A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition

Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp

A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition Lingjie Meng a,b, Jiawei Xiang a,n, Yanxue Wang b, Yongying Jiang a, Haifeng Gao a a b

College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou 325035, PR China School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China

a r t i c l e i n f o

abstract

Article history: Received 12 February 2014 Received in revised form 9 May 2014 Accepted 6 June 2014

Defective rolling bearing response is often characterized by the presence of periodic impulses, which are usually immersed in heavy noise. Therefore, a hybrid fault diagnosis approach is proposed. The morphological filter combining with translation invariant wavelet is taken as the pre-filter process unit to reduce the narrowband impulses and random noises in the original signal, then the purified signal will be decomposed by improved ensemble empirical mode decomposition (EEMD), in which a new selection method integrating autocorrelation analysis with the first two intrinsic mode functions (IMFs) having the maximum energies is put forward to eliminate the pseudo lowfrequency components of IMFs. Applying the envelope analysis on those selected IMFs, the defect information is easily extracted. The proposed hybrid approach is evaluated by simulations and vibration signals of defective bearings with outer race fault, inner race fault, rolling element fault. Results show that the approach is feasible and effective for the fault detection of rolling bearing. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Morphological filter Translation invariant wavelet Improved EEMD Rolling bearing Denoising Fault diagnosis

1. Introduction Rolling bearings cover a broad range of rotary machines and plays a crucial role in the modern manufacturing industry. The failures of rolling bearing can result in the deterioration of machine performance and it is significant to accurately and easily detect the existence and severity of a fault in the bearing. As the vibration signal carrying a great deal of information representing the mechanical equipment's health conditions, the use of vibration analysis has been established as the most common and reliable method of analysis in the field of condition monitoring and diagnostics of rotating machinery [1–4]. Additionally, the vibration signal is ordinarily non-stationary and non-linear, and the fault features are always immersed in heavy noise; therefore, the feature extraction of bearing fault signals is a relatively important problem. Conventional signal processing techniques, such as time-domain statistical analysis, Fourier transform, short-time Fourier transform (STFT), Wigner–Viller distribution (WVD), etc., are based on the assumption that the signals are stationary and linear [5–7], which is not in compliance with the actual situation. Wavelet transform (WT) has been a good choice to deal with the

n

Corresponding author. E-mail address: [email protected] (J. Xiang).

http://dx.doi.org/10.1016/j.ymssp.2014.06.004 0888-3270/& 2014 Elsevier Ltd. All rights reserved.

Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

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non-stationary signals [8–11]. However, WT suffers from the following disadvantages, such as the appropriate selections of the base function and certain frequency bands with defect information. Empirical mode decomposition (EMD) has been recently developed in fault diagnosis of rotating machinery [12–14]. EMD is based on the local characteristic time scales of a signal and could decompose the complicated signal into a set of complete and almost orthogonal intrinsic mode functions (IMFs) [15–20]. EMD is a self-adaptive signal processing method that can be applied to non-linear and non-stationary process perfectly. However, one of the major drawbacks of EMD is the mode mixing problem [21,22]. To alleviate this problem, ensemble empirical mode decomposition (EEMD) is developed by Wu and Huang [23]. However, in practical applications of EEMD, some problems need to be solved, e.g., the reducing of the narrowband impulses and random noises embedded in original signal, and the eliminating of the undesirable pseudo IMFs. To reduce the narrowband impulses, the morphological filter has been widely used because of its adaptive and robust performance in restraining positive and negative impulse [24,25]. To reduce the random noises, the translation invariant wavelet denoising method can inhibit the pseudo-Gibbs phenomenon and the random noises effectively [26]. To extract the real components from the IMFs obtained by EEMD, Peng et al. [27] proposed a simple method which uses the correlation coefficients of IMFs and the original signal as a criterion. All the correlation coefficients will be compared with a hard threshold (a ratio of the maximal correlation coefficients). However, in practical applications, the criteria of the ratio have not been defined clearly. The too big or too small ratios will lead to the elimination of real components or the failure of removing the pseudo low-frequency components, respectively. Therefore, the more feasible and effective method for the selection of IMFs need to be developed necessarily. For the above reasons, this paper presents a hybrid approach for the rolling bearing fault diagnosis. The combination of morphological filter and translation invariant wavelet is taken as the pre-filter process unit of EEMD. Then a new selection method integrating autocorrelation analysis with the first two IMFs having the maximum energies is proposed to eliminate the pseudo low-frequency components of IMFs. Applying the envelope analysis on the preserved real IMFs, the defect information is easy to be extracted. The paper is organized as follows. We briefly describe the fundamental theory of translation invariant wavelet and morphological filter in Sections 2.1 and 2.2, respectively. In Section 2.3, the combination of both methods is applied to a simulated signal to remove the narrowband impulses and random noises. The fundamental theory of EEMD and the proposed IMFs selection method is shown in Sections 3.1 and 3.2, respectively, and then a simulation analysis is carried out to validate the effectiveness of the selection method. In Section 4, the hybrid approach is verified using the vibration signals of defective bearings with outer race fault, inner race fault, and rolling element fault, respectively. Finally, the conclusions are drawn in Section 5. 2. Translation invariant wavelet and morphological filter 2.1. A brief introduction of translation invariant wavelet The wavelet denoising method has been most commonly used, especially the soft-threshold denoising method [28]. However, the traditional wavelet methods may result in visual artifact on discontinuities of signals at some circumstances, namely pseudo-Gibbs phenomenon, which lead to location discontinuity. If applying the translation invariant wavelet, this drawback would be alleviated [26]. Briefly, the process can be summarized as follows: Let H n ¼ fhj0 rh r ng denote the shift quantity, and Sh denote the circulant shift by h. For a signal xðtÞð0 r t rnÞ, the time domain translation results by Sh are shown as ðSh xÞt ¼ xðt þ hÞmod n

