fault detection of high-speed train wheelset bearing based ...researcharticle fault detection of...

Research ArticleFault Detection of High-Speed Train Wheelset Bearing Based onImpulse-Envelope Manifold

Zhe Zhuang1 Jianming Ding1 Andy C Tan2 Ying Shi1 and Jianhui Lin1

1State Key Laboratory of Traction Power Southwest Jiaotong University Chengdu 610031 China2LKC Faculty of Engineering and Science Universiti Tunku Abdul Rahman 43000 Kajang Malaysia

Correspondence should be addressed to Jianming Ding fdingjianming126com

Received 26 May 2017 Accepted 12 October 2017 Published 3 December 2017

Academic Editor Sara Muggiasca

Copyright copy 2017 Zhe Zhuang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A novel fault detection method employing the impulse-envelope manifold is proposed in this paper which is based on thecombination of convolution sparse representation (CSR) and Hilbert transform manifold learning The impulses with differentsparse characteristics are extracted by the CSR with different penalty parameters The impulse-envelope space is constructedthroughHilbert transform on the extracted impulsesThemanifold based on impulse-envelope space (impulse-envelopemanifold)is executed to learn the low-dimensionality intrinsic envelope of vibration signals for fault detection The analyzed results basedon simulations experimental tests and practical applications show that (1) the impulse-envelope manifold with both isometricmapping (Isomap) and locally linear coordination (LLC) can be successfully used to extract the intrinsic envelope of the impulseswhere local tangent space analysis (LTSA) fails to perform and (2) the impulse-envelope manifold with Isomap outperforms thosewith LLC in terms of strengthening envelopes and the number of extracted harmonics The proposed impulse-envelope manifoldwith Isomap is superior in extracting the intrinsic envelope strengthening the amplitude of intrinsic envelope spectra and enlargingthe harmonic number of fault-characteristic frequencyThe proposed technique is highly suitable for extracting intrinsic envelopesfor bearing fault detection

1 Introduction

Train bogie is one of the crucial subsystems of high-speedtrain and consists of many critical mechanical componentsone of which is wheelset bearing Due to the demandingworking conditions surrounding the wheelset bearing (suchas alternating contact stresses heavy loads and wheel-railshock) the faults on the component surface of wheelsetbearing are easily generated The vibration and shock excitedby the bearing faults could endanger the running safety of thehigh-speed train Thus it is important to detect symptom ofits faults at an early stage to ensure safe operation of the train

The traditional detection of bearing faultsmainly involvesgrease or oil monitoring acoustic emission techniqueshotbox detection and vibration signal monitoring [1] Thestandards require a level-threemaintenance approval of high-speed train certification before the wheelset bearing can bedisassembledThismakes grease or oil monitoring unsuitablefor wheelset bearing fault detection The attenuation of

transient elastic waves generated by a bearing fault restrictswide application of acoustic emission techniques in bearingfault detection [2] Hotbox detection is commonly used inpractice When the temperature of bearing housing exceeds apreset threshold the hotbox detector sets an alarm Howeverhotbox detector is only sensitive to severe faults for examplebearing burn-off [1] Not only can the axle-box accelerationsignals be conveniently and reliablymeasured at relatively lowcost but also they carry vital information about the healthstate of the bearing faults [3 4] Consequently vibrationsignal monitoring has become an effective and feasibledetection technique for wheelset bearing faults especially atthe incipient stage

The impulse series or periodic impulses embedded in thebearing vibration signals carry essential information of thebearing conditionThe amplitudes of these impulses inducedby bearing faults are modulated by the variances of theposition and direction of forces applied on rollers [5 6] Thefault-characteristic frequencies of the bearing are modulated

HindawiShock and VibrationVolume 2017 Article ID 2104720 17 pageshttpsdoiorg10115520172104720

2 Shock and Vibration

by the slippage of rolling elements and the fluctuation ofwheelset rotational speeds [7 8] The impulses generatedby bearing faults are transient impulses containing a widerange of frequencies with very short time duration This caneasily excite multimodel resonance responses of the structureand sensor [9] The impulses generated by bearing faultsare usually masked by background noises and structuralvibration [10 11] In addition the impulses generated bybearing faults are mixed with those caused by the wheel-rail interaction when the wheel tread has defects or is out ofroundness These nonlinear and nonstationary modulationcharacteristics multimodel effects noise interferences andimpulse-mixture make it difficult and complex to extractthese impulses from the measured vibration signals Extract-ing impulses has long been a challenge in the field of faultdetection and diagnosis

To effectively tackle this problem many advanced signalprocessing techniques have been proposed including empir-ical model decomposition (EMD) [12 13] wavelet transform(WT) [14 15] and compressive sensing (CS) [16 17] Amongthem EMD is suitable for analyzing nonlinear and nonsta-tionary signals and models the analyzed signal as the sumover a set of intrinsic model functions (IMFs) and a residual[12] EMD has been successfully applied in the field of faultdiagnosis failure detection damage identification and healthmonitoring [18 19] The shortcomings of EMD are the lackof theoretical foundation [20] sensitivity to noises samplingerrors [21] and model mixtures [10] These have adverseeffects on the performance for fault detection To alleviatethese problems the variants of EMD such as EEMD bivariateempirical mode decomposition (BEMD) and multivariateempirical mode decomposition (MEMD) [22ndash24] have beendeveloped Moreover there is a lack of theory to clarify theseproblemsWavelet analysis is conducted by the inner productof the measured vibration signals and wavelet basis providesthe time-scale information of the impulses Both continuouswavelet transform (CWT) and discrete wavelet transform(DWT) have been successfully applied for fault detection ofrotational machines with multiresolution [25 26] The hugecomputational costs and redundant coefficients of CWT limitits wide application as compared to DWT which has a fasteralgorithm [27]Wavelet packet transform (WPT) is proposedto improve the decomposition performance of WT on high-frequency band which contains useful information for faultdetection [28] However the decomposition quality of theDWT and WPT is influenced by the selection of motherwavelet [29] The shift-variance [30] and the low oscillation[31] of DWT and WPT result in distortion and containnonsparse representation of the impulses

CS consists of sparse representation and dictionary con-struction With sparse representation models the signalsare the linear combinations of basis elements or atoms in aredundant dictionary Dictionary design is adapted to self-feature the vibration signals to match well with the high-levelstructures of the impulses As far as sparse representationis concerned the exact resolution of sparse representationproves to be an NP-hard problem [32] and the approxi-mate solutions based on greedy-based matching pursuit [33]

and convex optimal-based basis pursuit [34] are consid-ered instead Dictionary construction includes manuallypredefined dictionary and dictionary learning Dictionarylearning includes regular dictionary learning [35] and shift-invariant dictionary learning (SIDL) [36 37] For excellentperformances of CS on representing signals (such as self-adaption sparsity and super-resolution) the CS based onthe predefined dictionaries and sparse representation is usedto detect faults on bearings and gear boxes and outperformsEMD and WT [38 39] Compared to predefined dictionaryand regular dictionary learning SIDL has shift-invariance[36 37]

The convolution sparse representation (CSR) based onalternating direction method of multipliers (ADMM) wasfirst proposed in 2016 and is a novel research on CSbased on pursuit and SIDL [38] CSR provides an excellentframework for extracting impulses induced by bearing faultsand wheel-rail interactions However the performances ofCSR on extracting impulses are heavily influenced by itspenalty parameter which determines the sparsity of theextracted impulses When the penalty parameter is verylarge the extracted impulse is very sparse and the numberof the extracted impulses is far less than the true numberof impulses [39] Thus this can easily lead to the loss ofimpulses containing fruitful fault-information Converselythe extracted impulses could be far more than the true num-ber of impulses As such this results in impulse corruptionsTo completely extract impulses with the least corruptionsis very difficult under the condition of a single penaltyparameter Hence in this paper the CSRs with differentpenalty parameters are jointly used to extract impulses in theframework of manifold learning

Manifold learning projects the high-dimensional datainto a lower-dimensional feature space by preserving thelocal neighborhood structures Manifold learning mainlyinvolves convex and nonconvex techniques Convex tech-nique involves full spectrum methods such as isometricmapping (Isomap) [40] diffusion maps [41] and sparsespectral methods (which include local tangent space analysis(LTSA) [42] and local linear embedding (LLE) [43]) Non-convex technique mainly includes locally linear coordination(LLC) [44] and Sammon mapping [45] Recently manifoldlearning has been successfully applied in fault diagnosis Themanifolds based on different spaces such as scale space ofWT and WPT [46 47] IMF space of EMD [48] and time-frequency space [49] are used to extract impulses Thesemanifold methods have successfully discovered the intrinsicstructures of impulses embedded in the measured vibrationsignals

Hence this paper aims to fully exploit the frameworkfor extracting impulses with CSR which provides lower orminimum adverse influences that the inappropriate selectionof penalty parameter of CSR bringsThis novel fault detectionmethod known as impulse-envelope manifold is proposedbased on the combination of CSR Hilbert transform andmanifold learning The impulses with different sparsity char-acteristic are extracted by the CSR with different penaltyparameters The impulse-envelope spaces are spanned by theHilbert transform on the extracted impulses The manifold

