radiation noise separation of internal combustion engine

Research ArticleRadiation Noise Separation of Internal Combustion EngineBased on Gammatone-RobustICA Method

Jiachi Yao1 Yang Xiang1 Sichong Qian1 and Shuai Wang12

1School of Energy and Power Engineering Wuhan University of Technology Wuhan 430063 China2The Second Ship Design Institute of Wuhan Wuhan 430063 China

Correspondence should be addressed to Yang Xiang yxiangwhuteducn

Received 12 July 2017 Revised 15 October 2017 Accepted 1 November 2017 Published 26 November 2017

Academic Editor Chao Tao

Copyright copy 2017 Jiachi Yao et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In the internal combustion engine noise source separation process the combustion noise and the piston slap noise are found tobe seriously aliased in time-frequency domain It is difficult to accurately separate them Therefore the noise source separationmethod which is based on Gammatone filter bank and robust independent component analysis (RobustICA) is proposed The6-cylinder internal combustion engine vibration and noise test are carried out in a semianechoic chamber The lead coveringmethod is adopted to isolate the interference noise from numbers 1 to 5 cylinder parts with only the number 6 cylinder partsleft bare Firstly many mode components of the measured near-field radiated noise signals are extracted through the designedGammatone filter bank Then the RobustICA algorithm is utilised to extract the independent components Finally the spectrumanalysis the continuouswavelet time-frequency analysis the correlation functionmethod and the drag test are employed to furtheridentify the separation results The research results show that the frequency of the combustion noise and the piston slap noise arerespectively concentrated at 4025Hz and 1725Hz Compared with the EWT-RobustICA method the separation results obtainedby the Gammatone-RobustICA method have very fewer interference components

1 Introduction

The internal combustion engine as power heart is widelyused in ships vehicles and other means of transportationWith the development of internal combustion engine toheavy load high speed and light direction its vibration noiseproblem is becoming more and more serious which hasbecome themain vibration noise source of ships and vehiclesBy reducing the level of vibration and noise of the internalcombustion engine the working performance of the internalcombustion engine can be improved and the peoplersquos livingenvironment can be ameliorated [1] In order to draw upthe vibration and noise reduction program of the internalcombustion engine the first step is to accurately separate andidentify the noise sources of the internal combustion engineMany parts of the internal combustion engine can producenoise According to the source of the internal combustionengine the noise can be divided into mechanical noisecombustion noise and aerodynamic noise [2ndash4] Mechanicalnoise mainly includes piston slap noise air valve knock

noise gear meshing noise and fuel injection pump noiseCombustion noise is caused by the change of the cylinderpressure Aerodynamic noise includes intake noise exhaustnoise and fan noise

Currently there are many scholars who utilised the cyclicWiener filtering method [5] blind source separation method[6ndash8] improved spectrofiltermethod [9] speed-varying filter[10] and othermultichannelmethods to separate and identifythe noise sources of the internal combustion engine

When the multichannel method is adopted to separateand identify the noise sources of the internal combustionengine the multiple channel noise signals of the internalcombustion engine need to be measured However in theactual engineering test by the limit of cost and installationconditions it is necessary to use a few sensors to achievethe same noise source separation effect Therefore scholarsstudied the single channel method to separate and identifythe noise sources of internal combustion engine For exampleZhang et al [11] adopted the ensemble empirical mode de-composition the coherent power spectrum analysis and the

HindawiShock and VibrationVolume 2017 Article ID 7565041 14 pageshttpsdoiorg10115520177565041

2 Shock and Vibration

improved analytic hierarchy process to separate and identifythe noise sources of the diesel engine Bi et al [12] utilised theEEMD-RobustICAmethod to separate the combustion noisepiston slap noise and exhaust noise of the gasoline engine

When the above single channel method is employed toseparate and identify the noise source of the internal combus-tion engine the first step is to decompose the single channelnoise signal by the EEMD algorithm However EEMD-based single channel method has many defects [13ndash15] TheEMD algorithm lacks rigorous mathematical derivation TheEEMD algorithm is required to add Gaussian white noisebefore each step of the EMD algorithm Therefore the cal-culation cost of the EEMD algorithm is very large Moreoverwhen the EEMD algorithm is applied to decompose the noisesignal the endpoint effect and modal aliasing problems willalso exist In recent years empirical wavelet transform (EWT)[16] variational mode decomposition (VMD) [17] and therelated improved methods are proved to be useful and bettertools to decompose the signal For example Yao et al [18]utilised variationalmode decomposition and robust indepen-dent component analysis to separate the noise source of dieselengine Moreover these methods are widely used in bearingfault diagnosis [19ndash21]

In the real world the human auditory system can distin-guish the mixed speech signals in a noisy environment Atpresent there are many scholars establishing the computa-tional auditory scene analysis model and algorithm based onthe human ear hearing system to separate and identify themixed speech signals [22] The speech signals and the radi-ated noise signals of the internal combustion engine belongto the separable aliasing sound signalsThus the noise sourceof the internal combustion engine can be separated andidentified by the human ear hearing model Moreover theGammatone filter bank is a widely used human ear hearingmodel [23ndash26] Therefore the Gammatone hearing filterbank can be introduced into the separation and identificationof the internal combustion engine noise sources

In this paper the lead covering method is utilised toisolate the noise interference from 1 to 5 cylinders with onlythe number 6 cylinder part left bare The WP10-240 six-cylinder four-stroke high speed internal combustion enginevibration and noise test are carried out in a semianechoicchamber The Gammatone-RobustICA method is proposedto separate and identify the combustion noise and the pistonslap noise of the number 6 cylinder

The paper is organized as follows In Section 2 basictheory methods (such as the cochlear basement membranemodel the Gammatone filter bank and the robust indepen-dent component analysis) are described In Section 3 thesimulation analysis is carried out In Section 4 an internalcombustion engine noise and vibration test is introduced InSection 5 separation and identification methods are adoptedto separate and identify the noise sources of an internalcombustion engine Finally Section 6 presents conclusions

2 Basic Theory

21 Cochlear Basement Membrane Model of the Auditory Sys-tem The human auditory system includes the auditory

periphery and the auditory center [27 28] The auditoryperiphery consists of outer ear middle ear and inner earThe inner ear consists of semicircular canal vestibule andcochlear implant The speech signals are through the outerear middle ear and ear bone to the cochlear The cochleartransforms the mechanical energy of sound waves to neuralcoding signals and through the auditory nerve into theauditory center Then the hearing will be produced

In the auditory system the cochlear as the human audi-tory receptor is one of the most important parts The soundsignal processing of the human ear is achieved by the fre-quency decomposition of cochlear basement membrane Itcannot only convert different frequencies of the sound signalsinto different basement membrane positions but also switchdifferent sound intensity into different basement membranevibration amplitude Thus the cochlear can complete thecoding according to the sound frequency and the soundintensity

In the auditory model a set of overlapping band-passfiltersrsquo bank is usually used to simulate the cochlear basementmembrane Suppose there are119873 filters The 119894th filter is ℎ(119905 119894)The response of the basement membrane to the signal 119909(119905) isdefined as follows

119910 (119905 119894) = 119909 (119905) lowast ℎ (119905 119894) (1)

where 119910(119905 119894) is the output of the basement membrane lowastrepresented the convolution

The characteristic of the Gammatone filter bank is highlyconsistent with the auditory characteristic which can wellsimulate the basement membrane frequency selectivity andspectral analysis characteristics Thus the Gammatone filterbank is widely adopted as the cochlear basement membranemodel