ð1Þ

where mod represents the modulus after division. Since the circulant shift is invertible, the reverse shift ðSh Þ  1 is represented by ðSh Þ  1 ¼ S  h

ð2Þ

If T represents the processing operation using the threshold denoising process, the final purified signal after a single shift processing is represented by x^ ¼ S  h ðTðSh xÞÞ

ð3Þ

where x^ is the final purified signal. Considering the contradiction that there may be several discontinuities in the signal, the best shift for one discontinuity might be the worst shift for another discontinuity. Therefore, the method of multiple average of circulant shift processing is usually adopted. The process is represented by x^ ¼ Aveh A H S  h ðTðSh xÞÞ

ð4Þ

where Ave is the average operation, H is the translation range and the biggest H is n. However, according to the above description, the shift parameter h has not been explicitly defined. More precisely, it appears that all the possible values of the shift parameter h need to be considered but not necessary. In fact, Beylkin [29] has already given a rapid way to perform the translation invariant wavelet transform for any possible h. The wavelet coefficients set obtained on any odd shift parameter h is equal to those using only a single circulant shift, whereas the wavelet coefficients set obtained on any even shift parameter h is equal to those without shift. Therefore, we can calculate Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

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the discrete wavelet transform (DWT) of the original signal as well as the single circulant shift signal, and then repeat the same DWT process at each decomposition level. Finally, all the possible wavelet coefficients on the whole shift parameters h are obtained. Reconstructing the low frequency scaling coefficients and the processed wavelet coefficients using the threshold shrinkage method, the final denoised signal is obtained. In addition, in order to obtain a good continuity, the soft-threshold shrinkage is employed in this paper, and the original signal will be decomposed into three levels with the ‘Sym8’ wavelet.

2.2. A brief introduction of morphological filter The morphological method was initially introduced in image processing by Serra [30], and later on, it was used in other areas such as signal processing [31–34]. The basic concept of morphological signal processing is to modify the shape of a signal, by transforming it through its intersection with another object called the structuring elements (SEs). There are four basic morphological operations, namely dilation, erosion, closing and opening, which form the foundation of the morphological method. Let f ðnÞ be the original 1-D discrete signal which is the function over a domain F ¼ ð0; 1; ⋯; N 1Þ, andgðmÞ be the SEs which is the discrete function over a domain G ¼ ð0; 1; ⋯; M  1ÞðM rNÞ. The above four basic operations can be defined as follows: Dilation ðf  gÞðnÞ ¼ max ff ðn  mÞ þ gðmÞg f1 rn rN; 1 r m r Mg