Shock and Vibration 3

based of the impulse-envelope spaces is used to discoverthe low-dimensionality intrinsic envelope of bearing faultsimpulses embedded in vibration signals for fault detectionThe results show that the proposed method is capable ofdetecting bearing faults through simulations experimentaltests and a practical test This paper is organized as followsThe basic theory of impulse-envelope manifold is introducedin Section 2 Simulation validation is executed in Section 3Experiment verifications are demonstrated in Section 4Section 5 illustrates the practical application of the proposedmethod Section 6 provides the conclusion of the paper

2 Basic Theory of Impulse-Envelope Manifold

21 Impulse Extraction by CSR CSR models a signal asthe sum of a set of convolutions of atoms with the sparsecoefficients defined as

d119898 x119896119898 = argmind119898 x119896119898

12119870sum119896=1

1003817100381710038171003817100381710038171003817100381710038171003817s119896 minus119872sum119898=1

d119898 lowast x11989611989810038171003817100381710038171003817100381710038171003817100381710038172

119865

+ 120582 119870sum119896=1

119872sum119898=1

1003817100381710038171003817x11989611989810038171003817100381710038171 (1)

where s119896 isin R119899 are 119896th analyzed vibration signals 119899 is length ofanalyzed signal d119898 isin R119901 is a set of atoms 119901 is length of atomx119896119898 isin R119899minus119901+1 are sparse coefficients related to a given signals119896 and atom d119898 120582 isin R+ is penalty parameter119870 is number ofinterval signals s119896 and119872 is number of atoms d119898

The sparse coefficients x119896119898 are resolved by the shift-invariance sparse coding (SISC) of (1) when the signals s119896 andatoms d119898 are given The SISC can be expressed as

x119896119898 = argmin12119870sum119896=1

1003817100381710038171003817100381710038171003817100381710038171003817s119896 minussum119896 d119898 lowast x11989611989810038171003817100381710038171003817100381710038171003817100381710038172

119865

+ 120582 119870sum119896=1

119872sum119898=1

1003817100381710038171003817x11989611989810038171003817100381710038171 (2)

In (2) the different sparse coefficients x119896119898 are decoupledwith respect to different analyzed signals s119896 the sparsecoefficients x119898 corresponding to signals s can be individuallysolved by

x119898 = argminx119898

121003817100381710038171003817100381710038171003817100381710038171003817s minussum119896 d119898 lowast x119898

10038171003817100381710038171003817100381710038171003817100381710038172

119865

+ 120582 119872sum119898=1

1003817100381710038171003817x11989810038171003817100381710038171 (3)

The atoms d119898 are obtained by SIDL using (1) when thesignal s119896 and sparse coefficients x119896119898 are known The SIDL isdescribed as

d119898 = argmind119898

12119870sum119896=1


119865

(4)

such that d119898 = 1forall119898The details on SISC and SIDL of CSR based on alter-

nating direction method of multipliers (ADMM) can be

found in [38] The atoms d120582119898 are learned from the intervalsignals s119896 isin R119899 (119896 = 1 2 119870) through interleavediterations of SISC and SIDL of CSR with different penaltyparameters 120582 The sparse coefficients x120582119898 associated with thesignals s = [s1119879 s119870119879]119879 isin R119899119870 are obtained throughSISC based on the learned atoms d120582119898 Hence the impulsesI120582119898 with different sparsity characteristic are extracted by theconvolution of atoms d120582119898 and associated sparse coefficients x120582119898and are expressed as

I120582119898 =119872sum119898=1

d120582119898 lowast x120582119898 (5)

22 Impulse-Envelope Space Construction The characteristicinformation on bearing faults is contained in the envelopeof the extracted impulses The Hilbert transform h120582119898 of theextracted impulses I120582119898 is defined as [50]

h120582119898 = 2120587 intinfin

minusinfin

I120582119898 (119905)119905 minus 120591 119889120591 =1120587119905 I120582119898 (119905) (6)

The Hilbert transform can be viewed as a filter of unityamplitude and phase plusmn90∘ depending on the sign of thefrequency of input signal spectrumThe real signal I120582119898 and itsHilbert transform h120582119898 can form a complex signal called theanalytical signal

z120582119898 = I120582119898 + jh120582119898 (7)

The envelope E120582119898 of the complex signal z120582119898 is defined as

E120582119898 = 10038161003816100381610038161003816I120582119898 + jh12058211989810038161003816100381610038161003816 = radic(I120582119898)2 + (h120582119898)2 (8)

Suppose 120582119894 = 1205821 + 05(119894 minus 1) (119894 = 1 2 119873) and 1205821 =1 in this paper 119873 is determined when the number ofthe nonzero elements of sparse coefficients x120582119873+05119898 equalszero The impulse-envelope space IES is spanned by all theenvelopes z120582119894119898 and expressed as

IES119898 = [E1205821119898 E1205822119898 sdot sdot sdot E120582119873119898 ] isin R119899119870times119873 (9)

23Manifold Learning Based on Impulse-Envelope Space Theimpulse-envelopemanifold transforms the impulse-envelopespace IES119898 with high-dimensionality 119873 in (9) into a newintrinsic impulse-envelope space I119898 with dimension 119889 whileretaining the geometry structure of the impulse-envelopespace IES119898 as much as possible In this paper 119889 is equal to1 because there is only one-type impulse in every impulse-envelope space Manifold learning involves convex and non-convex techniques Convex technique includes full spectrumand sparse spectral methods All manifold leaning has itsadvantages and shortcomings In this paper the manifoldlearning based on impulse-envelope space is conducted forthe first time and no references are available Hence theIsomap with full spectrum methods the LTSA in sparsespectral methods and the LLC in nonconvex techniques are


Analyzed signals

ENT

Extracting impulseswith different sparsity

Hilbert transform

Impulse-envelope space

Manifold learning

Low-dimensionalityintrinsic envelope

Envelope spectra

Figure 1 Fault detection flowchart of the impulse-envelope manifold

selected to learn the low-dimensionality intrinsic structuresof the impulse-envelope embedded in high-dimensionalityimpulse-envelope space The detailed algorithms of IsomapLTSA and LLC can be found in [40] [42] and [44]respectively In addition the nearest neighbors 120581 in manifoldlearning are set as the length of atom 11990124 Estimation of the Number of the Atom Type (ENA)The number of atoms 119872 is not determined in (1) insteadit is based on prior vibration mechanism of the impulsesgenerated by bearing faults [5] An impulse can be com-pletely described by two parameters namely the resonancefrequency and damping coefficientThe resonance frequencycan identify different atoms So the dominant frequenciesof the atoms are used to estimate the number of atoms 119872Considering the defects of outer race inner race roller andwheel tread generally the number119872 is preset as 4 inwheelsetbearing fault detection The true value of 119872 is obtainedvia iteratively executing the CSR The dominant frequencies119891119898 (119898 = 1 2 119872) of each atom are extracted by Fouriertransform If the difference of any two dominant frequenciesis more than the frequency resolution 119891119904119901minus1 (119891119904 denotes thesampling frequency) this illustrates that there are119872 atomsOtherwise 119872 = 119872 minus 1 and the operation is repeated toexecute CSR and calculate the dominant frequencies until thedifference of any two dominant frequencies is more than thefrequency resolution The final value of 119872 is output as theestimated value of the number of atoms

25 Fault Detection Based on Impulse-Envelope ManifoldThe schematic of fault detection based on impulse-envelopemanifold is summarized and shown in Figure 1

The proposed impulse-envelope manifold methodincludes the following

Step 1 Input the analyzed signals

Step 2 Estimate the number of atom types using dominantfrequency analysis

Step 3 Extract the impulses with different sparsity character-istic using (1) to (5)

Step 4 Construct the impulse-envelope space using (9)

Step 5 Execute the manifold learning based on impulse-envelope space to learn the low-dimensionality intrinsicenvelope

Step 6 Use envelope spectra of the intrinsic envelope to judgethe bearing fault

3 Simulation Validation

To illustrate the effectiveness of the proposed method theacceleration responses 119886(119905) induced by a bearing fault are sim-ulated using the impulse function of a massndashspringndashdampersystem [5] and are expressed as

119886 (119905) = 119871sum119897=1

119860 119897119890minus120573(119905minus119897119879119901) cos [120596 (119905 minus 119897119879119901)] 119906 (119905 minus 119898119897119879119901) (10)

where 119860 119897 represents the amplitude of the 119897th fault impulsewhich is set as 0000000005 119879119901 represents the reciprocalof fault-character frequency 119891119901 which is set as 491 Hz 120573is the structural damping coefficient set as 1200Nsm 120596 isthe nature frequency which is 2000Hz and 119871 represents thenumber of the simulated impulses which is 39

