Measurement 45 (22) 38 322 Contents lists available at SciVerse ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement Faulty bearing signal recovery from large noise using a hybrid method based on spectral kurtosis and ensemble empirical mode decomposition Wei Guo, Peter W. Tse, Alexandar Djordjevich 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, Tat Chee Ave., Kowloon Tong, Hong Kong article info abstract Article history: Received 8 November 2 Received in revised form 26 October 2 Accepted 5 January 22 Available online 24 January 22 Keywords: Ensemble empirical mode decomposition Spectral kurtosis Signal filtering Bearing fault diagnosis Time frequency analyses are commonly used to diagnose the health of bearings by processing vibration signals captured from the bearings. However, these analyses cannot be guaranteed to be robust if the bearing signals are overwhelmed by large noise. Ensemble empirical mode decomposition (EEMD) was developed from the popular empirical mode decomposition (EMD). However, if there is large noise, it may be difficult to recover impulses from large noise. In this paper, we develop a hybrid signal processing method that combines spectral kurtosis (SK) with EEMD. First, the raw vibration signal is filtered using an optimal band-pass filter based on SK. EEMD method is then applied to decompose the filtered signal. Various bearing signals are used to validate the efficiency of the proposed method. The results demonstrate that the hybrid signal processing method can successfully recover the impulses generated by bearing faults from the raw signal, even when overwhelmed by large noise. Ó 22 Elsevier Ltd. All rights reserved.. Introduction Rolling bearings are the most important elements in rotating machinery. Unfortunately, bearings frequently fall out of service for various reasons, such as unexpected heavy loads, inadequate or unsuitable lubrication, careless handling, and ineffective sealing. The occurrence of serious bearing faults in a machine may cause a decrease in performance. In the worst case, this results in downtime costs, significant damage to other parts of the machine, or even catastrophic failure []. Hence, the analysis of bearing vibration signals has attracted great attention in the field of condition monitoring and fault diagnosis, as these signals give rich information for the early detection of bearing failures. However, in the early stage of bearing failure, the amplitude or energy of the defects in the vibration signal is somewhat weak, and is often overwhelmed or concealed Corresponding author. Tel.: +852 3442 843; fax: +852 3442 45. E-mail address: meptse@cityu.edu.hk (P.W. Tse). by large noise and other structural vibrations. The recovery of the bearing vibration signal from noise while preserving its important features, including the defect features, remains a challenging problem for both signal processing and statistics [2]. Several linear filtering methods that are easy to design and implement, such as the Wiener filter and the Kalman filter, have been proposed to reduce the noise. However, in practice, machine processes often contain complex, non-stationary, noisy, and nonlinear characteristics [3], and adaptive signal processing techniques may be more suitable for vibration signal processing and analysis. The most popular signal processing methods for vibration analysis are envelope analysis [4] and wavelet transforms [5 7]. Although envelope analysis is effective in many cases, the method requires the designer to know the band filter around a resonance frequency, and it is ineffective in the presence of a high noise level [8]. One of the main problems with the wavelet transform and wavelet packet methods is the non-adaptive basis. A mother wavelet must 263-224/$ - see front matter Ó 22 Elsevier Ltd. All rights reserved. doi:.6/j.measurement.22..
W. Guo et al. / Measurement 45 (22) 38 322 39 be carefully chosen so that the content of her daughter wavelets are largely similar to that of the analyzed signal to ensure good results. Although many new and complicated basic functions have been proposed to improve the effectiveness of wavelet-based methods [9 ], to date no general guideline has been proposed for the correct selection of a mother wavelet. At the same time, little attention has been paid to the inherent deficiencies of the wavelet transform, such as border distortion and energy leakage [2,3]. The ensemble empirical mode decomposition (EEMD) [4] was developed from the popular empirical mode decomposition (EMD) [5,6], which is an adaptive signal analysis method and represents a nonlinear and non-stationary signal as the sum of some signal components with amplitude and frequency modulated parameters [7], called intrinsic mode functions (IMFs) [5]. In EEMD method, white noise is introduced to help to separate disparate time scales and improve the decomposition performance of the normal EMD method. The ensemble means are chosen as the final results to minimize the effect caused by the added white noise. With the strategy of adding white noise to the analyzed signal, EEMD method can be used as a nonlinear and adaptive filter that can extract weak periodic or quasi-periodic signals from noisy signals, and especially faulty bearing signals in the presence of large noise. However, in some extreme cases, such as when the real bearing signal is completely overwhelmed by large noise, it is difficult for the EEMD to identify the impacts generated by faulty bearing elements. This is because the