ð5Þ

Erosion ðf ΘgÞðnÞ ¼ min ff ðn þmÞ  gðmÞg f1 r n rN; 1 rm r Mg

ð6Þ

Closing ðf gÞðnÞ ¼ ðf  g ΘgÞðnÞ

ð7Þ

Opening ðf 3gÞðnÞ ¼ ðf Θg  gÞðnÞ

ð8Þ

where  , Θ,  and 3 denote the dilation, erosion, closing and opening operations, respectively. Ordinarily, the background noises are composed of random peaks and valleys. The morphological opening operation mainly smoothes and inhibits the noise of the signal's peaks, and can eliminate the scatters and burrs. The closing operation mainly eliminates the noise of the signal's valleys and can bridge the small grooves of the signal. Opening and closing are not mutually inverse functions, so they can be combined together to filter noise. The opening–closing F OC and closing–opening F CO filters are defined as F OC ðf ðnÞÞ ¼ ðf 3ggÞðnÞ

ð9Þ

F CO ðf ðnÞÞ ¼ ðf g3g ÞðnÞ

ð10Þ

F OC and F CO filters have all the features of the opening and closing operation. Although they can restrain positive and negative impulses, statistic bias still exists. Because of the opening operator's expansibility and the closing operator's contractibility, the output magnitude of the F OC filter becomes small, while the output magnitude of the F CO filter is large. In this case, the average weighted combination of close–opening and open–closing operation is adopted and defined as f^ ðnÞ ¼ ½F OC ðf ðnÞ Þ þ F CO ðf ðnÞ Þ=2

ð11Þ

where f^ is the purified signal. SE is another sticking point except the morphological operators; the attributes of SEs are controlled by its shape, height (amplitude), and length (domain). There are various kinds of SEs, such as flat SEs, triangular SEs and semicircular SEs. In the present study, the flat SE is used because it is the simplest and appears to be quite appropriate for detecting impulses [35–37]. In order to retain the shape characters of the signal entirely, all the heights of the flat SE are defined as zero [38,39]. All the studies show that the length of SEs is important for the morphological method, and the scholars developed various rules or guidelines for choosing the length of SEs [36–39]. For denoising, the selected length of SEs should be far less than that of signal, and greater than that of the narrowband impulses. In general, the width of pulsed noises in vibration signal is very narrow. Therefore, the SEs length is usually selected as the length of several sampling points [40]. According to Ref. [41], the SEs length selected in Sections 2.3 and 4 is three and five, respectively. Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

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2.3. The combination of morphological filter and translation invariant wavelet Evidently, there are two combination forms, translation invariant wavelet–morphological filter and morphological filter– translation invariant wavelet. To study the performances of those different combination forms, simulations will be carried using the following four denoising methods, respectively: (1) (2) (3) (4)

The The The The

morphological filter–translation invariant wavelet (marked as M–T); translation invariant wavelet–morphological filter (marked as T–M); morphological filter separately (marked as M); and translation invariant wavelet separately (marked as T).

Suppose the simulated signal xðtÞ is xðtÞ ¼ x1 ðtÞ þx2 ðtÞ þ x3 ðtÞ

ð12Þ

where x1 ðtÞ is the original signal represented by two harmonic waves as x1 ðtÞ ¼ sin ð2π 15tÞ þ 0:9 sin ð2π 30tÞ

ð13Þ

x2 ðtÞ is the Gaussian noise (signal to noise ratio SNR¼10 dB), and x3 ðtÞ is a series of alternating positive and negative impulses. Suppose the sampling frequency is 1024 Hz and the sampling points are 1024, the time domain waveforms of the original signal x1 ðtÞ and the noisy signal xðtÞ are shown in Fig. 1a and b, respectively. We can clearly see that the original signal is immersed in heavy noises. The denoising results of using the four methods are shown in Fig. 2a–d. The contrasts of the effects are measured by the signal to noise ratio (SNR) and the root mean square error (RMSE), which are defined as follows: ( ) 2 ∑N i ¼ 1 x ðiÞ SNR ¼ 10 log 10 ð14Þ ^ 2 ∑N i ¼ 1 ðxðiÞ  xðiÞÞ RMSE ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N ∑ ðxðiÞ  x^ ðiÞÞ2 Ni¼1

ð15Þ

where xðiÞ ði ¼ 1; 2; ⋯; NÞ is the original signal, the signal length is N, and x^ ðiÞ ði ¼ 1; 2; ⋯; NÞ is the purified signal. The results are shown in Table 1. As shown in Fig. 2a–c, the morphological filter can effectively eliminate the narrowband impulses almost completely, and the random noises to a certain extent as well. In contrast, Fig. 2d performs unsatisfactorily for the removal of narrowband impulses when using the translation invariant wavelet separately. From Table 1, the M–T has the maximum SNR (18.9734) and the minimum RMSE (0.1071); therefore, the M–T is the best choice for signal denoising.