The fault simulation signal with minus7 dB signal-to-noiseratio (SNR) is shown in Figure 2 which are generated bymixing the fault response in (10) with white noises Thelow-dimensionality intrinsic impulse-envelopes are extractedfrom the noise signals as shown in Figure 3(b) and byusing the proposed impulse-envelopemanifold shown in Fig-ure 3(d) Through comparisons the manifolds with Isomapand LLC can successfully extract the impulse-envelope ofthe noise signals based on the impulse-envelope space thenumber of the extracted impulse-envelopes is 39 which areshown in Figures 3(a) and 3(c) and is equal to the presetvalue 119871 of simulation impulses However LTSA fails tolearn the impulse-envelope from the impulse-envelope spaceMeanwhile the fault-characteristic frequency 119891119901 and its 20-order harmonics are extracted by the spectra of the intrinsicimpulse-envelope as shown in Figures 3(b) and 3(d) Theamplitudes of the extracted intrinsic envelope by Isomapare larger than the ones by LLC as a result the amplitudes


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Figure 2 Simulation signals (a) the original signals with periodic impulses and (b) the signals with added white noise (SNR = minus7 dB)

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Figure 3The intrinsic impulse-envelopes extracted by the impulse-envelopemanifold and their envelope spectra (a) impulse-envelope withIsomap and (b) the envelope spectra of (a) (c) impulse-envelope with LLC and (d) the envelope spectra of (c) (e) impulse-envelope withLTSA and (f) the envelope spectra of (e)

of the envelope spectra by Isomap are also larger than theones obtained by LLC This shows that the impulse-envelopemanifold with Isomap has a better performance in extractingthe envelopes than the LLC

To compare the manifolds with Isomap based on twoother envelope spaces spanned by the Hilbert transform of

IMFs in EEMD and multiscale decomposition signals inWPT the decomposition results obtained by EEMD andWPT from processing the signals in Figure 2(b) are shown inFigures 4 and 5 respectively The number of ensembles andthe amplitude of the added white noise are two parametersneeded to be set when the EEMDmethod is used Generally


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(IMF2)(IMF1)

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10

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Figure 4 IMFs obtained by EEMD

when the signal is dominated by high-frequency componentsthe noise amplitude needs to be smaller And when the signalis dominated by low-frequency components the noise ampli-tude should be increased In this paper the amplitude of theadded white noise is 02 times the standard deviation of thesignal and the number of ensembles is set as 400 accordingto 119873 = (119886119890)2 where 119873 is the ensemble number a is theamplitude of the added white noise and 119890 is the standarddeviation of error which is defined as 001 [51] Daubechieswavelet (Db8) is selected as themotherwavelet ofWPTdue toits wide application in engineering signal processing [52 53]The intrinsic impulse-envelopes are extracted by themanifoldwith Isomap based on both IMF-envelope and multiscaleenvelope spaces and the results are shown in Figure 6 TheIMF-envelope space extracted 12 harmonics of the fault-characteristic frequency while multiscale envelope space has5-order harmonics (the number of harmonics is lower than20 in the impulse-envelope space) The amplitudes of theenvelope and envelope spectra obtained by the manifoldwith Isomap based on IMF-envelope andmultiscale envelopespace are less than the impulse-envelope space with Isomapand are almost the same as the impulse-envelope space withLLC These results show that the impulse-envelope spaceoutperforms the IMF-envelope andmultiscale envelope spacein extracting the intrinsic impulse-envelope

4 Experimental Verification

Figure 7 shows the wheelset bearing test bench used for thepractical tests The test bench consists of a motor driving

Table 1 The parameters of the test rolling bearing

Rollernumber

Roller diameter(mm)

Pitch diameter(mm)

Contact angle(rad)

19 269 180 01571

wheel loading device wheelset and axle box The motordelivers the driving power with different motor speeds Thedriving power is conveyed to the driving wheel throughrubber belts The traction power of the driving wheel isthen transmitted to the wheelset The artificial faults areintroduced on the bearing outer race and on a roller as shownin Figure 8The artificially faulted roller bearing is installed inthe axle box and an accelerometer ismounted on the housingThe parameters of the faulty bearing are listed in Table 1

41 Result and Discussion Fault Detection with an OuterRace Fault Thevibration signalsmeasured from thewheelsetbearing test bench are shown in Figure 9 and those with anartificially simulated fault on the bearing outer race are shownin Figure 8(a)

The intrinsic impulse-envelopes learned by the impulse-envelopemanifold with Isomap LLC and LTSA are shown inFigure 10 The impulse-envelope manifold with Isomap andLLC successfully detects the fault-characteristic frequency ofan outer race defect and with 7 harmonics However theimpulse-envelope manifold with LTSA fails to extract the


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Figure 5 Multiscale signals obtained by WPT

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Figure 6 The intrinsic envelopes extracted by the manifold with Isomap and their envelope spectra (a) on IMF-envelope space of EEMD(b) the envelope spectra of (a) (c) on multiscale envelope space of WPT and (d) the envelope spectra of (c)


Motor

Driving wheel

Axle box and bearing

WheelsetLoading device

Sensor

Axle box

Figure 7 Photos of the test bench and measurement sensor

(a) (b)

Figure 8 Photos of the artificial faults on outer race (a) and roller (b)

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Figure 9 Measured vibration signals of bearing outer race fault

fault-characteristic frequency or its harmonics The ampli-tudes of the intrinsic envelope with Isomap are larger thanthe ones obtained by LLC Furthermore the amplitudes ofthe envelope spectra with Isomap are larger than the onesobtained with LLC These show that the impulse-envelopemanifold with Isomap is superior to the one with LLC inextracting the intrinsic envelopes with weak impulses Thefault-characteristic frequency of an outer race defect 119891BPFO isexpressed as

119891BPFO = 1198731198872 (1 minus 119861119889119875119889 cos (120601))119891119908 (11)

where 119873119887 is the number of rollers 119861119889 is the roller diameter119875119889 is the pitch diameter 120601 is the contact angle and 119891119908 is thebearing rotation speed

For comparison with the two other spaces spanned byHilbert transform of the IMFs in EEMD and multiscaledecomposition signals in WPT the results obtained by themanifold with Isomap based on the IMFs-envelope space

and multiscale envelope space are shown in Figure 11 Themanifold with Isomap based on envelope of IMFs extractsthe fault-characteristic frequency of the outer race fault andhas 7 harmonics (the number of the extracted harmonics isthe same as the impulse-envelope with Isomap and LLC)However the manifold with Isomap based on the multiscaleenvelope space extracts the fault-characteristic frequencyof outer race with only 2 harmonics The amplitudes ofthe intrinsic envelope obtained by the manifold based onthe IMF-envelope space and multiscale envelope space areless than the ones obtained by the impulse-envelope man-ifold with Isomap These results illustrate that the impulse-envelope space outperforms the spaces spanned by theenvelopes of IMFs and multiscale decomposition signals onextracting the impulses generated by faults on the outer race

42 Results and Discussion Fault Detection with a Fault onthe Roller The vibration signals collected from the wheelset


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lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)

Figure 10 The intrinsic envelopes learned by the impulse-envelope manifold and their envelope spectra (a) impulse-envelope with Isomap(b) the envelope spectra of (a) (c) impulse-envelope with LLC (d) the envelope spectra of (c) (e) impulse-envelope with LTSA and (f) theenvelope spectra of (e)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)

Figure 11 The intrinsic envelopes extracted by the manifold with Isomap and their envelope spectra (a) IMFs-envelope space of EEMD (b)the envelope spectra of (a) (c) multiscale envelope space of WPT and (d) the envelope spectra of (c)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20

Figure 12 Vibration signals of a bearing roller fault

0

NLZ NLZNLZ LZ LZLZLZ

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)

NLZ NLZNLZ LZ LZLZ LZ

0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)

Figure 13 The intrinsic envelopes extracted by the impulse-envelope manifold and their envelope spectra (a) the impulse-envelope withIsomap (b) the envelope spectra of (a) (c) the impulse-envelope with LLC (d) the envelope spectra of (c) (e) the impulse-envelope withLTSA and (f) the envelope spectra of (e)

bearing test bench with a fault on the roller of the wheelsetbearing (Figure 8(b)) are shown in Figure 12

The intrinsic envelopes learned from the vibration signalare shown in Figure 12 and the impulse-envelope manifoldis shown in Figure 13 The impulse-envelope manifold withboth Isomap and LLC can well learn the low-dimensionalityintrinsic envelopes from the measured vibration signalsAccording to the motion relationship of rollers and racesshown in Figure 14 they will generate 7 impulses from

B1 to H1 in the load zone (LZ) of the wheelset bearingIn Figures 13(a) and 13(b) there are seven (7) impulses inthe load zone of the wheelset bearing For the wheelsetbearing the forces applied on the faulty roller are too smallto excite the impulses due to the lack of contant forcesin no-bearing case In Figures 13(a) and 13(c) when thedefective roller enters the LZ there are 7 impulses On theother hand when the defective roller leaves the LZ thereare no visible impulses Among the seven impulses from B1


G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘

Figure 14The relativemotion between the rollers and races and theload zone (LZ)

to H1 impulse B1 and impulse H1 appear to lie at the edgeof LZ of the wheelset bearing There is a gap between theraces and defective roller when the roller lies in impulse E1The gap is caused by the symmetrical structure of the twonormal rollers corresponding to impulse F1 and impulse D1Consequently the envelope amplitudes of impulses B1 H1and E1 are less than those of impulses C1 D1 F1 and G1The envelope spectra of the intrinsic envelopes obtained byimpulse-envelope manifold with both Isomap and LLC cancapture the fault-characteristic frequency of roller 119891BPFO andits 2-order harmonics The fault-characteristic frequency ofroller 119891BPFO is expressed as

