Making EEMD more effective in extracting bearing fault features for intelligent bearing fault diagnosis by using blind fault component separation

Abstract

Rolling element bearings are widely used in machinery, such as cooling fan, railway axle, centrifugal pump, transaction motor, gas turbine engine, wind turbine gearbox, etc., to support rotating shafts. Bearing failures will accelerate failures of other adjacent components and finally result in the breakdown of systems. To prevent any unexpected accidents and reduce economic loss, condition monitoring and fault diagnosis of rolling element bearings should be immediately conducted. Ensemble empirical mode decomposition (EEMD) as an improvement on empirical mode decomposition is a data-driven algorithm to adaptively decompose vibration signals collected from the casing of machinery for bearing fault feature extraction without the requirement of expertise and thus its easy usage attracts much attention in recent years from readers and engineers. The direct applications of EEMD to preprocessing bearing fault signals for intelligent bearing fault diagnosis can be found in lots of publications and conferences every year. However, such applications are not always effective in extracting bearing fault features because the Fourier spectrum of the first intrinsic mode function is too wide and contains many unwanted strong low-frequency periodic components. In this paper, according to results from the analyses of industrial railway axle bearing fault signals, we experimentally show that the direct use of EEMD is not always effective in extracting bearing fault features. Further, to make EEMD more effective, we introduce the concept of blind fault component separation to separate low-frequency periodic vibration components from high-frequency random repetitive transients, such as bearing fault signals. Results show that the idea of blind fault component separation is much helpful in enhancing the effectiveness of EEMD in extracting bearing fault features in the case of industrial railway axle bearing fault diagnosis.

Keywords

Ensemble empirical mode decomposition intelligent bearing fault diagnosis fault feature extraction blind fault component industrial railway axle

1 Introduction

Machine fault diagnosis is a recent hot topic to identify different faults of engineering systems and critical components, such as diesel engine [1], valve actuator [2], etc. Rolling element bearings are the most critical components used in machinery, such as cooling fan, railway axle, centrifugal pump, transaction motor, gas turbine engine, wind turbine gearbox, etc., to support rotating shafts. Their failures will accelerate failures of other adjacent components and finally result in failures of systems [3, 4]. Thus, condition monitoring and fault diagnosis of rolling element bearings attract much attention from readers and engineers to prevent any unexpected accidents and reduce economic loss [5, 6]. When there is a defect on the surface of either an outer race or an inner race, impacts generated by rollers striking the defect excite resonant frequencies of a machine over time and then repetitive transients are observed in vibration signals collected from the casing of the machine. Because of the interruptions from heavy noises and other unwanted vibration components, such as strong low-frequency periodic vibration components, bearing fault signals are easily overwhelmed and they are difficult to be directly recognized [7, 8]. Consequently, signal processing methods are required to preprocess bearing fault signals before condition monitoring and fault diagnosis of rolling element bearings are conducted [9, 10].

Empirical mode decomposition (EMD) [11] and its improvement called ensemble empirical mode decomposition (EEMD) [12] are two most popular and attractive signal processing methods for preprocessing bearing fault signals and they do not need complicated mathematical equations to be interpreted so that readers can quickly and easily understand their fundamental principles. More interestingly, EMD and EEMD are able to adaptively decompose a signal into some intrinsic mode functions (IMFs) without the requirement of expertise so that EMD and EEMD are easy-in-use in machine fault diagnosis to preprocess vibration signals collected from the casing of a machine. In recent years, many EMD and EEMD based diagnostic works have been reported [13]. Feng et al. [14] proposed EEMD based Teager energy spectrum for bearing fault diagnosis and EEMD based energy separation for fault diagnosis of wind turbine planetary gearboxes [15]. Lei et al. [16] proposed to use EEMD and wavelet neural network to achieve high diagnostic accuracies of locomotive roller bearings. In their further works, Lei et al. [17] proposed adaptive EEMD to overcome the mode mixing problem still existing in EEMD and they proposed the concept of sensitive IMFs for machine fault diagnosis [18]. Peng et al. [19, 20] used wavelet packets to preprocess vibration data prior to the use of EMD so as to increase the decomposition ability of EMD. By using the similar idea with those proposed by Peng et al. [19, 20], Guo et al. [21] proposed using spectral kurtosis instead of wavelet packets prior to the use of EEMD for extraction of bearing fault features. Furthermore, Guo et al. [22] investigated the influence of different parameters of EEMD on the decomposition performance of EEMD. He et al. [23] proposed a midpoint-based EMD for machine fault diagnosis and their results showed that their proposed midpoint based EMD is more effective than the envelope based EMD for decomposition of gearbox vibration signals. Yan and Gao [24] proposed using EMD based Hilbert transform to extract instantaneous frequency components for machine health monitoring. Zhang et al. [25] proposed using band-limited noises to efficiently fasten the calculation procedure of EEMD for decomposition of a signal mixture. Wang et al. [26] proposed an enhanced EEMD to automatically fuse IMFs with similar characteristics for realizing the concept of blind fault component separation. Yang and Yu [27] proposed the combination of IMFs obtained by EMD and then employed SVM for intelligent bearing fault diagnosis. Cheng et al. [28] used the integration of EMD and autoregressive model for bearing fault diagnosis. Malik and Sharma [29] proposed using EMD to decompose post fault current signals and then employed artificial neural networks to classify different faults existing in a transmission line.