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Fig. 1. The time domain waveform of the original signal and the noisy signal. (a) the original signal x1 (t) and (b) the noisy signal x(t).

Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

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Fig. 2. Comparison of denoised results obtained by different denoising algorithms. (a) M-T, (b) T-M, (c) M and (d) T. Table 1 The SNR and RMSE results of the four denoising methods. Evaluation index

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3. Improved ensemble empirical mode decomposition 3.1. Principles of EMD and EEMD EMD is an adaptive and efficient method applied to decompose non-linear and non-stationary signals [20]. Although EMD is well known and widely used, it suffers from a major drawback of mode mixing. Mode mixing is defined as ‘a single IMFs either consisting of signals of widely disparate scales, or a signal of a similar scale residing in different IMFs components’ [21]. To overcome this problem, a new noise-assisted data analysis method, EEMD, is proposed, which defines the real IMF components as the mean of an ensemble of trials. Each trial consists of the decomposition results of the signal plus a white noise of finite amplitude [23]. The detailed procedure of EEMD is as follows: (1) add a white noise series to the signal; (2) decompose the signal with added white noise into IMFs using traditional EMD; (3) return to step (1), and redo steps (1) and (2) for a predefined number of trials, each time with different white noise series of the same amplitude; and (4) obtain the ensemble mean of the corresponding IMFs as the final result as EEMD

p

xðtÞ þ nðtÞ - ∑ cj ðtÞ þ rðtÞ

ð16Þ

j¼1

where xðtÞ is the original signal, nðtÞ is the artificial added white noise, p is the IMF number of EEMD, cj ðtÞ is the IMFj and rðtÞ is the residuals. In addition, the added noise and the number of trials in the ensemble are two key parameters for the EEMD method. In this paper, the standard deviation of the added noise is 0.2 times that of the original signal, and the number of trials is 100, as suggested in Ref. [23]. 3.2. An integrated method for IMFs selection Because IMFs are almost the orthogonal representations for the original signal, the real components will have good correlations with the signal, whereas the pseudo components will not. To eliminate those pseudo components, Peng et al. [27] employed the correlation coefficients μi (i ¼ 1; 2; ⋯p;p is the number of IMFs) of IMFs and the signal as a criterion to decide which IMFs should be retained and which IMFs should be removed. To avoid eliminating the real IMFs with low Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

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amplitude, all IMFs and the signal will be normalized. Let xðtÞ denote the original signal, the normalization process is shown as follows: x0 ðtÞ ¼ ðxðtÞ  meanðxðtÞÞÞ=stdðxðtÞÞ

ð17Þ

0

where x ðtÞ is the normalized signal, the operations mean and std represent the mean value and the standard deviation of the original signal, respectively. Then, all the correlation coefficients μi will be compared with a hard threshold λ. The λ can be a ratio of the maximal μi as

λ ¼ maxðμi Þ=η ði ¼ 1; 2⋯; pÞ

ð18Þ

where η is a 1.0 bigger ratio factor and recommended as 10 in Ref. [27]. The method described above is straightforward and reasonable. However, in practical applications, the criteria of η have not been defined clearly. Too big or too small values of η will lead to the failure of removing the pseudo low-frequency components or the incorrect removing of real components, respectively. These situations will be performed in Section 4.1. To overcome this problem, the integrated method is developed. It is well known that the autocorrelation is the cross-correlation of a signal with itself [42]. One application of autocorrelation in signal processing is to strengthen the periodicity of signal. The characteristic signal of a faulty rolling bearing acts as a series of periodic impulses [33,37,43]. Therefore, we can take the advantage of autocorrelation to strengthen the periodicity of the signal and the IMFs as well. Meanwhile, the difference between the real components and the pseudo components will be increased. Then, we can extend the idea in Ref. [27] that we can use the correlation coefficients between the autocorrelation of IMFs and the original signal as a criterion to decide which IMFs should be retained and which IMFs should be eliminated. Additionally, all IMFs include different frequency bands ranging from high to low, and the first few IMFs will cover a wide frequency range at the high-frequency part. Considering that high-frequency band of vibration signal contains the key fault information of rolling bearing, the fault characteristics could be extracted from the first numbers of IMFs [16,44,45]. Therefore, the first two IMFs will be reserved simultaneously in the proposed integrated method. The process of integrated method proposed can be described as follows: (1) (2) (3) (4)

calculate the autocorrelation of both the original signal and each IMFs, and normalized; obtain all correlation coefficients μi (i ¼ 1; 2; ⋯p, p is the number of IMFs); compare all μi with a hard threshold λ (the λ is calculated by Eq. (18); and inspect whether the first two IMFs are reserved; if not, reserve the first two IMFs simultaneously.

