excel in measuring a shaft bending away from theprobe location [47] Unbalance and misalignment problemsare the types of problems that can be detected by the dis-placement probe For the measured vibration frequenciesabove 1 kHz the amplitude is usually lost in the noise level[47] It has the advantages of a good dynamic range within aspecific frequency range reasonable sensitivity and a simplepostprocessing circuit with negligible maintenance How-ever it is difficult to install susceptible to shocks and sometraditional displacement sensors are not calibrated for un-known metal materials [37] Sarhan et al [49] used thedisplacement sensor in monitoring the cutting forces of themachining center under different cutting conditions Sai-mon et al [50] developed a low-cost fiber optic displacementsensor (FODS) for industrial applications that is immune toelectromagnetic interference +e capability of a fiber opticdisplacement sensor in capturing the amplitude and fre-quency of vibration was studied by Binu et al [51] and basedon the results this sensor can solve many sensing problemsin aircraft


55 LDV LDV is a noncontact optical measurement in-strument that can be applied to determine the vibrationvelocities of any points on the surface of a particular ma-chine [52 53] +e working mechanism of LDV is based onthe laser Doppler concept where a frequency-modulatedcoherent laser beam is reflected from a vibrating surface andDoppler shift of the reflected beam is compared with thereference beam Currently a higher power infrared (in-visible) fiber laser is more popular in LDV compared to theHe-Ne laser+e introduction of this technology has fulfilledthe goal of achieving long-range measurements withoutcompromising the signal quality [54] Continuous-scan laserDoppler vibrometry (CSLDV) has accelerated the mea-surement at many points +e laser beam will scan con-tinuously along a defined path across a structure accordingto the desired scan frequencies One major advantage ofLDV is the ease of changing the measurement point whichcan be done by just deflecting the laser beam Despite thatthe application of LDV in machine monitoring and diag-nosis is limited because of the price and portability factors

6 Feature ExtractionSignal ProcessingMethod(RQ 2)

Figure 4 shows the feature extractionsignal processing stageinvolved in this study It can be divided into time frequencyand time domain frequency analysis +e time domainanalysis involves the statistical features of peak root-mean-square (RMS) crest factor and kurtosis +e frequencydomain analysis consists of fast Fourier transform (FFT)cepstrum analysis envelope analysis and spectrum analysiswhereas time-frequency domain analysis can be divided intoWT HilbertndashHuang transform (HHT) WignerndashVille dis-tribution (WVD) short-time Fourier transform (STFT) andPower Spectral Density (PSD)

7 Time Domain Analysis

+e simplest vibration analysis for machine diagnosis is usedto analyze the measured vibration signal in the time domainVibration signals obtained are a series of values representingproximity velocity and acceleration and in time domainanalysis the amplitude of the signal is plotted against time

Although other sophisticated time domain approaches havebeen used the approach of visually looking at the timewaveform should not be underestimated because numerousinformation can be obtained in this manner +is infor-mation includes the presence of amplitudemodulation shaftunbalance transient and higher-frequency components[55] However simply looking into these vibration signalscannot segregate the variations in vibration signals fordifferent machine failures due to the noisy data especially atthe early stage of failure +us a signal processing method isrequired to obtain the important information from the timedomain signals by converting the raw signals into appro-priate statistical parameters such as peak RMS crest factorand kurtosis Several statistical parameters are usuallyextracted from the time domain signal so that the mostsignificant parameter which can effectively differentiatebetween healthy and defective machine vibration signalscan be chosen [56] In this article the statistical parametersof peak RMS crest factor and kurtosis are discussed and theadvantages and disadvantages of each parameter can be seenin Table 5

71 Peak +e peak is the maximum value of the signal v(t)over measured time and can be defined as [55]

peak |v(t)|max (1)

If there is a presence of impacts the peak values of thevibration signal will vary Under a fault condition the peakvalue increases +e faultrsquos severity and type can be assessedbased on the amplitudes of the corresponding peaks Peakvalue feature was studied by Lahdelma and Juuso [57] todiagnose bearing and gear faults in the machine +e pro-posed approach is suitable for online analysis as the re-quirements for frequency range are small Shrivastava andWadhwani [58] used statistical parameters such as peakRMS crest factor and kurtosis to diagnose the rotatingelectrical machine Although all parameters can differentiatebetween healthy and faulty conditions they concluded thatdetermining the type of faults in this manner is not veryefficient Igba et al [39] used the peak values approach inmonitoring the condition of wind turbine gearboxes becausefaults can be detected based on the changes in their values

Table 4 +e advantages and disadvantages of various sensors used in vibration analysis for machine monitoring and diagnosis

Sensors Advantages DisadvantagesPiezoelectricaccelerometer

Lightweight high sensitivity goodfrequency dynamic range

Needs electronic integration to acquire velocity and displacement datavulnerable to interference from the external environment

MEMSaccelerometer

Cheaper than piezoelectric sensorrequires low processing power high

sensitivitySuffers from poor signal-to-noise ratio

Velocitytransducer

Can operate without any external devicegenerally costs less than other sensors

Limited operational frequency range most velocity transducers are proneto reliability problems at operational frequency of more than 121degC

Displacementsensor

Good sensitivity simple postprocessingcircuit with negligible maintenance Succeptible to shock difficult to install

LDV

Ease of changing the measurementpoints ability to provide long-rangemeasurements without compromising

the signal quality

Extremely high cost limited portability


+is approach can also counter the limitations of the RMSfeature where the RMS is not significantly affected by low-intensity vibrations

72 RMS RMS value presents the power content in vi-bration and useful in detecting an imbalance in rotatingmachinery According to Vishwakarma et al [59] this is thesimplest and effective technique to detect faults especiallyimbalance in rotating machines However detecting thefaults at the early stage is still a problem in this method andthis technique is only appropriate for the analysis of a singlesinusoid waveform +e RMS value is more suitable forsteady-state applications and analysis of single sinusoidwaveform [1] RMS is preferred over peak value due to thepeak valuersquos sensitivity to noise RMS value of a pure si-nusoid is equal to the area under the half-wave which is0707 RMS value can be represented by

RM

1T

1113946T2

T1

v(t)dt

1113971

(2)

where T represents time duration and v(t)is the signalReferring to Igba et al [39] the RMS method has twodisadvantages +e first one is the RMS values of a vibrationsignal are not affected by the isolated peaks in the signalreducing its sensitivity towards incipient gear tooth failureNext it is also not significantly affected by short bursts oflow-intensity vibrations +is will produce some compli-cations in detecting the early stages of bearing failureBartelmus et al [60] applied the RMS values as a diagnosticfeature to diagnose gearbox fault where the models of thebehavior of gearboxes that correlate the transmission errorfunction and load variation are presented Sheldon et al [61]used the RMS feature in diagnosing wind turbine gearboxand stated that applying the RMS feature is not recom-mended in detecting early stages of bearing failure RMS wasamong the statistical parameters applied by Krishnakumariet al [62] in fault diagnostics of the spur gear +e pa-rameters are then combined with fuzzy logic and diagnosticsaccuracy was found to be 95 where DT reduces the de-mand for human expertise Other applications of RMSvalues in vibration analysis for machine monitoring can beseen in Table 6 [63 64]

73 Crest Factor A crest factor is the ratio of the peak valueof the input signal to the RMS value and is represented asfollows [55]

Crest Factor peakRMS

(3)

For a pure sine wave the crest factor will be2

radic 1414

and for normally distributed random noise the value will beapproximately 3 Compared to peak and RMS values thecrest factor is usually used when measurements are con-ducted at different rotational speeds because it is inde-pendent of speed Crest factors are also reliable only in thepresence of significant impulsiveness [1] Jiang et al [65]employed the crest factor features and SVM to diagnose gear

faults It was found that the crest factor is the most sensitivefeature for gear failure and by applying this feature theachieved diagnostic accuracy is 9333 Shrivastava andWadhwani [58] applied the crest factor values along withother time domain features for the fault detection and di-agnosis of rotating electrical machines +ey found that thecrest factor feature is unable to classify between healthybearing bearing with defective ball and bearing with de-fective outer race Aiswarya et al [66] used the crest factorfeature along with other time domain features to diagnosefaults in the turbo pump of a liquid rocket engine Combinedwith the SVM method in the fault classification stage theproposed method can diagnose the fault effectively with100 accuracy

74 Kurtosis Kurtosis is a nondimensional statisticalmeasurement of the number of outliers in distributionand in vibration analysis it corresponds to the number oftransient peaks A high number of transient peaks and ahigh kurtosis value may be indicative of wear Kurtosis isnot sensitive to running speed or load and its effective-ness is dependent on the presence of significant impul-siveness in the signal [67] Kurtosis feature can providethe information regarding the non-Gaussianity or im-pulsiveness of the vibration signals [68 69] In machinecondition monitoring applications kurtosis is usuallypreferable to crest factor but the latter is more widelyused +is is because the meters that can record the crestfactor value are easily available and more affordablecompared to the kurtosis meter Kurtosis was among thefive parameters applied by Fu et al [70] to be incorporatedwith the unsupervised AI method in diagnosing rollingbearing Based on the results the proposed method wasfound to have a sensitive reflection on fault identificationsincluding a slight fault Runesson [67] employed thekurtosis along with RMS value in monitoring the con-dition of a mechanical press +e results demonstratedthat kurtosis generally is not reliable but contains someuseful information in the monitoring of the gearbox of themechanical press machine Other research studies thatapplied the kurtosis approach in vibration analysis formachine monitoring can be seen in Table 6 [63 71]

8 Frequency Domain Analysis

Most real-world signals can be broken down into a com-bination of unique sine waves Each sine wave will appear asa vertical line in the frequency domain where the height andposition of the line represent the amplitude and frequencyrespectively In frequency domain analysis the amplitude isplotted against frequency and compared to the time domainand the detection of the resonant frequency component iseasier +is is one of the reasons why frequency domainmethods are favorable in detecting faults in the machine[59] Several characteristics of the signal that are not visiblein the perspective of time domain can be observed usingfrequency domain analysis However frequency analysis isnot suitable for signals whose frequencies vary over time


+e advantages and disadvantages of each frequency domainmethod can be seen in Table 7

81 FFT Fourier transform (FT) converts a signal f(t) inthe time domain to the frequency domain generating thespectrum F(ω) FT is given by

F(ω) Ff(t) 1113946infin

minusinfinf(t)e

minus iωtdt (4)

where ω is the frequency and t is the time It can be con-verted back to time domain from the frequency domain byinverse Fourier transform (IFT) +is can be obtained as

f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)

FFT is an efficient and widely used algorithm to obtainthe FT of discretized time signals +e FFT plot of fault-freeindustrial machines consists of only one peak which rep-resents the natural frequency of the operating machine+us defect in the machine can be identified when there is apresence of other peaks aside from the natural frequencypeak in the plot However Goyal and Pabla [37] claimed thatduring the conversion between domains there is a little loss

of time information FFT is also unable to investigate thetransient features efficiently in time and can predict the faultbut cannot determine the severity of fault [3] However it isthe quickest way to separate the frequencies of the signal forthe diagnosis process A combination of time domain signalanalysis and FFT is normally associated with diagnosing thelow-speed machine to produce more accurate results but themajor concern is its reliance on the magnitude of the faulthaving an effect on the carrier frequency [11] Saucedo-Dorantes et al [8] used the FFTand PSDmethod to diagnosethe fault in a gearbox and detect the bearing defect in theinduction motor +ey found that the proposed method canperfectly detect the presence of wear at low operating fre-quencies but is not suitable at high operating frequenciesPatel et al [72] proposed the FFTmethod as an analysis toolin monitoring a rotating machine and major faults such asmisalignment and bearing can be monitored in this mannerOther applications of FFTcan also be seen in Table 6 [23 73]

82 CepstrumAnalysis Cepstrum analysis was developed inthe 1960s and can be defined as the power spectrum of thelogarithm of the power spectrum [74] Cepstrum analysiscan be used to detect any periodic structure in the spectrum


FrequencyDomain

TimeDomain

Peak RMS CrestFactor

Kurtosis

FFT Cepstrum Envelope Spectrum

WT WVD HHT PSD STFT


Figure 4 +e feature extractionsignal processing stage of the proposed review article

Piezoelectricaccelerometer

AdhesiveMeasured surface

(a)

Measured surface

Mounting studVelocitytransducer

Drilled hole

(b)

Figure 3 Vibration measurement using (a) piezoelectric accelerometer by means of adhesive mounting and (b) velocity transducer stud-mounted on the machinersquos surface


Table 6 Various reported vibration analysis techniques in machine monitoring and diagnosis

