A novel signal compression method based on optimal ensemble ...

Journal of Sound and Vibration 332 (2013) 423–441

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Journal of Sound and Vibration journal homepage: www.elsevier.com/locate/jsvi

A novel signal compression method based on optimal ensemble empirical mode decomposition for bearing vibration signals Wei Guo, Peter W. Tse n The Smart Engineering Asset Management Laboratory and the Croucher Optical Nondestructive Testing Laboratory, Department of Systems Engineering and Engineering Management, City University of Hong Kong, 83 Tat Chee Ave., Kowloon Tong, Hong Kong

a r t i c l e i n f o

abstract

Article history: Received 5 January 2012 Received in revised form 21 August 2012 Accepted 21 August 2012 Handling Editor: K. Worden Available online 30 September 2012

Today, remote machine condition monitoring is popular due to the continuous advancement in wireless communication. Bearing is the most frequently and easily failed component in many rotating machines. To accurately identify the type of bearing fault, large amounts of vibration data need to be collected. However, the volume of transmitted data cannot be too high because the bandwidth of wireless communication is limited. To solve this problem, the data are usually compressed before transmitting to a remote maintenance center. This paper proposes a novel signal compression method that can substantially reduce the amount of data that need to be transmitted without sacrificing the accuracy of fault identification. The proposed signal compression method is based on ensemble empirical mode decomposition (EEMD), which is an effective method for adaptively decomposing the vibration signal into different bands of signal components, termed intrinsic mode functions (IMFs). An optimization method was designed to automatically select appropriate EEMD parameters for the analyzed signal, and in particular to select the appropriate level of the added white noise in the EEMD method. An index termed the relative root-mean-square error was used to evaluate the decomposition performances under different noise levels to find the optimal level. After applying the optimal EEMD method to a vibration signal, the IMF relating to the bearing fault can be extracted from the original vibration signal. Compressing this signal component obtains a much smaller proportion of data samples to be retained for transmission and further reconstruction. The proposed compression method were also compared with the popular wavelet compression method. Experimental results demonstrate that the optimization of EEMD parameters can automatically find appropriate EEMD parameters for the analyzed signals, and the IMF-based compression method provides a higher compression ratio, while retaining the bearing defect characteristics in the transmitted signals to ensure accurate bearing fault diagnosis. & 2012 Elsevier Ltd. All rights reserved.

1. Introduction In industry, remote condition monitoring systems are designed to collect data for remotely assessing the health condition of important machine elements. For example, rolling bearings are the most important elements in the vast majority of rotating machines. Serious bearing failure may cause downtime costs or significant damage to other parts of

n

Corresponding author. Tel.: þ852 3442 8431; fax: þ 852 3442 0415. E-mail address: [email protected] (P.W. Tse).

0022-460X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jsv.2012.08.017

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W. Guo, P.W. Tse / Journal of Sound and Vibration 332 (2013) 423–441

the machine, and even catastrophic failure [1]. Hence, it is vital to transmit vibration signals generated from the bearings in a monitored machine to the maintenance center for determining the health conditions of bearings. Unfortunately, the performance of remote monitoring is often affected by the problem of needing to transmit large amounts of data collected by sensors. To ensure diagnostic accuracy of rotating machines, sufficient vibration data are needed. A data acquisition system samples data through many channels simultaneously at a high sampling speed which is usually set at fifty thousand samples per second or higher. Therefore, the amount of data required for fault diagnosis is often massive [2]. However, the data transmission from a local source or a monitored machine to a remotely located maintenance center over wireless channels faces bottlenecks, such as limited bandwidth and long transmission time. To minimize the storage and transmission load, it is necessary to compress the collected raw data to an acceptable size prior to wireless transmission. The compression of data can be achieved by removing redundant and irrelevant information from the raw vibration data and compressing the data that can fit into the limited bandwidth and enable fast transmission. When the maintenance center receives the compressed data, it must ensure that the received data can be reconstructed back to its temporal waveform without losing any information that is vital for accurate fault diagnosis. The existing signal compression methods can be categorized into three types: direct data compression methods, parameter extraction methods and transformation methods. In direct compression methods, the signal is directly handled to provide the compression. Coding by time domain methods is based on the idea of extracting a subset of significant samples to represent the original signal [3,4]. Parameter extraction methods use a pre-processor to extract parameters or features of the signal and perform compression on them; for example, the compression method based on linear predictions or neural networks (e.g., [5,6]). Compression methods based on transformations (e.g., S transform [7], fractional Fourier transform [8], discrete cosine transform [9], and wavelet transform [10]) transform the signal in the time domain to another domain and then compress a small portion of the transform coefficients. Among the transform methods, wavelet transform has shown promising performance due to its good localization properties [2,11]. Various wavelet-based compression methods for one-dimensional signals have been proposed to compress the electrocardiograph signal (e.g., [12,13]) and speech signal [14], whereas only a few results [10,15–17] were the compression of vibration signals using wavelet transform. One of major problems with wavelet transform is their nonadaptive basis because the selection process of the best basis function is dominated by the signal components that are relatively large in a frequency band [18]. No general guidelines have been proposed for properly selecting the wavelet basis function [19]. Meanwhile, little attention has been paid to inherent deficiencies of the wavelet transform, such as border distortion, energy leakage, etc. [20,21]. An adaptive signal processing method, empirical mode decomposition (EMD) method [22,23] has recently been paid attention. This method represents nonlinear and non-stationary signals as sums of simpler components with amplitude and frequency modulated parameters [24]. It has no limitations in terms of basis function selection, energy leakage, parameter selection of model, and so on. It has been shown to be quite versatile in a broad range of applications for extracting signals from data generated in noisy nonlinear and non-stationary processes [25], e.g., [21,26,27]. The ensemble empirical mode decomposition (EEMD) [28] has been recently developed from the EMD method and can improve its scale separation. In relation to vibration signals collected from faulty bearings, the EEMD method can be employed to extract impulsive shocks, which are generated when a faulty rolling ball strikes either the inner race or outer race, or when balls strike a faulty outer or inner race, or even both races. This paper proposed a novel signal compression method based on the optimal EEMD method for bearing vibration signals. The method involves two steps. First, the EEMD method with parameter optimization is used to decompose a vibration signal collected from a faulty bearing, so that the signal component related to the defect characteristics can be separated from background noise and the other irrelevant signal components. The designed parameter optimization automatically selects appropriate EEMD parameters for the vibration signal to be analyzed. Second, a subset of significant samples is selected from this signal component for compression. The remainder of the paper is organized as follows. Section 2 provides a brief introduction to the EEMD method and a review of published methods for determining the EEMD parameters. Section 3 first gives an empirical strategy of the EEMD parameters and then presents an optimization method for the EEMD parameters. Section 4 proposes a signal compression method for the compression of bearing signals and compares it with the popular wavelet compression method. Fault diagnosis is conducted to verify whether the proposed compression results in the loss of defect characteristics in bearing signals. Section 5 applies the proposed methods to a vibration signal collected from a real traction motor. Finally, conclusions are drawn in Section 6.