However, the value of ratio factor η in Eq. (18) needs to be chosen reasonably. As it is known that the limiting correlation coefficient between the two variables is at most 1.0, generally speaking, if the correlation coefficient is greater than 0.5, we can conclude that there is a noticeable correlativity between the two variables according to the knowledge of statistics. In this case, the threshold 0.5 is half of limiting value 1, that is, the ratio factor η is 2 for Eq. (18). Extending this conceive, the hard threshold is set to the half of the maximal correlation coefficient of IMFs in the present study. In addition, the correlation coefficients between the normalized autocorrelation of IMFs and that of original signal are at most 1.0, the threshold 0.5 is the limiting value in the case of η ¼ 2. However, this is impossible because the maximal correlation coefficient is unlikely to be 1.0 in practice, and the threshold will adjust adaptively with the change of the maximal correlation coefficient for a certain signal. The simulations and experimental investigations below demonstrate that the ratio factor η ¼ 2 is reasonable. In order to make the advantage of the proposed selection method unique, the synthesized signal YðtÞ consisting of two components, x4 ðtÞ and δðtÞx5 ðtÞ, is constructed to simulate the characteristic of rolling bearing faults as YðtÞ ¼ x4 ðtÞ þ δðtÞx5 ðtÞ

ð19Þ

where x4 ðtÞ is the low frequency steady state signal x4 ðtÞ ¼ sin ð2π 50tÞ, x5 ðtÞ is the high frequency transient signal x5 ðtÞ ¼ 2 sin ð2π 250tÞ, δðtÞ is a switch operation defined as ( 1; t A ½0:048m  0:005; 0:048m þ 0:005 δðtÞ ¼ fm ¼ 1; 2; ⋯5g ð20Þ 0; t A others Suppose the sampling frequency is 1024 Hz and the sampling points are 256, the time domain waveform of the synthesized signal YðtÞ and its components x4 ðtÞ and δðtÞx5 ðtÞ are shown in Fig. 3(a-c), respectively. It can be seen that YðtÞ is a sine wave attached by small impulses. The decomposition results using EEMD are shown in Fig. 4, where r represents the residue component. IMF1 represents the small impulses, IMF2 and IMF3 represent the sine wave but both of them cannot separately describe the low frequency steady state signal x4 ðtÞ exactly, IMFs 4–7 and the residual component are the undesirable pseudo IMFs which have no obvious physical meaning. The combination signal of IMF2 and IMF3 is shown in Fig. 5; it is shown that the low frequency steady state signal x4 ðtÞ can be represented well. Therefore, the first three IMFs can approximate the simulation signal, and we think they are the real components that contain the ‘useful’ information. Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

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5

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Fig. 3. The time domain waveform of the simulated signal. (a) the Synthesized signal Y(t), (b) the low frequency steady state signal x4(t) and (c) the high frequency transient signal x5(t).

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When applying the proposed method for IMFs selection, we can automatically select the first three IMFs as the real components. Table 2 shows the correlation coefficients between the autocorrelation of the IMFs and the synthesized signal. According to the selection criterion, IMFs 1–3 should be preserved. The reconstructed signal using the preserved three IMFs is shown in Fig. 6a; it is seen that the original signal has been restored preferably. Measuring the RMSE defined above is 0.1076, and the result is acceptable by comparison with Table 1. The pseudo components including the end swing effect are evident in the new residue as shown in Fig. 6b. For these above reasons, the hybrid approach using morphological filter–translation invariant wavelet and improved EEMD is proposed. The complete process of the proposed method is shown in Fig. 7. Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

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Fig. 6. The time domain waveform of reconstructed signal and the final residue. (a) The reconstructed signal and (b) The final residue.

4. Experimental investigations In the section, the proposed approach is evaluated by defective bearings vibration signals. The vibration signals are acquired from the MFS-MG experimental platform as shown in Fig. 8. During the experimental investigations, the defective bearing of the type ER-12K is installed on the left side of the shaft and the normal bearing is on the right side. The specifications of the bearing are listed as follows: the pitch diameter of the bearing is 33.4772 mm; the number of rolling element is 8; the rolling element diameter is 7.9375 mm; and the contact angle is 01. A computer online monitoring system is available for data acquisition and the vibration signals of bearings with three fault types (including outer race fault, inner race fault and rolling element fault) were collected.