Authors Methodologies Findings

[63] Incorporated the RMS and kurtosis values in NN to diagnosethe rolling element bearings fault

+e proposed method can effectively diagnose the conditionusing only a few features of vibration data but the fault types

and severity level cannot be determined

[71] Applied the kurtosis and SVM method to diagnose rollerbearing fault

+e accuracy of the proposed method is 9375 and can beapplied even with a limited number of samples

[23] Used the FFTand PSDmethods to monitor the condition of themachine

A PC-based vibration analyzer incorporating the proposedmethod was developed

[73] Applied the FFT method to diagnose induction motor fault +e simulation results obtained from MATLABSimulink arein agreement with the experimental results

[78] Combined the cepstrum analysis and NNmethod to detect anddiagnose gear fault

NN can diagnose gear faults with high accuracy provided thatproper measured data are used

[79]Used two cepstrum analysis approaches namely automated

cepstrum editing procedure (ACEP) and cepstrumprewhitening (CPW) to detect bearing fault

CPW approach is more suitable for applications that do notrequire bandpass filtering but applying both approaches

without prior knowledge can lead to false result in detectingbearing faults

[81] Applied the envelope analysis to diagnose faults in rotatingmachines under variable speed conditions

Squared envelope method is an optimal approach in faultdiagnosis in terms of computational cost and simplicity

compared to the improved synchronous average (ISA) thecepstrum prewhitening (CPW) and the generalized

synchronous average (GSA)

[86] Used the envelope analysis to diagnose bearing faults +e squared envelope method is more suitable to analyze thecyclostationary signals compared to the envelope method

[90] Combined the higher-order spectrum analysis and SVM todiagnose faults in power electronic circuit +e proposed method achieved the accuracy of up to 99

[91] Applied the power spectrum analysis (PSA) and SVM todiagnose rolling bearing fault

Using the PSA with SVM classifier gives better result comparedto NN classifier

[100] Applied the WPT method to monitor the condition of themachine

Using the proposed method as input to a NN classifierproduced nearly 100 classification accuracy Also the

proposed method produced a better result compared to FFTwhen the data are corrupted by noise

[102] Combined the Hilbert transform and WPT to detect gearboxfault +e proposed method is capable of detecting early gar fault

[101] Applied a denoising method based on WT to diagnose rollingbearing and gearbox

+e proposed method is more effective and has moreadvantages compared to Donohorsquos soft-thresholding denoising

method

[103] Proposed an orthonomal DWT (ODWT) method to monitorand diagnose bearing faults at an early stage

+e proposed method outperforms the EEMD and Hilbertenvelope spectrum analysis method

[115] Applied the HHT and FT methods to diagnose machine fault HHT outperforms FT where FT can only differentiatecharacteristic frequency in low-frequency band

[116] Proposed a new local mean parameter to improve the HHTmethod to detect gearbox fault

Introducing the new parameter improves the HHTprocess andmakes the fault detection process simpler

[120] Applied the STFTmethod to diagnose faults in a hydroelectricmachine

+e basis for the effective fault diagnosis of hydroelectricmachines was proposed

Table 5 +e advantages and disadvantages of time domain methods

Time domainmethods Advantages Disadvantages

Peak Simple and easy technique Sensitive to noise

RMSSimple and easy technique directlyrelated to the energy content of the

vibration profileChanges in RMS vibrations are only sensitive to high-amplitude components

Crest factor Easily available and affordable crestfactor meter Only reliable in the presence of significant impulsiveness

Kurtosis

High performance in detectingperiodic impulse force highly

sensitive to shock can be assimilatedwith a shape factor independent of

the signal amplitude

Costly kurtosis meter can be erroneous


Table 6 Continued


[121] Combined STFT and SVM methods to diagnose faults ininduction motor

+e proposed method has a huge potential to diagnose faultintelligently in other real-time system applications

[122] Combined the STFT and nonnegative matrix factorization(NMF) methods to detect rolling bearing element fault

+e proposed method is able to determine the fault types andseverity and yields 993 accuracy superior to NN

[125] Applied the PSDmethod to diagnoseMassey Ferguson gearbox +e proposed method can reliably and quickly diagnosegearbox fault

[126] Used the PSD and SVM methods to diagnose gearbox faults +e proposed method achieved an accuracy of 9882 and9716 for spur and helical gearbox dataset respectively

[133] Used the SVM method to diagnose rolling bearing elementfault based on the fractal dimensions

SVM trained with 11 time domain statistical features and threefractal dimensions provides better results compared to the

SVM trained with only fractal dimensions or with time domainstatistical features

[134] Applied the SVM K-nearest neighbor (KNN) and Fischerlinear discriminant (FLD) methods to diagnose engine fault

+e performance of the SVMmethod is much better comparedto the KNN and FLD method

[135] Presented a real-time online monitoring approach for the discslitting machine based on WPT and SVM methods

Findings show that different types of disc slitting machinesrsquofaults can be successfully detected with an accuracy of 956

[64]RMS values were among the statistical features employed asinput parameters for the DNN to monitor the condition of

gearbox

It was found that the deep learning methods are superiorcompared to the NN method which has low robustness in

diagnosing the condition of gearbox

[145]

Compared the combination of GA with three types of NNnamely multilayer perceptron (MLP) radial basis function(RBF) and probabilistic neural network (PNN) to detect

bearing fault

+e combination of GA with MLP and PNN gave 100 successrate whereas RBF gave 9931 rate

[146] Applied the combination of EMD and NNmethods to diagnosethe roller bearing fault

+e proposed method can successfully diagnose roller bearingfault but has an end effect complication

[147] Combined the WPT GA NN and SVM methods to diagnosefault in diesel engine +e proposed method produced 100 classification accuracy

[148]Proposed a CNN approach that makes use of cyclic spectrummaps (CSMs) of raw vibration signal to diagnose the motor

bearing in the rotating machine

Based on the validation with benchmark vibration datacollected from bearing tests the proposed technique is superiorto its referenced methods in terms of the classification accuracy

[149] Proposed a distribution-invariant deep belief network(DIDBN) as a basis for intelligent fault diagnosis of machines

+e proposed method is able to achieve a high diagnosisaccuracy even with new working conditions

[150] Used the CNN method with 1D image of raw three-axisaccelerometer signal as the input

It was found that CNN trained with a higher number of kernelsin the first layer produced slightly better performance

[151]

Proposed a hybrid deep signal processing method to diagnosebearing faults in the machine where the signal processing

feature extraction and bearing fault diagnosis wereautomatically conducted

+e proposed method is superior to the manual extractionmethods and commonly used deep learning structures in termsof accuracy and it is not affected by the operation conditions

[152]Presented the augmented deep sparse autoencoder (ADSAE)method in diagnosing gear faults where data shifting technique

was incorporated to enhance the SAE model

Compared with other deep learning architectures the proposedmethod provides a higher accuracy (99) and only requires a

few raw vibration signal data

[62]Combined the decision tree and fuzzy logic methods to

diagnose spur gear fault based on the statistical features such asRMS crest factor and kurtosis

+e performance of the proposed method in diagnosing faultwas found to be 95

[160] Proposed the fuzzy logic method to diagnose the operation ofrotating machines

+e proposedmethod can easily diagnose the operational statusof the rotating system

[161] Applied the fuzzy logic method to monitor and diagnose thecondition of the pump

+e proposed method can successfully identify and classify thefaults of the five-plunger pump

[162] Proposed the combination of DWT and fuzzy logic to predictthe presence of misalignment in rotating machinery

+e proposed approach has an error of less than 1 inpredicting the degree of misalignment

[163] Developed a gas turbine vibration monitoring approach basedon TakagindashSugeno fuzzy logic

Expertsrsquo knowledge regarding the maintenance of the gasturbine in accordance to the vibration level detected can be

successfully expressed by the proposed method

[168]Proposed a combination of wavelet support vector machine(WSVM) and immune genetic algorithm (IGA) to diagnose

gearbox fault

+e proposed method yielded a better diagnostic accuracycompared to the SVM and NN method in addition to strong

generalization capability

[169] Combined the GA SVM and EEMDmethods to diagnose gearfaults

Incorporating the GA to select the parameter of SVM canimprove the generalization ability and classification accuracy of

the diagnostic system

[170] Applied the combination of GA and SVM in bearing faultdiagnosis

Applying the cross-validation method to optimize SVMoutperforms the SVM method optimized by GA in bearing

fault diagnosis


such as harmonics sidebands or echoes [66] +is allowsfaults such as bearing and localized tooth faults whichproduce low-level harmonically related frequencies to bedetected +ere are four types of cepstrum which are realcepstrum complex cepstrum power spectrum and phasespectrum but power cepstrum is the most widely usedcepstrum in machine diagnosis and monitoring Accordingto Goyal and Pabla [45] cepstrum analysis is important ingearbox diagnosis Dalpiaz et al [75] compared the cepstrumanalysis with other methods inmonitoring the condition of agearbox and found that cepstrum analysis is insensitive togear cracks To detect the rubbing phenomenon of thesliding bearing in the machine the cepstrum analysismethod was applied by Sako et al [76] It was found that theproposed approach can even detect mild rubbing which isdifficult to be achieved by using conventional abnormalitydiagnostic methods Experimental work was conducted byAralikatti et al [77] to diagnose the universal lathe machinewhere cepstrum analysis was employed to the time domainsignal +e vibration signal was obtained by a triaxial ac-celerometer It was concluded that analyzing the vibrationsignal in the frequency domain does not guarantee thepresence of a fault Other applications of cepstrum analysiscan be discovered in Table 6 [78 79]

83 Envelope Analysis Envelope analysis also known asamplitude demodulation or demodulated resonance anal-ysis was introduced by Mechanical Technology Inc [80]+is technique separates the low-frequency signal frombackground noise [59] Envelope analysis is made up of abandpass filtering and demodulation step that extracts thesignal envelope and its spectrum possibly contains thedesired diagnostic information [81] It is widely used inrolling element bearing and low-speed machine diagnosisand has the advantage of early detection of bearing problems[55 81] +e challenge of this approach is determining thebest frequency band to envelope Envelope analysis needs asharp filter and precise specification of the frequency bandfor filtering in order to work smoothly [55] Regardingbearing failure the noise components make the envelopeanalysis difficult to determine the fault +e introduction ofthe squared envelope analysis method has solved thisproblem where a squared envelope can be computed asshown in [82] It is highly preferable in analyzing thecyclostationary signals Rubini and Meneghetti [83] com-pared the envelope analysis with the wavelet transform (WT)method in diagnosing the incipient faults in ball bearings+e results demonstrated that after 30min (48000 cycles)the envelope analysis is no longer able to diagnose thepresence of the fault whereas theWTmethod is still relevantAn envelope analysis approach has also been applied byWidodo et al [84] to preprocess the vibration signals of low-speed bearing and thus determining the bearing charac-teristic frequencies +is method is then compared with theacoustic emission (AE) signal analysis and during the faultrecognition stage with the SVM technique it produces worseperformance than the AE approach Envelope analysis alsowas applied by Leite et al [85] to detect the bearing fault in

induction motor and the proposed method can efficientlydetect fault without any information regarding the modelApplication of envelope analysis in machine monitoring canalso be seen in Table 6 [81 86]

84 Spectrum AnalysisComparison Spectrum analysis isrelated to FFT in a way that FFT is often used in spectrumanalysis to transform the signal from time to frequencydomain [87] Spectrum comparison should be conducted ona logarithmic amplitude scale (dB) as the changes on alogarithmic axis can determine the state of the vibrationHowever ones have to deal with the small fluctuations of therotating speed of the machine [55] A fault that is able tochange the vibration signature significantly over a shortperiod of time can be determined by this method [88]Spectrum analysis is a complex analysis that even with theamount of literature available expert skills are still requiredto exploit the diagnostic capabilities of spectrum analysisCompared to the cepstrum analysis spectrum analysis doesnot provide any information regarding the time localizationof frequency component [77] Salami et al [38] haveemployed the spectrum analysis method for machine con-dition monitoring and it is observed that this approach canproduce smoothed and high-resolution spectral estimates ofthe vibration signals compared to the FFT approach +isspectral is useful for monitoring the state of machinesCiabattoni et al [89] proposed a novel statistical spectrumanalysis (SSA) where the spectral content of vibration signalswas calculated using FFT and then transformed into sta-tistical spectral images in diagnosing faults of rotatingmachines Other applications of spectrum analysis can beobserved in Table 6 [90 91]