2. Ensemble empirical mode decomposition (EEMD) 2.1. Brief introduction of EEMD The EEMD method [28] was developed from the EMD method [22,25]. It belongs to noise-assisted signal analysis methods and has been proven with better scale separation ability than the normal EMD method. The procedure of the


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EEMD method can be briefly summarized as follows: Step 1:Add white noise with a predefined noise amplitude to the signal to be analyzed. Step 2:Use the EMD method to decompose the newly generated signal. Step 3:Repeat the above signal decomposition with different white noise, in which the amplitude of the added white noise is fixed. Step 4:Calculate the ensemble means of the decomposition results as final results. Using this signal processing method, a multi-component signal, x(k), is decomposed into a finite number of intrinsic mode functions (IMFs) and a residue, xðkÞ ¼

n X

ci þ r,

(1)

i¼1

where n represents the number of the IMFs, ci is the ith IMF that is the ensemble mean of the corresponding IMFs obtained from all of decomposition processes, and r is the mean of the residues from all of decomposition processes. In each decomposition process, the added white noise helps to perturb the analyzed signal and enables the EMD method to visit all possible solutions in the finite neighborhood of the true final IMF [28]. Based on the property of zero mean of white noise, the added white noise can be cancelled out in the final ensemble mean if there are sufficient trials. Only the signal itself can survive in the final decomposition results. For more details about the EMD and the EEMD methods, please refer to Refs. [22,25,28]. 2.2. Review of EEMD parameter selection In the EEMD method, two critical parameters, the amplitude of the added white noise, AN, and the ensemble number, NE, need to be prescribed. The previous research about the method for selecting EEMD parameters can be summarized into the following points: First, the problem of the automatic selection of EEMD parameters is still unsolved and required further investigation. The amplitude of the added white noise was proven to be chosen appropriately for good performance of the EEMD method. Lei et al. [29–31] and Zhou et al. [32] convinced that there were no specific equations reported in the literature to guide the choice of EEMD parameters, especially the noise amplitude. Developing methods for automatically selecting the EEMD parameters aiming at different signals are thus needed in future research [29–31]. Second, the EEMD method was applied and developed for processing various signals, in which the EEMD parameters were set using trial and error or empirical values. Lei et al. [29–31] tried different noise amplitudes and selected from them. In most of cases (e.g., [33,34]), the noise amplitude was set to the empirical value suggested by Wu and Huang [28] or the authors’ empirical value without providing detailed explanations. Wu et al. [35] proposed an improved EEMD method without mentioning how to automatically select the appropriate EEMD parameters. ˇ Third, Zvokelj et al. [36,37], Chang and Liu [38], Zhang et al. [39], and Yeh et al. [40] independently introduced the signal-to-noise ratio (SNR) as a performance index to select the noise amplitude. The assumption of their methods is the ˇ analyzed signal or its power is known a priori. For real vibration signals, Zvokelj et al. [36,37] still used the empirical setting as proposed by Wu and Huang [28]. Niazy et al. [41] used relative root-mean-square error (RMSE) to evaluate the performances of EEMD when trying different levels of the added white noise, however, they did not give any guidance on how to select the appropriate noise level based on the relative RMSE. Having analyzed the characteristics of bearing vibration signals, an optimization method was designed to automatically select EEMD parameters for the target vibration signal. 3. Optimization for EEMD parameters 3.1. Observations on parameter setting Wu and Huang [28] described the effect of the added white noise and these two parameters satisfy the following equation that ln e þ

AN lnNE ¼ 0, 2

(2)

where e represents the standard deviation of error between the original signal and the corresponding IMF(s). The empirical setting is as follows: the amplitude of the added white noise is approximately 0.2 of a standard deviation of the original signal and the value of the ensemble is a few hundreds. This is not always usable for signal processing in different applications. Following many simulations and experiments, an empirical strategy has been devised for determining the EEMD parameters [42]. (1) The noise amplitude greatly influences the performance of the EEMD method with regard to scale separation. Once the noise amplitude is determined, increasing the ensemble number is helpful for reducing the remaining noise in each IMF.

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(2) Lower amplitude white noise will result in smaller errors. However, the noise amplitude should not be too low otherwise it may not introduce enough changes in the extremes of the decomposed signal and has little or no effect on separating completely different signal components in the original signal. (3) Once the noise amplitude is determined, when not considering the computation cost, a larger value of ensemble number will lead to a smaller error, which is mainly caused by the added white noise, especially for the high-frequency component. To some degree, continuing increasing the ensemble number results in only a minor change in errors. (4) When the signal is dominated by the high-frequency component, the high-frequency component is more easily separated from the low-frequency component and white noise with lower amplitude is able to separate the mixed modes. If the amplitude of the high-frequency component is higher, the amplitude of the added white noise should be appropriately increased. When the signal is dominated by low-frequency components, the amplitude of white noise should be higher. 3.2. Optimization for EEMD parameters With the above observations, it is critical to determine an appropriate noise amplitude in the EEMD method. It would be ideal to automatically find the optimal noise amplitude for the signal to be analyzed. In this paper, an index termed relative RMSE was introduced to evaluate the performances of the EEMD method with various noise amplitudes, and SNR was used to evaluate the remaining noise of decomposition results for various ensemble values. Based on such indices, an optimization method was designed for automatically selecting the appropriate EEMD parameters. Assume that the original vibration signal, xo(k), is composed of the main signal component(s) related to the feature of interest, background noise, and some low correlation signal components. Applying the EEMD method to the vibration signal, the IMF, cmax(k), having the highest correlation with the vibration signal and containing its main signal component, would be selected and used to evaluate the decomposition performance of EEMD method when setting different noise amplitudes. The desired decomposition will separate the main signal component from noise and other low-correlated signal components. The relative RMSE was introduced to evaluate the decomposition performance of EEMD under different noise amplitudes. It is defined as the ratio between the root-mean-square of the error and the root-mean-square of the original signal, where the error is the difference between the original signal, xo(k), and the selected IMF, cmax(k). It is expressed as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uP u ðx ðkÞcmax ðkÞÞ2 uk ¼ 1 o u Relative RMSE ¼ u , (3) N P t x2o ðkÞ k¼1

where N is the number of samples in the original signal. If the relative RMSE is very small and close to zero, it indicates that the selected IMF, cmax(k), is close to the original signal; that is to say, the selected IMF, cmax(k), contains not only the main component in the original signal but also part of noise and/or the other low-correlated or irrelevant signal components. Accordingly, the difference between the original signal and the selected IMF is small and the desired decomposition is not reached. However, there must be a value of noise amplitude that maximizes the relative RMSE. At this point, the selected IMF, cmax(k), only contains the main signal component, and is separated from noise and the other irrelevant signal components. The error is from the remaining components in the original signal, other than the selected IMF. This is the desired decomposition result and the corresponding noise amplitude is the optimal one. Hence, using this index, the appropriate noise amplitude can be determined. Considering that the above definition depends on the mean of the original signal, the definition of the relative RMSE is modified to remove the effect of non-zero mean and make the index independent of the mean value. It can be expressed as the following equation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uP u ðx ðkÞcmax ðkÞÞ2 uk ¼ 1 o u Relative RMSE ¼ u , (4) N P t ðxo ðkÞxo Þ k¼1

where xo is the mean of the original signal. For a signal with zero mean, Eq. (3) is the same to Eq. (4). The amplitude of the added white noise is related to the original signal, and thus it can be expressed as follows: AN ¼ LN so ,

(5)

where so is the standard deviation of the original signal and LN is the noise level of the added white noise. Thus, the optimization of the noise amplitude, AN, is equivalent to the optimization of the noise level, LN. A procedure for determining the optimal noise level is described as follows: Step 1:Set a small value of the initial ensemble number, for example, NE ¼10, and choose a relatively large value as the initial noise level, LN ¼ l0.