core algorithm of EEMD method is signal decomposition using EMD method, which is based on the existence of the extremes of a signal. When the signal is contaminated by large noise, the extremes of interest are hidden in the noise and EEMD method cannot discriminate the real bearing signal from the noise. A preprocessing method is thus needed for signal decomposition using EEMD method. Spectral kurtosis (SK) [8 2] has been proven to be efficient in detecting incipient faults buried in large noise, and offers a means of designing an optimal filter to extract faulty bearing signals. Based on the estimation of SK, filters, such as an optimal band-pass filter, are easier to implement and can recover the real bearing signal from the mask of large noise. However, there is a compromise between incipient detection ability and signal distortion, and in most cases the filtered signal still contains some noise. A signal with a higher signal-to-noise ratio can be obtained using other filters, but at the expense of further signal distortion. Applying EEMD method to the filtered signal allows the feature signal of the faulty bearing to be adaptively separated from the remaining noise without attenuating the signal amplitude or energy. In this paper, a hybrid signal processing method that combines spectral kurtosis (SK) with EEMD is proposed to recover faulty bearing signals from large noise. In this method, an optimal band-pass filter based on SK is first designed to filter the raw vibration signal to provide the necessary extremes for further signal decomposition. The filtered signal is then decomposed using EEMD method. The impulses generated by the faulty elements of the bearing are extracted from the noisy vibration signal. Noise and the other irrelevant components are thus separated from the real bearing signal. The visibility of the impulses from the faulty bearing is observably improved. The remainder of this paper is organized as follows. Section 2 briefly introduces EEMD method and compares its performance in decomposing vibration signals with EMD method. Section 3 first uses vibration signals collected from faulty bearings to analyze the individual performances of EEMD method and the filter based on SK. By considering the advantages and limitations of these methods in processing vibration signals masked by large noise, a hybrid signal processing method is proposed that combines the optimal band-pass filter based on SK and EEMD method to recover the signals of faulty bearings in large noise situations. Section 4 shows and analyzes the resultant signals by applying the proposed hybrid method to experimental and real vibration signals from faulty bearings installed in an experimental DC motor and a real traction motor. Section 5 conducts fault diagnoses on the resultant signals to validate the efficiency of the proposed hybrid method in terms of the detection of incipient bearing defects. Finally, conclusions are drawn in Section 6. 2. Ensemble empirical mode decomposition 2.. Brief introduction Ensemble empirical mode decomposition (EEMD) method [4] is developed from the popular empirical mode decomposition (EMD) method [5,6], which is an adaptive method to represent a nonlinear and non-stationary signal as the sum of signal components with amplitude and frequency modulated parameters and is also capable of revealing overlapping in both time and frequency components [7]. EEMD method provides the improvement over the normal EMD method and solves the problem of mode mixing when the analyzed signal contains high-frequency intermittent oscillations. It consists of sifting an ensemble of white-noise-added signals and treats the mean as the final result. Although each individual signal decomposition will generate a relatively noisy result, the added white noise is necessary to force the sifting process to visit all possible solutions in the finite neighborhood of real extreme and then generates different solutions for the final IMF [4]. Meanwhile, the zero mean of white noise is helpful for the cancellation of the added white noise in the final ensemble mean if there are sufficient trails. Hence, only the signal itself can survive in the final decomposition result. It is applicable for analyzing and identifying the vibrations in rotating machines. For more details about EEMD method, please refer to Ref. [4]. The procedure of the EEMD method is listed as follows: Step : Initialize parameters: the ensemble number, N E, and the amplitude of the added white noise, a, which is a fraction of the standard deviation of the signal to be analyzed. The index of the ensemble starts from, m =. Step 2: Perform the mth signal decomposition using the EMD method: decompose the white noise-added signal,