9 Time-Frequency Domain Analysis

Time and frequency domains are integrated into the time-frequency domain analysis +is means that the signal fre-quency component and their time-variant features can bedetermined simultaneously in this analysis Vibrationanalysis approaches mentioned before (time domain andfrequency domain methods) mostly rely on the stationaryassumption that is unable to detect the local features in timeand frequency domain simultaneously [92] +us suchmethods are inappropriate for nonstationary signal analysisAs mentioned before the time-frequency domain analysismethods discussed in this study include WT HHT WVDSTFT and PSD +e advantages and disadvantages of eachtime-frequency domain method can be seen in Table 8

91WT WTtechnique was first proposed byMorlet back in1974 [93] It is a linear transformation decomposing a timesignal into wavelets which are local functions of timeequipped with predetermined frequency content Instead ofsinusoidal functions wavelets are used as the basis [92 94]A suitable wavelet basis has to be chosen according to thesignal structure to avoid misleading diagnosis results WTprovides a superior time localization at high frequenciescompared to STFT WT is preferable when dealing with


nonstationary signals and in analyzing the transient signalfrom the measured vibration signal [95] According to Zouand Chen [96] the WT technique is highly sensitive tostiffness variation compared to WVD +e WTmethod canbe distinguished into discrete and continuous wavelettransform (DWTand CWT) In DWT the power of two actsas a scaling factor and it is typically applied through a pair oflowpass and highpass wavelet filters +e scaling factor isselected arbitrarily or via convolution for the CWT [45]Both DWTand CWTare referred to as standard WT whichcannot efficiently perform feature extraction of certain typesof signals due to its incapability to produce a sparse rep-resentation It has a low-frequency resolution for high-frequency components and poor time localization for low-frequency components+is gives birth to the wavelet packettransform (WPT) technique It is a more advanced form ofCWT where it further decomposes the detailed informationof the signal in the high-frequency region and improves thefrequency resolution making it applicable for the analysis ofvarious nonstationary signals Dalpiaz and Rivola [94] ap-plied the WT method in monitoring the condition of theautomatic packaging machine and found that WT is able todetermine the variation of vibration frequency contentwithin the machine cycle +e advantage of CWT is that ithas a finer scale parameter compared to the DWTmethodbut in terms of computational DWT is more efficient [97]Al-Badour et al [98] employed the CWT and WPT indetecting faults in rotating machinery WPT is actually anextension of the DWT method but with finer frequencyresolution +ey found that in terms of speed and spectralcharacterization of the vibration signal the WPTmethod isbetter than the CWTmethod Rangel-Magdaleno et al [99]applied the DWTmethod to detect the incipient broken barin the induction motor and the detection accuraciesachieved are 9655 for the unload conditions 805 for thehalf-load and 876 for the full-load condition Otherapplications of the WT technique can be found in Table 6[100ndash103]

92 WVD Wigner introduced the WVD method and Villeapplied it to process the signal and thus it was named theWignerndashVille distribution It is a specific case of the Cohenclass distributions which yields a time-frequency energydensity computed by correlating the signal with a time and

frequency translation of itself [104] +e WVD of a signalx(t)is represented aswhere xlowast is the conjugate of x and τ isthe delay variable WVD has several advantages such asbetter resolution than STFT excellent accuracy and windowfunction is not needed for its analysis [45] WVD is notdirectly used by researchers to determine the time-frequencystructures of signals because of the cross-term interferenceproblem [93]

WX(tω) 12π

1113946+infin

minusinfinx t +

τ2

1113874 1113875 middot xlowast

t minusτ2

1113874 1113875 middot eminus jτωdτ (6)

Staszewski et al [105] performed the fault detectionanalysis on the gearbox using the original WVDmethod andits weighted form and they claimed that compared to theoriginal WVD its weighted form can reduce interference inthe time-frequency domain with a cost of a reduction in thefrequency resolution Directional Wigner distribution(dWD) was specifically developed for transient complex-valued signal analysis and applied in rotating or recipro-cating machines by [106] Baydar and Ball [107] used thesmooth pseudo WVD technique on acoustic and vibrationsignals to diagnose the gearbox condition and the resultsshowed that acoustic signals were more effective in earlyfault detection compared to vibration signals An applica-tion of the WVD method in diagnosing induction machineswas demonstrated by Climente-Alarcon et al [104] By usingthis proposed technique more reliable diagnosis resultsmight be obtained in a situation where harmonics tracing isdifficult

93 HHT David Hilbert first introduced the Hilberttransform in 1905 +en Huang et al [108] introduced theHHT in 1998 to determine the characteristics of stationarynonstationary and transient signals HHT consists of em-pirical mode decomposition (EMD) of signals and Hilberttransform and by combining these two methods a Hilbertspectrum can be obtained where the faults in a runningmachine can be diagnosed [92] +us in this manuscriptany works regarding the EMD method fall into the HHTsection A complicated multicomponent signal can bebroken down into a series of intrinsic mode functions(IMFs) using this method By using the EMD technique acomplicated signal x(t) can be reconstructed with the helpof IMFs expressed as

Table 7 +e advantages and disadvantages of frequency domain methods

Frequency domainmethods Advantages Disadvantages

FFT Easy to implement fast technique Cannot efficiently analyze transient features in time

Cepstrum Analysis Easy to implement useful in side bandanalysis

Can only be applied to the well separated harmonics the fluctuations ofthe curve of the spectrum are averaged-out due to the filtering

Envelopeanalysis

Excellent application in bearing system workswell even in the presence of a small random

fluctuation

Can lead to a gross diagnosis error not suitable to be applied in the gearsystem

Spectrumanalysis

Useful in detecting signal that changessignificantly over a short period of time higherspectral estimation performance compared to

the FFT

Require expertsrsquo skills due to its complexity


x(t) 1113946infin

minusinfinci(t) + rn(t)dt (7)

where ci(t) is the th IMF and xn(t)is the residual signal thatrepresents the slowly varying or constant trend of thesignal [92] HHT has several advantages such as lowcomputational time and it does not associate with anyconvolution [45] However EMD which is the main partof HHT has certain drawbacks People might misinter-pret the result due to unenviable IMFs generated at thelow-frequency region and in addition to that the low-frequency componentsrsquo signals cannot be separated +usthe ensemble EMD (EEMD) method was introduced toovercome the limitation of EMD by introducing Gaussianwhite noise to the EMD [92 109] However in the low-frequency region the energy leakage and modal aliasingproblems still exist +is is what motivates Torres et al[110] to propose the complete EEMD with adaptive noise(CEEMDAN) method which can produce better modalfrequency spectrum separation outputs

Peng et al [111] introduced a better version of HHTthat incorporated the WPT technique to decompose thevibration signal into a set of narrowband signals +eproposed method was shown to have a better resolution inthe time and frequency domain compared to the wavelet-based scalogram Wu et al [112] employed the HHTapproach in diagnosing the looseness faults of rotatingmachinery and the proposed technique is successful indetermining the faults at different components of themachine Osman and Wang [113] proposed a normalizedHHT (NHHT) technique to tackle the problem ofselecting the appropriate distinctive IMF componentsespecially for bearing health condition monitoringHowever the EMD of the proposed method only pro-cesses signals over narrowbands Chen et al [114] pro-posed a combination of CEEMDAN and particle swarmoptimization least squares support vector machine (PSO-LSSVM) to improve the diagnosis accuracy of rollingbearings +e diagnosis accuracy of several rolling bear-ings fault types was improved by this method to 100Other applications of HHT in machine monitoring anddiagnosis can be observed in Table 6 [115 116]

94 STFT STFTwas pioneered by Gabor back in 1946 in thecommunication field [117] It has the ability to counter thelimitations of FFT and is mostly applied to extract thenarrowband frequency content in nonstationary or noisysignals [37] In the STFTmethod the initial vibration signalis broken down into time segments by windowing and thenFT is applied to each time segment [45] +e mathematicalequation for STFT is given by

STFT(f τ) 1113946infin

minusinfinx(t)ω(t minus τ)e

minus j2πftdt (8)

where x(t) is the interpreted signal and ω(t) is the windowfunction centered at time Τ STFT depends on the width ofthe window AA large window width is chosen to obtaingreater accuracy in frequency whereas to improve the ac-curacy in time a small window width is desired +e maindrawback of this approach is that it cannot achieve highresolution in the time and frequency domainsimultaneously

Safizadeh et al [118] proposed the STFT application inmachinery diagnosis and proved that although STFT pro-vides the time-frequency information with limited precisionand it is better than the conventional methods of machinediagnosis To avoid cross-term effects Burriel-Valencia et al[119] implemented the STFT method for fault diagnosis ofinduction machines where the spectrums in the frequencydomain in the relevant frequency band are filtered +eproposed method greatly reduced the computing time andmemory resources +e STFTmethod has also been appliedin fault diagnosis of hydroelectric machine [120] inductionmotor [121] and rolling element bearing [122] (refer toTable 6)

95 PSD PSD can be applied to measure the amplitude ofoscillatory signals in the time series data and determine theenergy strength of frequencies which may be useful forfurther analysis From the complex spectrum the one-sidedPSD can be computed in (ms2)2Hz as

PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)

Table 8 +e advantages and disadvantages of time-frequency domain methods

Time-frequencydomain methods Advantages Disadvantages

WTProvide a superior time localization at high frequenciescompared to STFT more flexible compared to STFT

availability of various wavelet functions

Suffers from the convolution of a priori basis functionswith the original signal difficult to choose the mother

wavelet type

WVD Has a good time and frequency resolution does not requirewindow function for its implementation Vulnerable to interference slower than STFT

HHT Has a good time and frequency resolution does not requirepriori basis functions

Result misinterpretation due to IMFs generated at thelow-frequency region

STFTStraightforward method and recommended for beginners

in the time-frequency analysis low computationalcomplexity

Constant frequency resolution for the whole signaldifficult to find a fast and effective algorithm to calculate

STFT

PSD Can be directly computed by FFT requires very littleprocessing power Frequency resolution is affected by the window size


where t2 minus t1 is the time range and X(f) is the complexspectrum of the vibration x(t) in a time range which can beexpressed in units of (ms2Hz) PSD can also be directlycalculated in the frequency domain if FFTof vibration signalis used by applying the following formula [123]

PSD Grms( 1113857

2

f (10)

where Grms is the root-mean-square of acceleration in acertain frequency f PSD can analyze the faulty frequencybands without facing a slip variation issue and does notnecessarily focus on one specific harmonic [124] It requiresvery little processing power and can be directly computed byFFT or by converting the autocorrelation function [45]

PSD technique has been used by Cusido et al [124]alongside WT to diagnose faults in induction machines andthe proposed technique can successfully diagnose faults forevery operating point of the induction motor However toimprove the diagnosis accuracy good knowledge to deter-mine the suitable mother wavelet and sampling frequenciesare still required Mollazade et al [123] also used the PSDvalues in the feature extraction stage and fuzzy logic in thefault recognition stage of fault diagnosis of hydraulic pumps+e classification accuracy of the proposed technique for1000 1500 and 2000 rpm conditions is 9642 100 and9642 respectively Other applications of PSD in machinemonitoring and diagnosis can be seen in Table 6 [125 126]

10 Fault RecognitionAI-Based Technique(RQ 3)

+e application of AI in vibration analysis for machinemonitoring and diagnosis has become increasingly popularand based on this review AI-based techniques contributeabout 57 of the overall vibration analysis method inmachine diagnosis and monitoring as shown in Figure 5

+is is because most of the techniques mentioned beforerequire huge expertise for successful implementation whichmakes them not suitable for common users [80] Further-more the expert is not immediately available +is is whereAI-based methods come in because a nonexpert user canmake reliable decisions without the presence of a machinediagnosis expert AI can be defined as any task performed bya program or a machine that is difficult enough that it re-quires intelligence to accomplish it [127] Several AI-basedmethods of vibration analysis for machine monitoring anddiagnosis are SVM NN fuzzy logic and GA

101 SVM SVM was initially introduced by Vapnik and isthe most widely used classification algorithm +is methodtransforms the data set or sample space to a high-dimen-sional kernel-induced feature space by nonlinear trans-formation and then determines the best hyperplane [1] +ebest hyperplane means the one with the largest marginbetween the two classes A and B as shown in Figure 6 +edata points from both classes that are closer to the hyper-plane and influence the position and orientation of thehyperplane are called support vectors

+e learning and test data for the SVM are obtained fromthe feature extraction process and after training the SVMalgorithm the SVM matrix was obtained [128] Optimiza-tion methods such as GA and particle swarm optimization(PSO) are usually incorporated with SVM in order to achievebetter results One of the reasons why SVM is widely appliedin vibration analysis for machine diagnosis is due to itscompatibility with large and complex datasets such as datacollected in the manufacturing industry [129] SVM is veryuseful as the number of features of classified entities will notaffect the performance of SVM [130]+is means that for thebase of the diagnosis system there is no limited number ofattributes that can be selected +ere is no requirement forexpertsrsquo knowledge in SVM as is the case with fuzzy logicand no layers are involved in SVM structure compared toNN