22 Gammatone Filter Bank TheGammatone filter bank is astandard cochlear auditory filter [29 30] It can simulate theband-pass filter characteristics of the basement membraneThe center frequency of each filter is logarithmically evenlydistributed on the frequency axis Suppose the center fre-quency of the 119894th filter is 119891119894 The time domain expression ofthe Gammatone filter is

119892119891119894 (119905) = 119905119873minus1 exp (minus2120587119861119905) cos (2120587119891119894119905 + 120593119894) 119906 (119905) (2)

where 119873 is the filter order 119891119894 is the filter center frequency120593119894 is the phase of the filter due to the phase of the soundsignals having small influence for hearing thus the phase 120593119894is usually set as zero 119906(119905) is the unit step function 119861 is theattenuation factor of filter It determines the decay rate of theimpulse response which is related to the bandwidth of thefilterThe bandwidth of the auditory band-pass filter dependson the center frequency It usually adopted the equivalentrectangular bandwidth (ERB) The calculation formula is

119861 = 1019ERB (119891119894) = 1019 (247 + 0108119891119894) (3)

The Gammatone filter bank is shown in Figure 1 Thetime domain waveform under different center frequencies119891119894 is shown in Figure 1(a) The corresponding amplitudefrequency response curve is shown in Figure 1(b)

Shock and Vibration 3

10 20 30 40 50 0 Time (ms)

100

259

496

847

1369

2143

3293

5000Ch

anne

l cen

ter f

requ

ency

(Hz)

(a) Time domain waveform of Gammatone function

minus50

minus40

minus30

minus20

minus10

0

Mag

nitu

de g

ain

(dB)

1000 2000 3000 4000 50000 Frequency (Hz)

(b) Amplitude frequency response curve of Gammatone function

Figure 1 Gammatone filter bank

MixedmatrixA

Source signals S(t)

Observed signalsX(t)

Estimated signals Y(t)

DemixingmatrixW

s1(t)

s2(t)

sn(t)

x1(t) y1(t)

x2(t) y2(t)

xn(t) yn(t)

middot middot middot middot middot middot middot middot middot

Figure 2 A common blind source separation process

23 Robust Independent Component Analysis The blindsource separation method is a powerful signal processingmethod [31] It can extract and recover the original signalswhich cannot be directly observed from several observedmixed signals Due to the fact that the source signal isunknown and unobserved and themixed system characteris-tics are unknown or only a small amount of prior knowledgeis known in advance it is a challenge to use the blind sourceseparation method to separate the source signals

Suppose the signals collected by the sensors are 119909(119896) =[1199091(119896) 1199092(119896) 119909119899(119896)]

119879 Then it is needed to find an in-verse system to reconstruct the original signals 119904(119896) =[1199041(119896) 1199042(119896) 119904119899(119896)]

119879 The output expression is

119910 (119896) = 119882119909 (119896) = 119882119860119904 (119896) (4)

A common blind source separation process is shown inFigure 2

The independent component analysis (ICA) is an impor-tant method to solve the blind source separation problemsThe FastICA algorithm is a widely used blind source sepa-ration algorithm which is proposed by the Hyvarinen [32]The FastICA algorithm has high convergence speed andreliability It is cubic convergence However it has some limi-tationsWhen the source signal spatial correlation is high theFastICA algorithm will have not good separation results andthe kurtosis based on higher order cumulant has its owndefects in the field value To solve these problems Zarzoso

and Comon [33] proposed the RobustICA algorithm whichhas excellent blind source separation effect The RobustICAalgorithm utilised the kurtosis as the objective functionThe kurtosis is an indicator to evaluate the non-Gaussiancharacteristic of the analysed signal The kurtosis is definedas

kurt (119910) =119864 1003816100381610038161003816119910

10038161003816100381610038164 minus 21198642 1003816100381610038161003816119910

10038161003816100381610038162 minus 10038161003816100381610038161003816119864 119910210038161003816100381610038161003816

2

1198642 100381610038161003816100381611991010038161003816100381610038162

(5)

Suppose the observed signal is 119883 The RobustICA algo-rithm does not need to carry out the whitening processfor the observed signal It only requires the mean value ofthe observed signal which is zero By RobustICA algorithmthe unmixed signal is 119910 = 119908119879119883 The specific calcula-tion process of the RobustICA algorithm is shown as fol-lows

Step 1 Counter 119899 = 1 Suppose the number 119873 of sourcesignals is the same with the number of observed signals

Step 2 119908119899 is randomly assigned as the initial value119908119899(0) andthe norm is 1 The number of iteration steps 119896 is set as 1

Step 3 Calculate the polynomial 119901(120583) = sum4119896=0 119886119896120583119896 The

largest root of the objective function is obtainedThe calcula-tion formula is 120583opt = argmax120583|119896(119908 + 120583119892)|

Step 4 Update the separation matrix 119908+119899 (119896) = 119908119899(119896 minus 1) +120583opt119892 And normalize 119908119899(119896) = 119908119899(119896)119908119899(119896)

Step 5 Repeat Steps 3 and 4 until the |119908119899(119896)119879119908119899(119896 minus 1)| is

sufficient and less than 1

Step 6 Orthogonal 119908+119899 = 119908119899 minus 119882119882119879119908+119899 Normalize 119908119899(119896) =119908119899(119896)119908119899(119896)

Step 7 Make 119899 = 119899 + 1 Then go back to Step 2 for nextiteration until 119899 = 119873


Calculate the correlation coefficient and select mode components

Measured noise signals

RobustICA

Drag testCWTSpectral analysis Coherence function method

Gammatone filter bank


Separation and identification results

middot middot middot



mmm3m2m1 mmminus1

mnm3m2m1 mnminus1

）1 ）2 ）3 ）nminus1 ）n

Figure 3 Calculation flow of the Gammatone-RobustICA method

24 Calculation Process of Gammatone-RobustICA MethodFor the measured single channel radiated noise signals theGammatone-RobustICA method is utilised to separate andidentify the noise sources First the different mode compo-nents of the measured signals are extracted by the Gamma-tone filter bank Because these different mode componentsare not always independent of each other thus the blindsource separation technique is still needed to further dealwith the separated signal components to extract the indepen-dent components Then the correlation coefficient betweenthe mode components and the measured signal is calculatedThe mode components which have a higher correlation coef-ficient with the measured signal are retained The retainedmode components and the measured signal are combinedtogether to form a new signal group The RobustICA al-gorithm is used to extract the independent componentsFinally the obtained separation results are further identi-fied through the spectral analysis the continuous wavelettransform (CWT) the coherence function method and thedrag test of internal combustion engine The calculationflow of the Gammatone-RobustICA method is shown inFigure 3

3 Simulation Analysis

In order to illustrate the performance of the Gammatone-RobustICAmethod some typical signals are selected to carryout the simulation analysis by MATLABThe selected typicalsignals (1198781 1198782 and 1198783) are shown as follows

1198781 = cos (2120587 ∙ 49 ∙ 119905)

1198782 = cos (2120587 ∙ 115 ∙ 119905)

1198783 = cos (2120587 ∙ 201 ∙ 119905)

119878 = 1198781 + 1198782 + 1198783

(6)

The sampling frequency of the selected signals is 3000Hzand the sampling number of the signals is 300 The timedomain waveform of the selected source signals is shown inFigure 4

For the mixed signal 119878 the Gammatone-RobustICAmethod and the EWT-RobustICA method are respectivelyutilised to separate the selected source signals 1198781 1198782 and 1198783

When using the Gammatone-RobustICA method thefrequency range of the Gammatone filter bank is set to


t (s)0 002 004 006 008 01

0 002 004 006 008 01

0 002 004 006 008 01

minus101

S3

minus101

S1

minus101

S2

Figure 4 Time domain waveform of the selected source signals

0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)