Besides the aforementioned works relevant to EMD and EEMD, the direct applications of EMD and EEMD to preprocessing bearing fault signals for intelligent bearing fault diagnosis can be found in lots of publications and conferences every year [13]. However, such direction applications of EMD and EEMD are not always effective in extracting bearing fault features because the Fourier spectrum of the first IMF is too wide and contains many unwanted strong low-frequency periodic components. In this paper, firstly, according to results from the analyses of industrial railway axle bearing fault signals, we experimentally show that the direct use of EEMD is not always effective in extracting bearing fault features. Secondly, we suggest using the concept of blind fault component separation to preprocess bearing fault signals prior to EEMD and bearing fault feature extraction used in intelligent bearing fault diagnosis. Blind fault component separation aims to separate low-frequency periodic vibration components from high-frequency random repetitive transients, such as bearing fault signals. At last, results show that our idea is much helpful in enhancing the effectiveness of EEMD in extracting bearing fault features in the case of industrial railway axle bearing fault diagnosis.

The organization of this paper is outlined as follows. In Section 2, the problem of EMD and EEMD for bearing fault diagnosis is formulated. In Section 3, the concept of blind fault component separation is introduced to preprocess bearing fault signals prior to the easy usage of EEMD and it makes EEMD more effective in extracting bearing fault features. In Section 3, a case study of industrial railway axle bearing fault diagnosis is provided to show that blind fault component separation is beneficial and helpful to the use of EEMD for bearing fault diagnosis. Conclusions are drawn at the last section.

2 Problem formulation of EEMD

EEMD is an easy-to-use and adaptive signal processing method to decompose a signal into some IMFs and it attracts much attention from readers and engineers to reprocess vibration signals collected from the casing of a machine for extracting bearing fault features. The fundamental principle of EEMD is introduced as follows.

Step 1. firstly, EEMD has two parameters including the amplitude a of white noises, which is a fraction L_N of the standard deviation of a signal x(n) to be analyzed, and the ensemble number N_E. Here, L_N can be regarded as an added noise level. In this step, an ensemble index m is initialized to 1.

Step 2. Conduct the m^th EMD on a signal x_m(n) corrupted by white noises, namely x_m(n) = x(n) + n_m(n), where n_m(n) is a time series of white noises with the pre-setting noise amplitude. For the m^th EMD, IMFs are denoted as c_i_,m, (i = 1, 2, \dots, N-1) and a residue, r_m. Here, N-1 is the number of IMFs. The details of EMD are well-known in the research field of adaptive signal processing and machine fault diagnosis [13]. For the details of EMD, please refer to reference [11] and a review article [13].

Step 3. Repeat Step 2 by increasing m = m + 1 until the ensemble index m reaches the ensemble number N_E.

Step 4. Calculate the ensemble mean of the i^th IMFs at different ensemble indices j = 1,2,\dots, N_E. Finally, the signal x(t) is decomposed as the sum of IMFs and a residue, i.e. $x (n) = \sum_{i = 1}^{N - 1} {\bar{c}}_{i} + \bar{r},$ (1) where ${\bar{c}}_{i}$ is the ensemble mean of the i^th IMFs at different ensemble indices and $\bar{r}$ is the ensemble mean of all residues. In reference [12], Wu and Huang pointed out that the relationship among the ensemble number N_E, the amplitude of the added white noise a, and the standard deviation of accumulative error e can be formulated as follows: $lne + (a / 2) \cdot ln N_{E} = 0 .$ (2)

It was recommended that the amplitude of the added white noise is approximately 0.2 of a standard deviation of the signal x(t) and the ensemble number N_E is a few hundreds. Additionally, it should be noted that, if the ensemble number N_E and the noise amplitude are set to 1 and 0, respectively, EEMD is reduced to EMD.