Poyhonen et al [130] implemented the SVM techniqueto diagnose faults in an electrical machine and the resultsshowed that the classification accuracy was high except forthe detection of eccentric rotors Tabrizi et al [131] com-bined the SVM with the WPT (for signal preprocessing) andEEMD (for feature extraction) methods to detect smalldefects on roller bearings under different operating condi-tions A classification tree kernel-based SVM has also beenemployed together with CWT to identify bearing faults andthis combination proves to be a promising method andsuperior to other SVM methods with common kernels indiagnosing the rolling element bearing fault [132] Pinheiroet al [128] used the SVM method for fault diagnosis of arotary machine and successfully detected several unbalancefaults However its performance is still questionable as asmall number of samples are used Further implementationof SVM in vibration analysis for machine diagnosis can befound in Table 6 [90 133ndash135]

102 NN NN is made up of a large number of richlyinterconnected artificial processing neurons called nodesconnected to each other in layers forming a network [136]NN has the ability to model processes and systems from rawvibration data extracted from frequency and time-frequencydomain techniques mentioned before [137] In the trainingstage of NN superior input variables might suppress theinfluence of the weak variables +us the data must beproperly processed and scaled before being fed into the NNNormalizing the raw vibration data to the values between 0and 1 can help to reduce the effect of the input variable [137]Training time increases according to the complexity of thenetwork and this directly affects the accuracy of the resultsDue to the robustness and efficiency in handling noisy datathe backpropagation neural network (BPNN) is widely usedin machine diagnosis [138] BPNN pioneered by Rumelhartand McClelland in 1986 is made up of three layers whichare input hidden and output layer [93] +e presence ofhidden layers gives the NN an ability to explain nonlinearsystems and the higher the number of hidden layers thedeeper the NN [139] Similar to the SVM method NN doesnot need a knowledge base to detect the location of the faultsunlike the fuzzy logic method Ertunc et al [140] compared


the performance of NN and the combination of NN andfuzzy logic which is known as adaptive neurofuzzy inferencesystems (ANFIS) Envelope analysis was applied for thesignal processing step +ey concluded that the ANFISmethod was superior to the NN especially in diagnosingfault severity Castelino et al [137] used the application ofNN in the vibration monitoring carried out on industrialrotary machines that were running in real operating con-ditions +e results showed that NN performed better fornonstationary signals in the time-frequency domain com-pared to the frequency domain Recently the deep learningor deep neural network (DNN) has been applied widely inmachine monitoring and diagnosis It is a type of NN thatcontains more than one hidden layer Compared to the NNand SVM method the DNN approach can adaptively learnthe hierarchical representation from raw data throughmultiple nonlinear transformations and approximatecomplex nonlinear functions instead of extracting the faultfeature manually [141] However due to its deep architec-ture a high number of parameters are involved which leadsto the risk of overfitting Widely applied DNN architecturesinclude autoencoders (AE) convolutional neural network(CNN) restricted Boltzmann machines and deep beliefnetworks Table 9 shows the comparison between NN anddeep learningDNN in machine monitoring and diagnosis

Hoang and Kang [142] applied the CNN techniquewhich is a class of DNN that is most commonly applied forimage analysis to diagnose the rolling element bearing inrotary machines Raw vibration signals in time domain areconverted into a 2D form for the CNN to perform vibrationimage classification +is method achieved 100 accuracy

using the bearing datasets from Case Western ReverseUniversity but hyperparameters for the CNNmodel can stillbe improved A combination of transfer learning and DNNhas been employed by Qian et al [143] in diagnosing therotating machines under different working conditionsTransfer learning focuses on how to store the knowledge orsolution obtained when solving a problem and apply it todifferent but related problems so that the amount of datacollection and training costs can be reduced [144] +eproposed method is robust and there is no requirement forfurther training when supplied with new datasets fromdifferent working conditions Similar applications can alsobe found in Table 6 [78 145ndash152]

103 Fuzzy Logic Compared to conventional logic fuzzylogic aims at modeling the imprecise modes of reasoning tomake rational decisions in an environment of uncertaintyand imprecision [153 154]+ere are four main stages of thefuzzy logic system which are fuzzification an inferencemechanism rule-base and defuzzification component +efuzzification stage converts the input data into fuzzy setsbefore the fuzzy inference stage makes a reliable conclusionbased on the rules created in the rule-base stage Finally thedefuzzification stage produces quantifiable results Fuzzylogic is associated with membership functions which role isto map the nonfuzzy input values to fuzzy linguistic termsand vice versa To obtain a diagnostic system with excellentsensitivity the rules andmembership functions can be tuned[155] However properly determine the fuzzy rules andoptimize the membership functions are the biggest challengein fuzzy logic Fuzzy logic is easier to implement comparedto SVM and NN Apart from that unlike other AI methodssuch as SVM andNN it does not rely on the datasets as thereis no training or testing stage in fuzzy logic In particularcases this method can only provide a general diagnosis asthe specific fault symptom of a machine cannot be regularlydetermined However this is the only available alternativewhen collecting the fault data is not possible [156] Lasurtet al [157] compared the performance of fuzzy logic withNN in fault diagnosis of electrical machines and theyclaimed that fuzzy logic performs better in detecting dif-ferent faults for a wide range of operating conditionscompared to NN Wu and Hsu [158] combined the methodof DWT and fuzzy logic to detect gear fault and the resultsobtained showed that the recognition rate of the proposedmethod is over 96 under various experimental conditionsMukane et al [159] applied the FFT method for signalprocessing and fuzzy logic for fault recognition in identi-fying machinery faults Multiple faults can be identified inthis manner including the severity of the faults Other ap-plications of fuzzy logic in vibration analysis for machinediagnosis can be found in Table 6 [160ndash163]

104 GA GA derived from a study of a biological systemcan solve both constrained and unconstrained optimiza-tion problems based on a natural selection process[164 165] At each step GA randomly selects the bestindividuals based on their quality from the current pop-ulation to become parents for the children of the next

5743

AI-MethodNon AI-Method

Figure 5 +e percentage difference between AI and non-AImethods in vibration analysis for machine diagnosis andmonitoring

Marging

Class B

Class A

Support Vector

SeparatingHyperplane

Figure 6 +e structure of SVM technique


generation in order to reach an optimal solution +is stepwill continue until a terminating condition is reached+ere are three main processes that occur at each GAnamely selection crossover and mutation GA is usuallyused to optimize the monitoring system parameters andboosting the speed and accuracy of fault diagnosis Samantaet al [145] presented a combination of ANN and SVM withGA for bearing fault detection Based on the result SVMperforms better than NN and GA helps to reduce thetraining time of both methods Han et al [166] used the GAin the process of diagnosing the induction motor and foundthat GA helps the diagnosis system to perform better bychoosing critical features and optimizing the networkstructure Hajnayeb et al [167] claimed that removingsome features from the input features will result in quickerand more accurate diagnosis systems GA is usuallycombined with other AI methods such as SVM fuzzy logicand NN In NN the GA can be used as an alternative tolearning the weight values and to optimize the topology of aNN For the fuzzy control the GA can be used to tune theassociated membership function parameters as well asgenerating the fuzzy rules +e applications of GA can alsobe observed in Table 6 [168ndash170] +e advantages anddisadvantages of each fault recognition method can be seenin Table 10

11 Discussion

More than 100 articles were discussed in this study coveringa topic associated with the vibration analysis in machinemonitoring and diagnosis in terms of instruments used inthe data acquisition stage feature extraction methods andfault recognition by AI techniques Because there is a largeamount of literature on this field a review of all the literatureis impossible and some papers might be omitted For thedata acquisition process and to answer the RQ 1 most of thestudies applied the simpler and cheaper alternative of thecomputer-based analyzer and with the help of DSP andFPGA this analyzer is nearly as good as the conventionalanalyzer Accelerometer is still the best sensor option forvibration analysis and this has been proved by most of thearticles reviewed However due to the high cost of the pi-ezoelectric accelerometer researchers are continuouslyworking towards the application of the MEMS accelerom-eter which can provide the same or better performanceVelocity transducer is preferable to be applied in diagnosinglow-speed machinery compared to accelerometers as theabsolute accelerations measured are much smaller in valuefor similar vibration displacements Noncontact sensors alsohave a huge potential in machine monitoring as mountingthe sensor on the machine is not a concern anymore which

in turn produces a more accurate measurement Howeverdue to its costly application it is not widely used LDV withmultichannel measurements is expected to be widely appliedin the future where the cost of implementing the LDV isreduced

Regarding the signal processing techniques (RQ 2) theworks on improving the detection and diagnosis of faults inthe time-frequency domain have attracted numerous at-tention from researchers +is is because it can be imple-mented to investigate the nonstationary signals as failuresignals are not repetitive at the earliest stage Usually thesenonstationary signals contain abundant information onmachine faults Time and frequency domain techniques formachine monitoring are based on the assumption of sta-tionary signals and this is not suitable for detecting short-duration dynamic phenomena especially in rotating ma-chinery However traditional methods should not beomitted as it is preferable in certain applications For low-speed machines envelope analysis is widely applied as it candetect low energy signals and the envelope spectrum isfurther analyzed using time-frequency domain methodssuch as WTand HHT where the noise level in the vibrationsignals is reduced To make use of the advantages of a certainmethod and to make up for the limitations some researchersapplied the fusion of certain techniques Based onFigures 7(a)ndash7(c) the most applied time frequency andtime-frequency domain methods in machine monitoringand diagnosis are RMS FFT and WT techniquesrespectively

To answer the RQ 3 researchers also move towardsimplementing the intelligence system in the vibrationanalysis for automated decision making and from thereview and referring to Figure 7(d) SVM is the most widelyused method mainly due to its high classification accuracyand low computational time Besides it was found that theapplication of the time domain parameters is directlyproportional to the applications of AI methods +is isbecause time domain features can improve the perfor-mance of AI methods and have a low computational costwhich would not put much computational burden on AImethods +e works on refining the algorithms for lowercomputational cost and easy implementation of the vi-bration analysis are still in progress for the AI-basedtechniques Based on the previous studies regarding vi-bration analysis for machine monitoring and diagnosismost of the reported studies applied the vibration analysismethod on one test rig or machine where the resultsproduced are excellent but the same performance cannot beguaranteed when applied to other machines +is alsoapplies to the environment where most of the reportedworks are conducted in a controlled environment and theperformance might differ if employed in an industrialsetting Similar cases applied to the fault recognition usingAI especially in SVM and NN methods +ese data-drivenmethods are based on the training of historically obtaineddatasets fed to the algorithm and when entirely newdatasets are used generalization issues might occur +usit is important to train the AI algorithms with appropriatediverse and optimized datasets It is also recommended to

Table 9 NN vs deep learningDNN

Characteristics NN Deep learningDNNPrior knowledge Required Not requiredComputational burden Lower HigherFeature extraction Manual AutomatedAccuracy Lower HigherRobustness Lower Higher


test the AI techniques at different operating or environ-mental conditions than the training datasets to counter thegeneralization problem It was discovered that almost 80of the previous studies applied the feature extraction orsignal processing techniques such as envelope analysisSTFT WT and HHT whether with the combination of AImethod or not Although these techniques achieved goodperformance in monitoring and diagnosing the machinecondition expert knowledge regarding signal processing isstill required Furthermore the feature extractor has to bereconstructed for every specific fault diagnosis task +is isone of the reasons researchers are migrating to the deeplearning approach where fault features are automaticallyextracted from the raw vibration signals

In terms of noise most of the reported existingmethods can effectively distinguish noise from vibrationsignals However this is based on the assumption ofGaussian distribution vibration signals In an industrialenvironment vibration signals are usually corrupted withnon-Gaussian noise due to the abnormal operation ofgears or bearings and random disturbances that occur inthe machine which is not widely considered in the re-ported techniques +is is because industrial machines arecomplex systems made up of various components such asshafts bearings and gearboxes which run simulta-neously +us some fault signatures are often covered bythe machine natural frequencies and submerged by highnon-Gaussian noise and as a result the faulty frequencies

Table 10 +e advantages and disadvantages several AI-based methods

AI-basedmethod Advantages Disadvantages

SVM Compatible with large and complex dataset highaccuracy

Difficult to determine the appropriate kernel to be appliedperform poorly when the data contain noise

