Xin Jianghui,An Mujin,Zhang Yu,Ren Cheng long

(1.Department of Vehicle Engineering,Nanjing University of Technology,Nanjing,211167,P.R.China;2.College of Energy and Power Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing,210016,P.R.China)

INTRODUCTION

The feature extraction of the mechanical vibration signal is a key point in malfunction diagnosis[1]. A lot of analytical methods are raised and applied to the feature extraction and analysis of vibration signal in mechanical system in order to meet the needs of modern engineering,such as the wavelet analysis[2],the high order statistics analysis[3-4]. They have their own unique advantages as well as some shortcoming especially when dealing with signals under strong-noise circumstances[5].

Empirical mode decomposition (EMD)method, which is a new signal processing method,is raised by a Chinese scientist Huang E in 1999[6]. The progressive decomposition is performed adaptively using the EMD method based on different time scales of the original signals[7],and a series of intrinsic mode function(IMF)components are created,which have different characteristic scales. The feature information of the original signals is obtained by analyzing every IMF.But when the signal are mixed with a plenty of noise[8],layers of EMD are increased, which not only reduces the computational efficiency,but also causes the losing of physical meaning in serious situation.

After considering the disadvantage of EMD method under strong background noise, the multi-autocorrelation processing is applied to each input signal of the system in this paper firstly.Then every IMF is obtained after conducting EMD method to the processed signals.Finally the Hilbert transform and the spectral analysis are used in IMFs which we care about,to get the feature of the inputs.Simulation and experiment show that this method is effective.

1 IMPROVED EMD WITH MULTI-AUTOCORRELATION

1.1 Preprocessing using multi-autocorrelation

In order to reduce the noise influence on the input signals,the multi-autocorrelation method is applied to the preprocessing for every input signal.The concrete steps are listed below.

(1)Assume that{x(t),t∈ T}is a time doma in data sequence,and define the first-order autocorrelation function (i.e., the second correlation function)as

(2)Calculate the mean of the first-order autocorrelation function R1 obtained from step(1), and then get the second-order autocorrelation function R2,shown as

(3)Similarly,calculate the mean of the second-order autocorrelation function R2 obtained from step(2),and then get the third-order autocorrelation function R3,shown as

Through multi-autocorrelation method,the preprocessing of the data is performed in order to reduce the impact of noise on the original input signal and prepare for EMD in the following step.

1.2 EMD method

EMD method decomposes the original signal to limit different IMFs and draws the physical meaning of the instant frequency of every IM F.IMFs must be suitable for the following conditions[9].

(1)In the entire data length,the number of extreme and over zero must be equal or the difference is one at most.

(2)At any data point,the average of the envelope of the local maximmum and the local minimum must be zero.

The decomposition steps[10]of a analytical signal s(t)is shown as below.

(1)Curve fit all maximum and minimum points the signal s(t)using two cubic spline curves,so all data points are between the two curves.

(2)Let m(t)represent the average of the two curves.Suppose h(t)=s(t)-m(t),so h(t)is an approximate IMF.Then repeat the upper step to take h(t)as the new s(t)until h(t)satisfies the conditions of IMF.The first IM F c1(t)is

(3)Set r(t)=s(t)-c1(t),and r(t)is used as the new s(t).Repeat steps(1-2)so that the second IMF c2(t)is obtained.Similarly,other IMFs are obtained,so,the final decomposition is

In Eq.(5),r(t)is the residual function,which is a monotone function and a constant,and shows the average tend of the original signal.

1.3 Procedures of improved EMD

According to the content mentioned above,the implementation procedures of the improved EMD using multi-autocorrelation and EMD are expressed as follows.

(1)Process multi-autocorrelation in every input signal to reduce the impact of noise and prepare for EMD.

(2)Decompose the preprocessed signals using EMD and obtain IM Fs.

(3)Carry on the Hilbert transform and the spectral analysis in IMFs which we care about and obtain the useful message of characteristic frequencies.