4.1. Analysis of the defective bearing with an outer race fault A typical vibration signal of defective bearing with an outer race fault is shown in Fig. 9. The measurement is performed with the sampling frequency of 12.8 kHz at the rotating speed of 1790 rpm. The frequency of rotor rotating f R is 29.83 Hz. Theoretically, the corresponding ball pass frequency in outer race (BPFO) is 90.96 Hz according to the specifications of the bearing. Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

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Bearings with accelerometers

Data acquisition

De-nosing Translation invariant wavelet

Morphological filter

Improved EEMD EEMD decomposition

Integrated method for IMFs selection

Analyze using the selected IMFs Fig. 7. The overall process of the proposed method.

From Fig. 9, it can be seen that due to the defect present in the rolling bearing, the vibration signal presents the periodicity impacts features, but there exist very serious ambient noises. Applying the M–T to filter the original signal, the purified signal is shown in Fig. 10. By comparing with Fig. 9, the ambient noises are effectively suppressed. Meanwhile, the periodicity impacts features are well reserved. In addition, it can be seen that the low frequency components in relation to the fault features have been retained; however, the high frequency components in relation to the natural frequency of the bearing have been removed. By applying the EEMD method to the purified signal, 12 IMFs are obtained. The decomposition results are given in Fig. 11a and b (1–6 IMFs are shown in Fig. 11a, 7–12 IMFs are shown in Fig. 11b). Form Fig. 11, it is not clear how many IMFs contain the ‘useful’ information; however, the impacts characteristics of the first three IMFs are evident. Applying the proposed selection method, the correlation coefficients μ between the normalized autocorrelation of IMFs and that of the original signal are shown in Table 3. In accordance with the selection criterion, it is just the first three IMFs that have been preserved. The envelope spectra of those selected IMFs are shown in Fig. 12a–c. From Fig. 12, the rotating frequency f s and the fault characteristic frequency as well as its multiplication frequencies (181.9 Hz and 272.8 Hz) are clearly revealed. There is a good match between the expected spectrum features and the actual situation associated with the bearing with an outer race fault. By contrast, applying the method in Ref. [27] for IMFs selection, the correlation coefficients μ between IMFs and the original signal are shown in Table 4. The value of ratio factor η are 10.0 (η1 ¼ 10, as used in Ref. [27]) and 2 (η2 ¼ 2, as used in this paper). When η1 ¼ 10, after selection the first seven IMFs are preserved. From Fig. 11, it is obvious that the pseudo lowfrequency components are still existent. By increasing the threshold, the value of η is 2 as used in this paper; after selection the IMFs 2–4 remains, but IMF1 is wrongly removed. The comparisons show that the integrated method proposed in this paper is more effective. 4.2. Analysis of the defective bearing with an inner race fault For the rotor with a rotating speed of 1792 rpm, vibration signal of the defective bearing with an inner race fault is shown in Fig. 13a, sampled with the frequency of 25.6 kHz. The corresponding ball pass frequency in the inner race (BPFI) is Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

L. Meng et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

10

Fig. 8. The MFS-MG experimental platform.

Amplitude(m/s 2)

0.2 0.1 0 -0.1 -0.2

0

0.1

0.2

0.3

0.4

0.5

0.6

Time(s)

Amplitude(m/s 2)

4

x 10

-3

3 2 1 0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 Frequency(Hz)

Fig. 9. The time domain waveform and frequency spectrum of the original signal. (a) the time domain waveform and (b) the frequency spectrum.

2

)

0.05

0

-0.05 0

0.1

0.2

0.3

0.4

0.5

0.6

Time(s)

Amplitude(m/s 2)

4

x 10

-3

3 2 1 0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 Frequency(Hz)

Fig. 10. The time domain waveform and frequency spectrum of the purified signal. (a) the time domain waveform and (b) the frequency spectrum.

Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

L. Meng et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

IMF2

IMF1

0 -0.02

0

0.5

0.05

IMF3

0.05

0.02

0 -0.05

0

IMF5 -3

IMF8

2

0 -2

0

-3

0

5

0

x 10

0.5

x 10

0

-4

5

0

Time(s)

0.5 Time(s)

0 -5

-3

0 -1

IMF12

-3

0 -1

0.5 Time(s)

Time(s)

IMF11

IMF10

x 10

1

0.5

Time(s) 1

0

-3

0

-3

0 -5

0.5 Time(s)

x 10

0.5

x 10

5

0 -2

0.5

x 10

0 -5

0.5 Time(s)

x 10

0

Time(s)

IMF9

IMF4 IMF7

2

0

-0.05

0.5

IMF6

5

0 -0.01

0

Time(s)

Time(s) 0.01

11

Time(s)

-5

0 -5

0.5

x 10

0

0.5 Time(s)

Fig. 11. The decomposition results using EEMD. (a) 1-6 IMFs and (b) 7-12 IMFs.