NN Fault tolerance process have a self-learning ability Havea strong capability to process data

Complicated design process takes a long time to process a largenetwork black box solution

Fuzzy logic Strong robustness simple design and easy to understand Difficult to obtain the knowledge rules difficult to determine theright membership function

GA Can process an extremely large range of data can beapplied for the optimization purpose High computing cost time-consuming procedure

3118

3615

PeakRMS

Crest FactorKurtosis

(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)

Figure 7 Percentage of methods used for (a) time domain (b) frequency domain (c) time-frequency domain and (d) AI-based approachesbased on the reported articles


become nondominant in the spectrum which makes themachine diagnosis and monitoring process more difficult[171 172]

For RQ 4 recent applications of smart machines present anew and huge challenge in monitoring and diagnosing theircondition+e presence of various sensors and communicationdevices in the smart machine will produce very noisy data+us research studies on a vibration technique that is preciseand robust and can handle a huge amount of noisy data ef-ficiently are desired Sometimes the collected vibration datafrom the sensors are insufficient for machine diagnosis andmonitoring+is is why the need for the Digital Twinmodelingapproach arises According to [173 174] the Digital Twinmodel can map various characteristics of the physical machineinto the virtual world to produce a digital replica of the ma-chine that is transferable detachable modifiable reproduciblerepeatable and erasable +us extrapolating the vibration dataacquired from the sensors is possible based on the mathe-matical representation of the machine By combining the AI-based data-driven approach and physics-based simulationmodel Digital Twin can obtain additional information re-garding the prediction of machine failures+is model can alsobe applied to run several simulations in different operationaland environmental conditions increasing the robustness of thediagnosis technique However producing an effective andproper Digital Twin model remains a challenge due to thenonlinear dynamics and uncertainty that occurs in the op-erating smart machines [175] +us works on constructing aDigital Twin model that can properly represent the actualconditions of the machine still can be explored In addition atechnique to monitor and diagnose the machinersquos conditionfrom a remote location without the need to visit the machine isworth exploring For AI-based techniques the performancecan be further evaluated by studying the effects of simultaneousfault occurrence on the machine In terms of AI algorithmsincorporating the transfer learning approach into the algorithmcan be further explored since the deep transfer learningmethodis still in its early stages Table 11 shows the most cited articlesreviewed in this manuscript for each method to answer the RQ5

12 Conclusion

Vibration analysis for machine monitoring and diagnosishas become cheaper and cheaper thanks to the emerging

technology and development in the data acquisition processand signal processing techniques including the instrumentapplied Nowadays even inexperienced users can conducteffective vibration monitoring without the presence of anexpert In this study we have conduct a systematic review ofvibration analysis for machine monitoring and diagnosiswhich can be divided into data acquisition feature extrac-tion and fault recognition stages Several RQs have beenanswered in this study which might provide useful infor-mation on this area From the study several key factors aredetermined

(i) With the advancement of powerful software and theInternet a computer-based analyzer is preferable inthe future due to its low cost and performancewhich is as good as the standalone analyzer

(ii) Noncontact sensor is the future of vibration analysisfor machine monitoring and diagnosis due to itsflexibility and independence of any mass-loadingeffects without compromising the signal quality

(iii) Time and frequency domain methods are suitablefor stationary signals and time-frequency domaintechniques are preferable for nonstationary signalsand early fault detection

(iv) Deep learning especially the deep transfer learningmethod is starting to be applied in vibrationanalysis for machine monitoring and diagnosis as ithelps in minimizing the requirement for expertknowledge in the complicated feature extractionstep Traditional AI methods such as SVM NN andfuzzy logic still require expert knowledge in thefeature extraction stage of newly fed datasets

(v) Traditional time domain features such as RMS andcrest factor are still relevant in the future and itsapplication with AI will continue to increase

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 no conflicts of interest

Table 11 +e most influencing articles for each methods

Methods Articlesrsquos name Numberof citation

Time domainFault diagnostics of rolling element bearing using the NNmethod and the time domain features of RMSand kurtosis conducted by [63] From the results the proposed method can still effectively diagnose the

machine even with the reduced number of inputs762

Frequency domainA research conducted by [86] to study the relationship between the classical envelope analysis andspectral correlation analysis in the diagnostics of bearing faults It was shown that the envelope analysis

provided the same results as the complex spectral correlation function613

Time-frequencydomain

A study on applying the CWT method in the feature extraction of mechanical vibration signalsconducted by [101] +e results proved that the proposed method is more effective than the Donohorsquos

ldquosoft-thresholding denoisingrdquo method1050

AI Similar to [63] 762


Acknowledgments

+e authors would like to thank Synvue Sdn Bhd (1236749-D) for insights and feedback of the project development+is work was supported by the Collaborative Research inEngineering Science and Technology (CREST) under grant304PELECT6050424C121

References

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[2] D H C de Sa So D P Viana A A de Lima et al ldquoDi-agnostic and severity analysis of combined failures composedby imbalance and misalignment in rotating machinesrdquo In-ternational Journal of Advanced Manufacturing Technologyvol 114 no 9 pp 3077ndash3092 2021

[3] S Kumar M Lokesha K Kumar and K Srinivas ldquoVibrationbased fault diagnosis techniques for rotating mechanicalcomponents review paperrdquo in Proceedings of the Interna-tional Conference on Advances in Manufacturing Materialsand Energy Engineering pp 1ndash6 Karnataka India June 2018

[4] R Ranjan S K Ghosh and M Kumar ldquoFault diagnosis ofjournal bearing in a hydropower plant using wear debrisvibration and temperature analysis a case studyrdquo Proceed-ings of the Institution of Mechanical Engineers - Part EJournal of Process Mechanical Engineering vol 234 no 3pp 235ndash242 2020

[5] A Glowacz ldquoVentilation diagnosis of angle grinder usingthermal imagingrdquo Sensors vol 21 no 8 p 2853 2021

[6] A Glowacz R Tadeusiewicz S Legutko et al ldquoFault di-agnosis of angle grinders and electric impact drills usingacoustic signalsrdquo Applied Acoustics vol 179 p 108070 2021

[7] D N Brown and T Jensen ldquoMachine-condition monitoringusing vibration analysisrdquo 2020 httpswwwbksvcommediadocbo0253pdfAvailable

[8] J J Saucedo-Dorantes M Delgado-Prieto J A Ortega-Redondo R A Osornio-Rios and R D J Romero-Tron-coso ldquoMultiple-fault detection methodology based on vi-bration and current analysis applied to bearings in inductionmotors and gearboxes on the kinematic chainrdquo Shock andVibration vol 2016 Article ID 5467643 13 pages 2016

[9] W-B Zoungrana A Chehri and A Zimmermann ldquoAu-tomatic classification of rotating machinery defects usingmachine learning (ml) algorithmsrdquo Human Centred Intel-ligent Systems vol 189 pp 193ndash203 2020

[10] S Elango J G Aravind and S Boopathi ldquoVibration analysisof bearing by using mechanical stethoscoperdquo InternationalJournal of Advanced Science and Research vol 3 no 1pp 1137ndash1149 2018

[11] Y H Kim A C C Tan and V Kosse ldquoCondition moni-toring of low-speed bearings - a reviewrdquo Australian Journalof Mechanical Engineering vol 6 no 1 pp 61ndash68 2008

[12] M Vishwakarma R Purohit V Harshlata and P RajputldquoVibration analysis amp condition monitoring for rotatingmachines a reviewrdquo in Proceedings of the 5th InternationalConference of Materials Processing and Characterizationpp 2659ndash2664 Elsevier Hyderabad India March 2016

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[14] A Aherwar ldquoAn investigation on gearbox fault detectionusing vibration analysis techniques a reviewrdquo AustralianJournal of Mechanical Engineering vol 10 no 2 pp 169ndash183 2012

[15] A S Sait and Y I Sharaf-Eldeen ldquoA review of gearboxcondition monitoring based on vibration analysis techniquesdiagnostics and prognosticsrdquo Rotating Machinery StructuralHealth Monitoring Shock and Vibration Volume 5 vol 5pp 307ndash324 2011

[16] I Sadeghi H Ehya J Faiz and H Ostovar ldquoldquoOnline faultdiagnosis of large electrical machines using vibration signal-areviewrdquo inrdquo in Proceedings of the 2017 International Con-ference on Optimization of Electrical and Electronic Equip-ment (OPTIM) amp 2017 Intl Aegean Conference on ElectricalMachines and Power Electronics (ACEMP) pp 470ndash475Brasov Romania May 2017

[17] B Kitchenham S Charters D Budgen et al Guidelines forPerforming Systematic Literature Reviews in Software Engi-neering UK Tech Rep Keele University and University ofDurham Keele England 2007

[18] K Shahzad P Cheng and B Oelmann ldquoArchitecture ex-ploration for a high-performance and low-power wirelessvibration analyzerrdquo IEEE Sensors Journal vol 13 no 2pp 670ndash682 2012

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[20] M Nuawi S Abdullah A Ismail and N Kamaruddin ldquoAnovel analysis (i-kaz 3d) for three axial vibration signal inbearing condition monitoringrdquo Statistics vol 6 no 7pp 318ndash322 2008

[21] S Kumar R Sehgal R Kumar and S Bhandari ldquoVibrationsanalysis of 4 jaw flexible coupling considering unbalancing intwo planesrdquo International Journal of Science and Technologyvol 1 no 11 pp 602ndash608 2012

[22] Q He andD Du ldquoA new dual-channel analyzer for vibrationof rotary machinerdquo in Proceedings oif the ASME PowerConference pp 253ndash256 Orlando FL USA May 2008

[23] S A Ansari and R Baig ldquoA pc-based vibration analyzer forcondition monitoring of process machineryrdquo IEEE Trans-actions on Instrumentation and Measurement vol 47 no 2pp 378ndash383 1998

[24] A Gani and M-J E Salami ldquoA labview based data acqui-sition system for vibration monitoring and analysisrdquo inProceedings of the Student Conference on Research and De-velopment pp 62ndash65 Shah Alam Malaysia July 2002

[25] P Bilski and W Winiecki ldquoA low-cost real-time virtualspectrum analyzerrdquo in Proceedings of the IEEE Instrumentationand Measurement Technology Conference pp 2216ndash2221Ontario Canada May 2005

[26] G Betta C Liguori A Paolillo and A Pietrosanto ldquoA dsp-based fft-analyzer for the fault diagnosis of rotating machinebased on vibration analysisrdquo IEEE Transactions on Instru-mentation and Measurement vol 51 no 6 pp 1316ndash13222002

[27] J D J Rangel-Magdaleno R D J Romero-TroncosoR A Osornio-Rios E Cabal-Yepez and A Dominguez-Gonzalez ldquoFpga-based vibration analyzer for continuous cncmachinery monitoring with fused fft-dwt signal processingrdquoIEEE Transactions on Instrumentation and Measurementvol 59 no 12 pp 3184ndash3194 2010


[28] C Rodriguez-Donate R Romero-Troncoso A Garcia-Perez and D A Razo-Montes ldquoFpga based embeddedsystem for inductionmotor failure monitoring at the start-uptransient vibrations with waveletsrdquo in Proceedings of theInternational Symposium on Industrial Embedded Systemspp 208ndash214 Le Grande Motte France June 2008

[29] G Betta C Liguori and A Pietrosanto ldquoAmulti-applicationfft analyzer based on a dsp architecturerdquo IEEE Transactionson Instrumentation and Measurement vol 50 no 3pp 825ndash832 2001

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[36] S Xianzhong J Zhuangde L Peng G Lin and J XingdongldquoA novel pvdf based high-gn shock accelerometerrdquo inProceedings of the 7th International Symposium on Mea-surement Technology and Intelligent Instruments pp 107ndash110 HuddersfieldEngland April 2005

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[39] J Igba K Alemzadeh C Durugbo and E T EirikssonldquoAnalysing rms and peak values of vibration signals forcondition monitoring of wind turbine gearboxesrdquo Renew-able Energy vol 91 pp 90ndash106 2016

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[50] S M Saimon N H Ngajikin M S Omar et al ldquoA low-costfiber based displacement sensor for industrial applicationsrdquoTELKOMNIKA (Telecommunication Computing Electronicsand Control) vol 17 no 2 pp 555ndash560 2019

[51] S Binu V P Mahadevan Pillai and N ChandrasekaranldquoFibre optic displacement sensor for the measurement ofamplitude and frequency of vibrationrdquo Optics amp LaserTechnology vol 39 no 8 pp 1537ndash1543 2007

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[54] S J Rothberg M S Allen P Castellini et al ldquoAn inter-national review of laser Doppler vibrometry making lightwork of vibration measurementrdquo Optics and Lasers in En-gineering vol 99 pp 11ndash22 2017