119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)

On the contrary the impulse-envelope manifold withLTSA is unable to extract the intrinsic envelopes of the vibra-tion signals or capture the fault-characteristic frequency ofroller and its harmonics For comparison the results obtainedby the manifold with Isomap based on the IMFs-envelopespace and multiscale envelope space are shown in Figure 15However the manifold based on the two spaces is unableto extract the intrinsic envelope of the vibration signalsThe results show that the impulse-envelope manifold hasexcellent performance in extracting the intrinsic envelopes ofthe impulses induced by bearing faults

5 Practical Application in High-Speed TrainWheelset Bearing

To test the capability of the proposed impulse-envelopemanifold for fault detection the technique was tested onthe data obtained from an operating high-speed train An

accelerometer installed on axle box was used to gather theaxle vibrations as shown in Figure 16

51 Results and Discussion Figure 17 shows the vibrationsignals collected from the axle box of an operating high-speedtrain running at a speed of 200Kmh with a defective rollerin wheelset bearing

There are two kinds of atoms obtained by ENT Consider-ing atom 1 the intrinsic envelopes learned from the vibrationsignals are shown in Figure 17 and after processing by theproposed impulse-envelopemanifold the results are shown inFigure 18 The impulse-envelope manifold with both Isomapand LLC can successfully extract the intrinsic envelopes of theimpulses induced by a roller fault When the defective rollerenters the LZ of the wheelset bearing there are 7 impulsesfrom impulse-envelope 119861119894 to impulse-envelope 119867119894 (119894 =2 3 8) When the defective roller leaves the LZ of thebearing there are no impulses due to the lack of contact forcebetween the defective roller and races and hence no resultingenvelopes appear From the configurations of the bearingand relative motion of the rollers and the races the intrinsicenvelopes vary alternatively when the defective roller entersand leaves the LZ of the wheelset bearing as shown inFigure 14 Figure 18(e) shows that the impulse-envelopemanifold with LTSA cannot extract the intrinsic envelopesof the signals On the contrary the intrinsic envelope spectrashown in Figures 18(b) and 18(d) can well extract the fault-characteristic frequency 119891BSF and its 3 harmonics Figure 19is an enlarged view from 012 to 028 sec of Figures 18(a) and18(b) Among the seven envelopes (B3 to H3) in Figure 19(b)the amplitude of envelope E3 is less than other envelopesThe amplitude of the envelope B3 is larger than envelope C3and envelope D3 and is different from the previous analysisdiscussed in Section 42The reason is the LZ variance causedby the wheel-rail longitudinal forces to strengthen the shockeffects on the defective roller at the positions of envelopesB3 and H3 during actual operation of the high-speed trainThe impulse-envelope manifold with both Isomap and LLCclearly shows the novel vibration phenomenon with doubleenvelopes of the waveform as shown in Figure 19

Referring to atom 2 the intrinsic impulse-envelopeslearned by the proposed impulse-envelope manifold areshown in Figure 20 The impulse-envelope manifolds withboth Isomap and LLC can efficiently extract the envelopes ofthe impulses induced by the unevenness of wheelset treadThe envelope spectra in Figures 20(b) and 20(d) capture 46 and 75 times the rotational frequency of wheelset bearingThese show that the impulse-envelope technique providesan excellent capability of isolating the impulses generated bybearing faults and the defects of wheel tread

For comparison the 2-dimensionality outputs of themanifold with Isomap based on the envelope space of IMFsin EEMD are shown in Figure 21 According to prior descrip-tion two types of atoms are embedded in vibration signalsshown in Figure 17 with the resulting dimensionality of themanifold set as 2 for the 2-dimensionality outputs of theman-ifold with Isomap based on the envelope space of multiscaledecomposition signals inWPTwhich are shown in Figure 22


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box

Figure 16 Location of accelerometer on the axle box

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18

Figure 17 Real vibration signal obtained from the axle box

The impulse-envelope manifold based on the two-envelopespace can extract the fault-characteristic frequency119891BSF andits 2-order harmonics (less than 3-order harmonics in theimpulse-envelope space) but is unable to isolate the impulsesgenerated by wheel tread unevenness Through comparisonof Figure 21 and Figure 22 Figure 22(c) clearly exhibits theappearance of impulses The locally zoomed figure from 018to 026 sec of Figure 22(c) is shown in Figure 23 The double

envelopes in an envelope waveform are weakened by wavelettransform as compared to Figure 19

6 Conclusion

The novelty of combining the outstanding properties ofCSR and impulse-envelope manifold through Hilbert trans-form to extract impulses of defective roller bearings isdemonstrated in this paper Through a series of simulation


0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192

60 NLZ LZ NLZ LZ NLZ LZ NLZ LZ NLZ LZ NLZ LZ NLZ LZ

(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３

3f４４ fBSF + 3fTFT 2fBSF + 3fTFT 3fBSF + 3fTFT

(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10

NLZ LZ NLZ LZ NLZ LZ NLZ LZ NLZ LZ NLZ LZ NLZ LZ

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT

2fBSF + 3fTFT 3fBSF + 3fTFT

(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)

Figure 18The intrinsic envelope extracted by the impulse-envelopemanifold corresponding to atom 1 (a) the impulse-envelopewith Isomap(b) the Hilbert envelope spectra of (a) (c) the impulse-envelope with LLC (d) the Hilbert envelope spectra of (c) (e) the impulse-envelopewith LTSA and (f) the Hilbert envelope spectra of (e)

0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)

Figure 19 Enlarged view of intrinsic envelope from 018 to 026 sec (a) corresponding to Figure 18(a) (b) corresponding to Figure 18(b)

studies experimental tests and real case data of a defectivewheelset bearing of a high-speed train the results confirmthe capability of the proposed technique The results clearlyshow that while both impulse-envelope manifolds with bothisometric mapping (Isomap) and locally linear coordination(LLC) can successfully extract the intrinsic envelope of theimpulses caused by bearing fault and unevenness wheeltread the Isomap outperforms LCC in terms of strengthand number of extracted harmonics When comparing withEEMD and WPT the proposed technique shows superiority

in extracting the intrinsic envelope and enlarging the numberof harmonics of fault-characteristic frequency

The proposed impulse-envelope manifold also discoversa novel phenomenon for the first time of double envelopewhich is caused by a roller defect in an envelope waveformThis discovery is beneficial to estimate the size of the faultHowever a point to note is that the computational cost ofIsomap is much higher than LLC and consequently is a topicfor future research to resolve the computational cost problem


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)

Figure 20The intrinsic envelope of wheelset bearing vibration extracted by the impulse-envelope manifold corresponding to atom 2 (a) theimpulse-envelope with Isomap (b) the Hilbert envelope spectra of (a) (c) the impulse-envelope with LLC (d) the Hilbert envelope spectraof (c) (e) the impulse-envelope with LTSA and (f) the Hilbert envelope spectra of (e)

0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)

Figure 21 The intrinsic envelope extracted from the envelope space of IMFs (a) corresponding to dimensionality 1 (b) the Fourier spectraof (a) (c) corresponding to dimensionality 2 and (d) the Fourier spectra of (c)


0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)

Figure 22The intrinsic envelope extracted from the envelope space ofmultiscale decomposition signals (a) corresponding to dimensionalityof 1 (b) the Fourier spectra of (a) (c) corresponding to dimensionality of 2 and (d) the Fourier spectra

05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018

Figure 23 The locally zoomed plot of Figure 22(c)

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This project is supported by National Natural Science Foun-dation of China (Grant no 51305358) the Research Fundof State Key Laboratory of Traction Power (Grant no2015TPL T17) and the Fundamental Research Funds for theCentral Universities (Grant no 2682017CX011)

References

[1] H R Cao F Fan K Zhou and Z J He ldquoWheel-bearingfault diagnosis of trains using empirical wavelet transformrdquoMeasurement vol 82 pp 439ndash449 2016

[2] Z Peng N J Kessissoglou and M Cox ldquoA study of the effectof contaminant particles in lubricants using wear debris andvibration condition monitoring techniquesrdquoWear vol 258 no11-12 pp 1651ndash1662 2005

[3] H Ocak K A Loparo and F M Discenzo ldquoOnline tracking ofbearing wear using wavelet packet decomposition and proba-bilistic modeling a method for bearing prognosticsrdquo Journal ofSound and Vibration vol 302 no 4-5 pp 951ndash961 2007

[4] Y Lei Z He Y Zi and X Chen ldquoNew clustering algorithm-based fault diagnosis using compensation distance evaluationtechniquerdquo Mechanical Systems and Signal Processing vol 22no 2 pp 419ndash435 2008

[5] M Liang and I Soltani Bozchalooi ldquoAn energy operatorapproach to joint application of amplitude and frequency-demodulations for bearing fault detectionrdquoMechanical Systemsand Signal Processing vol 24 no 5 pp 1473ndash1494 2010

[6] J Shi M Liang D-S Necsulescu and Y Guan ldquoGeneralizedstepwise demodulation transform and synchrosqueezing fortime-frequency analysis and bearing fault diagnosisrdquo Journal ofSound and Vibration vol 368 pp 202ndash222 2016