Table 3 The correlation coefficients between the autocorrelation of IMFs and that of the original signal. IMF1 μ

IMF2

IMF3

IMF4

IMF5

IMF6

0.0238

0.8215

0.8750

0.3510

0.0751

0.0204

IMF7

IMF8

IMF9

IMF10

IMF11

IMF12

μ

0.0333

0.0069

0.0151

0.0033

0.0043

0.0055

λ

maxðμi Þ=η ¼ 0:8750=2 ¼ 0:4375

147.84 Hz and the frequency of rotor rotating f s is 29.87 Hz. The purified signal using M–T is shown in Fig. 13b. By comparing Fig. 13a with 13b, we get to know that the periodicity impacts features caused by fault are strengthened and the ambient noises are effectively suppressed. Applying the EEMD, 12 IMFs are obtained and will not be shown in the present study. Calculating the correlation coefficients μ between the normalized autocorrelation of IMFs and that of the original signal, the results are shown in Table 5. In accordance with the selection criterion, the first four IMFs are retained as the real components. The envelope spectra of IMF1 containing the most abundant fault feature frequency in the four retained IMFs are shown in Fig. 14. From Fig. 14, the BPFI together with its harmonics and the side frequencies modulated by the rotor rotating frequency are prominent. Therefore, we can conclude that there exists an inner race fault in the bearing. 4.3. Analysis of the defective bearing with a rolling element fault For the sampling frequency of 12.8 kHz, the vibration signal of the rolling element bearing with a rolling element fault is measured at the rotor of rotating speed of 2390 rpm. The ball spin frequency (BSF) is 79.36 Hz. The original vibration signal Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

L. Meng et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

Amplitude(m/s 2)

12

2

fs

BPFO

2BPFO

3BPFO

1 0

0

50

100

150

200

250

300

200

250

300

250

300

Amplitude(m/s 2)

Frequency(Hz)

20

fs

BPFO

10 0

0

50

100

150

Amplitude(m/s 2)

Frequency(Hz)

10

BPFO

fs

2BPFO

5 0

0

50

100

150

200

Frequency(Hz)

Fig. 12. The envelope spectrum of the first three IMFs. (a) IMF1, (b) IMF2 and (c) IMF3.

Table 4 The correlation coefficients between IMFs and the original signal. IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

0.1167

0.7584

0.7853

0.4067

0.2315

0.1190

IMF7

IMF8

IMF9

IMF10

IMF11

IMF12

μ

0.0939

0.0567

0.0337

0.0275

0.0232

0.0226

λ

maxðμi Þ=10 ¼ 0:07853

μ

maxðμi Þ=2 ¼ 0:39265

Amplitude(m/s 2)

1 0.5 0 -0.5 -1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.4

0.5

0.6

Time(s)

Amplitude(m/s 2)

0.2 0.1 0 -0.1 -0.2

0

0.1

0.2

0.3 Time(s)

Fig. 13. The time domain waveform of the original signal and the purified signal.

Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

L. Meng et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

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Table 5 The correlation coefficients between the autocorrelation of IMFs and that of the original signal. IMF1

IMF2

0.0111 IMF7

μ

0.0361

λ

maxðμi Þ=η ¼ 0:6836=2 ¼ 0:3418

IMF4

IMF5

IMF6

0.0775

0.6836

0.5214

0.1783

0.0633

IMF8

IMF9

IMF10

IMF11

IMF12

0.0159

0.0132

0.0538

0.0599

0.0096

12

4BPFI+fs

4BPFI

3BPFI+fs

3BPFI-fs

2BPFI-fs

6

2BPFI

BPFI

BPFI-fs

Amplitude(m/s 2)

8

3BPFI

fs

10

BPFI+fs

μ

IMF3

4 2 0

0

100

300

200

400

500

600

700

Frequency(Hz) Fig. 14. The envelope spectrum of IMF1.