3 W. Guo et al. / Measurement 45 (22) 38 322 x m = x + n m, where n m is the added white noise with the presetting amplitude, and x is the signal to be analyzed. The decomposition result is some simple signal components called intrinsic mode functions (IMFs) [5], c i,m, i =,2,..., N IMF, and a non-zero low-order residue, r m, where N IMF is the number of IMFs obtained in each decomposition. Step 3: Repeat Step 2 with m = m + until the index m reaches the presetting ensemble number, N E. Step 4: Obtain the final decomposition results by calculating the means of corresponding IMFs and the residue obtained from each signal decomposition process. 2.2. Parameter setting As the procedure for EEMD method indicates, two critical parameters, the amplitude of the added white noise and the ensemble number need to be prescribed. These parameters directly affect the decomposition performance of EEMD method. Wu and Huang [4] gave the relationship among the ensemble number, N E, the amplitude of the added white noise, a, and the standard deviation of error, e, by using the equation, lne +(a/2) lnn E =. The empirical setting is as follows: the amplitude of the added white noise is approximately.2 of a standard deviation of the original signal and the value of ensemble is a few hundreds. This is not always applicable for signals in various applications. Following many simulations and experiments, an empirical strategy has been devised for determining the parameter setting of EEMD method [2]. () The amplitude of the added white noise greatly influences the performance of EEMD method with regard to scale separation. The white noise with smaller amplitude added to the signal to be analyzed will result in smaller errors. However, the noise amplitude should not be too small; otherwise, it may not introduce enough changes in the extremes of the signal and will take little or no effect on separating completely different modes in the signal. (2) Once the noise amplitude is determined, when not considering the computation cost, a larger value for the ensemble number will lead to smaller errors, which are mainly caused by the added white noise, especially for the high-frequency signal component. To some degree, continuing to increase the ensemble number will result in only a minor change in errors. (3) When the signal is dominated by the high-frequency signal component, the high-frequency component is more easily separated from the low-frequency signal component and lower noise amplitude is able to separate the mixed modes. If the peak value of the high-frequency component is higher, the noise amplitude should be appropriately increased. When the signal is dominated by the low-frequency signal components, the noise amplitude should be larger. 2.3. Comparisons with EMD method The main improvement of EEMD method is that this method removes the problem of mode mixing in EMD method, which is defined as one or more IMFs consisting of oscillations of dramatically disparate scales and it is often caused by the intermittency of the driving mechanisms [4]. In this section, using EEMD method and the aforementioned strategy for parameter setting, two vibration signals are used to compare the decomposition performances of EMD and EEMD methods. One vibration signal, shown in Fig. a, was collected from a motor with a defect in one of the bearing elements. The decomposition results after applying EMD and EEMD methods to the vibration signals are shown in Fig. b and c, respectively. To save space, for each method only the first nine IMFs are shown in the corresponding figure. The other IMFs have very small amplitudes and are not displayed. With EEMD method, the low-frequency signal component is completely contained in the IMF8 shown in Fig. c. The impulses related to the features of the faulty bearing are mainly distributed in the first two IMFs. With EMD method, the decomposition results are shown in Fig. b. Part of the low-frequency component is mixed with oscillations in the IMF7 and the wave in the IMF8 is irregular and nonperiodic. This indicates that EMD method is very sensitive to noise or oscillations. Regardless of which method was used, the majority of the impulses generated by the faulty bearing elements reside in IMFs. A comparison of the two IMFs in the top diagrams of Fig. b and c shows that the IMF in the latter figure is clearer. It may be caused by the cancellation effect associated with the ensemble mean. The decomposition result obtained using EEMD method is thus much better than that obtained using EMD method. The other vibration signal was collected from a blower [22] and is shown in Fig. 2a. It can be seen that this vibration signal is dominated by the low-frequency signal component, whereas the vibration signal in the former example is dominated by the high-frequency signal component. EMD and EEMD methods were again used to decompose this vibration signal and the decomposition results are shown in Fig. 2b and c, respectively. With the EMD method, IMF6 includes two time scales, and the low-frequency signal component is divided into two parts that have a similar scale but are contained in different IMFs (IMF6 and IMF7). In contrast, with EEMD method the same signal component is only distributed in IMF6, as shown in Fig. 2c. This example also indicates that EEMD method has a better decomposition performance than EMD method. 3. A hybrid method based on spectral kurtosis and EEMD 3.. Problem analysis The recovery of a real signal from large noise, while preserving its important faulty features is a challenging problem for the condition monitoring and fault diagnosis of rotating machines. Although EEMD method improves the scale separation ability of EMD method, both methods are based on the existence of extremes to discriminate different signal components. When the signal of interest is completely overwhelmed by large noise, there may be a lack of necessary extremes for EEMD method to separate the real