Note that the magnitude at each frequency makes no sense,which aims to obtain the characteristics in frequency domain.

2 SIMULATION ANALYSIS

2.1 Simulation conditions

The simulation signal is an AM-FM signal without noise,shown as

Therefore,the frequency of AM-FM part of s1(t)is

The fundamental frequency of this part is 10 Hz, the following part sin80πt is at the frequency of 40 Hz.

Fig.1 shows the original signal of AM-FM without noise in the time domain. Fig.2 represents the corresponding expression after conducting multi-autocorrelation. Every IMF after EMD is shown in Fig.3.And the results after Hilbert transform and spectrum analysis are displayed in Fig.4.

Fig.1 Original AM-FM signal without noise

Fig.2 AM-FM signal after multi-autocorrelation without noise

Fig.3 Every IM F after EMD method without noise

Fig.4 Characteristic frequencies whithout noise

In order to observe the capability to extract characteristic of the original signals under strong noise conditions,a random noise which has zero mean and variance of 25is added to Eq.(6).And Figs.5-6 show the outcomes of the original and after conducting multi-autocorrelation in time domain.

Fig.5 Original AM-FM signal with noise

Fig.6 AM-FM signal after multi-autocorrelation with noise

Figs.7-8 show every IMF after processing EMD and the results after Hilbert transform and spectrum analysis respectively.

Fig.7 Every IM Fafter EM D method with noise

Fig.8 Characteristic frequencies with noise

Through the above simulations,it is clearly shown that the improved EMD method has good performance in extracting characteristic of the input signals under the strong noise conditions.

2.2 Performance test

In order to reflect the performance of the improved EMD method,the comparison is made between the results using the direct Hilbert-Huang transform[9]and the improved EMD method.Results are shown in Figs.9-10.

Fig.9 Signal characteristic using improved EMD method

Fig.10 Signal characteristic using Hilbert-Huang transformation

A conclusion is drawn from Fig.8 that when the source signal is mixed with a strong noise,using the improved EMD method, the characteristic can be extracted.While Figs.9-10 cannot show the feature clearly and even bring false features at the frequencies of 30,100,and 110 Hz.

The spectrum obtained from the improved EMD method can express the feature of signals mixed with strong noise which has zero mean.

3 EXPERIMENT AND RESULT ANALYSIS

When a vehicle is moving,it can severely affect riding comfort if the reis a serious vibration in the vehicle cab. Signal acquiring using traditional fault diagnosis method can bring strong background noise, which raises the difficulty when anglicizing.In this paper,the improved EMD is applied to the researches of the vehicle vibration signals and the further vibration fault diagnosis of vehicle cab.

According to the design parameters of the vehicle and the vibration situation,as well as the requirement of analyzing and processing, the sampling frequency is settled as 5 k Hz.Firstly,the ICP accelerometer is mounting in the corresponding location where the vibration is easy to be tested.After moving the vehicle at the speed of 45 km/h in the B-class road surface,the data is acquired.Finally the test data is analyzed.

Only 10 240 points are picked and used to draw the vibration signal of test vehicle cab floor,shown in Fig.11.Fig.12 is a series of time sequence processing by multi-autocorrelation and Fig.13 is IMFs after conducting the EMD method.Just like simulation,the characteristic message is obtained by processing Hilbert transform and spectrum analysis,shown in Fig.14.

Fig.11 Cab signal at vibration speed

Fig.12 Cab signal af ter multi-autocorrelation method

Similarly,10 240 points of the signal on the bridge are chosen at the speed of 45 km/h to conduct analysis.The input signals of the vehicle bridge in time domain and after multi-autocorrelation are shown in Figs.15-16,respectively.Fig.17 shows every IMF.

In Fig.18, the characteristic message is obtained by conducting Hilbert transform and spectrum analysis to every IM F.At the frequency of 3.36 Hz,the greater magnitude is shown,which indicates that the feature part is at this frequency point.

