更全的杂志信息网

Variational Mode Decomposition for Rotating Machinery Condition Monitoring Using Vibration Signals

更新时间:2016-07-05

0 Introduction

Failures in Engineering systems are basically due to the rotating components,such as the gears,bearings,turbines,shafts and rotors.Prolonged operation in harsh working conditions causes these components to deteriorate,especially the gears and bearings.In most cases,sudden failures are a major problem in industries in which such failures cause losses in finance,equipment and resources.Hence,maintaining and sustaining the rotating machinery components is very important for ensuring safe operation and avoiding fatalities.Condition monitoring technology offers a good solution for industrial staff when maintaining their assets[1].Vibration-based monitoring is one of the most popular condition monitoring technologies,and has been used in many industries because of its simple,low implementation cost and effectiveness compared with other monitoring technologies.

Much research has been carried out over recent decades to produce a more effective and efficient rotating machinery monitoring process.In recent condition monitoring investigation,the combination of signal processing method and machine learning algorithms have been widely used[1,2].The signal processing method is very important for ensuring the accuracy of the information,and characteristics used in the analysis process and in the machine learning algorithm help to reduce human interpretation errors and provide automated monitoring strategies.Empirical mode decomposition (EMD),introduced by Huang et al.,is a well-known signal processing method used in monitoring studies due to its ability to analyse non-linear and non-stationary signals,and to address the limitations of the traditional fast Fourier transform (FFT)method[36]as well.The EMD method has been combined with many machine learning algorithms for rotating machinery monitoring,such as neural network,Bayesian,support vector machine(SVM)and extreme learning machine(ELM)[711].

However,the EMD method suffers from a mode mixing problem and an end effect problem,which in most rotating machinery applications are due to the complexity of the rotating machinery signals characteristic[12,13].In order to address the issue of the EMD method,there are many improvised versions of the method that have been proposed,such as ensemble EMD(EEMD)[14],complementary EEMD (CEEMD)[5],partial EEMD(PEEMD)[15] and local mode decomposition(LMD)[16].The EEMD method has been used with neural network,artificial bee colony(ABC)and SVM[1719].For the CEEMD method,SVM and ELM have been used as a combination for monitoring strategies[20,21]. For PEEMD and LMD,variable predictive mode-based class discrimination(VPMCD),neural network and SVM have been used[2224].However,the end effect and the mode mixing problems still occurred in these improvised methods,which can lead to inefficient and inaccurate monitoring and diagnosis process[24,25].

Recently,an adaptive and non-recursive signal processing method called the variational mode decomposition (VMD)has been proposed by Dragomiretskiy et al.[26].The VMD method has overcome the limitations of the EMD method by having a unique decomposition procedure as compared with other decomposition procedures.However,the VMD method requires certain parameters to be determined,particularly the number of modes to be reconstructed.This becomes a problem for the VMD method,as an inaccurate set of mode numbers will affect the decomposition result.This problem is still considered as open for the VMD method[26,27].Zhang et al.have used the number of dominant frequency characteristics of the signals as the number of modes for the VMD method[28].Recently,Li et al.have used the locally weighted scatter plot smoothing method(LOWESS),which locates the number of major peaks in the envelope spectrum,and uses this as the mode number for the VMD method[27].In addition,Zhang et al.have proposed a selection method based on a correlation and energy ratio to select the mode number for the VMD method[29].

This study therefore aims to propose a mode selection number for the VMD method based on the statistical parameter ratio(SPR)plot.This proposed method is more effective in determining the mode number for the VMD method,especially when used for complex signal characteristics when compared with a selection method based on dominant frequency characteristics and major peaks in the envelope spectrum.The method can also be used as an alternative for the selection method based on correlation and energy ratio,and it will provide a better visualization in selecting the mode number for the VMD method.The statistical characteristics are used here as input for the ELM algorithm for fault classification,and the result has been compared with artificial neural network(ANN).The comparison between features extracted from the original signals,intrinsic mode functions (IMFs)and variational mode functions(VMFs)have also been compared.