The problem of EEMD is that the Fourier spectrum of the first IMF is too wide so that bearing fault features are possible to be overwhelmed by strong low-frequency periodic vibration components. An example, in which EEMD fails to extract industrial railway axle bearing fault features, is given in the following to show that the direct use of EEMD is not always effective in bearing fault feature extraction. In Fig. 1 (a), the temporal signal of an industrial railway axle bearing outer race fault signal is plotted.

Fig.1

Temporal signals in the case of the industrial outer race defects: (a) a railway axle bearing outer race fault signal; (b) the first IMF obtained by EEMD; (c) the second IMF obtained by EEMD; (d) the third IMF obtained by EEMD.

After EEMD is directly applied to process the railway axle bearing outer race fault signal, the first three IMFs are plotted in Fig. 1 (b) to (d) and their corresponding Fourier spectra are plotted in Fig. 2 (a) to (c), respectively. In Fig. 2 (a), it is clear to see that the first IMF covers a too wide frequency range from a very high-frequency of 4500 Hz to a very low-frequency of 500 Hz. To extract bearing defect frequencies, such as bearing outer race defect frequency and its harmonics, squared envelope spectrum analysis is further conducted on the IMFs in Fig. 1 (b) to (d). The squared envelope spectra of the first three IMFs are respectively plotted in Fig. 3 (a) to (c), where no bearing defect frequencies can be clearly detected. Hence, in this instance, the direct use of EEMD to extracting bearing fault features fails to provide any useful signatures for the fault diagnosis of the railway axle bearing.

Fig.2

Frequency spectra of the first three IMFs obtained by EEMD in the case of the industrial outer race defects: (a) the frequency spectrum of the first IMF; (b) the frequency spectrum of the second IMF; (c) the frequency spectrum of the third IMF.

Fig.3

Squared envelope spectra of the first three IMFs in the case of the industrial outer race defects: (a) the squared envelope spectrum of the first IMF; (b) the squared envelope spectrum of the second IMF; (c) the squared envelope spectrum of the third IMF.

3 Making EEMD more effective in extracting bearing fault features for intelligent bearing fault diagnosis by using blind fault component separation

In Section 2, we have experimentally shown an instance study, in which EEMD fails to extract bearing fault features due to the interruption of the low-frequency periodic components. In this section, we will propose a simple and effective strategy to make EEMD more effective in extracting bearing fault features. Our idea is inspired by blind fault component separation, which aims to separate low-frequency periodic vibration components from high-frequency random repetitive transients, such as bearing fault signals. In other words, the influence of low-frequency periodic vibration components are partly removed from an original vibration mixture before high-frequency random repetitive transients are to be further analyzed. Nowadays, some algorithms including a short-time Fourier transform based algorithm [30], auto-regressive (AR) filtering [31], active noise cancellation [31], an adaptive eigenvector algorithm [32], continuous wavelet transform [33], etc, are available to realize blind fault component separation. Except AR filtering, other algorithms are able to directly extract repetitive transients, especially bearing fault signals. Hence, in this paper, auto-regressive (AR) filtering is adopted to remove the influence of low-frequency periodic components and retain only random components prior to the use of EEMD. The fundamental equation of AR filtering is given as follows [34]: $x (n) = - \sum_{p = 1}^{p = q} a (p) x (n - p) + v (n),$ (3)

where v (n) is a random part. The parameters a (p) of an AR filter are obtained by solving the Yule-Walker equations via the Levinson-Durbin recursion algorithm [34]. q is the order of AR filtering which is determined by minimizing Akaike information criterion. In bearing fault diagnosis, according to our expertise, an AR order of 50 to 100 is sufficiently large [35]. The Fourier transform of Equation (3) can be written as: $v (f) = x (f) a (f) .$ (4) where v (f) is the Fourier spectrum of the random part v (n); x (f) is the Fourier spectrum of the signal x (n); a (f) is the Fourier spectrum of the AR filter.

In Equation (4), only random components, namely bearing fault signals, are retained after AR filtering is conducted. Then, EEMD is further used to decompose the reprocessed signal into IMFs. At last, squared envelope spectrum analysis is conducted on IMFs to identify different bearing faults [8]. The flowchart of the proposed idea is summarized in Fig. 4.