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Step 2:Perform the signal decomposition using the EEMD method and calculate the relative RMSE. It is unnecessary to extract all of the IMFs to find the optimal noise level, as only the IMF with the largest correlation coefficient relative to the signal is used to calculate the relative RMSE. During the process of signal decomposition, when the correlation coefficient of the current IMF is sufficiently small, the decomposition stops. Step 3:Decrease the noise level, LN, and retain the initial ensemble number for the next decomposition. Repeat step 2 until the change in the relative RMSE is negligible. Step 4:The optimal noise level is the value that maximizes the relative RMSE, where the maximal relative RMSE is arrived at by determining the maximum numerically. Once the optimal noise level is determined, the remaining task is to choose an appropriate value for the ensemble number. Too large a value of ensemble number will lead to a higher computation cost. Too small a value will not be enough to cancel out the noise remaining in each IMF. Here, the widely accepted and used measure, the signal-to-noise ratio (SNR), was introduced to determine the appropriate ensemble number. The procedure is to fix the optimal noise level and increase the ensemble number until the change in the SNR value is relatively small. The following section used various vibration signals to illustrate the proposed optimization method and verify its effectiveness. 3.3. Experiments-vibration signal decomposition Two vibration signals were collected from faulty bearings and then decomposed using the optimal EEMD method. This is also pre-processing for further signal compression. 3.3.1. The rationale for experiment setup To verify the proposed methods on the effectiveness for remote bearing monitoring, two types of experiments were set up. The first type of experiments was performed in a controlled environment, such as a laboratory using a smaller electric motor running with a bearing. The intention of such experiments is to ensure that the desired tests can be conducted successfully on a smaller motor before performing real tests on expensive traction motors used in real trains. The second type of experiments was conducted using a real and expensive traction motor, which would be described in Section 5. In the first type of experiments, each vibration signal was collected from a rolling bearing built into an experimental electric motor with a shaft rotation speed of 1400 rpm, which is shown in Fig. 1(a). The motor was constructed similar to the structure of the traction motor used in electrical trains. The tested bearings used in the experiments are SKF 1206 KTN9. An example bearing is shown in Fig. 1(b). Its specification is shown in Table 1. Vibration signals were picked up by fixing a piezo-electric accelerometer on the motor as shown in Fig. 1(a). The accelerometer was vertically mounted on the

Accelerometer

Tested bearing

Fig. 1. Experiment setup and faulty components of the tested bearings. (a) An electric motor with a rotation speed of 1400 rpm, (b) Tested bearing (SKF 1206 EKTN9), (c) An outer race defect, and (d) An Inner race defect.

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Table 1 Specification of faulty bearings used in experiments. Parameter

Value

Ball diameter, d Pitch diameter, D No. of balls, Nb Contact angle, a Shaft rotation speed

8 mm 47 mm 14 0 1400 rpm

Relative RMSE

0.8

Noise level = 0.2 0.6 0.4 0.2 0

2

1

0.1 Noise level

0.01

0.001

Fig. 2. Relative RMSEs when adding the white noise with various noise levels to the vibration signal from the bearing with an inner race defect. The optimal noise level for this signal is 0.2.

top of the bearing housing. The selected area was made flat and smooth to ensure effective coupling. The tested bearings worked at the same rotation speed and with no load. The sampling frequency was set to 80 kHz. In the experiments, the faulty bearings include: a bearing with an inner race defect, and a bearing with multiple defects (outer-race and inner-race defects). The faulty outer and inner races are shown in Fig. 1(c) and (d), respectively, in which the positions of defects are marked by circles. 3.3.2. Vibration signal decompositions The same initial values of EEMD parameters were set for experimental signals. First, a relatively large value was chosen as the initial noise level, i.e., l0 ¼2, and the initial ensemble number was set as 10. When the noise level is in this range, 2 rLN r0.1, the noise level is decreased in step of 0.1; when 0.1 oLN r0.01, the decreasing step is 0.01; when 0.01 oLN r0.001, the decreasing step is 0.001. That is, when the noise level is 0.1, the level of the added white noise for the next signal decomposition should be 0.09. If the decreasing step for each interval of noise level is too small, it will lead to a huge computation cost. After applying the optimal EEMD method to the above vibration signals, the relative RMSEs and the corresponding selected IMFs for the faulty bearings are illustrated as follows. 3.3.2.1. Decomposition of the signal from a bearing with an inner race defect. Fig. 3(a) displays the vibration signal collected from a bearing with an inner race defect. Applying the EEMD method with the parameter optimization to this vibration signal, the relative RMSEs for various noise levels are shown in Fig. 2. Here, the noise level decreasing from a relatively large value to a small value is to show the variation of relative RMSE in a wide range of noise level. In this experiment, at the noise level of 0.2, the maximal relative RMSE was arrived at by determining the maximum numerically, and thus the optimal noise level for this vibration signal is 0.2. Adding white noise with this optimal level, the selected IMF, cmax(k), is shown in Fig. 3(b). Its kurtosis is 12.86. For comparisons with the optimal value, white noise with three non-optimal levels (LN ¼1.4, 2, and 0.009) were individually added to the vibration signal and decomposed. The selected IMFs for these noise levels and their kurtosis values are shown in Fig. 3(c)–(e). The noise level corresponding to Fig. 3(d) is the initial noise level. When the noise level is less than 0.009 (a small noise level), the change on the relative RMSE is very small. The noise level, LN ¼1.4, was randomly chosen to compare with the case of setting the optimal noise level. The comparison of these IMFs and their corresponding kurtosis values indicates that setting the optimal noise level produces the best decomposition performance. In Fig. 3(b), the impulsive component in the selected IMF1 is clear and separated from noise and the other irrelevant components, whereas in Fig. 3(c)–(e) there is still a lot of noise in the selected IMFs. In Fig. 3(d), particularly, some impulses are difficult to find in the selected IMF. This demonstrates that the proposed optimization method for automatically selecting the appropriate noise level is practicable. 3.3.2.2. Decomposition of the signal from a bearing with multiple defects (the outer-race and inner-race defects). The second experimental signal, shown in Fig. 5(a), was collected from a faulty bearing in which there were defects on both the outer and the inner races. The relative RMSEs for different noise levels are shown in Fig. 4. The optimal noise level for this signal


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Amplitude (mV)

The vibration signal from the bearing with an inner race defect 2

0

-2

0

0.04

0.08

0.12

0.16

0.2

Amplitude (mV)

IMF1, LN = 0.2, kurtosis = 12.86

2 0

-2 0 2

0.1 IMF1, LN = 2, kurtosis = 8.55

0.2 Amplitude (mV)

Amplitude (mV)

Amplitude (mV)

Time (s)

0

-2

0

0.1 Time (s)

0.2


2 0

-2

0

2

0.1 0.2 IMF1, LN = 0.009, kurtosis = 3.98

0

-2

0

0.1 Time (s)

0.2

Fig. 3. The vibration signal in (a) from the bearing with an inner race defect and the corresponding selected IMFs when setting the optimal noise level in (b) and three non-optimal noise levels in (c)–(e).