1 Method Theory

1.1 Variational mode decomposition

The performance of the VMD method mainly depends on the accuracy of the input parameters,which comprise the balancing parameter (α),the time-step of dual ascent(τ),the number of mode(K),the initial omega(ω )and the tolerance.Some of the input parameters have a standard value.For example,the tolerance has a typical value of 1×10-6,theωis 0(allωwill start with 0)and theτis 0for noise-slack as mentioned by Ref.[26].Theαcan be set to 1 500to have a good decomposition result,as stated by Zhang et al.[29]The number of mode is an important parameter for the VMD method.This is due to the mode number determining the number of the VMF that will be reconstructed by the VMD method.Initiating an inaccurate number of mode will cause the under-decomposed and over-decomposed problem of the VMD method,as well as potential information losses from the input signal.Therefore,it is very important to have a good mode selection method for the VMD method.

The three data sets have been used to compare the two different machine learning algorithms.For ELM,the sample was normalized as required by the algorithm.The overall performance of these three datasets is described in Table 4for ELM,and in Table 5for ANN.Set 1defines VMD-ELM and VMD-ANN,set 2defines Signal-ELM and Signal-ANN,while set 3defines EMDELM and EMD-ANN.In Table 4,A is defined as an average accuracy of between 1to 200neurons.B is defined as the average when the neurons are set to eight(to run 30times with the neurons set to eight in order to avoid the tweak problem)and C is the accuracy value when the neurons are eight.By default,aparticular number of neurons is equal to the number of features.

where fis the maximum frequency deviation,fAMthe component of amplitude-modulated frequency,and fFMthe component of frequencymodulated frequency.

试验鸡来自北京市华都峪口禽业有限责任公司,挑选体重相近、体况健康的9周龄“京红1号”蛋种鸡1 260只,饲养试验在华都峪口禽业有限责任公司鲍官庄养殖基地进行。

The VMD method relies on three basic concepts,i.e.,Wiener filtering,heterodyne demodulation and one-dimensional Hilbert transform.The method decomposed an input signal into different modes with a specific scale by assuming that each mode is a finite bandwidth signal with a pulse at the centre.Firstly,VMD uses Hilbert transform to obtain the single spectrum for each mode and to transfer the spectrum of each mode to the fundamental frequency by using exponential correction.This will evaluate the bandwidth of each mode and construct the constraint model of the variational problem.

whereωkis the centre frequency of the mode,and fis the input signal.A quadratic penalty term and Lagrange multiplier,λoperator was introduced to convert the constraint problem into a non-constraint problem.

The proposed selection method was then applied to the simulated signals.This is shown in the SPR plot in Fig.4,which consists of eight different SPR plots.To gain an adequately improved visualization for selecting the mode number,the SPR plot has been reduced to two plots consisting of RMS and shape factors,as shown in Fig.5.Hence these two SPR plots can provide better visualization and thus they avoid confusion in selecting the mode number for the VMD method.This is because the mode number will be selected based on the first point,where the plot starts to attain a steady state or a similar value.In this case the mode selected for the simulated signals is 4,referring to Fig.5.

The above equation found a sub-problem in the sub-optimization method,called the alternate direction method of multipliers (ADMM).The solution to the sub-problem using Eq.(6)with respect to ukand Eq.(7)with respect toωk

湖州一个富家儿媳,丈夫死后想改嫁,而公公不允许,迫她守寡。她便向“疙瘩老娘”求援,“疙瘩老娘”开价是一字百两银子,向她要了一千六百两银子,写了张十六字的状子。

By substituting the solution with the sub-optimization method,the full algorithm for the VMD method was established as the following expression[26]

Section 1: Comparison of the imaging techniques from biological aspects

1.2 Extreme learning machine

ELM is a simple and efficient algorithm for training single-hidden layer feedforward neural networks (SLFNs),as proposed by Huang et al.[30].SLFNs consist of the input layer,a hidden layer and an output layer,in which the input layer has n neurons corresponding to the ninput variables,the hidden layer has I neurons and the output layer has mneurons corresponding to the moutput variables.The algorithm randomly generates the connection weight between the input and the hidden layers,as well as the threshold of the hidden layer neurons without any adjustment in the training process.It also obtains the optimal solution by adjusting the number of hidden layer neurons.ELM provides better generalization performance at extremely fast learning speeds as compared to traditional feedforward network learning algorithms[30].ELM helps to resolve some of the issues of conventional gradient-based algorithms for SLFNs,such as algorithms becoming unstable,and diverges when the leaning rate is too large.The algorithm converges slowly when the learning rate is small,and stops at the local minima if it is located far above the global minima,which is undesirable,over-trained and time-consuming[30].The algorithm of ELM can be summarized as follows.