(a) Separation results of the Gammatone-RobustICA method

0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)

(b) Separation results of the EWT-RobustICA method

Figure 5 Comparison of simulation signal separation results

45Hzndash205Hz and the channel number is set to 3 By theGammatone filter bank the three mode components ofthe mixed signals can be extracted Then the RobustICAalgorithm is adopted to further extract the independentcomponents from the three mode components The separa-tion results of Gammatone-RobustICAmethod are shown inFigure 5(a)

From Figures 4 and 5(a) it can be seen that the IC1 IC2and IC3 are respectively corresponding to 1198781 1198782 and 1198783The results obtained by Gammatone-RobustICA method aresimilar to the time domain waveforms of the source signals

When using EWT-RobustICA method the separationresults of EWT-RobustICAmethod are shown in Figure 5(b)From Figures 4 and 5(b) it can be seen that IC1 IC2 andIC3 are respectively corresponding to 1198781 1198782 and 1198783 But

Table 1 Specific parameters of the WP10-240 type diesel engine

Characteristics ParametersEngine type In-line engineCylinder number 4Stroke number 6Cylinder diameter times stroke 126mm times 130mmFiring order 1-5-3-6-2-4Maximum output power 175 kWRated power speed 2200 rpmCompression ratio 17 1Maximum torque 1000NsdotmMaximum torque speed 1200ndash1600 rpm

2mm lead plate

Figure 6 Lead cover of the internal combustion engine

the IC2 has some difference with the 1198782 This can be seenfrom the red circle in Figure 5(b) Thus it can be consideredthat Gammatone-RobustICA method has a better separationeffect than EWT-RobustICA method

4 Experimental Investigation

41 Test Platform The noise and vibration test of internalcombustion engine are carried out in a fully enclosed semi-anechoic chamber The size of the semianechoic chamber islength 704m timeswidth 679m times height 595mThe free soundfield radius is not less than 2 meters and the backgroundnoise is 18 dB

Test bench contains theWP10-240 type high speed dieselengine transmission shaft Germanyrsquos Siemens 1PL6 ACmotor console and other related accessories The specificparameters of the WP10-240 type high speed diesel engineare shown in Table 1

The internal combustion engine has six cylinders It willproduce many vibration and noise sources It is very difficultto directly separate all the noise sources of the internalcombustion engine Therefore the lead covering method isutilised to isolate the noise from the numbers 1ndash5 cylindersand only the number 6 cylinder parts are exposed The noisesource of the specified number 6 cylinder is separated andidentified The lead cover of the internal combustion engineis shown in Figure 6

42 Test Conditions The internal combustion engine is nor-mally operated at a rated speed of 2200 rpm Thus it is nec-essary and meaningful to separate and identify the noise


WP10-240 typediesel engine

1 2 3 4 5 6

Motor

Computer

Semianechoic chamber

Charge amplifier

NI cDAQ9172NI9234NI9205

LabVIEW integrated data acquisition system

Microphone

Accelerometer

TDC sensor

Cylinder pressure sensor

Lead coverAccelerometer

Figure 7 Vibration and noise measuring system of internal combustion engine

Table 2 Internal combustion engine test conditions

Test conditions Speed (rpm) Percentage of load ()(1) Normal condition 2100 0(2) Drag condition 2100 0

sources of the internal combustion engine at the rated speedHowever in the internal combustion engine test benchthe coupling equipment of the internal combustion enginehas some problems The internal combustion engine cannotreach the rated speed In the test the actual speed of theinternal combustion engine is 2100 rpm

Moreover when the internal combustion engine is in dragcondition the internal combustion engine will not producethe combustion noise and will only produce the mechanicalnoise However it is difficult to measure the independentpiston slap noise because many moving parts of an internalcombustion engine will produce noise According to therelevant knowledge of internal combustion engine whenthe piston impacts the inner wall of the cylinder it willproduce the vibration and then the vibration will furtherproduce piston slap noise Thus the frequency of the pistonslap vibration can be utilised to assess the accuracy of theseparated piston slap noise The test conditions of internalcombustion engine are shown in Table 2

43 Measuring System and Measuring Point ArrangementThe vibration and noise measuring system of internal com-bustion engine is shown in Figure 7 The measuring systemincludes the NI 9234 and NI 9205 acquisition module thatthe highest sampling rate can be up to 512 kHzThe LC0158Taccelerometers are adopted to measure the cylinder headvibration and the piston slap vibration that the sensitivityis 30mVg the range is 166 g and the frequency range is0ndash15 kHz The type of the cylinder pressure sensor is Kistler7013C that the range is 25MPa with a single channel chargeamplifier 5018A1000 The DGO9767CD electret microphoneis applied to measure the noise signals that the sensi-tivity is 50mVPa and the frequency response range is20Hzndash20 kHz

Accelerometer forpiston slap vibration

Figure 8 Measured position of piston slap vibration

In fact due to the limitation of the test conditions itis difficult to measure the independent combustion noiseAccording to the related knowledge of internal combustionengine the combustion noise is related to the drastic changeof cylinder pressure Drastic change of cylinder pressure cancause vibration of cylinder head and body surface and thenthe vibration will produce the combustion noise Thus thecorrelation function of cylinder pressure and cylinder headvibration can be used to determine the frequency of thecombustion noise and then further evaluate the accuracy ofseparated combustion noise

Due to the fact that the structure of internal combustionengine and movement trajectory of piston are known beforethus the place of the piston slap occurring can be determinedaccording to the structure of internal combustion engine andmovement trajectory of piston The measured position of thepiston slap vibration is corresponding to the position that thepiston impacts the inner wall of the cylinder The measuredposition of the piston slap vibration is shown in Figure 8

TheDGO9767CDelectretmicrophone is arranged at 1 cmdistance away from the number 6 cylinder body side TheLC0158T accelerometer is arranged at the piston slap place


Microphone for cylinder bodyside near field radiated noise



Figure 9 Specific arrangement of the measuring point

0 120 240 360 480 600 720

0 120 240 360 480 600 720

0 120 240 360 480 600 720

minus505

p1

(MPa

)

minus100

10

p2

(Pa)

minus500

50

a (g

)

Crank angle (∘A)

Figure 10 Cylinder pressure cylinder head vibration accelerationand cylinder body side near-field radiated noise signals

to measure the piston slap vibration when the internal com-bustion engine is in drag conditionThe specific arrangementof measuring point is shown in Figure 9

In the test the highest frequency of the internal combus-tion engine radiated noise is below 8000Hz According tothe sampling theorem the sampling frequency is greater thantwice the highest frequency of the analysed signals Thus thesampling frequency can be set to 256 kHz

The number 6 cylinder is set as the research objectWhen the internal combustion engine is in 2100 rpm and no-load condition the cylinder pressure signals (1199011) cylinderhead vibration acceleration signals (119886) and the cylinder bodyside near-field radiated noise signals (1199012) are measured It isshown in Figure 10

5 Separation and Identification ofthe Near-Field Radiated Noise

In this part the Gammatone-RobustICA method and theEWT-RobustICA method are respectively used to separateand identify the noise sources of the cylinder body side near-field radiated noise

In the process of the noise and vibration test the mea-sured noise signalmay have random error components whichwill affect the subsequent calculation results In order toreduce the random error components the pretreatment suchas eliminate trend items and slip average is carried out onthe measured noise signal The preprocessed noise signal isshown in Figure 11

120 240 360 480 600 7200Crank angle (∘A)

minus10

0

10

p (P

a)