Relative RMSE

0.8

Noise level = 1.2 0.6 0.4 0.2 0

2

1

0.1 Noise level

0.01

0.001

Fig. 4. Relative RMSEs when adding the white noise with various noise levels to the vibration signal from the bearing with outer-race and inner-race defects. The optimal noise level for this signal is 1.2.

is 1.2. The selected IMF (IMF1) is shown in Fig. 5(b) and the kurtosis value is 25.27. Selecting the noise level, LN ¼1.3, produces the second highest relative RMSE. The corresponding selected IMF and its kurtosis are shown in Fig. 5(c). With the noise level of LN ¼2 or LN ¼0.009, the selected IMFs shown in Fig. 5(d) and (e) contain more noise than previous decomposition results. Their kurtosis values are also smaller: 14.10 and 9.46, respectively. Therefore, the optimal noise level for this vibration signal is 1.2. Having determined the optimal noise level, the next step was to select an appropriate value for the ensemble number. In the experiments, the SNR was used to measure the remaining noise in the selected IMF and then determine the appropriate ensemble number. The higher the SNR value, the cleaner the signal. An example is used to illustrate the variation in the SNR as the ensemble number increases. The example signal from the bearing with an inner race defect is shown in Fig. 3(a) and its optimal noise level is 0.2. The SNR values for the increased ensemble values are shown in Fig. 6. As shown in this figure, when the ensemble number is less than 100, increasing the ensemble number accelerates the increase in the SNR value. When the ensemble number is larger than 150, the change in the SNR value is relatively small. Further increasing the ensemble number is ineffective for improving the SNR value. The real optimization process thus stopped at this point, NE ¼150. Therefore, for the bearing with an inner race defect, the corresponding vibration signal in Fig. 3(a), better decomposition performance can be obtained by setting the optimal noise level, LN ¼0.2, and the ensemble number, NE ¼150. Table 2 lists the correlation coefficients between the original vibration signal and all IMFs obtained using the optimal EEMD method. The first three coefficients are much larger than the others, and the fourth coefficient is smaller. The coefficients of the other IMFs are close to zeros. To save space, only the first four IMFs are given here. The top diagram

430


Amplitude (mV)

The vibration signal from the bearing with outer-race and inner-race defects 3

0

-3

0

0.04

0.08

0.12

0.16

0.2

IMF1, LN = 1.2, kurtosis = 25.27 Amplitude (mV)

3 0 -3

0

3

0.1 IMF1, LN = 2, kurtosis = 14.10

0.2

0 -3

0

0.1 Time (s)

0.2


3 0 -3 0

Amplitude (mV)

Amplitude (mV)

Amplitude (mV)

Time (s)

3

0.1 0.2 IMF1, LN = 0.009, kurtosis = 9.46

0 -3 0

0.1 Time (s)

0.2

Fig. 5. The vibration signal in (a) from the bearing with outer-race and inner-race defects and the corresponding selected IMFs when setting the optimal noise level in (b) and three non-optimal noise levels in (c)–(e).

1.2

SNR (dB)

1.15 1.1 1.05 1 0.95 10

50

100 150 200 Ensemble number

250

300

Fig. 6. SNR values for various ensemble numbers when adding the optimal white noise (LN ¼0.2) to the signal from the bearing with an inner race defect.

Table 2 The correlation coefficients between the vibration signal from the inner-race-defect bearing and all IMFs obtained using the optimal EEMD method. Correlation coefficient IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 IMF10 IMF11 IMF12

0.8461 0.7927 0.1901 0.0118 0.0005 0.0008 0.0004 0.0002 0.0003 0.0000 0.0002 0.0000

Amplitude (mV)


431

The vibration signal from the bearing with an inner race defect 2 0 -2 IMF1 2 0 -2 IMF2 2 0 -2 IMF3 1 0 -1 IMF4 0.1 0 -0.1 0 0.04 0.08 0.12 0.16 0.2 Time (s)

The vibration signal from the bearing with outer and inner race defects 3 0

Amplitude (mV)

-3 3

IMF1

0 -3 3

IMF2

0 -3 1

IMF3

0 -1 1

IMF4

0 -1

0

0.04

0.08 0.12 Time (s)

0.16

0.2

Fig. 7. Vibration signals collected from various faulty bearings and their corresponding first four IMFs decomposed using the optimal EEMD method. (a) The vibration signal from the bearing with an inner race defect and the first four IMFs and (b) The vibration signal from the bearing with outer-race and inner-race defects and the first four IMFs.

of Fig. 7(a) shows the original vibration signal and the remaining four diagrams show the first four IMFs extracted from the original signal. The decomposition results for the other vibration signal are shown in Fig. 7(b). The top diagram of Fig. 7(b) is the original vibration signal. The remaining diagrams in this figure show main decomposition results, IMF1–IMF4. Comparing the original vibration signal from each faulty bearing with the corresponding selected IMF (IMF1), it is clear that noise and the other irrelevant signal components are removed and the extracted impulses in IMF1 are closely related to the characteristics of the faulty bearing.

3.3.3. Computation time analysis and stepped-up strategies The EEMD method with parameter optimization is a repeated signal decomposition process. To analyze computation time for the parameter optimization, the following assumptions are made: 1) When setting the initial ensemble number and any value of noise level, the time of signal decomposition using the EEMD method is T1. 2) When optimizing the noise level, the number of levels between the initial noise level and the final level is N1; i.e., the signal decomposition using EEMD is repeated N1 times to find the optimal noise level. 3) When searching an appropriate ensemble number for the signal to be analyzed, each ensemble number between the initial value and the final value is a multiple of the initial ensemble number, ni (i¼ 1,2,y).