W. Guo et al. / Measurement 45 (22) 38 322 3 5 5-5 - -5..2.3.4.5.6.7.8.9. (a) A vibration signal collected from a faulty bearing, which is dominated by the high-frequency signal - - IMF 5-5 2-2 IMF5 - IMF6 - IMF7 -.5 IMF8 -.5.5 IMF9 -.5..2.3.4.5.6.7.8.9. (b) The first nine IMFs obtained using EMD method, in which the mode mixing exists in IMF7 IMF - - 5-5 2-2 IMF5 - IMF6 - IMF7 -.5 IMF8 -.5.5 IMF9 -.5..2.3.4.5.6.7.8.9. (c) The first nine IMFs obtained using EEMD method Fig.. A vibration signal collected from a faulty bearing and the comparison of the respective first nine IMFs obtained using EMD and EEMD methods. signal from the noise. In real cases, the faulty feature in the early stage of a bearing failure is often weak and hidden by background noise. The noise often embodies strong vibrations from several competing sources (e.g., improper installation and surfacing of the mounted sensors, random impacts from friction and contact forces, external disturbances) which span a large frequency range and strongly mask the signal of interest [9]. For a vibration signal with an extremely low signal-to-noise ratio, EEMD method may not extract the desired signal components from the noisy vibration signal. In the following, some experimental signals are used to illustrate this limitation of EEMD in recovering the faulty bearing signal masked by large noise. In the experiments, the vibration signals were collected from faulty bearings that covered four types of common faults: an outer race defect, an inner race defect, a ball defect, and a multiple defect (outer and inner race defects). Each tested bearing (SKF 26 EKTN9) was installed in a DC motor with a speed of 4 rpm, which is shown in Fig. 3a. As the figure shows, the vibration signal was measured by vertically mounting a piezo-electric accelerometer on the top of the bearing housing in each case. The sampling frequency for data acquisition was set to 8 khz. The specification of the tested bearings is given in Table. The faulty elements of the tested bearings are shown in Fig. 3c e, in which the position of the defect on each element is circled. Although the DC motor in the experiments has a relatively simple structure, it adequately serves to simulate such cases in real motors, such as a traction motor. A DC motor is the mainstay of electric traction motors, which are widely used in electrical trains. The bearings installed in a traction motor support the driving shaft of the motors. During tests, the traction motor is generally removed from the train and insulated from other elements in the train. The intention of firstly performing the experiments on the small DC motor was to ensure that the desired tests could be conducted successfully before the real test was carried out on an expensive traction motor. The vibration signals collected from the bearings in the small DC motor contained inherent background noise. To simulate large noise in a real case, a Gaussian white noise was added to
32 W. Guo et al. / Measurement 45 (22) 38 322.3 -.2 5 5 2 25 3 Samples (a) A vibration signal collected from a garden blower [22], which is dominated by the low-frequency signal. IMF -.. -.. -.. -.. IMF5 -..2 IMF6 -.2.2 IMF7 -.2 5 5 2 25 3 Samples (b) The first seven IMFs obtained using EMD method, in which the mode mixing exists in IMF6. IMF -.. -.. -.. -.. IMF5 -..2 IMF6 -.2.2 IMF7 -.2 5 5 2 25 3 Samples (c) The first seven IMFs obtained using EEMD method Fig. 2. A vibration signal collected from a garden blower [22] and the comparison of the respective first seven IMFs obtained using EMD and EEMD methods. Accelerometer Tested bearing (a) A experimental DC motor (b) The tested bearing (SKF 26 EKTN9) (c) A defect on an outer race (d) An defect on an inner race (e) A defect in a ball Fig. 3. Experimental setup and faulty elements of the tested bearings, in which the defect on each element is circled. each vibration signal collected in the experiments. Following these experiments, a vibration signal collected from a real traction motor was analyzed, the result of which will be presented in Section 4.2.
W. Guo et al. / Measurement 45 (22) 38 322 33 Table Specifications of the faulty bearings used in the experiments. Parameter Value Ball diameter, d 8mm Pitch diameter, D 47 mm No. of balls, N b 4 Contact angle, a Shaft rotation speed 4 rpm Fig. 4 shows the raw vibration signals from faulty bearings. The impulses related to the features of the faulty bearings were almost completely masked by noise. Applying EEMD method to each vibration signal resulted in its decomposition into thirteen IMFs. The correlations of the IMFs with the original signal were calculated to evaluate the significance of each signal component to the original signal. To measure the strength of the relationship between the raw vibration signal and each IMF, the index of the correlation coefficient was introduced. Table 2 lists the correlation coefficients between the bearing vibration signals and their corresponding IMFs obtained using EEMD method only. The first four IMFs for each faulty bearing have higher correlation coefficients with the raw vibration signal than the other IMFs. Thus, to save space, only the first four IMFs for each faulty bearing are displayed in Fig. 5. Fig. 5a shows the first four IMFs decomposed from the vibration signal from the bearing with an outer race defect. Part of the noise in the raw vibration signal was filtered out and resides in IMF. The periodic impulses are still masked by some noise and distributed in. A small portion of impulses and noise were distributed in. IMF,, and have larger correlation coefficients with the raw signal, which are.866,.666, and.47, respectively. This is because they are main components in the raw signal. As mentioned above, to simulate the real vibration signals, each experimental signal is composed of the vibration signal collected from the DC motor, the