Figure 11 Preprocessed noise signal

51 Gammatone-RobustICA Method When the Gamma-tone-RobustICA method is utilised to separate and identifythe noise source of the internal combustion engine the firststep is to design an appropriate Gammatone filter bank toextract various mode components of the preprocessed noisesignal It is necessary to predefine the two important param-eters of the Gammatone filter bank the center frequencyrange and the number of channels For the center frequencyrange on the one hand the frequency range of humanaudible sounds is 20Hzndash20 kHz On the other hand thefrequency range of the internal combustion engine radiatednoise is usually below 8000Hz Thus the center frequencyof the Gammatone filter bank is set to 20Hzndash8000Hz Forthe number of channels of the Gammatone filter bank onthe one hand considering the calculation accuracy and thecomputing costs the higher the number of channels is thehigher the accuracy of the calculation is and the higher thecost of the computation is thus the number of channels ofthe Gammatone filter bank should not be too much On theother hand according to the related knowledge of internalcombustion engine the noise sources of internal combustionengine are combustion noise piston slap noise air valveknock noise gear meshing noise fuel injection pump noiseand so forth After considering these factors the number ofchannels of the Gammatone filter bank is set to 11

By the Gammatone filter bank the mode componentsfrom the preprocessed noise signal can be obtained Thedecomposition results are shown in Figure 12

In order to improve the efficiency of the calculation themode components with large correlation with the prepro-cessed noise signal need to be selected to carry out the nextstep calculation

Suppose the correlation coefficient between the modecomponents and the preprocessed noise signal is 119903119894 (119894 =1 2 119899) 119899 is the number of the mode componentsCorrelation coefficient 119903 is defined as follows

119903119883119884 =cov (119883 119884)

radic119863 (119883)radic119863 (119884) (7)

where 119883 represents the source signal 119884 represents the sepa-ration component cov(119883 119884) represents the covariance of 119883and 119884 119863(119883) and 119863(119884) represent the variance of 119883 and 119884respectively

According to Pearson correlation coefficient theory [34]the correlation coefficient is in the range of minus1 to +1 If thecorrelation coefficient is greater than zero there is a positivecorrelation between the two variables On the contrarythere is a negative correlation In general if the correlationcoefficient is greater than 03 the two variables are correlated


m1

m2

m3

m4

m5

m6

m7

m8

m9

m10

m11

120 240 360 480 600 7200Crank angle (∘A)

Figure 12 Decomposition results by the Gammatone filter bank

In order to select the mode components the threshold 120582is set to determine whether the mode component is retainedor not But the internal combustion engine has many noisesources and there are many noise disturbances in the mea-surement process Thus if the threshold of the correlationcoefficient is set to 03 the selected mode components will beless and the separated independent noise source informationwill not be sufficient In order to obtain more sufficientindependent noise source information in the actual study thethreshold of the correlation coefficient needs to be set smallerHere the threshold of the correlation coefficient is defined asfollows

120582 =max (119903119894)

120578 119894 = 1 2 119899 (8)

where 120578 is the ratio factor and 120578 is set to 100The calculation results of the correlation coefficient

between the mode components and the preprocessed noisesignal are shown in Table 3

From Table 3 it can be seen that the maximum correla-tion coefficient is 01256 Thus if the correlation coefficientis more than 001256 it should be retained On the contraryif the correlation coefficient is less than 001256 it should betaken out Through analysing it can be determined that m2m3m4m5m6m7m9 andm11 should be retained andm1m8 andm10 should be taken out

Due to the fact that the retained mode components arenot always independent of each other the RobustICA algo-rithm needs to be used to extract the independent compo-nents The retained mode components and the preprocessed

Table 3 Correlation coefficient between themode components andthe preprocessed noise signal

Mode components Correlation coefficientm1 00001m2 00925m3 00987m4 00903m5 00539m6 01256m7 00902m8 00011m9 00392m10 00098m11 00215

IC1

IC2

IC3

IC4

IC5

IC6

IC7

IC8

IC9

120 240 360 480 600 7200Crank angle (∘A)

Figure 13 RobustICA calculation results

noise signal are combined together to form a new signalgroupThen the RobustICA algorithm is employed to extractthe independent components The calculation results areshown in Figure 13

According to the relevant knowledge of internal combus-tion engine the fuel combustion in the cylinder can causedrastic pressure change in the cylinder and it caused the com-bustion noise Thus the combustion noise is high frequencysignal Through analysing the nine components the IC6 isthe high frequency signalThus it can be preliminarily judgedthat the IC6 component is the combustion noise


The mechanical noise of internal combustion engine isusually below 3500Hz [35] Through analysing the Robus-tICA calculation results the frequency of IC9 is below3500Hz Thus it can be preliminarily judged that the IC9component is the piston slap noise

Apart from IC6 and IC9 as for the rest 7 componentsthey may be the air valve knock noise gear meshing noisefuel injection pump noise or other noise sources Ideally allthe noise sources of the internal combustion engine should beseparated and identified However since the noise sources areseriously mixed with each other it is difficult to separate andidentify all the noise sources and they need further researchFor example the air valve knock noise is mainly caused bythe impact of valve opening and closing and timing of valveopening and closing can be determined according to thetiming of inlet and exhaust of internal combustion engineMoreover through arranging the vibration sensor and theacoustic sensor near the valve and combining the timing ofvalve opening and closing the air valve knock noise can befurther studied The gear meshing noise is generated by thecollision and friction between teeth during the gear meshingprocess Every turn of the gear can produce the collisionand friction thus the gear meshing noise can be furtherstudied The fuel injection pump noise is mainly caused bythe oil pressure change during the oil spraying process Thefuel injection pump noise can be studied through oil injec-tion pressure and burning time of internal combustion en-gine

Considering that combustion noise and piston slap noiseare the main noise sources of internal combustion enginethus the paper is mainly on the separation and identificationof combustion noise and piston slap noise

TheFFT (Fast Fourier Transform) andCWT(ContinuousWavelet Transform) are combined to further identify the sep-aration results The calculation results are shown in Figures14 and 15 The correlation function of cylinder pressure andcylinder head vibration is shown in Figure 16

From Figure 14 it can be seen that the frequency ofIC6 component focuses on 4025Hz and the time domainwaveform of IC6 component has great change at 390∘CAFrom Figure 14(c) the frequency energy is large aroundthe 390∘CA and it is mainly concentrated around 4000HzAccording to the prior knowledge of the internal combustionengine the ignition sequence of the internal combustionengine is 1-5-3-6-2-4 The ignition angle of the number 6cylinder is around 390∘CA Due to the fact that the number1ndash5 cylinders are covered by lead the frequency energyof the number 6 cylinder is bigger than the number 1ndash5cylinders Moreover from Figure 16 cylinder pressure andcylinder head vibration have a good correlationnear 4000HzThe combustion noise is mainly caused by the change ofcylinder pressure Near 4000Hz themain information aboutcombustion noise is includedThus it can be determined thatthe IC6 component is the combustion noise

From Figure 15 it can be seen that the frequency of IC9component focuses on 1725Hz Combined with Figure 16the correlation function of cylinder pressure and cylinderhead vibration is not good near 1725Hz From Figure 15(c)the frequency energy is huge around the 390∘CA It is

IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)

(a) Time domain waveform

Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT

Figure 14 Time domain waveform FFT and CWT of IC6 by theGammatone-RobustICA method

corresponding with the ignition angle of the number 6cylinder In order to further confirm the noise componentof the IC9 the internal combustion engine drag test iscarried out By the drag test the piston slap vibration signalis measured separately The FFT of IC9 and piston slapvibration is shown in Figure 17 From Figure 17 the IC9spectrum is very consistent with the piston slap vibrationspectrum Combined with Figure 18 correlation function ofIC9 can be seen and piston slap vibration is basically greaterthan 05 and therefore it can be considered that IC9 andpiston slap vibration have a good correlation Thus it can bedetermined that the IC9 component is mainly the piston slapnoise


IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT

Figure 15 Time domain waveform FFT and CWT of IC9 by the Gammatone-RobustICA method

543 6 71 2 80Frequency (kHz)

0

05

1

r

Figure 16 Correlation function of cylinder pressure and cylinderhead vibration

IC9 spectrumPiston slap vibration spectrum

0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)

Figure 17 FFT of IC9 and piston slap vibration

52 EWT-RobustICA Method In this part the EWT-Robus-tICA method is used to separate the noise source of internalcombustion engine Firstly the EWT algorithm is applied

1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r

Figure 18 Correlation function of IC9 and piston slap vibration

to decompose the preprocessed noise signal The calculationresults are shown in Figure 19

After the preprocessed noise signal is decomposed bythe EWT algorithm empirical modal components can beobtained But it may have some false empirical modal com-ponents Thus it is necessary to remove the false empir-ical modal components Hence the correlation coefficientbetween empirical modal components and preprocessednoise signal is utilised to determine whether the empiricalmodal component is removed or not The correlation coef-ficient between empirical modal components and prepro-cessed noise signal is shown in Table 4

From Table 4 it can be seen that the maximum value ofthe empiricalmodal components is 08532Thus if the empir-ical modal components are less than 008532 it should beremoved Therefore F3 F4 F5 F6 F7 F8 and F9 should beremovedThen the remaining F1 and F2 and the preprocessednoise signal are combined together to form a new signalgroup The RobustICA algorithm is utilised to extract the

Shock and Vibration 11F1

F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)

Figure 19 EWT calculation results

Table 4 Correlation coefficient between empirical modal compo-nents and preprocessed noise signal

Empirical modal components Correlation coefficientF1 08532F2 05144F3 00712F4 00569F5 00525F6 00214F7 00146F8 00159F9 00071

independent componentsThe RobustICA calculation resultsare shown in Figure 20

By analysing it can be preliminarily judged that theIC1 component and the IC2 component are the combustionnoise and the piston slap noise Then the FFT and CWT areutilised to further analyse the IC1 component and the IC2component The calculation results are shown in Figures 21and 22

From Figure 21 it can be seen that the amplitude ofIC1 component has great change around 390∘CA and theignition sequence of the number 6 cylinder is at 390∘CAThefrequency range of the IC1 component is concentrated around4000Hzndash6700Hz Combined with Figure 16 the correlationfunction of cylinder pressure and cylinder head vibration isgood at 4000Hzndash5000Hz but the correlation function is notgood at 5000Hzndash6700HzThus it can be considered that theIC1 component is mainly the combustion noise However it

IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)

Figure 20 Calculation results by the RobustICA

IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P

a)Crank angle (∘A)


4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004

03 4 5 6 7 8Frequency (kHz)

(b) FFT

1 5 6 2 43

Interference components

120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT

Figure 21 Time domain waveform FFT and CWT of IC1 by theEWT-RobustICA method


IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2

Interferencecomponents

(c) CWT


has many interference components as shown in the circle inFigure 21(c)

From Figure 22 the amplitude of IC2 component hasgreat change at 390∘CA It is consistent with the ignitionangle of the number 6 cylinder The frequency of the IC2component focuses on 1350Hz 1725Hz and 2100Hz In theinternal combustion engine drag test the independent pistonslap vibration signal is measured Moreover the FFT ofIC2 and piston slap vibration is shown in Figure 23 FromFigure 23 it can be seen that the frequency of piston slapvibration is concentrated at 1700Hz But the frequency ofIC2 is concentrated at 1350Hz 1725Hz and 2100Hz It hassome difference with the IC2 component Combined withFigure 24 the correlation function of IC2 and piston slap


1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)


vibration is not very goodThus it can be determined that theIC2 component has some interference components except forthe piston slap noise component It can be seen in the yellowcircle in Figure 22(c)

53 Comparison Discussion When adopting the Gamma-tone-RobustICA method to separate the combustion noiseand piston slap noise the calculation results are shown inFigures 14 and 15 The frequencies of combustion noise andpiston slap noise are concentrated at 4025Hz and 1725Hzrespectively When utilising the EWT-RobustICA methodthe separated combustion noise and piston slap noise areshown in Figures 21 and 22 Comparing Figure 14 withFigure 21 it can be seen that there are many other frequencycomponents except for the 4025Hz components in Figure 21Comparing Figure 15 with Figure 22 it can be seen thatthere are many other frequency components except for the1725Hz components in Figure 22 Moreover from Figure 17the IC9 spectrum is consistent with the piston slap vibra-tion spectrum while in Figure 23 the IC2 spectrum hassome difference with the piston slap vibration spectrumTherefore compared with the EWT-RobustICA method theGammatone-RobustICAmethod can get more pure combus-tion noise and piston slap noiseTheGammatone-RobustICAmethod has a better separation and identification effect thanthe EWT-RobustICA method

6 Conclusions

(1) In the aspect of the internal combustion engine test thelead covering method is adopted to wrap the numbers 1ndash5cylinders and only the number 6 cylinder parts are exposedIt can effectively insulate the interference noise from thenumbers 1ndash5 cylinders Thus it is conducive to separating


and identifying the noise sources of the specified number 6cylinder

(2) Inspired by the human auditory system the Gamma-tone-RobustICA method is proposed to separate and iden-tify the combustion noise and the piston slap noise Com-pared with the EWT-RobustICA method the proposedGammatone-RobustICA method has a better separationeffect The separation results obtained by the Gammatone-RobustICA method have very fewer other interference com-ponents

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China China (Grant no 51279148)

References

[1] A Ruiz-Padillo D P Ruiz A J Torija and A Ramos-RidaoldquoSelection of suitable alternatives to reduce the environmentalimpact of road traffic noise using a fuzzy multi-criteria decisionmodelrdquo Environmental Impact Assessment Review vol 61 pp8ndash18 2016

[2] X Zhao Y Cheng L Wang and S Ji ldquoReal time identificationof the internal combustion engine combustion parametersbased on the vibration velocity signalrdquo Journal of Sound andVibration vol 390 pp 205ndash217 2017

[3] E G Giakoumis D C Rakopoulos and C D RakopoulosldquoCombustion noise radiation during dynamic diesel engineoperation including effects of various biofuel blends A reviewrdquoRenewable amp Sustainable Energy Reviews vol 54 pp 1099ndash11132016

[4] D Sachau S Jukkert and N Hovelmann ldquoDevelopment andexperimental verification of a robust active noise control systemfor a diesel engine in submarinesrdquo Journal of Sound andVibration vol 375 pp 1ndash18 2016

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

[6] C Serviere J-L Lacoume and M El Badaoui ldquoSeparation ofcombustion noise and piston-slap in diesel engine - Part IISeparation of combustion noise and piston-slap using blindsource separation methodsrdquo Mechanical Systems and SignalProcessing vol 19 no 6 pp 1218ndash1229 2005

[7] Z-Y Hao Y Jin and C Yang ldquoStudy of engine noise based onindependent component analysisrdquo Journal of Zhejiang Univer-sity vol 8 no 5 pp 772ndash777 2007

[8] X Wang F Bi C Liu X Du and K Shao ldquoBlind source sepa-ration and identification of internal combustion engine noisebased on independent component and wavelet analysisrdquo inProceedings of the 2nd Annual Conference on Electrical andControl Engineering ICECE 2011 pp 113ndash116 China September2011