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To generate desired decomposition results, one needs to set different parameters and repeat the signal decomposition using the normal EEMD method. The corresponding computation time, to, would be t o ¼ T 1 N1 þ T 1 n1 þ T 1 n2 þ þT 1 ni þ , where the first term is the computation time for optimizing the noise level, and the rest is the computation time for searching an appropriate ensemble number for the analyzed signal. The computation cost of the EEMD parameter optimization is heavy because it takes a long time to generate the irrelevant signal components in the signal to be extracted. Therefore, a number of strategies were introduced to shorten the computation time and speed up the optimization process. The signal collected from the bearing with an inner race defect was used as an example to illustrate these strategies and the computation time. The platform was a Lenovo ThinkPad X220 laptop computer with Intel Core i7-2620M CPU at 2.70 GHz and 4 GB memory, running Windows 7 Home Premium 64-bit and MATLAB R2011a. These stepped-up strategies for the EEMD parameter optimization are summarized as follows: 3.3.3.1. Decreasing the iteration number of the sifting process in EMD method. In the sifting process of EMD, a low but fixed value of iteration number can be set to obtain each IMF. Ten for the sifting number was suggested in Ref. [28]. Such setting can eliminate unpleasant effect caused by the extra sifting, at the same time, speeds up the sifting process for obtaining each IMF. For the example signal collected from the bearing with an inner race defect, when using the commonly used three-threshold stopping criterion [43] and executing signal decomposition one time, the total iteration number for obtaining all of IMFs is 598 and the computation time is 11.2 s. If fixing the iteration number to 10, the computation time for all of IMFs is 4.1 s and smaller than the former. 3.3.3.2. Extracting only part of the IMFs when optimizing the noise level. When optimizing the EEMD parameters, it is not necessary to extract all of the IMFs, as only the IMF with the largest correlation coefficient relative to the analyzed signal is used to calculate the relative RMSE. Therefore, each signal decomposition in EEMD stops when the correlation coefficient of the current IMF is much smaller than those of the previous IMFs. This strategy also accords with the property of the bearing vibration signal. When decomposing the vibration signal collected from a faulty bearing, the bearing signal of interest is a high-frequency signal generated by the resonance of the faulty bearing and usually distributes in one of the first few IMFs. The rest of IMFs are mainly generated by background noise, other machine component(s) and/or extra sifting of EMD. For the above example signal, as shown in Table 2, the correlation coefficients between the first three IMFs and the original vibration signal are much larger than those of the last IMFs. The forth coefficient is smaller. The correlation coefficients of IMF5-IMF12 close to zeros. During the optimization, the signal decomposition stops generating the other signal components when obtaining IMF4. It reduces the computation time for each signal decomposition of EEMD. 3.3.3.3. Setting a low value of initial ensemble number when optimizing the noise level. As mentioned in Section 3.1, during the optimization process, changing the noise level has more effect on the extraction of the main component, whereas changing the ensemble number only influences the remaining noise in the main component. The above vibration signal was used as an example and the result is shown in Fig. 8. This figure shows the relative RMSEs (real line) for various noise levels when setting a relatively low value of initial ensemble number, for example, NE ¼10, as well as the relative RMSEs (dash-dotted line) when setting the empirical ensemble value, for example, NE ¼100. When optimizing the noise level, setting a large value as the initial ensemble number takes much time on repeating the signal decomposition, whereas the variation trend of the index is not changed greatly. 3.3.3.4. Stopping criterion for optimizing the noise level. The above experimental results show the relative RMSEs when the same initial and final noise levels are set for each vibration signal. In fact, when optimizing the noise level, there is no need

Relative RMSE

0.7

NE = 10

NE = 100

0.6 0.5 0.4 0.3 0.2 2

1 Noise level

0.1

Fig. 8. Relative RMSEs for setting two ensemble numbers, NE ¼10 and NE ¼100, when adding the white noise with various noise levels to the vibration signal from the bearing with an inner race defect.


433

to decrease it to a small value because a small amount of noise has no effect on improving the decomposition performance. As shown in Fig. 3(e), IMF1 obtained by setting LN ¼0.009 (a small value) still contains much noise and is close to the original vibration signal. Therefore, the noise level optimization process stops when the change in the relative RMSE becomes negligible. For the above example signal, the optimization of noise level stops at the noise level of 0.01 because the decrease of the relative RMSE at this noise level is smaller than the previous, in which the relative RMSEs are 0.060 (setting LN ¼0.04), 0.041 (setting LN ¼0.03), 0.030 (setting LN ¼0.02), and 0.028 (setting LN ¼0.01), and the corresponding changes are 32%, 27%, and 7%. Using the above strategies, the computation time of optimizing the noise level is 9.0 min. 3.3.3.5. A very small decreasing step in the noise level is unnecessary. The experimental results indicate that a very small decreasing step in the noise level is not necessary, as shown in Fig. 5(b) and (c). The former shows IMF1 obtained by setting the noise level at 1.2, which is the optimal level. The latter shows IMF1 obtained by setting the noise level at 1.3, which generates the second-highest relative RMSE and is the second-best noise level. The kurtosis values of these two IMF1s are close. If using a decreasing step smaller than the current value of 0.1, much time would be spent generating similar results to that in Fig. 5(c) yet this would contribute little to the improvement of the decomposition performance. 3.3.3.6. Only the selected IMF is considered when finding the appropriate ensemble number. When finding the appropriate ensemble number, for each ensemble number the signal decomposition stops once the selected IMF is obtained. For the signal used in the example, only the first IMF was used to calculate the SNR value and find the appropriate ensemble number. The corresponding computation time was shortened accordingly. When applying the above strategies to decompose the example signal, the process for extracting irrelevant IMFs was omitted and the total computation time for parameter optimization was 16.1 min. By employing a higher-performance computer, less computation time would be used. Although the optimal EEMD method executes the signal decompositions more times than other signal decomposition methods, such as the popular wavelet transform method, the optimal EEMD method can automatically find the appropriate parameters for the vibration signal to be analyzed and adaptively decompose the signal. Hence, it is suitable for signal processing in remote condition monitoring systems. 4. Vibration signal compression After applying the optimal EEMD method, the vibration signals collected from faulty bearings were decomposed into various signal components and the impulsive shocks in the vibration signals were distributed in the selected IMFs. In this section, the compression of bearing signals will be performed on the selected IMFs. Its compression performances are evaluated and compared with the wavelet compression method. 4.1. Compression performance measures To evaluate the data compression method reliably, two critical issues need to be considered: the amount of compression and the distortion measure of the reconstruction. The amount of compression is commonly measured by a factor known as compression ratio (CR), which is defined as the ratio between the size of the original file and the size of the compressed file: Compression ratio ¼

So , Sc

(6)

where So is the size of the original file, and Sc is the size of the compressed file. It can also be expressed to measure the saving percentage (SP) of the original file, where SP is given by the following equation: Saving percentage ¼

So Sc 100%: So

(7)

The percentage RMS (root-mean-square) difference (for short, PRD) [44] is one of the most popular distortion measures. It is to measure how closely the reconstruction resembles the original. It is given by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uP u ðx ðkÞxr ðkÞÞ2 uk ¼ 1 o PRD ¼ u 100%, (8) u N P t x2o ðkÞ k¼1

where xo(k) (k¼ 1,2,y,N) is the original signal, xr(k) (k ¼1,2,y,N) is the reconstructed signal, N is the number of samples in the original signal. In practice, the performance measures of a compression method are not limited to these indices. Depending on the nature of applications, other statistical indices and analysis methods can also be introduced.