[7] Q Han and F Chu ldquoNonlinear dynamic model for skiddingbehavior of angular contact ball bearingsrdquo Journal of Sound andVibration 2015

[8] G He K Ding and H Lin ldquoFault feature extraction of rollingelement bearings using sparse representationrdquo Journal of Soundand Vibration vol 366 pp 514ndash527 2016


[9] L Cui NWu C Ma and HWang ldquoQuantitative fault analysisof roller bearings based on a novel matching pursuit methodwith a new step-impulse dictionaryrdquo Mechanical Systems andSignal Processing vol 68-69 pp 34ndash43 2016

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

[11] Y Shao and K Nezu ldquoDesign of mixture de-noising fordetecting faulty bearing signalsrdquo Journal of Sound andVibrationvol 282 no 3-5 pp 899ndash917 2005

[12] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[13] H C Wang J Chen and G M Dong ldquoFeature extraction ofrolling bearingrsquos early weak fault based on EEMD and tunableQ-factor wavelet transformrdquo Mechanical Systems and SignalProcessing vol 48 no 1-2 pp 103ndash119 2014

[14] W Su FWang H Zhu Z Zhang and Z Guo ldquoRolling elementbearing faults diagnosis based on optimal Morlet wavelet filterand autocorrelation enhancementrdquo Mechanical Systems andSignal Processing vol 24 no 5 pp 1458ndash1472 2010

[15] X Wang Y Zi and Z He ldquoMultiwavelet denoising withimproved neighboring coefficients for application on rollingbearing fault diagnosisrdquoMechanical Systems and Signal Process-ing vol 25 no 1 pp 285ndash304 2011

[16] L Cui J Wang and S Lee ldquoMatching pursuit of an adaptiveimpulse dictionary for bearing fault diagnosisrdquo Journal of Soundand Vibration vol 333 no 10 pp 2840ndash2862 2014

[17] X F Chen Z Du J Li X Li and H Zhang ldquoCompressedsensing based on dictionary learning for extracting impulsecomponentsrdquo Signal Processing vol 96 pp 94ndash109 2014

[18] W-L Chiang D-J Chiou C-W Chen J-P Tang W-K Hsuand T-Y Liu ldquoDetecting the sensitivity of structural damagebased on the Hilbert-Huang transform approachrdquo EngineeringComputations (SwanseaWales) vol 27 no 7 pp 799ndash818 2010

[19] R Yan and R X Gao ldquoHilbert-huang transform-based vibra-tion signal analysis for machine health monitoringrdquo IEEETransactions on Instrumentation and Measurement vol 55 no6 pp 2320ndash2329 2006

[20] S A Bagherzadeh and M Sabzehparvar ldquoA local and onlinesifting process for the empirical mode decomposition and itsapplication in aircraft damage detectionrdquo Mechanical Systemsand Signal Processing vol 54 pp 68ndash83 2015

[21] H Jiang C Li and H Li ldquoAn improved EEMD with multi-wavelet packet for rotating machinery multi-fault diagnosisrdquoMechanical Systems and Signal Processing vol 36 no 2 pp 225ndash239 2013

[22] F Jiang Z Zhu W Li G Zhou and G Chen ldquoFault identifica-tion of rotor-bearing systembased on ensemble empiricalmodedecomposition and self-zero space projection analysisrdquo Journalof Sound and Vibration vol 333 no 14 pp 3321ndash3331 2014

[23] G Rilling P Flandrin P Goncalves and J M Lilly ldquoBivariateempirical mode decompositionrdquo IEEE Signal Processing Lettersvol 14 no 12 pp 936ndash939 2007

[24] J Fleureau A Kachenoura L Albera J-C Nunes and LSenhadji ldquoMultivariate empirical mode decomposition andapplication to multichannel filteringrdquo Signal Processing vol 91no 12 pp 2783ndash2792 2011

[25] 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

[26] Y Qin B Tang and J Wang ldquoHigher-density dyadic wavelettransform and its applicationrdquo Mechanical Systems and SignalProcessing vol 24 no 3 pp 823ndash834 2010

[27] G Cai X Chen and Z He ldquoSparsity-enabled signal decom-position using tunable Q-factor wavelet transform for faultfeature extraction of gearboxrdquo Mechanical Systems and SignalProcessing vol 41 no 1-2 pp 34ndash53 2013

[28] Y Lei J Lin Z He and Y Zi ldquoApplication of an improvedkurtogram method for fault diagnosis of rolling element bear-ingsrdquo Mechanical Systems and Signal Processing vol 25 no 5pp 1738ndash1749 2011

[29] Y Lei Z He and Y Zi ldquoApplication of the EEMD method torotor fault diagnosis of rotatingmachineryrdquoMechanical Systemsand Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[30] I W Selesnick R G Baraniuk and N G Kingsbury ldquoThedual-tree complex wavelet transformrdquo IEEE Signal ProcessingMagazine vol 22 no 6 pp 123ndash151 2005

[31] IW Selesnick ldquoWavelet transformwith tunableQ-factorrdquo IEEETransactions on Signal Processing vol 59 no 8 pp 3560ndash35752011

[32] A M Tillmann ldquoOn the computational intractability of exactand approximate dictionary learningrdquo IEEE Signal ProcessingLetters vol 22 no 1 pp 45ndash49 2015

[33] J A Tropp ldquoGreed is good algorithmic results for sparseapproximationrdquo Institute of Electrical and Electronics EngineersTransactions on Information Theory vol 50 no 10 pp 2231ndash2242 2004

[34] M A T Figueiredo R D Nowak and S J Wright ldquoGradientprojection for sparse reconstruction application to compressedsensing and other inverse problemsrdquo IEEE Journal of SelectedTopics in Signal Processing vol 1 no 4 pp 586ndash597 2007

[35] K Engan K Skretting and J H Husoslashy ldquoFamily of iterativeLS-based dictionary learning algorithms ILS-DLA for sparsesignal representationrdquoDigital Signal Processing vol 17 no 1 pp32ndash49 2007

[36] H Liu C Liu and Y Huang ldquoAdaptive feature extractionusing sparse coding for machinery fault diagnosisrdquoMechanicalSystems and Signal Processing vol 25 no 2 pp 558ndash574 2011

[37] H Tang J Chen and G Dong ldquoSparse representation basedlatent components analysis formachinery weak fault detectionrdquoMechanical Systems and Signal Processing vol 46 no 2 pp 373ndash388 2014

[38] B Wohlberg ldquoEfficient algorithms for convolutional sparserepresentationsrdquo IEEE Transactions on Image Processing vol 25no 1 pp 301ndash315 2016

[39] J Ding F Li J Lin B Miao and L Liu ldquoFault detectionof a wheelset bearing based on appropriately sparse impulseextractionrdquo Shock and Vibration vol 2017 pp 1ndash17 2017

[40] J B Tenenbaum V de Silva and J C Langford ldquoA globalgeometric framework for nonlinear dimensionality reductionrdquoScience vol 290 no 5500 pp 2319ndash2323 2000

[41] S Lafon and A B Lee ldquoDiffusion maps and coarse-graining Aunified framework for dimensionality reduction graph parti-tioning and data set parameterizationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 28 no 9 pp1393ndash1403 2006

[42] Z Zhang and H Zha ldquoPrincipal manifolds and nonlineardimensionality reduction via tangent space alignmentrdquo SIAMJournal on Scientific Computing vol 26 no 1 pp 313ndash338 2004

[43] S T Roweis and L K Saul ldquoNonlinear dimensionality reduc-tion by locally linear embeddingrdquo Science vol 290 no 5500pp 2323ndash2326 2000


[44] W YThe and S T Roweis ldquoAutomatic alignment of hidden rep-resentationsrdquo in In Advances in Neural Information ProcessingSystems vol 15 pp 841ndash848 2002

[45] J W Sammon Jr ldquoA nonlinear mapping for data structureanalysisrdquo IEEE Transactions on Computers vol C-18 no 5 pp401ndash409 1969

[46] J Wang Q B He and F R Kong ldquoAutomatic fault diagnosisof rotating machines by time-scale manifold ridge analysisrdquoMechanical Systems and Signal Processing vol 40 no 1 pp 237ndash256 2013

[47] Q He ldquoVibration signal classification by wavelet packet energyflow manifold learningrdquo Journal of Sound and Vibration vol332 no 7 pp 1881ndash1894 2013

[48] Z Su B Tang L Deng and Z Liu ldquoFault diagnosis methodusing supervised extended local tangent space alignment fordimension reductionrdquoMeasurement vol 62 pp 1ndash14 2015

[49] X Ding and Q He ldquoTime-frequency manifold sparse recon-struction a novel method for bearing fault feature extractionrdquoMechanical Systems and Signal Processing vol 80 pp 392ndash4132016

[50] B Boashash ldquoEstimating and interpreting the instantaneousfrequency of a signal I Fundamentalsrdquo Proceedings of the IEEEvol 80 no 4 pp 520ndash538 1992

[51] 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

[52] J-D Wu and C-H Liu ldquoInvestigation of engine fault diagnosisusing discrete wavelet transform and neural networkrdquo ExpertSystems with Applications vol 35 no 3 pp 1200ndash1213 2008