Fig.4

The flowchart of the proposed idea for making EEMD more effective in extracting bearing fault features for intelligent bearing fault diagnosis.

4 A case study of industrial railway axle bearing fault diagnosis

All experiments introduced in this paper were conducted in the State Key Laboratory of Traction Power, at the Southwest Jiaotong University [36]. Two kinds of industrial railway axle bearing fault signals were collected to verify the effectiveness of the proposed idea. The platform of the experiments is plotted in Fig. 5 (a) and the industrial railway axle bearing defects are shown in Fig. 5 (b) and (c), respectively. Moreover, it should be noted that these bearing defects were not artificially seeded and they were found in an in-service industrial train. According to the different combinations of different industrial bearing defects, the first bearing fault signal to be analyzed is a railway axle bearing outer race fault signal plotted in Fig. 1 (a) and the second bearing fault signal is a railway axle multiple bearing fault signal caused by the outer race defects and the roller defect. In all experiments, the shaft rotation frequency and the sampling frequency were set to f_r = 10.28Hz and F_s = 10kHz, respectively. The bearing outer race defect frequency, the cage frequency/the fundamental train frequency and the ball spinning frequency were calculated as f_O = 83.23Hz, f_C = 4.39Hz and f_BS = 33.93Hz, respectively.

Fig.5

The experimental platform and two kinds of bearing defects found in an in-service train: (a) the design of the experimental platform; (b) three industrial bearing outer race defects; (c) an industrial bearing roller defect.

In Section 2, it is found that the direct use of EEMD fails to provide any bearing fault signatures for the fault diagnosis of the industrial railway axle bearing outer race. Following this analysis, we conduct the AR filtering with the order of 50 to preprocess the railway axle bearing outer race fault signal and we plot the reprocessed signal in Fig. 6 (a). After that, the signal reprocessed by the AR filtering is further processed by using EEMD. The first three IMFs and their corresponding frequency spectra are plotted in Figs. 6 and 7, respectively. In Fig. 7(a), the high-frequency vibration components are much more outstanding compared with the frequency spectrum plotted in Fig. 2 (a). To extract bearing fault features, squared envelope spectrum analysis is applied to process the first three IMFs plotted in Fig. 6 (b) to (d) and the squared envelope spectra of the first three IMFs are shown in Fig. 8 (a) and (c), respectively. In Fig. 8 (a) and (b), the bearing outer race defect frequency f_O = 83.23 Hz and its first harmonic are clear to be detected, which connotes that the bearing suffered from the bearing outer race defects.

Fig.6

Temporal signals after AR filtering is conducted in the case of the industrial outer race defects: (a) the temporal signal of the railway axle bearing outer race fault signal preprocessed by AR filtering; (b) the first IMF obtained by EEMD; (c) the second IMF obtained by EEMD; (d) the third IMF obtained by EEMD.

Fig.7

Frequency spectra after AR filtering is conducted in the case of the industrial outer race defects: (a) the frequency spectrum of the first IMF; (b) the frequency spectrum of the second IMF; (c) the frequency spectrum of the third IMF.

Fig.8

Squared envelope spectra after AR filtering is conducted in the case of the industrial outer race defects: (a) the squared envelope spectrum of the first IMF; (b) the squared envelope spectrum of the second IMF; (c) the squared envelope spectrum of the third IMF.

In the second instance, the temporal signal of a railway axle multiple fault signal caused by the industrial outer race defects and the industrial roller defect is plotted in Fig. 9 (a) and it is directly processed by using EEMD firstly. The first three IMFs obtained by using EEMD are plotted in Fig. 9 (b) to (d), respectively. The frequency spectra and the squared envelope spectra of the first three IMFs are plotted in Figs. 10 and 11, respectively. In Fig. 11, the outer race defect frequency f_O = 83.23 Hz and its harmonics indicate the existence of the outer race defects. At the same time, the cage frequency f_C = 4.39 Hz and the ball spinning frequency f_BS = 33.93 Hz and its several harmonics indicate the occurrence of the roller defect. Consequently, in the second instance, both the bearing outer race defects and the bearing roller defect are successfully detected by using EEMD.

Fig.9

Temporal signals in the case of the multiple industrial bearing defects: (a) the temporal signal of a railway axle multiple fault signal; (b) the first IMF obtained by EEMD; (c) the second IMF obtained by EEMD; (d) the third IMF obtained by EEMD.