Given a training dataset with pclasses{xiyi },i=1,…,Nand yi ∈Rp.xi∈Rqis a qdimensional data point.If Gx)is an infinitely differentiable activation function in the hidden layer,then the output of SLFN is express as

where Lis the number of hidden notes,and ajand bjthe jth hidden node′s learning parameter assigned randomly.βj ∈ Rp is the output weight vector.The SLFN output of the matrix form can be and expressed as

where

where His called the hidden layer output matrix of the network.Hijrepresents the jth hidden node with respect to the input samples,xi·β=There-fore,the objective function of ELM can be expressed as

where H and Y = Penrose generalized inverse of matrix H.The above output weight matrixβminimizes the cost

2 The Proposed Method

The VMD method is a modern decomposition tool which decomposes the vibration signal into sets of sub-signals called VMFs.The sub-signals define amplitude modulated and frequency modulated(AM-FM)signals,as described in Eq.(1),and the total practical VMF Bandwidth,BWas estimated using Eq.(3)according to Carson′s rule,Eq.(2)[26].

For a healthy spectrum,the dominant consists of 1×GMF,2×GMF and 3×GMF.For a faulty signal,the dominant consists of previous GMF frequencies with the addition of a sub-harmonic occurring at 500Hz.Hence,the PSM approach gives the number of mode for the healthy signals as three and for the faulty signals it is four.In the comparison,the mode number for the healthy signals will be set to three,and for faulty signals it will be set to four.Fig.11summarizes the comparison between the PSM approach and the proposed selection method based on SPR.The results are shown in Table 2.The performance was calculated based on Eq.(19)

The simulated signals have been generated and used to validate the performance of the proposed selection method.Eq.(15)describes the simulated signals

Fig.1 Flowchart of the proposed method

Table 1 Statistical parameters

Statistical parameter Equation RMSNn=1 xn()2 N Range maxx()-min(x)Skewness 1 N Nn=1(xn()-x31 N Nn=1 xn()-x( )2 3)Kurtosis 1 N Nn=1(xn()-x41 N Nn=1 xn()-x( )2 4)Crest factor max xn1 N Nn=1 xn)2 Shape factor1 N Nn=1 xn)2 1 N Nn=1 xn)Impulse factor max xn)1 N Nn=1 xn)Margin factor max xn)1 N N(∑n=1xn) )2

Here,a selection method based on SPR has been proposed,as shown in Fig.1.The statistical parameter used in this paper is described in Table 1,in which xn)represents a time series of signals of the nth signal sample.In a recent study,Zhang et al.have proposed a selection method based on the correlation and energy ratio,which also provided a good selection method for the VMD method[29].This method calculates the correlation and energy ratio between each VMF and input signal and selects the high value for use in the correlation and energy ratio plot.Here,SPR calculates the ratio between the sum of the VMFs and the input signal to produce the SPR plot.Therefore,the selection method using SPR can provide an alternative approach to selecting the mode number for the VMD method.It also provides better visualization for selecting the mode number.

A Gaussian white noise is added to the simulated signals with a signal-to-noise(SNR)ratio of 30.The simulated signals are then iteratively decomposed using the VMD method of different mode set numbers,ranging from 1to 10.The other parameters used were initially set to the standard value,as described earlier.The statistical parameter ratios are then calculated and plotted against the number of modes.Fig.2shows the simulated signals as described in Eqs.(15—18).

Fig.2 Simulated signals

The simulated signals in Fig.2were decomposed into three different decomposition results with the number of modes set to 3,4and 5in order to simulate the problem of the VMD method when using inaccurate mode numbers.Based on the result in Fig.3,the under-decomposed problem occurred when the decomposition was three,and where the component of the simulated signals was mixed within the reconstructed mode.When the mode is 4then the decomposition result is good,as all the components of the simulated signals were reconstructed with the fourth mode,as Gaussian noise,added.When the mode is 5,then over-decomposition occurred with an extra mode having been reconstructed,although not significantly affecting the components of the simulated signals.It can thus be concluded that the underdecomposed must be avoided in the VMD method,whereas the over-decomposed is fine,although it is better to avoid this for the sake of ensuring the accuracy of the decomposition result.