background noise and the additive white noise. Using EEMD method, the raw signal was decomposed to some signal components. The first three IMFs correspond to the noise and the bearing signal in the raw signal and thus have larger correlation coefficients though the raw signal is noisy. is the remainder of the raw signal, which is indicated by its lower correlation coefficient with the raw signal. The other IMFs (IMF5 ) are mainly caused by the extra sifting during the signal decomposition and their correlation coefficients are thus closer zeros. As Fig. 5a shows, in, the periodic impulses in relation to the characteristics of the outer race defect are clearer than the original signal. However, the decomposition results for the other faulty bearings are not as good as the result for the bearing with the outer race defect. Fig. 5c shows the first four IMFs for the bearing with a ball defect. Fig. 5d shows the first four IMFs for the bearing with the outer and the inner race defects. These figures show that part of the impulses was recovered from the large noise and reside in one of the IMFs, but there is still some noise in this IMF. For the signal from the bearing with an inner race defect, the first four IMFs are shown in Fig. 5b. It is difficult to observe the impulses in the first four IMFs. Although some noise was removed from the raw signal, the impulses related to the characteristics of the inner race defect are still buried in noise. This is because the impacts are caused by the inner race defect and the decomposition method lacks the necessary extremes of interest. As Fig. 3a shows, the accelerometer was mounted on the top of the bearing housing, which is a further distance from the inner race than from the outer race. Accordingly, the vibration signal collected was rather weak and easily buried in large noise. A comparison of the original signals shown in Fig. 4a and b shows that necessary extreme are lacking in the signal shown in Fig. 4b, which rendered EEMD method inefficient. For signals with a low signal-to-noise ratio, it is preferable to design a detector to find weak signals buried in large noise to facilitate signal decomposition, which is precisely what spectral kurtosis (SK) does. The SK has been proven to be a powerful statistical index for the indication of incipient bearing faults even in the presence of strong masking noise. It is large in frequency bands in which the impulsive bearing fault signal is dominant, and is effectively zero, where the spectrum is dominated by stationary components [8,9]. Hence, based on the advantages of the SK, a filter was designed to pre-process the raw signal and remove part of the noise. The following section discusses the performance of an optimal band-pass filter based on SK in recovering signals from large noise. 3.2. Spectral kurtosis [8 2] Since SK is a statistical tool which indicates the presence of series of transients and their locations in the frequency domain, it can be used as a defect indicator. The idea is to compute the SK and check in each frequency band for abnormally high values which may suggest the presence of an incipient fault. The maximum SK provides the references for the optimal center frequency and bandwidth of a band-pass filter, which can extract the narrowband transients buried in the broad-band background noise. The estimation for SK can be built from the short time Fourier transform (STFT) of the signal to be analyzed. For more details about the SK and the filter implementation, please refer to Refs. [8 2,23]. The filtered signals obtained by applying the optimal band-pass filter to various bearing signals are shown in Fig. 6a d. The kurtosis value of each filtered signal is marked in the caption of the figure. It can be seen that most of the impulses are separated from the noise. The kurtosis values of the filtered signals are higher than the kurtosis values of the raw signals, the latter of which are given in Fig. 4. Hence, the impacts caused by faulty elements in the bearings are recovered from large noise. However, the filtered signal for each faulty bearing still contains some noise. Using other filters, such as a matched filter, may further improve the signal-to-noise ratio of the filtered signal, but at the expense of further signal distortion. For the signal from the bearing with multiple defects, rather weak vibration signals may be attenuated, which makes fault diagnosis inaccurate. As with EEMD method, the
34 W. Guo et al. / Measurement 45 (22) 38 322 3-3.2.4.6.8..2.4.6.8.2 (a) A vibration signal collected from a bearing with an outer race defect (Kurtosis = 3.69) 3-3.2.4.6.8..2.4.6.8.2 3 (b) A vibration signal collected from a bearing with an inner race defect (Kurtosis = 3.7) -3.2.4.6.8..2.4.6.8.2 3 (c) A vibration signal collected from a bearing with a ball defect (Kurtosis = 4.48) -3.2.4.6.8..2.4.6.8.2 (d) A vibration signal collected from a bearing with outer and inner race defects (Kurtosis = 4.74) Fig. 4. Experimental vibration signals collected from four faulty bearings, which are overwhelmed by large noise. filtered signal provides the necessary extremes for the signal decomposition, and the method is thus suitable for further separating the feature signal of a faulty bearing from noise. 3.3. Hybrid signal processing method based on SK and EEMD By analyzing the individual performances of the foregoing two methods, a hybrid signal processing method that combines the two methods is proposed. The optimal band-pass filter based on SK is first employed to remove some noise from the raw signal, and the EEMD method is then used to decompose the filtered signal to separate the signal of interest (the impulses related to the bearing faults) from the noise, which allows good detection of the defects but at the same time minimizes the distortion of the impulses. Finally, a clean signal from the faulty