[55] I Howard ldquoA review of rolling element bearing vibra-tionrsquodetection diagnosis and prognosisrdquo Report for theDefence Science and Technology Organization Canberra(Australia) Report no DSTO-RR-0013 October VictoriardquoDSTO Aeronautical and Maritime Research LaboratoryTech Rep Melbourne Victoria Australia 1994

[56] P Gangsar and R Tiwari ldquoMulticlass fault taxonomy inrolling bearings at interpolated and extrapolated speedsbased on time domain vibration data by svm algorithmsrdquoJournal of Failure Analysis and Prevention vol 14 no 6pp 826ndash837 2014

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[59] M Vishwakarma R Purohit V Harshlata and P RajputldquoVibration analysis amp condition monitoring for rotatingmachines a reviewrdquo Materials Today Proceedings vol 4no 2 pp 2659ndash2664 2017

[60] W Bartelmus F Chaari R Zimroz and M HaddarldquoModelling of gearbox dynamics under time-varying non-stationary load for distributed fault detection and diagnosisrdquoEuropean Journal of Mechanics - A Solids vol 29 no 4pp 637ndash646 2010

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[63] B Samanta and K R Al-Balushi ldquoArtificial neural networkbased fault diagnostics of rolling element bearings usingtime-domain featuresrdquo Mechanical Systems and SignalProcessing vol 17 no 2 pp 317ndash328 2003

[64] Z Chen X Chen C Li R-V Sanchez and H Qin ldquoVi-bration-based gearbox fault diagnosis using deep neuralnetworksrdquo Journal of Vibroengineering vol 19 no 4pp 2475ndash2496 2017

[65] L Jiang Y Liu X Li and A Chen ldquoGear fault diagnosisbased on svm and multi-sensor information fusionrdquo Journalof Central South University vol 41 no 6 pp 2184ndash21882010

[66] N Aiswarya S Suja Priyadharsini and K Moni ldquoAn effi-cient approach for the diagnosis of faults in turbo pump ofliquid rocket engine by employing fft and time-domainfeaturesrdquo Australian Journal of Mechanical Engineeringvol 16 no 3 pp 163ndash172 2018

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[69] J Hebda-Sobkowicz R Zimroz and A Wyłomanska ldquoSe-lection of the informative frequency band in a bearing faultdiagnosis in the presence of non-Gaussian noise-comparisonof recently developed methodsrdquo Applied Sciences vol 10no 8 p 2657 2020

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[71] K H Zhu X G Song and D X Xue ldquoRoller bearing faultdiagnosis based on imf kurtosis and svmrdquo Advanced Ma-terials Research vol 694-697 pp 1160ndash1166 2013

[72] H K Patel D Shah and A Raghuwanshi ldquoReal timemachine health monitoring and vibrational analysis using fftapproachrdquo International Journal of Engineering and Ad-vanced Technology vol 8 no 5 pp 1833ndash1836 2019

[73] T Ameid A Menacer H Talhaoui and I Harzelli ldquoBrokenrotor bar fault diagnosis using fast fourier transform appliedto field-oriented control induction machine simulation andexperimental studyrdquo International Journal of AdvancedManufacturing Technology vol 92 no 1ndash4 pp 917ndash9282017

[74] Y Liu Z Jiang H Haizhou and J Xiang ldquoAsymmetricpenalty sparse model based cepstrum analysis for bearingfault detectionsrdquo Applied Acoustics vol 165 p 107288 2020

[75] G Dalpiaz A Rivola and R Rubini ldquoGear fault monitoringcomparison of vibration analysis techniquesrdquo in Proceedingsof the 3rd International Conference Acoustical and VibratorySurveillance Methods and Diagnostics Techniques pp 623ndash632 Las Vegas NV USA January 1998

[76] T Sako K Tokumo and O Yoshie ldquoRubbing detection ofsliding bearings in early stage by frequency modulationanalysisrdquo Electronics and Communications in Japan vol 97no 12 pp 11ndash23 2014

[77] S S Aralikatti K Ravikumar and H Kumar ldquoFault diag-nosis of single point cutting tool using spectrum cepstrumand wavelet analysisrdquo in Proceedings of the 1st InternationalConference on Manufacturing Material Science and Engi-neering pp 1ndash9 Telangana India August 2019

[78] H Li Y Zhang and H Zheng ldquoGear fault detection anddiagnosis under speed-up condition based on order ceps-trum and radial basis function neural networkrdquo Journal ofMechanical Science and Technology vol 23 no 10pp 2780ndash2789 2009

[79] C Peeters P Guillaume and J Helsen ldquoA comparison ofcepstral editing methods as signal pre-processing techniquesfor vibration-based bearing fault detectionrdquo MechanicalSystems and Signal Processing vol 91 pp 354ndash381 2017

[80] R B Randall Frequency Analysis Bruel and KjaerCopenhagen Denmark 1987

[81] D Abboud J Antoni S Sieg-Zieba and M EltabachldquoEnvelope analysis of rotating machine vibrations in variablespeed conditions a comprehensive treatmentrdquo MechanicalSystems and Signal Processing vol 84 pp 200ndash226 2017

[82] D Ho and R B Randall ldquoOptimisation of bearing diagnostictechniques using simulated and actual bearing fault signalsrdquoMechanical Systems and Signal Processing vol 14 no 5pp 763ndash788 2000

[83] R Rubini and U Meneghetti ldquoApplication of the envelopeand wavelet transform analyses for the diagnosis of incipientfaults in ball bearingsrdquo Mechanical Systems and SignalProcessing vol 15 no 2 pp 287ndash302 2001

[84] AWidodo E Y Kim J-D Son et al ldquoFault diagnosis of lowspeed bearing based on relevance vector machine andsupport vector machinerdquo Expert Systems with Applicationsvol 36 no 3 pp 7252ndash7261 2009

[85] V C M N Leite J G B Da Silva G F C Veloso et alldquoDetection of localized bearing faults in induction machinesby spectral kurtosis and envelope analysis of stator currentrdquoIEEE Transactions on Industrial Electronics vol 62 no 3pp 1855ndash1865 2014

[86] R B Randall J Antoni and S Chobsaard ldquo+e relationshipbetween spectral correlation and envelope analysis in thediagnostics of bearing faults and other cyclostationary ma-chine signalsrdquo Mechanical Systems and Signal Processingvol 15 no 5 pp 945ndash962 2001

[87] J Trout ldquoVibration analysis explainedrdquo 2020 httpswwwreliableplantcomvibration-analysis-31569[Online] Avail-able

[88] P J Loughlin and G D Bernard ldquoCohen-posch (positive)time-frequency distributions and their application to ma-chine vibration analysisrdquo Mechanical Systems and SignalProcessing vol 11 no 4 pp 561ndash576 1997

[89] L Ciabattoni F Ferracuti A Freddi and A MonteriuldquoStatistical spectral analysis for fault diagnosis of rotatingmachinesrdquo IEEE Transactions on Industrial Electronicsvol 65 no 5 pp 4301ndash4310 2017

[90] J Cui Y-R Wang and Q Liu ldquo+e technique of powerelectronic circuit fault diagnosis based on higher-order


spectrum analysis and support vector machinesrdquo In Pro-ceedings of the Chinese Society of Electrical Engineeringvol 27 no 10 pp 62ndash66 2007

[91] T Guishuang S Wang and C Zhang ldquoA method for rollingbearing fault diagnosis based on the power spectrum analysisand support vector machinerdquo in Proceedings of the IEEE 10thInternational Conference on Industrial Informaticspp 546ndash549 Beijing China July 2012

[92] Z Feng M Liang and F Chu ldquoRecent advances in time-frequency analysis methods for machinery fault diagnosis areview with application examplesrdquo Mechanical Systems andSignal Processing vol 38 no 1 pp 165ndash205 2013

[93] Y Wei Y Li M Xu and W Huang ldquoA review of early faultdiagnosis approaches and their applications in rotatingmachineryrdquo Entropy vol 21 no 4 p 409 2019

[94] G Dalpiaz and A Rivola ldquoCondition monitoring and di-agnostics in automatic machines comparison of vibrationanalysis techniquesrdquo Mechanical Systems and Signal Pro-cessing vol 11 no 1 pp 53ndash73 1997

[95] B Bao Liu S-F Ling and Q Qingfeng Meng ldquoMachinerydiagnosis based on wavelet packetsrdquo Journal of Vibrationand Control vol 3 no 1 pp 5ndash17 1997

[96] J Zou and J Chen ldquoldquoA comparative study on time-ndashfrequency feature of cracked rotor by wignerndashville distri-bution and wavelet transformrdquo Journal of Sound andVibration vol 276 no 1-2 pp 1ndash11 2004

[97] A Giantomassi F Ferracuti S Iarlori G Ippoliti andS Longhi ldquoElectric motor fault detection and diagnosis bykernel density estimation and kullback-leibler divergencebased on stator current measurementsrdquo IEEE Transactionson Industrial Electronics vol 62 no 3 pp 1770ndash1780 2015

[98] F Al-Badour M Sunar and L Cheded ldquoVibration analysisof rotating machinery using time-frequency analysis andwavelet techniquesrdquo Mechanical Systems and Signal Pro-cessing vol 25 no 6 pp 2083ndash2101 2011

[99] J Rangel-Magdaleno H Peregrina-Barreto J Ramirez-Cortes R Morales-Caporal and I Cruz-Vega ldquoVibrationanalysis of partially damaged rotor bar in induction motorunder different load condition using dwtrdquo Shock and Vi-bration vol 2016 Article ID 3530464 11 pages 2016

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

[101] J Lin and L Qu ldquoFeature extraction based on morlet waveletand its application for mechanical fault diagnosisrdquo Journal ofSound and Vibration vol 234 no 1 pp 135ndash148 2000

[102] X Fan and M J Zuo ldquoGearbox fault detection using hilbertand wavelet packet transformrdquo Mechanical Systems andSignal Processing vol 20 no 4 pp 966ndash982 2006

[103] W Fan Q Zhou J Li and Z Zhu ldquoA wavelet-based sta-tistical approach for monitoring and diagnosis of compoundfaults with application to rolling bearingsrdquo IEEE Transac-tions on Automation Science and Engineering vol 15 no 4pp 1563ndash1572 2017

[104] V Climente-Alarcon J A Antonino-Daviu M Riera-Guasp R Puche-Panadero and L Escobar ldquoApplication ofthe Wigner-Ville distribution for the detection of rotorasymmetries and eccentricity through high-order har-monicsrdquo Electric Power Systems Research vol 91 pp 28ndash362012

[105] W J Staszewski K Worden and G R Tomlinson ldquoTime-frequency analysis in gearbox fault detection using thewigner-ville distribution and pattern recognitionrdquo

Mechanical Systems and Signal Processing vol 11 no 5pp 673ndash692 1997

[106] Y-S Han and C-W Lee ldquoDirectional Wigner distributionfor order analysis in rotatingreciprocating machinesrdquoMechanical Systems and Signal Processing vol 13 no 5pp 723ndash737 1999

[107] N Baydar and A Ball ldquoA comparative study of acoustic andvibration signals in detection of gear failures using wigner-ville distributionrdquoMechanical Systems and Signal Processingvol 15 no 6 pp 1091ndash1107 2001

[108] N E Huang Z Shen S R Long et al ldquo+e empirical modedecomposition and the hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[109] S Huang XWang C Li and C Kang ldquoData decompositionmethod combining permutation entropy and spectral sub-stitution with ensemble empirical mode decompositionrdquoMeasurement vol 139 pp 438ndash453 2019

[110] M E Torres M A Colominas G Schlotthauer andP Flandrin ldquoA complete ensemble empirical mode de-composition with adaptive noiserdquo in Proceedings of the IEEEInternational Conference on Acoustics Speech and SignalProcessing (ICASSP) pp 4144ndash4147 Prague Czech RepublicMay 2011

[111] Z K Peng P W Tse and F L Chu ldquoA comparison study ofimproved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo Me-chanical Systems and Signal Processing vol 19 no 5pp 974ndash988 2005

[112] T Wu Y Chung and C Liu ldquoldquoLooseness diagnosis ofrotating machinery via vibration analysis through hil-bertndashhuang transform approachrdquo Journal of Vibration andAcoustics vol 132 no 3 pp 1ndash9 2010

[113] S Osman and W Wang ldquoA normalized hilbert-huangtransform technique for bearing fault detectionrdquo Journal ofVibration and Control vol 22 no 11 pp 2771ndash2787 2016