Fig.3 Decomposition results with different mode numbers

Fig.4 SPR plot for the simulated signals

Fig.5 Selected SPR plot for a simulated signal

专科护士SOP培训不仅可为教师培养提供科学计划,同时为教学科学管理提供依据,促进专科护士培训质量的提升。SOP以程序性文件的方式为护理教学管理提供了依据[11-12]。SOP对专科护士培训内容进行了优化和细化,每个教学任务由谁来做、怎么做、达到什么标准均明确规定。这有利于由护理部牵头的护理教学质量管理团队对专科护士培训SOP的执行情况进行管理,可促进专科护士培训管理向目标化和规范化方向发展 [13]。

To further validate the proposed selection method using SPR,more complex signals have been used.These are the online gearbox vibration signals downloaded from Acoustic and Vibration database provided by Bechhoefer[31].Both the healthy and the faulty signals are shown in Fig.6.The proposed selection method then applies to both the healthy and faulty signals and to the SPR plot shown in Figs.7,8.

Fig.6 Online gearbox vibration signals

Fig.7 SPR plot for the healthy signals

Fig.8 SPR plot for faulty signal

Fig.7(a)and Fig.8(b)show all eight SPR plots for the signals.The skewness and margin factor plots have been removed as it does not show a good relation between sum of VMFs and input signals.Hence there are a further six SPR plots that need to be considered.After looking in detail at the six SPR plots,only three,which are RMS,shape factor and impulse factor,can be used based on their consistencies and adequate visualization.Finally,we decided to use only RMS and shape factor and removed impulse factor to avoid confusion during the selection process.In addition,RMS and shape factor provide very good visualization for selecting the mode number.The final SPR plots are shown in Fig.7 (d)and Fig.8(d).However,these steps may need to be repeated when new sets of signals are used because this may produce a different SPR plot,thus resulting in yet another SPR plot that is suitable for use.For this study RMS and shape factor will be used.

To select the mode number,the first point at which the plot starts to become steady,and the RMS and shape factor become similar in value is selected as the mode number for the corresponding signals.This is based on the similarities concept between the sum of VMFs and the input signals,at which particular point the value will become either one or close to one.The similarities concept basically defines when the VMD method decomposes a signal into sets of VMFs and the combination of VMFs produces a signal which is similar to the input signals.Therefore,the healthy and faulty signals shown in Fig.6will have 11modes and 12modes,respectively,as shown in Fig.7 (d)and Fig.8 (d).Fig.9shows an extra example of healthy and faulty signals.The selected mode number for the healthy signal is 9 while for the faulty signal it is 10.

如图4所示,根据真无功功率(正弦式无功功率)定义公式无功功率Q=ΣU(n)I(n)sin(θ),无功功率计量算法与有功类似,只是电压信号采用移相90度之后的。测量带宽主要受到数字移相滤波器的带宽限制,ATT7022B无功功率的测量带宽也可高达21次谐波。

(4)可频繁启停及正反转切换:在有制动单元及制动功率满足要求情况下,启停及正反转切换每小时可达一千次以上;

Fig.9 Example of another online gearbox signals

3 Rotating Machinery Monitoring

To further validate the performance of the proposed selection method,a comparison between SPR and traditional peak searching method(PSM)has been presented.As mentioned earlier,the gearbox vibration signals used in this paper have been downloaded from Acoustic and Vibration database provided by Bechhoefer[31].The PSM method is a basic traditional method used to determine the mode number for the signals which had been used in the early implementation of VMD in rotating machinery applications[28,32].In this method,the number of dominant frequencies in the frequency spectrum is used as the number of modes for the VMD method.Basically,the dominant frequency corresponds to the gear mesh frequency(GMF)for gear applications and the inner and outer race fault frequency,and the ball pass frequency and the ball spin frequency for bearing applications.Recently,an advanced PSM has been proposed by Li et al.[27]using LOWESS,in which the number of modes are determined based on the number of peaks on the envelope spectrum.For comparison,the PSM used is the traditional PSM method using the frequency spectrum.