Fig.10

Frequency spectra in the case of the multiple industrial bearing defects: (a) the frequency spectrum of the first IMF; (b) the frequency spectrum of the second IMF; (c) the frequency spectrum of the third IMF.

Fig.11

Squared envelope spectra of the first three IMFs in the case of the multiple industrial bearing defects: (a) the squared envelope spectrum of the first IMF; (b) the squared envelope spectrum of the second IMF; (c) the squared envelope spectrum of the third IMF.

Fig.12

Temporal signals after AR filtering is conducted in the case of the multiple industrial bearing defects: (a) the temporal signal of a railway axle multiple fault signal preprocessed by AR filtering; (b) the first IMF obtained by EEMD; (c) the second IMF obtained by EEMD; (d) the third IMF obtained by EEMD.

Fig.13

Frequency spectra after AR filtering is conducted in the case of the multiple industrial bearing defects: (a) the frequency spectrum of the first IMF; (b) the frequency spectrum of the second IMF; (c) the frequency spectrum of the third IMF.

Fig.14

Squared envelope spectra after AR filtering is conducted in the case of the multiple industrial bearing defects: (a) the squared envelope spectrum of the first IMF; (b) the squared envelope spectrum of the second IMF; (c) the squared envelope spectrum of the third IMF.

For a comparison, the multiple bearing fault signal reprocessed by using AR filtering with an order of 50 is plotted in Fig. 12 (a). Then, EEMD is applied to process the signal reprocessed by using AR filtering and the first three IMFs are plotted in Fig. 12 (b) to (d), respectively. The frequency spectra and the squared envelope spectra of the first three IMFs after AR filtering are plotted in Figs. 13 and 14, respectively. In Fig. 14 (a), the high-frequency vibration components of the first IMF are much more outstanding than those shown in Fig. 10 (a).

In Fig. 14 (a), it is observed that the outer race defect frequency f_O = 83.23 Hz and its several harmonics are much clearer than those obtained by using EEMD only in Fig. 11 (a), which experimentally demonstrates that the blind fault component separation is beneficial to using EEMD for the extraction of the bearing fault features. As a result, from the two instances relevant to the industrial railway axle bearing fault feature extraction, it is concluded that indeed the blind fault separation makes EEMD more effective in extracting the bearing fault features, such as the bearing defect frequencies and their harmonics. Furthermore, statistical parameters of the frequency spectra containing the outstanding bearing defect frequencies obtained by using blind fault component separation and EEMD are potential to improve prediction accuracies of intelligent bearing fault diagnosis methods [37].

5 Conclusion

In this paper, by considering the common problem existing in the extraction of the bearing fault features by using EEMD, we introduced the concept of blind fault component separation to provide a simple and useful solution for making EEMD more effective in extracting the bearing fault features. Our idea aimed to separate the strong low-frequency periodic vibration components from the high-frequency random repetitive transients, such as the bearing fault signals, before EEMD was used to process the bearing fault signals. In the first instance, we experimentally showed that the direct use of EEMD failed to extract the bearing outer race fault features, namely the bearing outer race defect frequency and its harmonics. By contrast, with the aid of the AR filtering, which is one of the blind fault component separation algorithms, EEMD was able to decompose the industrial railway axle bearing outer race fault signal into the first three IMFs which further exhibited the occurrence of the outer race fault features. Consequently, the blind fault component separation made EEMD more effective in extracting the bearing outer race fault features. In the second instance, the results showed that the help of AR filtering made the multiple bearing fault features more outstanding. In this paper, according to our experimental results and analyses, we suggested that in future readers and engineers should consider using the concept of blind fault component separation prior to the use of EEMD, which is potentially beneficial to increasing prediction accuracies of intelligent bearing fault diagnosis because outstanding bearing features are extracted by using blind fault component separation and EEMD. In near future, we will consider how to improve the decomposition performance of EEMD and make EEMD work for fault diagnosis of rolling element bearings without using the concept of blind fault component separation.

Footnotes

Acknowledgments

This research work was partly supported by National Natural Science Foundation of China (Project No. 51505307), General Research Fund (Project No. CityU 11216014), Sichuan Province Research Fund (Project No. 2017JY0127 and szjj2016-015) and the research grants council theme-based research scheme under Project T32-101/15-R. The authors would like to thank anonymous reviewers for their valuable comments on our manuscript.

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