[114] W Chen J Li Q Wang and K Han ldquoFault feature ex-traction and diagnosis of rolling bearings based on waveletthresholding denoising with ceemdan energy entropy andpso-lssvmrdquo Measurement vol 172 Article ID 108901 2020

[115] Z Y Xuan and M Ge ldquoApplication of the hilbert - huangtransform for machine fault diagnosticsrdquo Applied Mechanicsand Materials vol 182-183 pp 1484ndash1488 2012

[116] M Rezaee and A Taraghi Osguei ldquoImproving empiricalmode decomposition for vibration signal analysisrdquo Pro-ceedings of the Institution of Mechanical Engineers - Part CJournal of Mechanical Engineering Science vol 231 no 12pp 2223ndash2234 2017

[117] D Gabor ldquo+eory of communication part 1 the analysis ofinformationrdquo Journal of the Institution of Engineers Elec-tronics vol 93 no 26 pp 429ndash441 1946

[118] M Safizadeh A Lakis and M +omas ldquoUsing short-timefourier transform in machinery diagnosisrdquo in Proceedings ofthe 4thWSEAS International Conference on Electronic SignalProcessing and Control pp 1ndash7 Rio de Janeiro Brazil April2005

[119] J Burriel-Valencia R Puche-Panadero J Martinez-RomanA Sapena-Bano and M Pineda-Sanchez ldquoShort-frequencyfourier transform for fault diagnosis of induction machinesworking in transient regimerdquo IEEE Transactions on In-strumentation and Measurement vol 66 no 3 pp 432ndash4402017


[120] Z Wu Y Li H Liu and L Liu ldquoApplication of short-timefourier transform in the vibration analysis of the large hy-droelectric machinerdquo Journal of Hydroelectric Engineeringvol 24 no 6 pp 115ndash120 2005

[121] T P Banerjee S Das J Roychoudhury and A AbrahamldquoImplementation of a new hybrid methodology for faultsignal classification using short -time fourier transform andsupport vector machinesrdquo in Soft Computing Models inIndustrial and Environmental E Corchado P NovaisC Analide and J Sedano Eds Springer Berlin Germanypp 219ndash225 2010

[122] H Gao L Liang X Chen and G Xu ldquoFeature extractionand recognition for rolling element bearing fault utilizingshort-time fourier transform and non-negative matrix fac-torizationrdquo Chinese Journal of Mechanical Engineeringvol 28 no 1 pp 96ndash105 2015

[123] K Mollazade H Ahmadi M Omid and R Alimardani ldquoAnintelligent combined method based on power spectraldensity decision trees and fuzzy logic for hydraulic pumpsfault diagnosisrdquo International Journal of Intelligent Systemsand Technologies vol 3 no 4 pp 251ndash263 2008

[124] J Cusid L Romeral J A Ortega J A Rosero and A GarciaEspinosa ldquoFault detection in induction machines usingpower spectral density in wavelet decompositionrdquo IEEETransactions on Industrial Electronics vol 55 no 2pp 633ndash643 2008

[125] K Heidarbeigi H Ahmadi and M Omid ldquoFault diagnosisof massey ferguson gearbox using power spectral densityrdquo inProceedings of the 18th International Conference on ElectricalMachines pp 1ndash4 Vilamoura Portugal September 2008

[126] M Heydarzadeh N Madani and M Nourani ldquoGearboxfault diagnosis using power spectral analysisrdquo in Proceedingsof the IEEE International Workshop on Signal ProcessingSystems pp 242ndash247 Dallas TX USA October 2016

[127] D Dou and S Zhou ldquoComparison of four direct classifi-cation methods for intelligent fault diagnosis of rotatingmachineryrdquo Applied Soft Computing vol 46 pp 459ndash4682016

[128] A A Pinheiro I M Brandao and C Da Costa ldquoVibrationanalysis in turbomachines using machine learning tech-niquesrdquo European Journal of Engineering Research andScience vol 4 no 2 pp 12ndash16 2019

[129] O AlShorman M Irfan N Saad et al ldquoA review of artificialintelligence methods for condition monitoring and faultdiagnosis of rolling element bearings for induction motorrdquoShock and Vibration vol 2020 Article ID 8843759 20 pages2020

[130] S Poyhonen M Negrea A Arkkio H Hyotyniemi andH Koivo ldquoSupport vector classification for fault diagnosticsof an electrical machinerdquo in Proceedings of the 6th Inter-national Conference on Signal Processing pp 1719ndash1722Beijing China October 2002

[131] A Tabrizi L Garibaldi A Fasana and S MarchesielloldquoEarly damage detection of roller bearings using waveletpacket decomposition ensemble empirical mode decom-position and support vector machinerdquo Meccanica vol 50no 3 pp 865ndash874 2015

[132] C Wu T Chen R Jiang L Ning and Z Jiang ldquoA novelapproach to wavelet selection and tree kernel constructionfor diagnosis of rolling element bearing faultrdquo Journal ofIntelligentManufacturing vol 28 no 8 pp 1847ndash1858 2017

[133] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on svms and fractal

dimensionrdquo Mechanical Systems and Signal Processingvol 21 no 5 pp 2012ndash2024 2007

[134] A Moosavian H Ahmadi and A Tabatabaeefar ldquoFaultdiagnosis of main engine journal bearing based on vibrationanalysis using Fisher linear discriminant k-nearest neighborand support vector machinerdquo Journal of Vibroengineeringvol 14 no 2 pp 894ndash906 2012

[135] Y Zhu Q Yan and J Lu ldquoFault diagnosis method for discslitting machine based on wavelet packet transform andsupport vector machinerdquo International Journal of ComputerIntegrated Manufacturing vol 33 no 10-11 pp 1118ndash11282020

[136] J Runge and R Zmeureanu ldquoForecasting energy use inbuildings using artificial neural networks a reviewrdquo Energiesvol 12 no 17 p 3254 2019

[137] M R Castelino H S Kumar P P Srinivasa and G S VijayldquoArtificial neural network-based vibration signal analysis ofrotary machines-case studiesrdquo in Proceedings of the Inter-national Conference on Emerging Trends in Engineeringpp 211ndash218 Karnataka India July 2014

[138] G Zurita V Sanchez and D Cabrera ldquoA review of vibrationmachine diagnostics by using artificial intelligencemethodsrdquoRevista Investigacirsquoon and Desarrollo vol 1 no 16pp 102ndash114 2016

[139] M A Korany H Mahgoub O T Fahmy and H M MaherldquoApplication of artificial neural networks for response sur-face modelling in hplc method developmentrdquo Journal ofAdvanced Research vol 3 no 1 pp 53ndash63 2012

[140] H M Ertunc H Ocak and C Aliustaoglu ldquoAnn-and anfis-based multi-staged decision algorithm for the detection anddiagnosis of bearing faultsrdquo Neural Computing amp Applica-tions vol 22 no 1 pp 435ndash446 2013

[141] Y Chen X Qin J Wang C Yu and W Gao ldquoFedHealth afederated transfer learning framework for wearable health-carerdquo IEEE Intelligent Systems vol 35 no 4 pp 83ndash93 2020

[142] D-T Hoang and H-J Kang ldquoRolling element bearing faultdiagnosis using convolutional neural network and vibrationimagerdquo Cognitive Systems Research vol 53 pp 42ndash50 2019

[143] W Qian S Li J Wang Y Xin and H Ma ldquoA new deeptransfer learning network for fault diagnosis of rotatingmachine under variable working conditionsrdquo in Proceedingsof the 2018 Prognostics and System Health ManagementConference pp 1010ndash1016 Chongqing China October 2018

[144] F Yang W Zhang L Tao and J Ma ldquoTransfer learningstrategies for deep learning-based phm algorithmsrdquo AppliedSciences vol 10 no 7 p 2361 2020

[145] B Samanta K R Al-Balushi and S A Al-Araimi ldquoArtificialneural networks and genetic algorithm for bearing faultdetectionrdquo Soft Computing vol 10 no 3 pp 264ndash271 2006

[146] Y Yu and C Junsheng ldquoA roller bearing fault diagnosismethod based on emd energy entropy and annrdquo Journal ofSound and Vibration vol 294 no 1-2 pp 269ndash277 2006

[147] F Bi and Y Liu ldquoFault diagnosis of valve clearance in dieselengine based on bp neural network and support vectormachinerdquo Transactions of Tianjin University vol 22 no 6pp 536ndash543 2016

[148] M M M Islam and J-M Kim ldquoMotor bearing fault di-agnosis using deep convolutional neural networks with 2danalysis of vibration signalrdquo Advances in Artificial Intelli-gence Springer in Proceedings of the Canadian Conferenceon Artificial Intelligence pp 144ndash155 May 2018

[149] S Xing Y Lei S Wang and F Jia ldquoDistribution-invariantdeep belief network for intelligent fault diagnosis of


machines under new working conditionsrdquo IEEE Transac-tions on Industrial Electronics vol 68 no 3 pp 2617ndash26252020

[150] D Kolar D Lisjak M Pajak and D Pavkovic ldquoFault di-agnosis of rotary machines using deep convolutional neuralnetwork with wide three axis vibration signal inputrdquo Sensorsvol 20 no 14 p 4017 2020

[151] M He and D He ldquoA new hybrid deep signal processingapproach for bearing fault diagnosis using vibration signalsrdquoNeurocomputing vol 396 pp 542ndash555 2020

[152] L Xueyi L Jialin Q Yongzhi and H David ldquoSemi-su-pervised gear fault diagnosis using raw vibration signal basedon deep learningrdquo Chinese Journal of Aeronautics vol 33no 2 pp 418ndash426 2020

[153] L A Zadeh ldquoFuzzy logicrdquo Computer vol 21 no 4pp 83ndash93 1988

[154] J Serrano-Guerrero F P Romero and J A Olivas ldquoFuzzylogic applied to opinion mining a reviewrdquo knowledge-basedsystemsrdquo Knowledge-Based Systems vol 222 Article ID107018 2021

[155] P Jayaswal A K Wadhwani and K B MulchandanildquoMachine fault signature analysisrdquo International Journal ofRotating Machinery vol 2008 pp 1ndash10 2008

[156] J M F Salido and S Murakami ldquoA comparison of twolearning mechanisms for the automatic design of fuzzy di-agnosis systems for rotating machineryrdquo Applied SoftComputing vol 4 no 4 pp 413ndash422 2004

[157] I Lasurt A F Stronach and J Penman ldquoA fuzzy logicapproach to the interpretation of higher order spectra ap-plied to fault diagnosis in electrical machinesrdquo in Proceedingsof the 19th International Conference of the North AmericanFuzzy Information Processing Society pp 158ndash162 AtlantaGA USA July 2000

[158] J-D Wu and C-C Hsu ldquoFault gear identification usingvibration signal with discrete wavelet transform techniqueand fuzzy-logic inferencerdquo Expert Systems with Applicationsvol 36 no 2 pp 3785ndash3794 2009

[159] R V Mukane N M Gurav S Y Sondkar andN C Fernandes ldquoLabview based implementation of fuzzylogic for vibration analysis to identify machinery faultsrdquo inProceedings of the International Conference on ComputingCommunication Control and Automation pp 1ndash5 PuneIndia August 2017

[160] R F M Marcal M Negreiros A A Susin andJ L Kovaleski ldquoDetecting faults in rotating machinesrdquo IEEEInstrumentation and Measurement Magazine vol 3 no 4pp 24ndash26 2000

[161] J Wang and H Hu ldquoVibration-based fault diagnosis ofpump using fuzzy techniquerdquo Measurement vol 39 no 2pp 176ndash185 2006

[162] A Umbrajkaar and A Krishnamoorthy ldquoVibration analysisusing wavelet transform and fuzzy logic for shaft mis-alignmentrdquo Journal of Vibroengineering vol 20 no 8pp 2855ndash2865 2018

[163] B Alili A Hafaifa and A Iratni ldquoFaults detection based onfuzzy concepts for vibrations monitoring in gas turbinerdquoDiagnostyka vol 21 no 4 pp 67ndash77 2020

[164] J Kusyk C S Sahin M Umit Uyar E Urrea and S GundryldquoSelf-organization of nodes in mobile ad hoc networks usingevolutionary games and genetic algorithmsrdquo Journal ofAdvanced Research vol 2 no 3 pp 253ndash264 2011

[165] S Katoch S S Chauhan and V Kumar ldquoA review ongenetic algorithm past present and futurerdquo MultimediaTools and Applications vol 80 no 5 pp 8091ndash8126 2021

[166] T Han B S Yang and Z J Yin ldquoFeature-based fault di-agnosis system of induction motors using vibration signalrdquoJournal of Quality in Maintenance Engineering vol 13 no 2pp 163ndash175 2007