434


4.2. Signal compressions and performance comparison 4.2.1. IMF-based signal compression After applying the optimal EEMD method, the impulses generated by the faulty bearing are distributed in the selected IMF and are separated from noise and other irrelevant signal components in the original signal. Such an IMF has a higher kurtosis value and thus can be compressed more efficiently than the original vibration signal can. The selected IMF (IMF1) for the bearing with the inner race defect is used to illustrate the compression process. Fig. 9(a) shows the original vibration signal (real line) and its extremes (crosses), which include the maxima and the minima of this IMF. Compared with this original signal, Fig. 9(b) shows IMF1 (real line) extracted from the original signal in Fig. 9(a) and the extremes (crosses) of this IMF1, in which the impulses caused by the faulty bearing component are much cleaner than that in the original signal. The distribution for most of extremes in IMF1 is centered around zero. A few extremes with large amplitudes are enough to indicate the positions and the amplitudes of the impulses. This means that almost all of the meaningful extremes related to the defect characteristics are concentrated in a small fraction of the total extremes, thus making efficient compression feasible. Based on such a clean bearing signal, a simple compression can be realized by discarding all but a small fraction of extremes. The original samples are thus represented by a small subset of the samples. This provides a compression ratio of roughly 2 M/N, where M is the number of the reserved extremes, N is the number of samples in the original signal, and the factor of 2 is for storing both the indices and the amplitudes of the reserved extremes, which can be used to reconstruct the IMF to be compressed. Therefore, the IMF-based compression method has two steps. First, the signal is decomposed using the optimal EEMD method. The IMF with the largest correlation coefficient is selected for signal compression. After identifying the extremes of the selected IMF, the extremes around zero are discarded. The compressed data file only contains the reserved important extremes along with their indices. Applying this compression method to vibration signals, the compression ratios (CRs) were calculated and are presented in Table 3. The selected IMFs to be compressed are shown in Fig. 10(a) and Fig. 11(a). Their corresponding reconstructed signals are shown in Fig. 10(b) and Fig. 11(b) For each reconstructed signal, the signal distortion is a measure of the difference between the selected IMF and the corresponding reconstructed signal. Table 3 also lists the percentage RMS differences (PRDs) of various bearing signals.

2

2

1.5

1.5 Amplitude (mV)

Amplitude (mV)

4.2.2. Comparison with wavelet compression Due to the compact support of basis functions used on the wavelet transform, wavelets have good energy concentration properties [2]. Performing the wavelet transform on the signal to be compressed, most of the wavelet coefficients are

1 0.5 0 -0.5

1 0.5 0 -0.5

-1

-1

-1.5

-1.5

-2

0

0.04

0.08 0.12 Time (s)

0.16

-2

0.2

0

0.04

0.08 0.12 Time (s)

0.16

0.2

Fig. 9. A vibration signal (real line) collected from a faulty bearing and the corresponding selected IMF (real line) along with their extremes (crosses). (a) A vibration signal from a bearing with an inner race defect and its extremes and (b) IMF1 extracted from the signal in (a) and the extremes of IMF1.

Table 3 Compression performances using the IMF-based and the wavelet-based compression methods.

IMF-based compression method Wavelet-based compression method

a

Defect position

CRa

SPb

PRDc

Maxd

PSDe

Inner race Outer & inner races Inner race Outer & inner races

13.16 13.52 2.07 9.96

92.40% 92.61% 51.75% 89.96%

24.28% 30.31% 24.72% 30.13%

1.38 1.95 1.03 1.43

8.80E 12 9.72E 12 1.10E 11 4.76E 12

CR: Compression ratio. SP: Saving percentage. c PRD: Percentage RMS (root mean square) difference. d Max: absolute maximum of the reconstructed signal. e PSD: Power spectral density of the reconstructed signal. b


435

The selected IMF (IMF1) for bearing signal with an inner race defect 2

Amplitude (mV)

0 -2 The reconstructed signal

2 0 -2 0

0.04

0.08 0.12 0.16 Time (s) Envelope spectrum of the reconstructed signal

0.2

0.1 Amplitude

201Hz≈BPFI 2× 0

0

200

3×

400 600 Frequency (Hz)

800

1000

Fig. 10. The selected IMF (IMF1) for the bearing with an inner race defect and the reconstructed signal as well as its envelope spectrum.

The selected IMF (IMF1) for bearing signal with outer & inner race defects

Amplitude (mV)

3 0 -3 The reconstructed signal

3 0 -3 0

0.08 0.12 0.16 Time (s) 141Hz≈BPFO Envelope spectrum of the reconstructed signal 2× BPFO

Amplitude

0.1

0.04

205Hz

≈ BPFI

0.2

3× BPFO 4× BPFO 5× BPFO 6× BPFO

0 0

200

400 600 Frequency (Hz)

800

1000

Fig. 11. The selected IMF (IMF1) for the bearing with outer-race and inner-race defects and the reconstructed signal as well as its envelope spectrum.

usually around zero and very few large coefficients exists. This means that almost all the information is concentrated in a small fraction of the coefficients, so that the signal can be efficiently compressed. To compare with the proposed IMF-based compression method, the popular wavelet compression method was also applied to the same vibration signals. Considering that the original vibration signals are noisy, they are processed in the sequence of wavelet de-noising and wavelet compression. For simply, wavelet threshold de-noising method was used to pre-process original vibration signals. A one-dimensional de-nosing function ‘wden’ (automatic 1-D de-noising) in MATLAB was firstly applied to each vibration signal. The recovered bearing signal was then compressed using Daubechies wavelet transform. The above signal processing, including the de-nosing and the compression of the vibration signal is based on wavelet transform. For simplicity, it is referred to as wavelet-based compression in the following discussion. The signal distortion comes from the difference between the de-noised signal and the reconstructed signal. Applying the wavelet-based compression method to

436


The vibration signal from the bearing with an inner race defect 2 0

Amplitude (mV)

-2 The reconstructed signal for the IMF-based compression

2 0 -2

The reconstructed signal for wavelet-based compression

2 0 -2

0

0.04

0.08 0.12 Time (s)

0.16

0.2

The vibration signal from bearing with outer and inner race defects 3 0

Amplitude (mV)

-3 3

The reconstructed signal for the IMF-based compression

0 -3 3

The reconstructed signal for wavelet-based compression

0 -3 0

0.04

0.08 0.12 Time (s)

0.16

0.2

Fig. 12. Vibration signals from various faulty bearings and their corresponding reconstructed signals for the IMF-based and the wavelet-based compression methods. (a) Original and reconstructed signals for the bearing with an inner race defect and (b) Original and reconstructed signals for the bearing with outer-race and inner-race defects.