W. Guo et al. / Measurement 45 (22) 38 322 35 Table 2 Correlation coefficients between raw bearing signals and their corresponding IMFs obtained using EEMD method only. Correlation coefficient S Outer S Inner S Ball S OI IMF.866.857.7866.862.666.64.653.639.47.49.4352.484.2967.2968.2732.2964 IMF5.28.22.2258.25 IMF6.497.496.5.53 IMF7.34.46.44. IMF8.73.79.746.742 IMF9.59.583.632.668 IMF.43.44.369.35 IMF.268.267.232.9.29.56.45.24.54.57.4.27 bearing is recovered from large noise and can be used for further signal analysis. The procedure for the hybrid method is briefly described as follows: Step : Filter the raw signal using an optimal band-pass filter based on SK and obtain the filtered signal. Step 2: Use EEMD method to decompose the filtered signal into IMFs. Step 3: Calculate the correlation coefficients between the IMFs and the filtered signal, and select the IMF that has the largest correlation coefficient as the resultant signal. 4. Experiments and application 4.. Experiments and results The proposed hybrid signal processing method was applied to noisy vibration signals. For each faulty bearing, the raw vibration signal was first processed using the band-pass filter based on SK. The filtered signals are shown in Fig. 6a d. The EEMD method was then used to decompose the filtered signals to further extract the impulses in relation to the bearing faults. Table 3 lists the correlation coefficients between the filtered signals and their corresponding IMFs. For each faulty bearing, the first four IMFs have much higher correlation coefficients than the others, and thus to save space, Fig. 7a d only show the first four IMFs for the faulty bearings. Using the hybrid signal processing method, the final result for the signal collected from the bearing with an outer race defect, as shown in Fig. 4a, is presented in Fig. 7a. After filtering and decomposition, the majority of the noise is distributed in, and only the periodic impulses reside in IMF. As indicated in Table 3, IMF has a larger 2-2 - - -.2.4.6.8..2.4.6.8 (a) The first four IMFs for the bearing with an outer race defect 2 IMF IMF -2 2-2 - -.2.2.4.6.8..2.4.6.8.2 (c) The first four IMFs for the bearing with a ball defect 2-2 - - IMF - -.2.4.6.8..2.4.6.8.2.2.4.6.8..2.4.6.8.2 (b) The first four IMFs for the bearing with an inner race defect 2-2 - - (d) The first four IMFs for the bearing with outer and inner race defects Fig. 5. Main decomposition results obtained by applying EEMD method to various vibration signals in the experiments. The impulses in relation to the bearing defects are still masked by noise. IMF
36 W. Guo et al. / Measurement 45 (22) 38 322 4-4.2.4.6.8..2.4.6.8.2 2 (a) The filtered signal for the bearing with the outer race defect (Kurtosis = 8.2) -2.2.4.6.8..2.4.6.8.2 4 (b) The filtered signal for the bearing with the inner race defect (Kurtosis = 3.97) -4.2.4.6.8..2.4.6.8.2 5 (c) The filtered signal for the bearing with the ball defect (Kurtosis = 8.39) -5.2.4.6.8..2.4.6.8.2 (d) The filtered signal for the bearing with outer and inner race defects (Kurtosis = 7.36) Fig. 6. The filtered signals obtained using an optimal band-pass filter based on spectral kurtosis. Compared with raw signals, the filtered signals have increased kurtosis values, however, they still contains some noise. correlation coefficient (.8994) than the other signal components and contains the main component in the filtered signal. Hence, IMF was taken as the final resultant signal recovered from the raw vibration signal, which can be proven by the comparison of the kurtosis values of various signals. Table 4 compares the kurtosis values of the raw signal, the filtered signal and the selected IMF for each bearing condition. For the bearing with an outer race defect, the kurtosis of the raw signal is 3.69, the kurtosis of the filtered signal is 8.2, and the kurtosis of IMF increases to.29, the last of which can clearly indicates the faulty state of the tested bearing. Similar observations can be made from the results corresponding to the bearings with an inner race defect and a ball defect, respectively. Fig. 7b shows the first four IMFs for the bearing with an inner race defect. IMF, which has the largest correlation coefficient (.8753), includes almost all of the impulses and was separated from the noise, which is mainly distributed in. The kurtosis value of the raw vibration signal collected from the bearing with an inner race defect is 3.7, whereas the kurtosis value of IMF, as shown in Fig. 7b, is 8.35. By applying the proposed hybrid signal processing method, the feature signal related to the inner race defect was successfully separated from the large noise and its kurtosis value improved remarkably. The proposed hybrid signal processing method provides a relatively clean signal for further signal analysis and fault diagnosis. Fig. 7c shows the first four IMFs for the bearing with a ball defect. IMF includes the main impulses and excludes the noise. The kurtosis value of IMF also increases rapidly from 4.48 (the kurtosis of the raw signal) to 4.2. Compared with the filtered signal, IMF has clearer periodicity, and the amplitudes of the impulses are almost unaffected.