[167] A Hajnayeb A Ghasemloonia S E Khadem andM HMoradi ldquoApplication and comparison of an ann-basedfeature selection method and the genetic algorithm ingearbox fault diagnosisrdquo Expert Systems with Applicationsvol 38 no 8 pp 10 205ndash10 209 2011

[168] F Chen B Tang and R Chen ldquoA novel fault diagnosismodel for gearbox based on wavelet support vector machinewith immune genetic algorithmrdquo Measurement vol 46no 1 pp 220ndash232 2013

[169] C Y Xiao B Q Shi Z J Hao and SM Zhu ldquoGear incipientdiagnosing based on eemd and genetic-support vector ma-chinerdquo Applied Mechanics and Materials vol 397-400pp 2104ndash2110 2013

[170] R Semil and P Jaiswal ldquoBearing fault diagnosis usingsupport vector machine with genetic algorithms based op-timization and k fold cross-validation methodrdquo Interna-tional Journal of Recent Technology and Engineering vol 8no 2 pp 3242ndash3250 2019

[171] A Afia C Rahmoune and D Benazzouz ldquoGear fault di-agnosis using autogram analysisrdquo Advances in MechanicalEngineering vol 10 no 12 Article ID 16878140188125342018

[172] J Nowicki J Hebda-Sobkowicz R Zimroz andA Wyłomanska ldquoDependency measures for the diagnosis oflocal faults in application to the heavy-tailed vibration sig-nalrdquo Applied Acoustics vol 178 Article ID 107974 2021

[173] T Fei C Jiangfeng Q Qinglin M Zhang H Zhang andS Fangyuan ldquoDigital twin-driven product designmanufacturing and service with big datardquo InternationalJournal of Advanced Manufacturing Technology vol 94no 9-12 pp 3563ndash3576 2018

[174] D Shangguan L Chen and J Ding ldquoA digital twin-basedapproach for the fault diagnosis and health monitoring of acomplex satellite systemrdquo Symmetry vol 12 no 8 p 13072020

[175] J Wang L Ye R X Gao C Li and L Zhang ldquoDigital twinfor rotating machinery fault diagnosis in smartmanufacturingrdquo International Journal of Production Re-search vol 57 no 12 pp 3920ndash3934 2019


machine monitoring and diagnosis is thermal imaginganalysis In this analysis an infrared camera is usually usedto detect many electrical faults in the machine based on thethermal anomalies +e thermal images obtained are usefulin detecting and locating the machinersquos faults However thistechnique is expensive and requires a longer time to processthe thermal images compared to processing the acoustic andvibration signals Vibration analysis is considered as the bestmethod in determining the machine condition [7]According to Saucedo-Dorantes et al [8] the percentage offault diagnosis techniques conducted with the means ofvibration analysis exceeds 82 Machines are mostly madeup of moving parts that generate unwanted vibration andwith vibration analysis and a decision on whether themachine can continue to operate or needs to be shut downand repaired can be made [3]

+e machinersquos condition can be determined by the vi-bration amplitude and frequency as both can reveal theseverity and source of the machine problem respectively [9]At first without the help of vibration equipment machineconditions can still be diagnosed with a human brain oftrained personnel coupled with the senses of touch andhearing which acts as a vibration analyzer However humanperception is somewhat limited and it is impossible to detectproblems that are beyond the capability of human senses oftouch and hearing +en vibration analysis was based on areal-time spectral analyzer and now it can be categorizedinto time frequency and time-frequency domain [10] Timeand frequency domain analysis analyses the time series ofdata with respect to time and frequency respectively Time-frequency domain analysis used both time and frequencydomains at the same time [3] Vibration analysis for mostmachine monitoring and diagnosis can be divided into low-speed and high-speed machines Because currently there isno universally accepted speed range to differentiate bothtypes of machines machines with rotating speeds up to600 rpm such as wind turbines and paper mills are con-sidered low-speed machines According to Kim et al [11]low-speed machines can be very time-consuming and moredifficult to monitor compared to high-speed machines as therotating elements and the fault is typically low unless thefault has reached above the background noise level Vi-bration monitoring of low-speed machines is highly asso-ciated with low-speed bearing in ensuring the reliability ofthe machine

+e vibration analysis for machine monitoring anddiagnosis typically consists of three main steps which aredata acquisition signal processing and fault recognitionTo date there are lots of techniques and instruments usedin each of the aforementioned steps and choosing the rightones might be quite challenging +is is because eachmethod and instrument have its characteristics advan-tages and disadvantages +ese methods can be dividedinto two main groups which are model-based and data-driven methods Model-based methods require an ana-lytical model of the system whereas data-driven methodsdo not need any assumption about the systemrsquos model Indata-driven methods advanced signal processing tech-niques are applied Because it is very difficult to model a

faulty system data-driven methods are widely applied inmachine diagnosis and monitoring compared to model-based methods +us the main contribution of this articleis the review of various data-driven vibration analysistechniques and instruments used for monitoring and di-agnosing the machines However due to a wide range oftechniques only the widely used ones are discussed in thisarticle +ere are several review articles regarding this areaand Table 1 discusses each of the review articles Based onTable 1 we aimed to fill the research gap in reviewing thevibration analysis for machine monitoring and diagnosiswhere the data acquisition system and comparison be-tween different vibration analysis techniques including thelatest deep learning approach are not discussed We alsoaimed to answer the following research questions de-scribed in Table 2

+is manuscript is organized as follows In the nextsection the research approach for this review article isdiscussed +en Sections 3ndash5 will follow the vibrationanalysis steps as shown in Figure 1 Firstly in Section 3the data acquisition stage is discussed +is stage involvesthe types of vibration sensors used to obtain the vibrationdata and analyzers for analyzing the acquired data +edata acquisition stage is not discussed in most of thepublished review articles Besides different sensormounting techniques are also discussed in this sectionSection 4 is about the signal processing or feature ex-traction methods performed by researchers over the yearsbased on the time frequency and time-frequency do-mains +e final stage in vibration analysis which is thefault recognition stage is discussed in Section 5 In thissection different AI-based methods such as supportvector machine (SVM) neural network (NN) includingdeep learning fuzzy logic and genetic algorithm (GA) inthe fault recognition step are discussed +e discussionsand findings of our review are explained in Section 6 andwe conclude our studies in Section 7

2 Research Approach

A comprehensive literature study was conducted to an-swer the five research questions A Systematic LiteratureReview (SLR) approach was employed to collect the rel-evant primary studies regarding the vibration analysis formachine monitoring and diagnosis [17] Firstly weclassified the articles and the selected papers were thenanalyzed and differentiated through the content analysismethod +e results can be classified into four maincategories

(1) Survey where review articles made by other re-searchers on vibration analysis for machine moni-toring and diagnosis are discussed

(2) Simulation where the performance of the proposedtechnique is evaluated through simulation methods

(3) Experimentreal-time deployments where themethods developed are applied experimentally or inreal environments








4 Analyzer







methods







methods











Start

Analyzer

Sensor

Time Domain

Frequency Domain


AI-Based

Data Acquisition


Fault Recognition

End














5 Sensor






English






Data Acquisition

SensorAnalyzer


VelocityTransducer

MEMSPiezoelectric



















peak |v(t)|max (1)






MEMSaccelerometer



Velocitytransducer



Displacementsensor


LDV


the signal quality





RM

1T

1113946T2

T1

v(t)dt

1113971

(2)




(3)


radic 1414










minusinfinf(t)e

minus iωtdt (4)


f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)





FrequencyDomain

TimeDomain


Kurtosis


WT WVD HHT PSD STFT





(a)

Measured surface


Drilled hole

(b)

































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References

































































































































































































4 Analyzer







methods







methods











Start

Analyzer

Sensor

Time Domain

Frequency Domain


AI-Based

Data Acquisition


Fault Recognition

End














5 Sensor






English






Data Acquisition

SensorAnalyzer


VelocityTransducer

MEMSPiezoelectric



















peak |v(t)|max (1)






MEMSaccelerometer



Velocitytransducer



Displacementsensor


LDV


the signal quality





RM

1T

1113946T2

T1

v(t)dt

1113971

(2)




(3)


radic 1414










minusinfinf(t)e

minus iωtdt (4)


f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)





FrequencyDomain

TimeDomain


Kurtosis


WT WVD HHT PSD STFT





(a)

Measured surface


Drilled hole

(b)

































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References






























































































































































































Start

Analyzer

Sensor

Time Domain

Frequency Domain


AI-Based

Data Acquisition


Fault Recognition

End














5 Sensor






English






Data Acquisition

SensorAnalyzer


VelocityTransducer

MEMSPiezoelectric



















peak |v(t)|max (1)






MEMSaccelerometer



Velocitytransducer



Displacementsensor


LDV


the signal quality





RM

1T

1113946T2

T1

v(t)dt

1113971

(2)




(3)


radic 1414










minusinfinf(t)e

minus iωtdt (4)


f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)





FrequencyDomain

TimeDomain


Kurtosis


WT WVD HHT PSD STFT





(a)

Measured surface


Drilled hole

(b)

































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References




























































































































































































5 Sensor






English






Data Acquisition

SensorAnalyzer


VelocityTransducer

MEMSPiezoelectric



















peak |v(t)|max (1)






MEMSaccelerometer



Velocitytransducer



Displacementsensor


LDV


the signal quality





RM

1T

1113946T2

T1

v(t)dt

1113971

(2)




(3)


radic 1414










minusinfinf(t)e

minus iωtdt (4)


f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)





FrequencyDomain

TimeDomain


Kurtosis


WT WVD HHT PSD STFT





(a)

Measured surface


Drilled hole

(b)

































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References









































































































































































































peak |v(t)|max (1)






MEMSaccelerometer



Velocitytransducer



Displacementsensor


LDV


the signal quality





RM

1T

1113946T2

T1

v(t)dt

1113971

(2)




(3)


radic 1414










minusinfinf(t)e

minus iωtdt (4)


f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)





FrequencyDomain

TimeDomain


Kurtosis


WT WVD HHT PSD STFT





(a)

Measured surface


Drilled hole

(b)

































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References


































































































































































































peak |v(t)|max (1)






MEMSaccelerometer



Velocitytransducer



Displacementsensor


LDV


the signal quality





RM

1T

1113946T2

T1

v(t)dt

1113971

(2)




(3)


radic 1414










minusinfinf(t)e

minus iωtdt (4)


f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)





FrequencyDomain

TimeDomain


Kurtosis


WT WVD HHT PSD STFT





(a)

Measured surface


Drilled hole

(b)

































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References





























































































































































































RM

1T

1113946T2

T1

v(t)dt

1113971

(2)




(3)


radic 1414










minusinfinf(t)e

minus iωtdt (4)


f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)





FrequencyDomain

TimeDomain


Kurtosis


WT WVD HHT PSD STFT





(a)

Measured surface


Drilled hole

(b)

































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References






























































































































































































minusinfinf(t)e

minus iωtdt (4)


f(t) Fminus 1

(F(ω)) 12π

1113946infin

minusinfinF(ω)e

iωtdω (5)





FrequencyDomain

TimeDomain


Kurtosis


WT WVD HHT PSD STFT





(a)

Measured surface


Drilled hole

(b)

































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References

























































































































































































































method














Kurtosis






Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References



























































































































































































Table 6 Continued
















gearbox



[145]


bearing fault












[151]





















gearbox fault








fault diagnosis













WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References






































































































































































































WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References






























































































































































































WX(tω) 12π

1113946+infin

minusinfinx t +

τ2


t minusτ2









Envelopeanalysis


fluctuation


Spectrumanalysis


the FFT



x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References



























































































































































































x(t) 1113946infin







minus j2πftdt (8)




PSD(f) 2|X(f)|

2

t2 minus t1( 1113857 (9)






wavelet type







STFT




PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References




























































































































































































PSD Grms( 1113857

2

f (10)
















5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References
































































































































































































5743



Marging

Class B

Class A

Support Vector





11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References




























































































































































































11 Discussion


















3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References





































































































































































































3118

3615

PeakRMS


(a)

39

21

19

21

FFTCepstrum

EnvelopeSpectrum

(b)

40

1314

258

WTWVDHHT

STFTPSD

(c)

3624

10

30

SVMNN

Fuzzy LogicGA

(d)





12 Conclusion








Data Availability















Acknowledgments


References





























































































































































































12 Conclusion








Data Availability















Acknowledgments


References



























































































































































































Acknowledgments


References









































































































































































































































































































































































































































































































































































































































































Documents

Vibration Analysis for Machine Monitoring and Diagnosis: A