the above vibration signals, the same performance measures, CR and PRD, were calculated and are also presented in Table 3. Their reconstructed signals are shown in the bottom diagrams of Fig. 12(a) and (b). For the bearing with an inner race defect, the original vibration signal is also shown in the top diagram of Fig. 12(a). After compressing this vibration signal, the reconstructed signals for the proposed IMF-based compression and the wavelet-based compression are shown in the middle and the bottom diagrams of Fig. 12(a), respectively. The CR, SP, and PRD using the IMF-based compression method are 13.16, 92.40%, and 24.28%, respectively. However, using the waveletbased compression method, the PRD is 24.72% which is close to 24.28%, and the CR is only 2.07 (SP ¼51.75%). The IMFbased compression method has a much higher compression ratio with a similar signal distortion. For another faulty bearing, the original vibration signal is shown in the top diagram of Fig. 12(b), and the reconstructed signals for these two compressions are displayed in the middle and the bottom diagrams of Fig. 12(b). The compression measures are shown in the rows denoted as ‘Outer & inner races’ in Table 3. Using the wavelet-based compression method, the CR is 9.96 (SP¼89.96%) and the PRD is 30.13%. In comparison, the proposed IMF-based compression provides a slightly better compression result, in which the CR is 13.52 (SP ¼92.61%) and the PRD is 30.31%. The comparisons of experimental results indicates that the performance of the IMF-based compression is better than the wavelet-based compression for the same vibration signal. In addition to the above two performance measures, the absolute maximum value and the power spectral density (PSD) were also calculated to compare the reconstructed signals for two compression methods, which are listed in the last two columns of Table 3. For example, for the bearing with the multiple defects, applying the wavelet-based compression method to this vibration signal, the absolute maximum value and the PSD of the reconstructed signal are 1.43 and 4.76E 12, respectively. Applying the IMF-based compression method to the same vibration signal, the absolute maximum value and the PSD of the reconstructed signal are higher, 1.95 and 9.72E 12, respectively. The difference on the maximum values can be directly observed from the reconstructed signals


437

Table 4 Calculation equations and theoretical values of bearing characteristic frequencies. Bearing characteristic frequency

Equation

Value

Ball pass frequency of the outer race (BPFO)

F or ¼ F r N2b ð1 Dd cos aÞ

136 Hz

Ball pass frequency of the inner race (BPFI)

F ir ¼ F r N2b ð1 þ Dd cos aÞ

192 Hz

Note: Fr, Nb, D, d, a represent the rotating frequency, the number of balls, the pitch diameter, the ball diameter and the contact angle, respectively.

shown in the middle and the bottom diagrams of Fig. 12(b), which corresponds to the IMF-based compression and the wavelet-based compression, respectively. The amplitude of the reconstructed signal in the middle diagram of Fig. 12(b) is larger than that in the bottom diagram. Although the wavelet compression executes the signal transform only one time and has higher computational efficiency, the IMF-based compression can compress various bearing vibration signals without considering the selection of the basis function and parameters, and also has better compression performance. It preserves not only the periodicity of the impulses but also their amplitudes. This compression method is demonstrated to be more applicable for remote condition monitoring systems.

4.3. Bearing fault diagnoses Fault diagnosis on the reconstructed signal is also a distortion measure of the bearing signal compression. Envelope spectral analysis has proven to be a good tool for the diagnosis of local faults in rolling bearings. It extracts the bearing characteristic defect frequencies (CDFs) along with the modulation, so that the fault type can be identified. In this section, the envelope spectral analysis was applied to the reconstructed signals for the IMF-based compression method to verify whether they still retain the features of the faulty bearings. Table 4 lists the equations [45] for calculating the characteristic frequencies of the faulty bearing and the results for the tested bearing whose specification is listed in Table 1. Using the envelope spectral analysis, the frequency spectra of the reconstructed signals from various faulty bearings are shown in Fig. 10(c) and Fig. 11(c). To display the CDFs clearly, the displayed frequency spectra are limited to the range of 0–1000 Hz. Applying the envelope spectral analysis to the reconstructed signals in Fig. 10(b) and Fig. 11(b), their frequency spectra are shown in Fig. 10(c) and Fig. 11(c), respectively. In Fig. 10(c), the CDF (201 Hz) for the inner race defect and its harmonics (2 and 3 BPFI) are identified, although there is a difference of 9 Hz between the identified value and the theoretical value (BPFI ¼192 Hz, listed in Table 4). From the frequency spectrum in Fig. 11(c), the defect-related frequencies – BPFO (141 Hz) of the outer race defect and its harmonics (2 and 3 BPFO), and BPFI (205 Hz) of the inner race defect – were clearly detected. The differences between the identified and the theoretical CDFs may be due to errors. One assumption in calculating the CDF is that there is no slippage between the shaft and the bearing, whereas in practice there is always some sliding and slippage, especially when the rolling element in the bearing wears out. Accordingly, this can lead to a small frequency error. Furthermore, variations in shaft rotation speed after heavy use also leads to the frequency difference. The results above demonstrate that the characteristic frequencies of faulty bearings can be detected by analyzing the reconstructed signals; accordingly, the types of defects can be determined. Therefore, the proposed IMF-based compression method can provide better compression performance, meanwhile well maintain the feature signal in the original vibration signal.

5. Application in a traction motor When a train company is performing tests on a traction motor, the motor will be removed from the train and re-installed back to the train after the completion of test. It is to ensure that the motor can be tested accurately without the influence caused by the train running on a rail. Once the purpose methods have been tested successfully, then the motor can be re-tested again when the train is running on a rail. A vibration signal was collected from such a traction motor to validate the proposed signal compression method. The motor comprises a 250 kg rotor supported by two rolling bearings, one of which is located on the drive end and the other is located on the non-drive end. Fig. 13(a) shows the schematic diagram (top view) of the traction motor. The motor was uncoupled from the gearbox throughout the experiment. The running speed of the motor was 1498 rpm (the rotation frequency was 25 Hz). Fig. 13(b) shows the traction motor and the tested bearing, a single row deep groove ball bearing (SKF 6215). The raw vibration signal was collected by an accelerometer that was close to the bearing housing of the motor and was magnet-mounted onto the motor at the axial direction, as shown in Fig. 13(b). The sampling frequency of data acquisition was 32.8 kHz. The specification and characteristic frequency of the tested bearing are listed in Table 5. A raw vibration signal from this motor is shown in the top diagram of Fig. 15(a).

438


Ball bearing SKF 6215

Top View Y Horizontal Traction Motor Z Vertical

X Axial

Accelerometer

Fig. 13. A traction motor and the tested bearing (SKF 6215). (a) Schematic diagram of the traction motor and (b) The traction motor, the tested bearing and the accelerometer. Table 5 Specification and characteristic frequency of the bearing (SKF 6215) in the traction motor. Parameter

Value

Bearing bore diameter Bearing outside diameter Race width Rotation speed of inner race Rotation frequency Sampling frequency No. of samples Ball pass frequency of the outer race (BPFO)

75mm 130mm 25mm 1498rpm 25Hz 32.8 kHz 4096 samples 114Hz

Relative RMSE 0.7

Noise level = 0.4

0.65 0.6 0.55 2

1

0.1 Noise level

0.01

Fig. 14. Relative RMSEs when adding the white noise with various noise levels to the vibration signal from the bearing in the traction motor.