[9] L Pruvost Q Leclere and E Parizet ldquoDiesel engine com-bustion and mechanical noise separation using an improved

spectrofilterrdquoMechanical Systems and Signal Processing vol 23no 7 pp 2072ndash2087 2009

[10] J Antoni N Ducleaux G Nghiem and S Wang ldquoSeparationof combustion noise in IC engines under cyclo-non-stationaryregimerdquoMechanical Systems and Signal Processing vol 38 no 1pp 223ndash236 2013

[11] J Zhang J Wang J Lin et al ldquoDiesel engine noise source iden-tification based on EEMD coherent power spectrum analysisand improved AHPrdquoMeasurement Science and Technology vol26 no 9 Article ID 095010 2015

[12] F Bi L Li J Zhang andTMa ldquoSource identification of gasolineengine noise based on continuous wavelet transform andEEMD-RobustICArdquoApplied Acoustics vol 100 pp 34ndash42 2015

[13] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety A Mathematical Physical ampamp Engineering Sciencesvol 454 pp 903ndash995 1998

[14] Z H Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis (AADA) vol 1 no 1 pp 1ndash41 2009

[15] M Zvokelj S Zupan and I Prebil ldquoEEMD-based multiscaleICA method for slewing bearing fault detection and diagnosisrdquoJournal of Sound and Vibration vol 370 pp 394ndash423 2016

[16] J Gilles ldquoEmpirical wavelet transformrdquo IEEE Transactions onSignal Processing vol 61 no 16 pp 3999ndash4010 2013

[17] K Dragomiretskiy and D Zosso ldquoVariational mode decompo-sitionrdquo IEEE Transactions on Signal Processing vol 62 no 3 pp531ndash544 2014

[18] J Yao Y Xiang SQian SWang and SWu ldquoNoise source iden-tification of diesel engine based on variational mode decom-position and robust independent component analysisrdquo AppliedAcoustics vol 116 pp 184ndash194 2017

[19] Y Wang R Markert J Xiang and W Zheng ldquoResearch onvariationalmode decomposition and its application in detectingrub-impact fault of the rotor systemrdquo Mechanical Systems andSignal Processing vol 60-61 pp 243ndash251 2015

[20] Z Li J Chen Y Zi and J Pan ldquoIndependence-orientedVMDtoidentify fault feature forwheel set bearing fault diagnosis of highspeed locomotiverdquo Mechanical Systems and Signal Processingvol 85 pp 512ndash529 2017

[21] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 pp 460ndash493 2017

[22] DWang L G Brown J and C DarwinComputational AuditoryScene Analysis Principles Algorithms and Applications IEEEPress 2008

[23] X-Z Zhang B W Ling C K Li and N C Leung ldquoOptimaldesign of continuous time irrational filter with a set of fractionalorder gammatone components via norm relaxed sequentialquadratic programming approachrdquo Digital Signal Processingvol 64 pp 28ndash40 2017

[24] S Tabibi A Kegel W K Lai and N Dillier ldquoInvestigating theuse of a Gammatone filterbank for a cochlear implant codingstrategyrdquo Journal of Neuroscience Methods vol 277 pp 63ndash742017

[25] H Yin V Hohmann and C Nadeu ldquoAcoustic features forspeech recognition based onGammatone filterbank and instan-taneous frequencyrdquo Speech Communication vol 53 no 5 pp707ndash715 2011


[26] E C Smith and M S Lewicki ldquoEfficient auditory codingrdquoNature vol 439 no 7079 pp 978ndash982 2006

[27] Q Zhou Y Wang L Yi Z Tan and Y Jiang ldquoMultisensoryInterplay Within Human Auditory Cortex New Evidencefrom Intraoperative Optical Imaging of Intrinsic SignalrdquoWorldNeurosurgery vol 98 pp 251ndash257 2017

[28] P Sun D Fox K Campbell and J Qin ldquoAuditory fatiguemodelapplications to predict noise induced hearing loss in human andchinchillardquo Applied Acoustics vol 119 pp 57ndash65 2017

[29] S Strahl and A Mertins ldquoAnalysis and design of gammatonesignal modelsrdquoThe Journal of the Acoustical Society of Americavol 126 no 5 pp 2379ndash2389 2009

[30] FMeriem H Farid BMessaoud and A Abderrahmene ldquoNewfront end based on multitaper and gammatone filters for robustspeaker verificationrdquo Lecture Notes in Electrical Engineering vol411 pp 344ndash354 2017

[31] C Chenot and J Bobin ldquoBlind separation of sparse sources inthe presence of outliersrdquo Signal Processing vol 138 pp 233ndash2432017

[32] A Hyvarinen ldquoFast and robust fixed-point algorithms for inde-pendent component analysisrdquo IEEE Transactions on NeuralNetworks and Learning Systems vol 10 no 3 pp 626ndash634 1999

[33] V Zarzoso and P Comon ldquoRobust independent componentanalysis by iterative maximization of the kurtosis contrastwith algebraic optimal step sizerdquo IEEE Transactions on NeuralNetworks and Learning Systems vol 21 no 2 pp 248ndash261 2010

[34] P Di Lena and LMargara ldquoOptimal global alignment of signalsbymaximization of Pearson correlationrdquo Information ProcessingLetters vol 110 no 16 pp 679ndash686 2010

[35] N Dolatabadi B Littlefair M De La Cruz S TheodossiadesS J Rothberg and H Rahnejat ldquoA transient tribodynamic ap-proach for the calculation of internal combustion engine pistonslap noiserdquo Journal of Sound and Vibration vol 352 Article ID12449 pp 192ndash209 2015

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



improved analytic hierarchy process to separate and identifythe noise sources of the diesel engine Bi et al [12] utilised theEEMD-RobustICAmethod to separate the combustion noisepiston slap noise and exhaust noise of the gasoline engine

When the above single channel method is employed toseparate and identify the noise source of the internal combus-tion engine the first step is to decompose the single channelnoise signal by the EEMD algorithm However EEMD-based single channel method has many defects [13ndash15] TheEMD algorithm lacks rigorous mathematical derivation TheEEMD algorithm is required to add Gaussian white noisebefore each step of the EMD algorithm Therefore the cal-culation cost of the EEMD algorithm is very large Moreoverwhen the EEMD algorithm is applied to decompose the noisesignal the endpoint effect and modal aliasing problems willalso exist In recent years empirical wavelet transform (EWT)[16] variational mode decomposition (VMD) [17] and therelated improved methods are proved to be useful and bettertools to decompose the signal For example Yao et al [18]utilised variationalmode decomposition and robust indepen-dent component analysis to separate the noise source of dieselengine Moreover these methods are widely used in bearingfault diagnosis [19ndash21]

In the real world the human auditory system can distin-guish the mixed speech signals in a noisy environment Atpresent there are many scholars establishing the computa-tional auditory scene analysis model and algorithm based onthe human ear hearing system to separate and identify themixed speech signals [22] The speech signals and the radi-ated noise signals of the internal combustion engine belongto the separable aliasing sound signalsThus the noise sourceof the internal combustion engine can be separated andidentified by the human ear hearing model Moreover theGammatone filter bank is a widely used human ear hearingmodel [23ndash26] Therefore the Gammatone hearing filterbank can be introduced into the separation and identificationof the internal combustion engine noise sources

In this paper the lead covering method is utilised toisolate the noise interference from 1 to 5 cylinders with onlythe number 6 cylinder part left bare The WP10-240 six-cylinder four-stroke high speed internal combustion enginevibration and noise test are carried out in a semianechoicchamber The Gammatone-RobustICA method is proposedto separate and identify the combustion noise and the pistonslap noise of the number 6 cylinder