[53] J Rafiee and P W Tse ldquoUse of autocorrelation of waveletcoefficients for fault diagnosisrdquo Mechanical Systems and SignalProcessing vol 23 no 5 pp 1554ndash1572 2009

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



by the slippage of rolling elements and the fluctuation ofwheelset rotational speeds [7 8] The impulses generatedby bearing faults are transient impulses containing a widerange of frequencies with very short time duration This caneasily excite multimodel resonance responses of the structureand sensor [9] The impulses generated by bearing faultsare usually masked by background noises and structuralvibration [10 11] In addition the impulses generated bybearing faults are mixed with those caused by the wheel-rail interaction when the wheel tread has defects or is out ofroundness These nonlinear and nonstationary modulationcharacteristics multimodel effects noise interferences andimpulse-mixture make it difficult and complex to extractthese impulses from the measured vibration signals Extract-ing impulses has long been a challenge in the field of faultdetection and diagnosis

To effectively tackle this problem many advanced signalprocessing techniques have been proposed including empir-ical model decomposition (EMD) [12 13] wavelet transform(WT) [14 15] and compressive sensing (CS) [16 17] Amongthem EMD is suitable for analyzing nonlinear and nonsta-tionary signals and models the analyzed signal as the sumover a set of intrinsic model functions (IMFs) and a residual[12] EMD has been successfully applied in the field of faultdiagnosis failure detection damage identification and healthmonitoring [18 19] The shortcomings of EMD are the lackof theoretical foundation [20] sensitivity to noises samplingerrors [21] and model mixtures [10] These have adverseeffects on the performance for fault detection To alleviatethese problems the variants of EMD such as EEMD bivariateempirical mode decomposition (BEMD) and multivariateempirical mode decomposition (MEMD) [22ndash24] have beendeveloped Moreover there is a lack of theory to clarify theseproblemsWavelet analysis is conducted by the inner productof the measured vibration signals and wavelet basis providesthe time-scale information of the impulses Both continuouswavelet transform (CWT) and discrete wavelet transform(DWT) have been successfully applied for fault detection ofrotational machines with multiresolution [25 26] The hugecomputational costs and redundant coefficients of CWT limitits wide application as compared to DWT which has a fasteralgorithm [27]Wavelet packet transform (WPT) is proposedto improve the decomposition performance of WT on high-frequency band which contains useful information for faultdetection [28] However the decomposition quality of theDWT and WPT is influenced by the selection of motherwavelet [29] The shift-variance [30] and the low oscillation[31] of DWT and WPT result in distortion and containnonsparse representation of the impulses

CS consists of sparse representation and dictionary con-struction With sparse representation models the signalsare the linear combinations of basis elements or atoms in aredundant dictionary Dictionary design is adapted to self-feature the vibration signals to match well with the high-levelstructures of the impulses As far as sparse representationis concerned the exact resolution of sparse representationproves to be an NP-hard problem [32] and the approxi-mate solutions based on greedy-based matching pursuit [33]

and convex optimal-based basis pursuit [34] are consid-ered instead Dictionary construction includes manuallypredefined dictionary and dictionary learning Dictionarylearning includes regular dictionary learning [35] and shift-invariant dictionary learning (SIDL) [36 37] For excellentperformances of CS on representing signals (such as self-adaption sparsity and super-resolution) the CS based onthe predefined dictionaries and sparse representation is usedto detect faults on bearings and gear boxes and outperformsEMD and WT [38 39] Compared to predefined dictionaryand regular dictionary learning SIDL has shift-invariance[36 37]

The convolution sparse representation (CSR) based onalternating direction method of multipliers (ADMM) wasfirst proposed in 2016 and is a novel research on CSbased on pursuit and SIDL [38] CSR provides an excellentframework for extracting impulses induced by bearing faultsand wheel-rail interactions However the performances ofCSR on extracting impulses are heavily influenced by itspenalty parameter which determines the sparsity of theextracted impulses When the penalty parameter is verylarge the extracted impulse is very sparse and the numberof the extracted impulses is far less than the true numberof impulses [39] Thus this can easily lead to the loss ofimpulses containing fruitful fault-information Converselythe extracted impulses could be far more than the true num-ber of impulses As such this results in impulse corruptionsTo completely extract impulses with the least corruptionsis very difficult under the condition of a single penaltyparameter Hence in this paper the CSRs with differentpenalty parameters are jointly used to extract impulses in theframework of manifold learning

Manifold learning projects the high-dimensional datainto a lower-dimensional feature space by preserving thelocal neighborhood structures Manifold learning mainlyinvolves convex and nonconvex techniques Convex tech-nique involves full spectrum methods such as isometricmapping (Isomap) [40] diffusion maps [41] and sparsespectral methods (which include local tangent space analysis(LTSA) [42] and local linear embedding (LLE) [43]) Non-convex technique mainly includes locally linear coordination(LLC) [44] and Sammon mapping [45] Recently manifoldlearning has been successfully applied in fault diagnosis Themanifolds based on different spaces such as scale space ofWT and WPT [46 47] IMF space of EMD [48] and time-frequency space [49] are used to extract impulses Thesemanifold methods have successfully discovered the intrinsicstructures of impulses embedded in the measured vibrationsignals

Hence this paper aims to fully exploit the frameworkfor extracting impulses with CSR which provides lower orminimum adverse influences that the inappropriate selectionof penalty parameter of CSR bringsThis novel fault detectionmethod known as impulse-envelope manifold is proposedbased on the combination of CSR Hilbert transform andmanifold learning The impulses with different sparsity char-acteristic are extracted by the CSR with different penaltyparameters The impulse-envelope spaces are spanned by theHilbert transform on the extracted impulses The manifold





d119898 x119896119898 = argmind119898 x119896119898

12119870sum119896=1

1003817100381710038171003817100381710038171003817100381710038171003817s119896 minus119872sum119898=1

d119898 lowast x11989611989810038171003817100381710038171003817100381710038171003817100381710038172

119865

+ 120582 119870sum119896=1

119872sum119898=1

1003817100381710038171003817x11989611989810038171003817100381710038171 (1)



x119896119898 = argmin12119870sum119896=1


119865

+ 120582 119870sum119896=1

119872sum119898=1

1003817100381710038171003817x11989611989810038171003817100381710038171 (2)


x119898 = argminx119898


10038171003817100381710038171003817100381710038171003817100381710038172

119865

+ 120582 119872sum119898=1

1003817100381710038171003817x11989810038171003817100381710038171 (3)


d119898 = argmind119898

12119870sum119896=1


119865

(4)




I120582119898 =119872sum119898=1

d120582119898 lowast x120582119898 (5)


h120582119898 = 2120587 intinfin

minusinfin

I120582119898 (119905)119905 minus 120591 119889120591 =1120587119905 I120582119898 (119905) (6)


z120582119898 = I120582119898 + jh120582119898 (7)


E120582119898 = 10038161003816100381610038161003816I120582119898 + jh12058211989810038161003816100381610038161003816 = radic(I120582119898)2 + (h120582119898)2 (8)





Analyzed signals

ENT


Hilbert transform


Manifold learning


Envelope spectra













119886 (119905) = 119871sum119897=1





0

4

8

Acce

lera

tionA

(msminus

2)

minus4

minus8

Time t (s)00000 02048 04096 06144 08192

(a)

0

6

12

Acce

lera

tionA

(msminus

2)

minus6

minus12

Time t (s)00000 02048 04096 06144 08192

(b)


0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(a)

Acce

lera

tionA

(msminus

2) fp

3fp5fp 7fp


2fp

4fp


0Frequency f (Hz)

200 400 600 800 100000

06

12

18

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

fp

3fp5fp 7fp

9fp 11fp13fp

15fp17fp 19fp

4fp

2fp

6fp


0Frequency f (Hz)

200 400 600 800 100000

03

06

(d)

Acce

lera

tionA

(msminus

2)

minus03

minus06

Time t (s)00000 02048 04096 06144 08192

06

03

00

(e)

Acce

lera

tionA

(msminus

2)

fp

15fp

0Frequency f (Hz)

200 400 600 800 10000000

0002

(f)






0

5

(IMF4)(IMF3)

(IMF2)(IMF1)

0

2

4

(IMF5)

0

1

2

(IMF6)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus10

minus06

minus35

minus70

minus1

minus2

minus12 minus10

minus05

Time t (s)00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

10

12

06

00

70

35

00

10

05

00






Rollernumber

Roller diameter(mm)

Pitch diameter(mm)

Contact angle(rad)

19 269 180 01571





0

5

0

2

4

0

2

4(38)

(37)

(36)

(35)

(34)

(33)

(32)

0

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus2

minus4

minus10

minus10

minus20

10

10

Time t (s)00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

20(31)

minus025

minus15

minus30

minus08

minus16

minus15

minus30

minus050

050

025

000

30

15

00

16

08

00

30

15

00


0

5

Acce

lera

tionA

(msminus

2)

minus10

minus15

minus5

Time t (s)00000 02048 04096 06144 08192

(a)