There were two faults in the tested traction motor. One fault was a motor eccentric problem due to poor workmanship on the clearance between the rotor and the stator. The other fault was an outer race defect that occurred in the bearing. Such two signal components can be observed from the frequency spectrum of the raw vibration signal. As shown in the top diagram of Fig. 15(b), the frequency spectrum of the vibration signal involves two main components, one signal component with low frequency at 920 Hz and the other signal component with high-frequency band centered around 12 kHz, the latter of which was generated by the faulty bearing. It is difficult to identify the fault-related impulses in the temporal waveform of the raw signal because it is overwhelmed by the dominant vibration generated by the motor eccentric. For the purpose of monitoring the bearing condition, it is necessary to extract the bearing signal from the raw vibration signal and then conduct the signal compression. The optimal EEMD method was applied to this raw vibration signal. The initial noise level and ensemble number are the same to the setting in the previous experiments. Fig. 14 shows the relative RMSEs when setting the noise level from the


439

A raw vibration signal from a traction motor

3 0 -3

IMF1

1.5

Amplitude (mV)

0 -1.5

IMF2

1.5 0 -1.5

IMF3

1.5 0 -1.5

IMF4

1.5 0 -1.5

0

0.02

0.04

0.06 0.08 Time (s)

0.1

0.12

Frequency spectrum of the raw vibration signal 0.6 Around 12kHz

920 Hz

0

Frequency spectrum of IMF1

0.3

Around 12kHz

Amplitude

0


0.05

0


0.4 920 Hz

0


0.4 920 Hz

0

0

2000

4000

6000 8000 10000 Frequency (Hz)

12000

14000

16000

Fig. 15. A raw vibration signal from the traction motor and the first four IMFs decomposed using the optimal EEMD method along with their frequency spectra. (a) A raw vibration signal and its main decomposition results, IMF1-IMF4 and (b) Frequency spectra of the signals shown in (a).

initial value to the final value. For the vibration signal from the traction motor, the relative RMSE reaches the maximum value where the noise level is 0.4. Hence, the optimal noise level should be LN ¼0.4. The ensemble number was selected as NE ¼100. Main decomposition results, IMF1–IMF4, are shown in Fig. 15(a) and their frequency spectra are shown in Fig. 15(b). As shown in these frequency spectra, IMF1 corresponds to the signal component of high-frequency band centered around 12 kHz, that is, the bearing signal was distributed in IMF1. IMF3 and IMF4 correspond to the signal component of low-frequency band at the frequency of 920 Hz. IMF2 is noise embedded in the raw signal. Because IMF1 contained the bearing signal, it was thus compressed for wireless transmission and then reconstructed for fault diagnosis. The compression ratio is 7.3, and the saving percentage is 86.3%. The reconstructed signal is shown in Fig. 16(b). Although the PSD of the reconstructed signal is 78%, comparing with IMF1 that is also shown in Fig. 16(a), the reconstructed signal which retains the impulses caused by the defective bearing outer race is shown in Fig. 16(b). Then the envelope spectral analysis was applied to the temporal waveform of Fig. 16(b) to convert the temporal impulses into its frequency components which are shown in Fig. 16(c). The displayed frequency spectrum is limited to the range of 0–2000 Hz. In Fig. 16(c), higher impulse is identified at 104 Hz (BPFO) and its harmonics (around 2 , 3 and 4 of BPFO). An inaccurate shaft speed after long use and an insufficient number of samples limits the frequency resolution and accounts for the difference between the theoretical BPFO (114 Hz) and the identified BPFO (104 Hz). The identification of BPFO from the reconstructed signal indicates that the proposed IMF-based signal compression method well retain the defect characteristics of the bearing signal. Therefore, the proposed signal compression method provides a much smaller file for data transmission, yet makes accurate fault diagnosis possible.

440


Amplitude (mV)

The selected IMF (IMF1) for the faulty bearing in the traction motor 1.5 0 -1.5 The reconstructed signal 1.5 0 -1.5

0

0.02

104Hz ≈ BPFO

0.2

0.04

0.06 0.08 Time (s)

0.1

0.12

Envelope spectrum for the reconstructed signal

Amplitude

2x 3x 4x

0

0

200 400 600 800 1000 1200 1400 1600 1800 2000 Frequency (Hz)

Fig. 16. The selected IMF (IMF1) for the faulty bearing in the traction motor and the reconstructed signal as well as its envelope spectrum.

6. Conclusions This paper presents a new signal compression method based on the optimal EEMD method for bearing vibration signals. An optimization method was designed for automatically selecting appropriate EEMD parameters for the vibration signal to be analyzed, so that the significant feature signal of the faulty bearing can be extracted from the original vibration signal and separated from background noise and the other signal components that are low-correlated or irrelevant to bearing faults. After applying the optimal EEMD method to each vibration signal, the impulses caused by bearing defect were distributed in the selected IMF. Such an IMF can be reconstructed by only a few its extremes with large amplitudes and thus can be efficiently compressed. The experimental results demonstrate that the proposed IMF-based compression method provides a higher compression ratio. This method extracts the important impulses relating to the bearing faults and reduces the size of vibration data for remotely transmitting to a bearing condition monitoring system. With the use of our method, shorter transmission time makes wireless data communication between remote maintenance center and inspected machines highly efficient, meanwhile maintains the accuracy of bearing fault diagnosis without the need to transmit an enormous amount of raw data. Furthermore, it also saves the processing time in the maintenance center for recovering feature signals from large amount of raw data. In future, the vibration signals generated by bearings installed a running traction motor can be collected and sent to the console of train driver via wireless means or to a remotely located maintenance center via power/signal transmission lines of the trains for performing prompt fault diagnosis. Hence, the time consuming and tedious practice of sending the entire data to the maintenance center and the unloading each traction motor for on-site bearing fault diagnosis becomes unnecessary.

Acknowledgements We acknowledge all the reviewers and the editor for their valuable comments. The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 122011) and a grant from City University of Hong Kong (Project No. 7008187). References ¨ ¨ [1] S. Ericsson, N. Grip, E. Johansson, L.E. Persson, R. Sjoberg, J.O. Stromberg, Towards automatic detection of local bearing defects in rotating machines, Mechanical Systems and Signal Processing 19 (2005) 509–535. [2] Z.K. Peng, F.L. Chu, Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography, Mechanical Systems and Signal Processing 18 (2004) 199–221. [3] M. Abo-Zahhad, B.A. Rajoub, An effective coding technique for the compression of one-dimensional signals using wavelet transforms, Medical Engineering and Physics 24 (2002) 185–199. [4] V. Kumar, S.C. Saxena, V.K. Giri, D. Singh, Improved modified AZTEC technique for ECG data compression: effect of length of parabolic filter on reconstructed signal, Computers and Electrical Engineering 31 (2005) 334–344. [5] N. Sriraam, Context-based near-lossless compression of EEG signals using neural network predictors, AEU—International Journal of Electronics and Communications 63 (2009) 311–320.


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