W. Guo et al. / Measurement 45 (22) 38 322 37 Table 3 Correlation coefficients between the filtered signals and their corresponding IMFs obtained using the hybrid signal processing method. Correlation coefficient S F-Outer S F-Inner S F-Ball S F-OI IMF.8994.8753.86.554.6222.7578.8262.9344.624.775.2936.7289.7.32.4.83 IMF5.3..2.46 IMF6..7.2.5 IMF7..7..3 IMF8.2.2..5 IMF9..3..3 IMF..3..4 IMF............3 Notes: S F-Outer, S F-Inner, S F-Ball and S F-OI are the filtered signals which were originally sampled from the bearings with an outer race defect, an inner race defect, a ball defect as well as a multiple defect (the outer and the inner race defects). The noise remaining in the filtered signal was separated and distributed in. The hybrid signal processing method thus identifies IMF as the resultant signal for this faulty bearing. For the bearing with multiple defects, i.e. the outer and the inner race defects, the first four IMFs are displayed in Fig. 7d, in which has the largest correlation value (.9344) and is finally selected as the resultant signal. Its kurtosis is 3.2, which is much larger than the kurtosis (4.74) of the raw signal. The foregoing experimental results prove that the proposed hybrid signal processing method is able to recover the feature signal related to bearing faults from large noise and provides a much cleaner signal for further analysis and fault diagnosis. The resultant signal has much a higher kurtosis value than the raw signal. The periodicity related to the bearing fault can be observed in the final resultant signal, and at the same time the amplitude or energy of the impacts has less distortion than the case when more complicated filters are used. In the following section, a vibration signal collected from a real traction motor is used to verify the performance of the proposed hybrid signal processing method. 4.2. Application of signal recovery from a bearing in a traction motor Another vibration signal collected from a real industrial motor (a traction motor) was used to verify the hybrid method. The traction motor is usually used in electrical trains to deliver the driving power to wheels. Generally, it is taken away from the train before the test and re-installed back IMF (Kurtosis =.29) 5-5 - - -.2.4.6.8..2.4.6.8 (a) The first four IMFs for the bearing with the outer race defect.2 4-4 - - IMF (Kurtosis = 4.2) -.2.4.6.8..2.4.6.8 (c) The first four IMFs for the bearing with the ball defect.2 IMF (Kurtosis = 8.35) 2-2 - - -.2.4.6.8..2.4.6.8 (b) The first four IMFs for the bearing with the inner race defect.2-5 -5 - IMF (Kurtosis = 3.2) -.2.4.6.8..2.4.6.8 (d) The first four IMFs for the bearing with outer and inner race defects.2 Fig. 7. Main decomposition results obtained by applying the hybrid signal processing method to vibration signals of various faulty bearings. The IMFs (bold in figures) have larger kurtosis values than that of the filtered signal.
38 W. Guo et al. / Measurement 45 (22) 38 322 Table 4 Kurtosis values of the signals for various faulty bearings. Kurtosis Raw signal Filtered signal Selected IMF A bearing with an outer race defect 3.69 8.2.29 A bearing with an inner race defect 3.7 3.97 8.35 A bearing with a ball defect 4.48 8.39 4.2 A bearing with outer and inner race defects 4.74 7.36 3.2 to the train after the test. It is to ensure that the motor can be tested accurately without the influence caused by the train running on a rail. Fig. 9a shows a traction motor and its bearing, which is a single row deep groove ball bearing (SKF 625). The motor comprised a 25 kg rotor supported by two rolling element bearings, the tested of which was located on the drive end. Fig. 9b shows the schematic diagram (top view) of the traction motor. The raw vibration signal was collected using an accelerometer that was close to the bearing housing of the motor and was magnet-mounted onto the motor at the axial direction. The running speed of the motor was 498 rpm (the rotation frequency was around 25 Hz). The data collected by the accelerometer were transmitted through a signal conditioner and a data acquisition card to a PC for further analysis. The sampling frequency was 4 khz. The specification and characteristic frequency of the tested bearing in the traction motor are listed in Table 6. The raw vibration signal collected from the tested bearing is shown in Fig. a. The periodic impulses are difficult to observe from the raw signal. It is thus necessary to extract the bearing signal from the raw vibration signal. First, the raw vibration signal was filtered using the optimal band-pass filter based on SK. The filtered signal is shown in Fig. b along with the kurtosis value of the signal. After filtering, the kurtosis value increases from 2.7 to 6.33. Using EEMD method, the filtered signal was then decomposed in some IMFs. The correlation coefficients of the first three IMFs with the filtered signal are.94,.59, and.4, respectively. Fig. c e shows the first three IMFs. The remaining signal components have very low correlation coefficients and are thus not displayed. As the figure shows, and mainly include the noise remaining in the filtered signal, and most of the impulsive part of the bearing signal resides in IMF, which has the highest correlation coefficient (.947) with the filtered signal and an increased kurtosis of 7.49. Using the proposed hybrid method, the signal of the faulty bearing was successfully recovered from the raw signal and IMF is the resultant signal that can be used for further fault diagnosis. 