Amplitude(m/s 2)

0.4 0.2 0 -0.2 -0.4

0

0.2

0.4

0.6

0.8

1

1.2

0.8

1

1.2

Time(s)

Amplitude(m/s 2)

0.1 0.05 0 -0.05 -0.1

0

0.2

0.4

0.6 Time(s)

Fig. 15. The time domain waveform of the original signal and the purified signal.

and the purified signal using the M–T denoising method are shown in Fig. 15a and b, respectively. The comparison shows the effectiveness of the denoising method. Applying the EEMD, 12 IMFs are obtained and will not be shown in the present study. Calculating the correlation coefficients μ between the normalized autocorrelation of IMFs and that of the original signal, the results are shown in Table 6. Using the proposed selection criterion, the IMF1, IMF2, IMF4 and IMF5 are retained as the real components. Applying the envelope analysis to the four retained IMFs, both the IMF4 and IMF5 contain the most distinct fault feature frequency. The envelope spectra of IMF4 and IMF5 are shown in Fig. 16a and b, respectively. From Fig. 16, the frequency of 79.36 Hz corresponding to characteristic frequency of rolling element fault is clearly identified. It reveals that the proposed hybrid method is effective for the fault detection of rolling bearing. Through the above experimental investigations, we can get to know that the M–T can effectively suppress the noises, and the proposed integrated method can appropriately select the real components from the IMFs. The results demonstrate that the proposed approach can effectively extract the fault features of defective bearings. Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i

L. Meng et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

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Table 6 The correlation coefficients between the autocorrelation of IMFs and that of the original signal. IMF2

IMF3

IMF4

IMF5

IMF6

0.0122

0.1465

0.2581

0.7796

0.8168

0.2582

IMF7

IMF8

IMF9

IMF10

IMF11

IMF12

μ

0.2276

0.0060

0.0072

0.0101

0.0129

0.0146

λ

maxðμi Þ=η ¼ 0:8168=2 ¼ 0:4084

μ

Amplitude(m/s 2)

10

BSF

IMF1

fs

5

0

0

20

40

60

80

100

120

140

160

180

200

140

160

180

200

Frequency(Hz)

fs

BSF

Amplitude(m/s 2)

10

5

0

0

20

40

60

80

100

120

Frequency(Hz)

Fig. 16. The envelope spectrum of IMF4 and IMF5.

5. Conclusion This paper proposes a hybrid approach for the fault detection of rolling element bearing. The morphological filter combining with translation invariant wavelet is taken as the pre-filter to denoise the narrowband impulses and random noises. An integrated method is proposed for the reasonable selection of the real components from IMFs obtained using EEMD. Its efficiency has been evaluated on simulation analysis and the experimental signals are measured from defective bearings with three characterized types faults. The results show that the proposed hybrid approach is feasible and effective for the fault detection of rolling bearing.

Acknowledgments The authors are grateful to the support from the National Natural Science Foundation of China (No. 51175097) and the Zhejiang Provincial Natural Science Foundation for Excellent Young Scientists (No. LR13E050002) and the Project sponsored by SRF for ROCS, SEM. References [1] M. Žvokelj, S. Zupan, I. Prebil, Non-linear multivariate and multiscale monitoring and signal denoising strategy using Kernel Principal Component Analysis combined with Ensemble Empirical Mode Decomposition method, Mech. Syst. Signal Process. 25 (2011) 2631–2653. [2] P.E. William, M.W. Hoffman, Identification of bearing faults using time domain zero-crossings, Mech. Syst. Signal Process. 25 (2011) 3078–3088. [3] S.F. Yuan, F.L. Chu, Fault diagnostics based on particle swarm optimisation and support vector machines, Mech. Syst. Signal Process. 21 (2007) 1787–1798. [4] Y. Lei, Z. He, Y. Zi, EEMD method and WNN for fault diagnosis of locomotive roller bearings, Expert Syst. Appl. 38 (2011) 7334–7341. [5] Z.K. Peng, F.L. Chu, Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography, Mech. Syst. Signal Process. 18 (2) (2004) 199–221. [6] Y.G. Lei, Z.J. He, Y.Y. Zi, Application of an intelligent classification method to mechanical fault diagnosis, Expert Syst. Appl. 36 (6) (2009) 9941–9948. [7] Y. Lei, J. Lin, Z. He, et al., A review on empirical mode decomposition in fault diagnosis of rotating machinery, Mech. Syst. Signal Process. 35 (1) (2013) 108–126.

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Please cite this article as: L. Meng, et al., A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition, Mech. Syst. Signal Process. (2014), http://dx.doi.org/ 10.1016/j.ymssp.2014.06.004i