1939年1月,国民党五届五中全会通过了《限制异党活动办法》,对共产党、民主团体、爱国民主人士和人民群众的言论行动实行严格的控制,实际上剥夺了人民群众抗战以来争得的某些民主权利。在9月9日举行的国民参政会第四次大会上,共产党和各抗日党派的参政员提出《请政府明令定期召集国民大会实行宪政案》。经过大家的努力,这个提案被通过。11月,国民党五届六中全会宣布于1940年11月12日召集国民大会。国民党曾借此大做文章,声称要实施宪政,还组织人讨论研究1936年5月5日颁布的《中华民国宪法草案》(即“五五宪草”)。但后来这些许诺都成了泡影。

Based on Fig.10,the number of peaks for the healthy signals is three,while for the faulty signals it is four.The number of peaks depends upon the dominant frequency on the spectrum.

Fig.10 Frequency spectrum of gearbox signals

我认为这部戏在思想上、实践上有一定的探索,但仅仅是上书还不够深厚,建议通过上书的引子来探讨中国改革开放中的工业改革和企业改革的思路和实践。

Table 2 Performance of the proposed mode determination method using statistical parameter ratio

Method SP1SP2SP3SP4SP5SP6SP7Ov Dataset Statistical parameter 0.91 0.99 0.98 0.95 0.94 0.98 0.92 0.95Healthy 2.16 0.96 0.99 1.22 1.22 1.00 0.91 1.00Faulty Peaks searching 1.52 0.97 1.02 0.88 0.89 1.02 0.83 0.87Healthy 1.83 0.94 0.98 1.19 1.16 0.98 0.88 0.96Faulty

Fig.11 Summary of the comparison

Based on Table 2,SP1is defined as the skewness,SP2as the kurtosis and SP3is defined as the crest factor;while SP4is defined as the shape factor,SP5as the impulse factor;SP6as the margin factor,SP7as the range;while Ov is the overall performance.The result,shown in Table 2,indicates that the proposed selection method using SPR provides a more accurate mode number than the traditional method.When the VMD method decomposes a signal into accurate sets of VMFs,the accuracy of the VMF characteristics,together with the input signal features,will have a high efficiency ratio value.The selection method using SPR recorded 0.956 0for the healthy signal and 1.001 3for the faulty signal,which outperforms the PSM method that recorded 0.872 1for the healthy signal and 0.961 7for the faulty signal.

To assess the condition of the gear,two machine learning algorithms have been used,which are ELM and ANN.Both healthy and faulty gear vibration signals have been used for experimental simulation in this paper.The type of fault in the gear systems is a wear fault,and is shown in Fig.12.The healthy and the faulty vibration signals have been divided into 120sample signals:60 samples for healthy and 60for faulty.Each signal sample will be decomposed by using the VMD method into sets of VMFs.The proposed method of determination using a statistical parameter ratio has also been used to determine the number of modes for each sample of healthy and faulty signals.The statistical parameter listed in Table 1,has,as distinct from the RMS,been used as input features for both ELM and ANN.The number of modes for each sample of the healthy and faulty signals has also been used as input features.Thus,there are eight features that have been used with two output targets,healthy and faulty.The detailed-on training and testing sample used for both ELM and ANN is summarized in Table 3.

Fig.12 Wear on gear system[31]

The input features summarized in Table 3 have been fed into ELM and ANN algorithms.The basic ELM algorithm used with the ELM type is set to a multi-classification and radial basis function,and has been used as an activation func-tion.For ANN,the basic ANN tools in MATLAB have been used with the default setting.The number of neurons has been set to eight for the ANN algorithm.To show the distinction and superiority of the mode determination method using a statistical parameter ratio,as well as the VMD method of gear fault diagnosis and classification,some comparisons have been made.As shown in Table 2,the data has been recorded into three different sets,totaling 360samples.Set 1represents the statistical features sample from the reconstructed VMD signal.The first and second modes have mainly been used for signal reconstruction of the VMD.This is due to the frequency characteristic of each VMF.Here,the interest frequency is within the 1×GMF,2×GMF and 3×GMF,which has been covered by the first and second modes of the VMD decomposition result.Both the healthy and faulty signals show similar VMF frequency characteristics,which ensures that the first and second modes are used for both healthy and faulty signals in this paper.Set 2represents the statistical features sample from the original signal without any decomposition method and Set 3represents the statistical features from the reconstructed EMD signal.A cross-correlation coefficient has been used to select the most significant IMFs.The first four highest cross-correlation coefficients have been used for the signal reconstruction of EMD.