0 0

0 4

0 8

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp 7fp 9fp

2fp

4fp

6fp 8fp10fp

(b)

0

2

Acce

lera

tionA

(msminus

2)

minus2

minus4

minus6

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp

2fp

4fp

08

04

00

(d)



Motor

Driving wheel



Sensor

Axle box


(a) (b)


0

Acce

lera

tionA

(msminus

2)

minus50

minus100

Time t (s)00000 02048 04096 06144 08192

50

100



119891BPFO = 1198731198872 (1 minus 119861119889119875119889 cos (120601))119891119908 (11)






0Ac

cele

ratio

nA

(msminus

2)

minus200

minus400

minus600

minus800

minus1000

Time t (s)00000 02048 04096 06144 08192

200

(a)

0Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)



0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













d119898 x119896119898 = argmind119898 x119896119898

12119870sum119896=1

1003817100381710038171003817100381710038171003817100381710038171003817s119896 minus119872sum119898=1

d119898 lowast x11989611989810038171003817100381710038171003817100381710038171003817100381710038172

119865

+ 120582 119870sum119896=1

119872sum119898=1

1003817100381710038171003817x11989611989810038171003817100381710038171 (1)



x119896119898 = argmin12119870sum119896=1


119865

+ 120582 119870sum119896=1

119872sum119898=1

1003817100381710038171003817x11989611989810038171003817100381710038171 (2)


x119898 = argminx119898


10038171003817100381710038171003817100381710038171003817100381710038172

119865

+ 120582 119872sum119898=1

1003817100381710038171003817x11989810038171003817100381710038171 (3)


d119898 = argmind119898

12119870sum119896=1


119865

(4)




I120582119898 =119872sum119898=1

d120582119898 lowast x120582119898 (5)


h120582119898 = 2120587 intinfin

minusinfin

I120582119898 (119905)119905 minus 120591 119889120591 =1120587119905 I120582119898 (119905) (6)


z120582119898 = I120582119898 + jh120582119898 (7)


E120582119898 = 10038161003816100381610038161003816I120582119898 + jh12058211989810038161003816100381610038161003816 = radic(I120582119898)2 + (h120582119898)2 (8)





Analyzed signals

ENT


Hilbert transform


Manifold learning


Envelope spectra













119886 (119905) = 119871sum119897=1





0

4

8

Acce

lera

tionA

(msminus

2)

minus4

minus8

Time t (s)00000 02048 04096 06144 08192

(a)

0

6

12

Acce

lera

tionA

(msminus

2)

minus6

minus12

Time t (s)00000 02048 04096 06144 08192

(b)


0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(a)

Acce

lera

tionA

(msminus

2) fp

3fp5fp 7fp


2fp

4fp


0Frequency f (Hz)

200 400 600 800 100000

06

12

18

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

fp

3fp5fp 7fp

9fp 11fp13fp

15fp17fp 19fp

4fp

2fp

6fp


0Frequency f (Hz)

200 400 600 800 100000

03

06

(d)

Acce

lera

tionA

(msminus

2)

minus03

minus06

Time t (s)00000 02048 04096 06144 08192

06

03

00

(e)

Acce

lera

tionA

(msminus

2)

fp

15fp

0Frequency f (Hz)

200 400 600 800 10000000

0002

(f)






0

5

(IMF4)(IMF3)

(IMF2)(IMF1)

0

2

4

(IMF5)

0

1

2

(IMF6)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus10

minus06

minus35

minus70

minus1

minus2

minus12 minus10

minus05

Time t (s)00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

10

12

06

00

70

35

00

10

05

00






Rollernumber

Roller diameter(mm)

Pitch diameter(mm)

Contact angle(rad)

19 269 180 01571





0

5

0

2

4

0

2

4(38)

(37)

(36)

(35)

(34)

(33)

(32)

0

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus2

minus4

minus10

minus10

minus20

10

10

Time t (s)00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

20(31)

minus025

minus15

minus30

minus08

minus16

minus15

minus30

minus050

050

025

000

30

15

00

16

08

00

30

15

00


0

5

Acce

lera

tionA

(msminus

2)

minus10

minus15

minus5

Time t (s)00000 02048 04096 06144 08192

(a)

0 0

0 4

0 8

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp 7fp 9fp

2fp

4fp

6fp 8fp10fp

(b)

0

2

Acce

lera

tionA

(msminus

2)

minus2

minus4

minus6

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp

2fp

4fp

08

04

00

(d)



Motor

Driving wheel



Sensor

Axle box


(a) (b)


0

Acce

lera

tionA

(msminus

2)

minus50

minus100

Time t (s)00000 02048 04096 06144 08192

50

100



119891BPFO = 1198731198872 (1 minus 119861119889119875119889 cos (120601))119891119908 (11)






0Ac

cele

ratio

nA

(msminus

2)

minus200

minus400

minus600

minus800

minus1000

Time t (s)00000 02048 04096 06144 08192

200

(a)

0Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)



0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Analyzed signals

ENT


Hilbert transform


Manifold learning


Envelope spectra













119886 (119905) = 119871sum119897=1





0

4

8

Acce

lera

tionA

(msminus

2)

minus4

minus8

Time t (s)00000 02048 04096 06144 08192

(a)

0

6

12

Acce

lera

tionA

(msminus

2)

minus6

minus12

Time t (s)00000 02048 04096 06144 08192

(b)


0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(a)

Acce

lera

tionA

(msminus

2) fp

3fp5fp 7fp


2fp

4fp


0Frequency f (Hz)

200 400 600 800 100000

06

12

18

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

fp

3fp5fp 7fp

9fp 11fp13fp

15fp17fp 19fp

4fp

2fp

6fp


0Frequency f (Hz)

200 400 600 800 100000

03

06

(d)

Acce

lera

tionA

(msminus

2)

minus03

minus06

Time t (s)00000 02048 04096 06144 08192

06

03

00

(e)

Acce

lera

tionA

(msminus

2)

fp

15fp

0Frequency f (Hz)

200 400 600 800 10000000

0002

(f)






0

5

(IMF4)(IMF3)

(IMF2)(IMF1)

0

2

4

(IMF5)

0

1

2

(IMF6)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus10

minus06

minus35

minus70

minus1

minus2

minus12 minus10

minus05

Time t (s)00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

10

12

06

00

70

35

00

10

05

00






Rollernumber

Roller diameter(mm)

Pitch diameter(mm)

Contact angle(rad)

19 269 180 01571





0

5

0

2

4

0

2

4(38)

(37)

(36)

(35)

(34)

(33)

(32)

0

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus2

minus4

minus10

minus10

minus20

10

10

Time t (s)00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

20(31)

minus025

minus15

minus30

minus08

minus16

minus15

minus30

minus050

050

025

000

30

15

00

16

08

00

30

15

00


0

5

Acce

lera

tionA

(msminus

2)

minus10

minus15

minus5

Time t (s)00000 02048 04096 06144 08192

(a)

0 0

0 4

0 8

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp 7fp 9fp

2fp

4fp

6fp 8fp10fp

(b)

0

2

Acce

lera

tionA

(msminus

2)

minus2

minus4

minus6

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp

2fp

4fp

08

04

00

(d)



Motor

Driving wheel



Sensor

Axle box


(a) (b)


0

Acce

lera

tionA

(msminus

2)

minus50

minus100

Time t (s)00000 02048 04096 06144 08192

50

100



119891BPFO = 1198731198872 (1 minus 119861119889119875119889 cos (120601))119891119908 (11)






0Ac

cele

ratio

nA

(msminus

2)

minus200

minus400

minus600

minus800

minus1000

Time t (s)00000 02048 04096 06144 08192

200

(a)

0Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)



0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

4

8

Acce

lera

tionA

(msminus

2)

minus4

minus8

Time t (s)00000 02048 04096 06144 08192

(a)

0

6

12

Acce

lera

tionA

(msminus

2)

minus6

minus12

Time t (s)00000 02048 04096 06144 08192

(b)


0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(a)

Acce

lera

tionA

(msminus

2) fp

3fp5fp 7fp


2fp

4fp


0Frequency f (Hz)

200 400 600 800 100000

06

12

18

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

fp

3fp5fp 7fp

9fp 11fp13fp

15fp17fp 19fp

4fp

2fp

6fp


0Frequency f (Hz)

200 400 600 800 100000

03

06

(d)

Acce

lera

tionA

(msminus

2)

minus03

minus06

Time t (s)00000 02048 04096 06144 08192

06

03

00

(e)

Acce

lera

tionA

(msminus

2)

fp

15fp

0Frequency f (Hz)

200 400 600 800 10000000

0002

(f)






0

5

(IMF4)(IMF3)

(IMF2)(IMF1)

0

2

4

(IMF5)

0

1

2

(IMF6)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus10

minus06

minus35

minus70

minus1

minus2

minus12 minus10

minus05

Time t (s)00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

10

12

06

00

70

35

00

10

05

00






Rollernumber

Roller diameter(mm)

Pitch diameter(mm)

Contact angle(rad)

19 269 180 01571





0

5

0

2

4

0

2

4(38)

(37)

(36)

(35)

(34)

(33)

(32)