Fig.13 IMFs of cab board using EMD method

Fig.14 Spectrum of IMFs after Hilbert transform and spectrum analysis

Fig.15 Signal of vehicle bridge at vibration speed

Fig. 16 Signal of vehicle bridge after multi-autocorrelation

It can be seen in Figs.11-18 that the main frequency component of the cab floor and vehicle bridge is 3.36 Hzat the speed of 45 km/h.

Fig.17 Every IMF using EMD method

Fig.18 IMFs after Hilbert transform and spectrum analysis

It is known that the radius of the vehicle wheel is 502 mm and the error of speedometer is 16%based on the paper of car′s inspection,so we calculate that the frequency of wheel rotation is 3.33 Hz which matches the conclusion acquired above.Based on this point,the wheel rotation frequency is the excitation frequency and the imbalance of wheel is the main excitation source to the cab vibration.By balancing and positioning every wheel, this cab vibration is reduced significantly after redoing the experiment,which indicates the accuracy and feasibility of the improved EMD method.

In summary,the improved EMD method is successfully used to extract characteristics of vibration signals,which indicates that the method can beef fectively applied to practical engineering.

4 CONCLUSIONS

The following conclusions can be drew through the above analysis:

(1)Various feature extraction methods have their own disadvantages,but more satisfactory results can be obtained by the combination of several methods.

(2)The multi-autocorrelation preprocessing before using EMD method for decomposed signals can reduce the impact of noise.

(3)Compared with other methods,using the improved EMD method,the characteristics can be extracted more efficiently and the frequency message can be clearly seen through Hilbert transform and spectrum analysis.

(4)By simulation and experiment, the improved EMD method is successfully used in extracting features of test signals especially when signals are mixed with strong background noise,which proves the validity and some engineering application of the method.

[1] Chen Jin, Jiang Ming. The state-of-art of the application of the higher-order cyclosta tion ary statistics in mechanical fault diagnosis[J].Journal of Vibration Engineering,2001,14(2):121-134.(in Chinese)

[2] Peng Zhike,Chu Fulei.Application of the wavelet transform in machine condition monitoring and fault diagnostics: A review with bibliography [J].Mechanical Systems and Signal Processing,2004,18(2):199-221.

[3] Lee SK,White P R.Higher-order time-frequency analysis and its application to fault detection in rotating machinery [J]. Mechanical Systems and Sig5nal Processing,1997,11(4):637-650.

[4] Tommy W SC, Tan H Z. HOS-based nonparametric and parametric methodologies for machine fault detection[J].IEEE Transactions on Industrial Electronics,2000,47(5):1051-1059.

[5] Tang Bao ping,Dong Shaojiang,Song Tao.Method for eliminating mode mixing of empirical mode decomposition based on the revised blind source separation original research article[J]. Signal Processing,2012,92(1):248-258.

[6] Russell JC, Lardner T J. Experimental determination of frequencies and tension for elastic cables [J]. Journal of Engineering Mechanics,ASCE,1998,124:1067-1072.

[7] Li H,Deng X,Dai H.Structural damage detection using the combination method of EM D and wavelet analysis [J]. Mechanical Systems and Signal Processing,2007,21(1):298-306.

[8] Lei Yaguo,He Zhengjia,Zi Yanyang.Application of the EEMD method to rotor fault diagnosis of rotating machinery original research article [J].Mechanical Systems and Signal Processing,2009,23(4):1327-1338.

[9] Liao Qingbin,Li Shunming.A novel method for feature extraction of rotating machinery vibration signals[J].China Mechanical Engineering,2006,17(16):1675-1679.(in Chinese)

[10]Zhong Youmin,Qin Shunren. Research on the uniform theoretical basis for Hilbert-Huang transform [J]. Journal of Vibration and Shock,2006,25(3):40-43.(in Chinese)