在考虑已明确电源基础上,根据电力电量平衡计算结果,2025年广东电力缺口约3 GW。根据《广东省能源发展“十三五”规划》,广东开工建设湛江核电一期2×1 250 MW机组;再考虑新增部分新能源装机,预计2025年广东无电力缺额。

Table 3 Training samples and testing samples details for ANN and ELM

AlgorithmDataTrain sample Test sample Operating conditionLabel ELM Set 1 Set 2 Set 3 45×9 15×9 Healthy 0 45×9 15×9 Faulty 1 45×9 15×9 Healthy 0 45×9 15×9 Faulty 1 45×9 15×9 Healthy 0 45×9 15×9 Faulty 1 ANN Set 165%of 120×9 15%/20%of 120×9 Set 265%of 120×9 15%/20%of 120×9 Set 365%of 120×9 15%/20%of 120×9 Healthy 0 Faulty 1 Healthy 0 Faulty 1 Healthy 0 Faulty 1

where kis the mode number, kt)the a non-decreasing function, kt)≥ 0,the envelope is non-negative A′kt)≥0.The change of envelope Akt)and the instantaneous frequency kt)are much slower than kt).Therefore,the mode component ukt)can be considered as a pure harmonic signal with amplitude Akt)and instantaneous frequency kt).

Table 4 Overall performance of datasets using ELM algorithm %

Method Training performance Testing performance Overall A B C A B C All VMDELM98.44 85.41 92.22 93.38 85.78 86.67 90.32 EMDELM98.66 89.07 84.44 91.75 77.67 70.00 85.27 Signal-ELM98.22 89.48 90.00 75.22 81.78 83.33 86.34

Table 5 Overall performance of datasets using ANN algorithm %

Method Train Validation Test Overall VMD-ANN 96.2 94.4 95.8 95.8 EMD-ANN 79.5 88.9 87.5 82.5 Signal-ANN 93.6 72.2 83.3 88.3

For all the data sets,VMD-ELM and VMDANN provide better classification accuracy(90.32%and 95.80%)when compared with Signal-ELM,Signal-ANN,EMD-ELM and EMDANN.This shows that the statistical parameter characteristics extracted from the reconstructed VMD signal are more accurate compared with those characteristics extracted from the original signals and the reconstructed EMD signal.It can be thus concluded that the decomposed signal using the VMD method helps to reduce signal noise and complexity without eliminating the use-ful information within the signal.Accurate parameters and the number of modes set for the VMD method are pivotal for ensuring the performance of the VMD method and for avoiding any elimination of the useful information following the decomposing process,thus reducing the accuracy of the VMD method in fault classification.Figs.13,14also show the performance of datasets with the ELM algorithm in terms of a different number of neurons,which in turn shows that the VMD-ELM outperforms the Signal-ELM and EMD-ELM.

Fig.13 Testing accuracy for datasets with different number of neurons

Fig.14 Training accuracy for datasets with different number of neurons

Tables 6—8show the confusion matrix for the ANN algorithm.Therefore,VMD with an accurate initial mode will provide better diagnosis and classification of gear applications.It thus offers better and more reliable machine condition monitoring for gear applications.