0

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus2

minus4

minus10

minus10

minus20

10

10

Time t (s)00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

20(31)

minus025

minus15

minus30

minus08

minus16

minus15

minus30

minus050

050

025

000

30

15

00

16

08

00

30

15

00


0

5

Acce

lera

tionA

(msminus

2)

minus10

minus15

minus5

Time t (s)00000 02048 04096 06144 08192

(a)

0 0

0 4

0 8

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp 7fp 9fp

2fp

4fp

6fp 8fp10fp

(b)

0

2

Acce

lera

tionA

(msminus

2)

minus2

minus4

minus6

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp

2fp

4fp

08

04

00

(d)



Motor

Driving wheel



Sensor

Axle box


(a) (b)


0

Acce

lera

tionA

(msminus

2)

minus50

minus100

Time t (s)00000 02048 04096 06144 08192

50

100



119891BPFO = 1198731198872 (1 minus 119861119889119875119889 cos (120601))119891119908 (11)






0Ac

cele

ratio

nA

(msminus

2)

minus200

minus400

minus600

minus800

minus1000

Time t (s)00000 02048 04096 06144 08192

200

(a)

0Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)



0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

(IMF4)(IMF3)

(IMF2)(IMF1)

0

2

4

(IMF5)

0

1

2

(IMF6)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus10

minus06

minus35

minus70

minus1

minus2

minus12 minus10

minus05

Time t (s)00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

10

12

06

00

70

35

00

10

05

00






Rollernumber

Roller diameter(mm)

Pitch diameter(mm)

Contact angle(rad)

19 269 180 01571





0

5

0

2

4

0

2

4(38)

(37)

(36)

(35)

(34)

(33)

(32)

0

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus2

minus4

minus10

minus10

minus20

10

10

Time t (s)00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

20(31)

minus025

minus15

minus30

minus08

minus16

minus15

minus30

minus050

050

025

000

30

15

00

16

08

00

30

15

00


0

5

Acce

lera

tionA

(msminus

2)

minus10

minus15

minus5

Time t (s)00000 02048 04096 06144 08192

(a)

0 0

0 4

0 8

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp 7fp 9fp

2fp

4fp

6fp 8fp10fp

(b)

0

2

Acce

lera

tionA

(msminus

2)

minus2

minus4

minus6

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp

2fp

4fp

08

04

00

(d)



Motor

Driving wheel



Sensor

Axle box


(a) (b)


0

Acce

lera

tionA

(msminus

2)

minus50

minus100

Time t (s)00000 02048 04096 06144 08192

50

100



119891BPFO = 1198731198872 (1 minus 119861119889119875119889 cos (120601))119891119908 (11)






0Ac

cele

ratio

nA

(msminus

2)

minus200

minus400

minus600

minus800

minus1000

Time t (s)00000 02048 04096 06144 08192

200

(a)

0Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)



0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

0

2

4

0

2

4(38)

(37)

(36)

(35)

(34)

(33)

(32)

0

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

Acce

lera

tionA

(msminus

2)

minus5

minus2

minus4

minus2

minus4

minus10

minus10

minus20

10

10

Time t (s)00000 02048 04096 06144 08192

Time t (s)00000 02048 04096 06144 08192

20(31)

minus025

minus15

minus30

minus08

minus16

minus15

minus30

minus050

050

025

000

30

15

00

16

08

00

30

15

00


0

5

Acce

lera

tionA

(msminus

2)

minus10

minus15

minus5

Time t (s)00000 02048 04096 06144 08192

(a)

0 0

0 4

0 8

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp 7fp 9fp

2fp

4fp

6fp 8fp10fp

(b)

0

2

Acce

lera

tionA

(msminus

2)

minus2

minus4

minus6

Time t (s)00000 02048 04096 06144 08192

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

fp 3fp 5fp

2fp

4fp

08

04

00

(d)



Motor

Driving wheel



Sensor

Axle box


(a) (b)


0

Acce

lera

tionA

(msminus

2)

minus50

minus100

Time t (s)00000 02048 04096 06144 08192

50

100



119891BPFO = 1198731198872 (1 minus 119861119889119875119889 cos (120601))119891119908 (11)






0Ac

cele

ratio

nA

(msminus

2)

minus200

minus400

minus600

minus800

minus1000

Time t (s)00000 02048 04096 06144 08192

200

(a)

0Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)



0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Motor

Driving wheel



Sensor

Axle box


(a) (b)


0

Acce

lera

tionA

(msminus

2)

minus50

minus100

Time t (s)00000 02048 04096 06144 08192

50

100



119891BPFO = 1198731198872 (1 minus 119861119889119875119889 cos (120601))119891119908 (11)






0Ac

cele

ratio

nA

(msminus

2)

minus200

minus400

minus600

minus800

minus1000

Time t (s)00000 02048 04096 06144 08192

200

(a)

0Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)



0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0Ac

cele

ratio

nA

(msminus

2)

minus200

minus400

minus600

minus800

minus1000

Time t (s)00000 02048 04096 06144 08192

200

(a)

0Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

40

20

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(b)

0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

minus20

Time t (s)00000 02048 04096 06144 08192

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

050

025

000

f０

2f０ 3f０

4f０5f０ 6f０ 7f０

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

030

015

000

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

00025

00000

(f)


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

50

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 120000

15

30f０

2f０

3f０

4f０

5f０

6f０ 7f０

(b)

0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus15

60

45

30

15

(c)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000 1200

f０

2f０

(d)



0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus20

minus40

60

40

20


0


Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

minus100

minus150

minus200

minus250

50

(a)

0

7

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

14 f）f３

2f３

(b)


0

4

8

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192 minus4

12

(c)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

06

03

00

f）f３

2f３

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

minus06

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

400 300200100

0002

0001

0000

(f)






G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










G1

D1F1E1

C1

269

180

N1

M1L1

K1

A2

C2

B2

J1

H1 B1

A1

27∘



119891BPFO = 119901119887119861119889 (1 minus11986121198891198752119889 cos

2 (120601))119891119908 (12)










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus30

minus60

30

(a)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

200 400 600 800 1000

10

05

00

(b)

05

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

minus15

minus20

1510

(c)

0Frequency f (Hz)

200 400 600 800 1000

Acce

lera

tionA

(msminus

2) 10

05

00

(d)


Accelerometer

Axle box


0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus18

minus36

54

36

18




6 Conclusion



0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

H3B3

H2

B2

B8H7

B7H6

B6H5

B5H4

B4

Acce

lera

tionA

(msminus

2)

minus60

minus120

minus180

Time t (s)00000 02048 04096 06144 08192


(a)

0

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

12f４４ f３ 2f３ 3f３


(b)

H3

B3H2

B2B8

H7B7

H6

B6

H5B5H4

B4

0

5

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)00000 02048 04096 06144 08192

10


(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

050

025

000

f４４ f３2f３ 3f３

fBSF + 3fTFT3fTFT


(d)

Acce

lera

tionA

(msminus

2)

minus02

minus04

minus06

minus08

Time t (s)00000 02048 04096 06144 08192

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

0002

0000

(f)


0

B3

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus100minus50

minus150minus200

Time t (s)

50

018 020 022 024 026

(a)

02468

H3

G3

F3E3D3C3

B3

Acce

lera

tionA

(msminus

2)

minus2

Time t (s)

10

018 019 020 021 022 023 024 025 026

(b)






0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus50

150

100

50

(a)

0

3

6

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

4fw

6fw

75fw

(b)

0

5

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus5

minus10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

027

018

009

000

4fw

6fw

75fw

(d)

Acce

lera

tionA

(msminus

2)

Time t (s)00000 02048 04096 06144 08192

minus02

minus04

04

02

00

(e)

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

100 200 300 400

0003

0002

0001

0000

(f)


0

Acce

lera

tionA

(msminus

2)

minus15

minus30

minus45

minus60

Time t (s)00000 02048 04096 06144 08192

15

(a)

0

1

2

Acce

lera

tionA

(msminus

2)

0Frequency f (Hz)

150 300 450 600

f４４

f３

2f３

3f４４

(b)

0

9

Acce

lera

tionA

(msminus

2)

minus9

minus18

Time t (s)00000 02048 04096 06144 08192

(c)

0Frequency f (Hz)

150 300 450 600

Acce

lera

tionA

(msminus

2) 10

05

00

f４４ f３2f３

(d)



0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




Acknowledgments


References
























































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

Acce

lera

tionA

(msminus

2)

minus5

minus10

minus15

Time t (s)00000 02048 04096 06144 08192

10

(a)

0Frequency f (Hz)

100 200 300 400 500 600

Acce

lera

tionA

(msminus

2) 10

05

00

f３

2f３

3f４４

fw

75fw

(b)

0

Acce

lera

tionA

(msminus

2)

minus10

Time t (s)00000 02048 04096 06144 08192

20

10

(c)Ac

cele

ratio

nA

(msminus

2)

0Frequency f (Hz)

100 200 300 400 500 600

18

09

00

f４４ f３2f３

3f４４

fBSF + 3fTFT

(d)


05

H3

G3

F3

E3

D3C3

B3

Acce

lera

tionA

(msminus

2)

minus5

Time t (s)

10152025

026025024023022021020019018




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









fault detection of high-speed train wheelset bearing based ...researcharticle fault detection of...

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