The paper is organized as follows In Section 2 basictheory methods (such as the cochlear basement membranemodel the Gammatone filter bank and the robust indepen-dent component analysis) are described In Section 3 thesimulation analysis is carried out In Section 4 an internalcombustion engine noise and vibration test is introduced InSection 5 separation and identification methods are adoptedto separate and identify the noise sources of an internalcombustion engine Finally Section 6 presents conclusions

2 Basic Theory

21 Cochlear Basement Membrane Model of the Auditory Sys-tem The human auditory system includes the auditory

periphery and the auditory center [27 28] The auditoryperiphery consists of outer ear middle ear and inner earThe inner ear consists of semicircular canal vestibule andcochlear implant The speech signals are through the outerear middle ear and ear bone to the cochlear The cochleartransforms the mechanical energy of sound waves to neuralcoding signals and through the auditory nerve into theauditory center Then the hearing will be produced

In the auditory system the cochlear as the human audi-tory receptor is one of the most important parts The soundsignal processing of the human ear is achieved by the fre-quency decomposition of cochlear basement membrane Itcannot only convert different frequencies of the sound signalsinto different basement membrane positions but also switchdifferent sound intensity into different basement membranevibration amplitude Thus the cochlear can complete thecoding according to the sound frequency and the soundintensity

In the auditory model a set of overlapping band-passfiltersrsquo bank is usually used to simulate the cochlear basementmembrane Suppose there are119873 filters The 119894th filter is ℎ(119905 119894)The response of the basement membrane to the signal 119909(119905) isdefined as follows

119910 (119905 119894) = 119909 (119905) lowast ℎ (119905 119894) (1)

where 119910(119905 119894) is the output of the basement membrane lowastrepresented the convolution

The characteristic of the Gammatone filter bank is highlyconsistent with the auditory characteristic which can wellsimulate the basement membrane frequency selectivity andspectral analysis characteristics Thus the Gammatone filterbank is widely adopted as the cochlear basement membranemodel

22 Gammatone Filter Bank TheGammatone filter bank is astandard cochlear auditory filter [29 30] It can simulate theband-pass filter characteristics of the basement membraneThe center frequency of each filter is logarithmically evenlydistributed on the frequency axis Suppose the center fre-quency of the 119894th filter is 119891119894 The time domain expression ofthe Gammatone filter is

119892119891119894 (119905) = 119905119873minus1 exp (minus2120587119861119905) cos (2120587119891119894119905 + 120593119894) 119906 (119905) (2)

where 119873 is the filter order 119891119894 is the filter center frequency120593119894 is the phase of the filter due to the phase of the soundsignals having small influence for hearing thus the phase 120593119894is usually set as zero 119906(119905) is the unit step function 119861 is theattenuation factor of filter It determines the decay rate of theimpulse response which is related to the bandwidth of thefilterThe bandwidth of the auditory band-pass filter dependson the center frequency It usually adopted the equivalentrectangular bandwidth (ERB) The calculation formula is

119861 = 1019ERB (119891119894) = 1019 (247 + 0108119891119894) (3)

The Gammatone filter bank is shown in Figure 1 Thetime domain waveform under different center frequencies119891119894 is shown in Figure 1(a) The corresponding amplitudefrequency response curve is shown in Figure 1(b)


10 20 30 40 50 0 Time (ms)

100

259

496

847

1369

2143

3293

5000Ch

anne

l cen

ter f

requ

ency

(Hz)


minus50

minus40

minus30

minus20

minus10

0

Mag

nitu

de g

ain

(dB)

1000 2000 3000 4000 50000 Frequency (Hz)



MixedmatrixA

Source signals S(t)



DemixingmatrixW

s1(t)

s2(t)

sn(t)

x1(t) y1(t)

x2(t) y2(t)

xn(t) yn(t)







119910 (119896) = 119882119909 (119896) = 119882119860119904 (119896) (4)




kurt (119910) =119864 1003816100381610038161003816119910

10038161003816100381610038164 minus 21198642 1003816100381610038161003816119910

10038161003816100381610038162 minus 10038161003816100381610038161003816119864 119910210038161003816100381610038161003816

2

1198642 100381610038161003816100381611991010038161003816100381610038162

(5)














RobustICA








mmm3m2m1 mmminus1

mnm3m2m1 mnminus1

）1 ）2 ）3 ）nminus1 ）n





1198781 = cos (2120587 ∙ 49 ∙ 119905)

1198782 = cos (2120587 ∙ 115 ∙ 119905)

1198783 = cos (2120587 ∙ 201 ∙ 119905)

119878 = 1198781 + 1198782 + 1198783

(6)





t (s)0 002 004 006 008 01

0 002 004 006 008 01

0 002 004 006 008 01

minus101

S3

minus101

S1

minus101

S2


0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)


0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)








2mm lead plate










1 2 3 4 5 6

Motor

Computer


Charge amplifier



Microphone

Accelerometer

TDC sensor



















0 120 240 360 480 600 720

0 120 240 360 480 600 720

0 120 240 360 480 600 720

minus505

p1

(MPa

)

minus100

10

p2

(Pa)

minus500

50

a (g

)

Crank angle (∘A)








120 240 360 480 600 7200Crank angle (∘A)

minus10

0

10

p (P

a)






119903119883119884 =cov (119883 119884)

radic119863 (119883)radic119863 (119884) (7)




m1

m2

m3

m4

m5

m6

m7

m8

m9

m10

m11

120 240 360 480 600 7200Crank angle (∘A)



120582 =max (119903119894)

120578 119894 = 1 2 119899 (8)







IC1

IC2

IC3

IC4

IC5

IC6

IC7

IC8

IC9

120 240 360 480 600 7200Crank angle (∘A)











IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT




IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10 20 30 40 50 0 Time (ms)

100

259

496

847

1369

2143

3293

5000Ch

anne

l cen

ter f

requ

ency

(Hz)


minus50

minus40

minus30

minus20

minus10

0

Mag

nitu

de g

ain

(dB)

1000 2000 3000 4000 50000 Frequency (Hz)



MixedmatrixA

Source signals S(t)



DemixingmatrixW

s1(t)

s2(t)

sn(t)

x1(t) y1(t)

x2(t) y2(t)

xn(t) yn(t)







119910 (119896) = 119882119909 (119896) = 119882119860119904 (119896) (4)




kurt (119910) =119864 1003816100381610038161003816119910

10038161003816100381610038164 minus 21198642 1003816100381610038161003816119910

10038161003816100381610038162 minus 10038161003816100381610038161003816119864 119910210038161003816100381610038161003816

2

1198642 100381610038161003816100381611991010038161003816100381610038162

(5)














RobustICA








mmm3m2m1 mmminus1

mnm3m2m1 mnminus1

）1 ）2 ）3 ）nminus1 ）n





1198781 = cos (2120587 ∙ 49 ∙ 119905)

1198782 = cos (2120587 ∙ 115 ∙ 119905)

1198783 = cos (2120587 ∙ 201 ∙ 119905)

119878 = 1198781 + 1198782 + 1198783

(6)





t (s)0 002 004 006 008 01

0 002 004 006 008 01

0 002 004 006 008 01

minus101

S3

minus101

S1

minus101

S2


0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)


0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)








2mm lead plate










1 2 3 4 5 6

Motor

Computer


Charge amplifier



Microphone

Accelerometer

TDC sensor



















0 120 240 360 480 600 720

0 120 240 360 480 600 720

0 120 240 360 480 600 720

minus505

p1

(MPa

)

minus100

10

p2

(Pa)

minus500

50

a (g

)