Table 6 Confusion matrix for EMD-ANN

Class Actual 1 2 1 50 11 Predicted 2 10 49 Conflict 0 0 Sensitivity/% 83.3 81.7 Accuracy/% 82.5

Table 7 Confusion matrix for Signal-ANN

Class Actual 1 2 1 58 12 Predicted 2 2 48 Conflict 0 0 Sensitivity/% 96.7 80.0 Accuracy/% 88.3

Table 8 Confusion matrix for VMD-ANN

Class Actual 1 2 1 59 4 Predicted 2 1 49 Conflict 0 0 Sensitivity/% 98.3 93.3 Accuracy/% 95.8

4 Conclusions

All experimental data were simulated by Acoustic and Vibration database(gear datasets)and used for the VMD method,as well as for the input for the machine learning algorithm.A statistical parameter ratio has been proved as a suitable and adequate indicator for determining the number of modes for the VMD method.However,the most suitable statistical parameter ratio needs to be selected first,based on the properties of the signal.For this research,RMS and shape factor are the most suitable as they provide improved visualization for determining the mode numbers.The machine learning algorithm has also been used to offer good,reliable machine condition monitoring techniques.VMD-ELM and VMD-ANN show better diagnostic and classification performance with an advantage of 5%—10%in accuracy.In summary,an accurate initial mode numbers set using a statistical parameter ratio and input features from the reconstructed VMD signal are found to be superior and more accurate,indicating that the proposed method can improve machine monitoring techniques.

Acknowledgements

The authors would like to extend their greatest gratitude to the Institute of Noise and Vibration UTM for funding the study under the Higher Institution Centre of Excellence(HICoE)Grant Scheme (No.R.K130000.7809.4J226).Additional funding for this research also comes from the UTM Research University Grant (No.Q.K130000.2543.11H36),and Fundamental Research Grant Scheme(No.R.K130000.7840.4F653)by the Ministry of Higher Education Malaysia.

References:

[1] HUI K H,HEE L M,LEONG M S,et al.Vibration condition monitoring:latest trend and review[J].Appl Mech Mater.Trans Tech Publications,2015,773/774:139-143.

[2] LEI Y,LIN J,ZUO M J,et al.Condition monitoring and fault diagnosis of planetary gearboxes:A review[J].Meas J Int Meas Confed,2014,48:292-305.

[3] HUANG N,SHEN Z,LONG S,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proc R Soc A Math Phys Eng Sci,1998,454:995,903.

[4] LI Y,XU M,WEI Y,et al.An improvement EMD method based on the optimized rational Hermite interpolation approach and its application to gear fault diagnosis[J].Meas J Int Meas Confed,2015,63:330-345.

[5] YEH J R,SHIEH J S.Complementary ensemble empirical mode decomposition:A novel enhanced data analysis method[J].Adv Adapt Data Anal,2010,2:135-156.

[6] SINGH D S,ZHAO Q.Pseudo-fault signal assisted EMD for fault detection and isolation in rotating machines[J].Mech Syst Signal Process,2016,81:202-218.

[7] SHEN Z,CHEN X,ZHANG X,et al.A novel intelligent gear fault diagnosis model based on EMD and multi-class TSVM[J].Meas J Int Meas Confed,2012,45:30-40.

[8] YU Y,YU Dejie,CHEN Junsheng.A roller bearing fault diagnosis method based on EMD energy entropy and ANN[J].J Sound Vib,2006,294:269-277.

[9] ASR M Y,ETTEFAGH M M,HASSANNEJAD R,et al.Diagnosis of combined faults in rotary machinery by non-naive Bayesian approach[J].Mech Syst Signal Process,2017,85:56-70.

[10]CHENG G,CHENG Y L,SHEN L H,et al.Gear fault identification based on Hilbert-Huang transform and SOM neural network[J].Meas J Int Meas Confed,2013,46:1137-1146.

[11]BENKEDJOUH T,RECHAK S.Intelligent prognostics based on empirical mode decomposition and extreme learning machine[C]∥Model Identif Control(ICMIC),2016 8th Int Conf.[S.l.]:[s.n.],2016,943-947.

[12]YANG Y,PAN H,MA L,et al.A roller bearing fault diagnosis method based on the improved ITD and RRVPMCD[J].Measurement,2014,55:255-264.

[13]FENG Z,MA H,ZUO M J.Vibration signal models for fault diagnosis of planet bearings[J].J Sound Vib,2016,370:372-393.

[14]HUANG N E,WU Z.Ensemble empirical mode decomposition:A noise-assisted data analysis method[J].Adv Adapt Data Anal,2009,1:1.