Crank angle (∘A)








120 240 360 480 600 7200Crank angle (∘A)

minus10

0

10

p (P

a)






119903119883119884 =cov (119883 119884)

radic119863 (119883)radic119863 (119884) (7)




m1

m2

m3

m4

m5

m6

m7

m8

m9

m10

m11

120 240 360 480 600 7200Crank angle (∘A)



120582 =max (119903119894)

120578 119894 = 1 2 119899 (8)







IC1

IC2

IC3

IC4

IC5

IC6

IC7

IC8

IC9

120 240 360 480 600 7200Crank angle (∘A)











IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT




IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












RobustICA








mmm3m2m1 mmminus1

mnm3m2m1 mnminus1

）1 ）2 ）3 ）nminus1 ）n





1198781 = cos (2120587 ∙ 49 ∙ 119905)

1198782 = cos (2120587 ∙ 115 ∙ 119905)

1198783 = cos (2120587 ∙ 201 ∙ 119905)

119878 = 1198781 + 1198782 + 1198783

(6)





t (s)0 002 004 006 008 01

0 002 004 006 008 01

0 002 004 006 008 01

minus101

S3

minus101

S1

minus101

S2


0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)


0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)








2mm lead plate










1 2 3 4 5 6

Motor

Computer


Charge amplifier



Microphone

Accelerometer

TDC sensor



















0 120 240 360 480 600 720

0 120 240 360 480 600 720

0 120 240 360 480 600 720

minus505

p1

(MPa

)

minus100

10

p2

(Pa)

minus500

50

a (g

)

Crank angle (∘A)








120 240 360 480 600 7200Crank angle (∘A)

minus10

0

10

p (P

a)






119903119883119884 =cov (119883 119884)

radic119863 (119883)radic119863 (119884) (7)




m1

m2

m3

m4

m5

m6

m7

m8

m9

m10

m11

120 240 360 480 600 7200Crank angle (∘A)



120582 =max (119903119894)

120578 119894 = 1 2 119899 (8)







IC1

IC2

IC3

IC4

IC5

IC6

IC7

IC8

IC9

120 240 360 480 600 7200Crank angle (∘A)











IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT




IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










t (s)0 002 004 006 008 01

0 002 004 006 008 01

0 002 004 006 008 01

minus101

S3

minus101

S1

minus101

S2


0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)


0 002 004 006 008 01

IC2

IC3

minus101

0 002 004 006 008 01minus1

01

minus101

IC1

002 004 006 008 010t (s)








2mm lead plate










1 2 3 4 5 6

Motor

Computer


Charge amplifier



Microphone

Accelerometer

TDC sensor



















0 120 240 360 480 600 720

0 120 240 360 480 600 720

0 120 240 360 480 600 720

minus505

p1

(MPa

)

minus100

10

p2

(Pa)

minus500

50

a (g

)

Crank angle (∘A)








120 240 360 480 600 7200Crank angle (∘A)

minus10

0

10

p (P

a)






119903119883119884 =cov (119883 119884)

radic119863 (119883)radic119863 (119884) (7)




m1

m2

m3

m4

m5

m6

m7

m8

m9

m10

m11

120 240 360 480 600 7200Crank angle (∘A)



120582 =max (119903119894)

120578 119894 = 1 2 119899 (8)







IC1

IC2

IC3

IC4

IC5

IC6

IC7

IC8

IC9

120 240 360 480 600 7200Crank angle (∘A)











IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT




IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1 2 3 4 5 6

Motor

Computer


Charge amplifier



Microphone

Accelerometer

TDC sensor



















0 120 240 360 480 600 720

0 120 240 360 480 600 720

0 120 240 360 480 600 720

minus505

p1

(MPa

)

minus100

10

p2

(Pa)

minus500

50

a (g

)

Crank angle (∘A)








120 240 360 480 600 7200Crank angle (∘A)

minus10

0

10

p (P

a)






119903119883119884 =cov (119883 119884)

radic119863 (119883)radic119863 (119884) (7)




m1

m2

m3

m4

m5

m6

m7

m8

m9

m10

m11

120 240 360 480 600 7200Crank angle (∘A)



120582 =max (119903119894)

120578 119894 = 1 2 119899 (8)







IC1

IC2

IC3

IC4

IC5

IC6

IC7

IC8

IC9

120 240 360 480 600 7200Crank angle (∘A)











IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT




IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














0 120 240 360 480 600 720

0 120 240 360 480 600 720

0 120 240 360 480 600 720

minus505

p1

(MPa

)

minus100

10

p2

(Pa)

minus500

50

a (g

)

Crank angle (∘A)








120 240 360 480 600 7200Crank angle (∘A)

minus10

0

10

p (P

a)






119903119883119884 =cov (119883 119884)

radic119863 (119883)radic119863 (119884) (7)




m1

m2

m3

m4

m5

m6

m7

m8

m9

m10

m11

120 240 360 480 600 7200Crank angle (∘A)



120582 =max (119903119894)

120578 119894 = 1 2 119899 (8)







IC1

IC2

IC3

IC4

IC5

IC6

IC7

IC8

IC9

120 240 360 480 600 7200Crank angle (∘A)











IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT




IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










m1

m2

m3

m4

m5

m6

m7

m8

m9

m10

m11

120 240 360 480 600 7200Crank angle (∘A)



120582 =max (119903119894)

120578 119894 = 1 2 119899 (8)







IC1

IC2

IC3

IC4

IC5

IC6

IC7

IC8

IC9

120 240 360 480 600 7200Crank angle (∘A)











IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT




IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















IC6

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

02

016

012

008

004

03 4 5 6 7 8

Frequency (kHz)

4025 Hz

(b) FFT

26351 4

120 240 360 480 600 72000

01

02

03

04

05

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT




IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










IC9

minus2

0

2

Am

plitu

de (P

a)

120 240 360 480 600 7200Crank angle (∘A)


Am

plitu

de (P

a)

FFT

0 1 2

025

02

015

01

005

03 4 5 6 7 8

Frequency (kHz)

1725 Hz

(b) FFT

1 5 43 6 2

120 240 360 480 600 72000

1

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



0

05

1

r



0

001

002

003

004

Am

plitu

de

1 2 3 4 5 6 7 80Frequency (kHz)



1 2 3 4 5 6 7 80Frequency (kHz)

0

05

1

r






F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










F2

F3

F4

F5

F6

F7

F8

F9

120 240 360 480 600 7200Crank angle (∘A)







IC1

IC2

0 120 240 360 480 600 720

IC3

Crank angle (∘A)


IC1

120 240 360 480 600 7200minus2

0

2

Am

plitu

de (P



4025 Hz

5100 Hz1150 Hz

5950 Hz6650 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

004


(b) FFT

1 5 6 2 43


120 240 360 480 600 72000

02

02

01

00

01

1

2

3

4

5

6

7

8 CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

(c) CWT



IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










IC2

minus2

0

2A

mpl

itude

(Pa)

120 240 360 480 600 7200Crank angle (∘A)


1350 Hz

2100 Hz

1725 Hz

Am

plitu

de (P

a)

FFT

0 1 2

002

006

008

01

012

014

004


(b) FFT

120 240 360 480 600 72000

02

04

06

08

1

2

3

4

5

6

7

8CWT

Crank angle (∘A)

Freq

uenc

y (k

Hz)

1 5 43 6 2


(c) CWT





1 2 3 4 5 6 7 80Frequency (kHz)

0

001

002

003

004

Am

plitu

de


0

05

1

r

1 2 3 4 5 6 7 80Frequency (kHz)




6 Conclusions







Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









radiation noise separation of internal combustion engine

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