[15]ZHENG J,CHENG J,YANG Y.Partly ensemble empirical mode decomposition:An improved noiseassisted method for eliminating mode mixing[J].Signal Processing,2014,96:362-374.

[16]SMITH J S.The local mean decomposition and its application to EEG perception data[J].J R Soc Interface,2005,2:443-454.

[17]YANG D,LIU Y,LI S,et al.Gear fault diagnosis based on support vector machine optimized by artificial bee colony algorithm[J].Mech Mach Theory,2015,90:219-229.

[18]LEI Y,HE Z,ZI Y.EEMD method and WNN for fault diagnosis of locomotive roller bearings[J].Expert Syst Appl,2011,38:7334-7341.

[19]ZHANG X,ZHOU J.Multi-fault diagnosis for rolling element bearings based on ensemble empirical mode decomposition and optimized support vector machines[J].Mech Syst Signal Process,2013,41:127-140.

[20]CHENG X,LI G,LI H.Research of planetary gear fault diagnosis based on multi-scale fractal box dimension of CEEMD and ELM[J].2017,63:45-55.

[21]LI X,DING F.Application of CEEMD-SVM in rolling bearing fault recognition[C]∥ 6th Int Conf Mechatronics.[S.l.]:Atlantis Press,2016,130:1497-1501.

[22]LI Z,WAN Z,XIONG X,et al.The application of LMD and BP neural network in gear fault diagnosis[J].[S.l.]:IEEE,2013:4609-4612.

[23]ZHANG J,MA W,LIN J,et al.Fault diagnosis approach for rotating machinery based on dynamic model and computational intelligence[J].Measurement,2015,59:73-87.

[24]ZHENG J.Rolling bearing fault diagnosis based on partially ensemble empirical mode decomposition and variable predictive model-based class discrimination[J].Arch Civ Mech Eng.Politechnika Wroc awska,2016,16:784-794.

[25]WEI Y,XU M,LI Y.A new gear fault diagnosis method based on improved local mean decomposition[M].Atl Press,2016,180:180-183.

[26]DRAGOMIRETSKIY K, ZOSSO D. Variational mode decomposition[J].IEEE Trans Signal Process,2014,62:531-544.

[27]LI Z,CHEN J,ZI Y,et al.Independence-oriented VMD to identify fault feature for wheel set bearing fault diagnosis of high speed locomotive[J].Mech Syst Signal Process,2017,85:512-529.

[28]ZHANG D,FENG Z.Application of variational mode decomposition based demodulation analysis in gearbox fault diagnosis[C]∥Conf Rec-IEEE Instrum Meas Technol Conf.Taipei,China:IEEE,2016.

[29]ZHANG M,JIANG Z,FENG K.Research on variational mode decomposition in rolling bearings fault diagnosis of the multistage centrifugal pump[J].Mech Syst Signal Process,2017,93:460-493.

[30]HUANG G B,ZHU Q Y,SIEW C K.Extreme learning machine:Theory and applications[J].Neurocomputing,2006,70:489-501.

[31]BECHHOEFER E.High speed gear dataset.Acoustics and Vibration Database[EB/OL].http://dataacoustics. com/measurements/gear-faults/gear-1/.[2013-05-18].(2016-10-15).

[32]MOHANTY S,GUPTA K K,RAJU K S.Comparative study between VMD and EMD in bearing fault diagnosis[C]∥Indusirial and Information System(ICIIS),9th International Conference.Gwalior:[s.n.],2014:2164-7011.

Muhd Firdaus Isham,Muhd Salman Leong,Meng Hee Lim,Zair Asrar Ahmad
《Transactions of Nanjing University of Aeronautics and Astronautics》2018年第1期文献

服务严谨可靠 7×14小时在线支持 支持宝特邀商家 不满意退款

本站非杂志社官网,上千家国家级期刊、省级期刊、北大核心、南大核心、专业的职称论文发表网站。
职称论文发表、杂志论文发表、期刊征稿、期刊投稿,论文发表指导正规机构。是您首选最可靠,最快速的期刊论文发表网站。
免责声明:本网站部分资源、信息来源于网络,完全免费共享,仅供学习和研究使用,版权和著作权归原作者所有
如有不愿意被转载的情况,请通知我们删除已转载的信息