5. Bearing fault diagnosis To verify whether each resultant signal recovered from the raw vibration signal maintained the defect features of the bearing, the resultant signals were analyzed using envelope spectral analysis to determine the fault types of the tested bearings. 5.. Bearing characteristic defect frequencies For a given rolling bearing, each time a rolling element in the bearing passes through the faulty surface, a series of impacts is generated. The resulting vibration repeats periodically at a rate. Hence, bearing characteristic defect frequencies have close relation with its characteristic frequencies, which are functions of its geometry and the rotation speed of the shaft in the motor. Given the geometry of a bearing, with the outer race stationary, the equations for calculating the characteristic frequencies of the bearing are given in Table 5. For the faulty bearings used in the experiments, the theoretical values of their characteristic frequencies are also shown in Table 5. For the bearing installed in the traction motor, its characteristic frequencies are shown in Table 6. Rolling bearing characteristic defect frequencies are the same as their characteristic frequencies, except for the characteristic frequency of the ball defect. The characteristic defect frequencies (CDFs) for the defects on the outer race and the inner race are BPFO and BPFO, respectively. The CDF for the ball defect is two times the BSF (2 BSF) because the defect on the ball(s) impacts both the outer and the inner races each time one revolution of the rolling element is made [24]. In fact, there may be differences between the theoretical and the real characteristic Table 5 Characteristic frequencies of the tested bearings in the DC motor. Characteristic frequency Equation Value Ball pass frequency on the F or ¼ F r N b 2 d D cos a 35 Hz outer race (BPFO) Ball pass frequency on the F ir ¼ F r N b 2 þ d D cos a 92 Hz inner race (BPFI) Ball spin frequency (BSF) F b ¼ F r D d2 cos 2 a 64.5 Hz 2d D 2 Note: F r, N b, D, d, and a represent the rotating frequency, the number of balls, the pitch diameter, the ball diameter and the contact angle, respectively. Table 6 Specifications and characteristic frequencies of the bearing (SKF 625) in the traction motor. Parameter Bearing bore diameter Bearing outside diameter Race width Shaft rotation speed Sampling frequency Ball pass frequency of an outer race (BPFO) Ball pass frequency of an inner race (BPFI) Value 75 mm 3 mm 25 mm 498 rpm 32.8 khz 4 Hz 6 Hz
W. Guo et al. / Measurement 45 (22) 38 322 39.25.2.5..5 36 Hz BPFO 2 3 2 4 6 8 4 Frequency (Hz) (a) Envelope spectrum of IMF for the bearing with the outer race defect 5 6 7.4.2..8.6.4.2 27 Hz 2xBSF 2 4 6 8 Frequency (Hz) (c) Envelope spectrum of IMF for the bearing with the ball defect..8.6 2 Hz BPFI 2.25.2.5 39Hz BPFO 2Hz BPFI 2 BPFO 3 BPFO.4..2.5 2 4 6 8 Frequency (Hz) (b) Envelope spectrum of IMF for the bearing with the inner race defect 2 4 6 8 Frequency (Hz) (d) Envelope spectrum of for the bearing with outer and inner race defects Fig. 8. Envelope spectra of the selected IMFs for various faulty bearings, in which the identified CDFs and their harmonics are marked in the figures. frequencies because the above calculations are made with the assumption of pure rolling contact between the rolling balls and the races. Meanwhile, other errors, e.g. errors in accurately determining the shaft speed, may result in the difference between the theoretical and the real frequencies. 5.2. Bearing fault diagnosis based on the selected IMFs The envelope spectral analysis based on the Hilbert transform has been proven to be a good tool for the diagnosis of local faults in rolling bearings. It extracts the characteristic defect frequencies of faulty bearings along with the modulation so that the type of defect can be determined. In the following, bearing fault diagnosis was conducted on the selected IMFs, i.e. the resultant signals obtained using the hybrid method, to verify their features in the frequency domain. theoretical value listed in Table 5, in which the BPFO is 35 Hz. Hence, the position of the defect on the outer race of the tested bearing was successfully determined. 5.2.2. Diagnosis of the bearing with an inner race defect When the envelope spectral analysis was applied to IMF for the bearing with the inner race defect, the frequency spectrum, as shown in Fig. 8b, revealed the frequency component at the characteristic frequency of the inner race defect of 2 Hz (BPFI) and its harmonic (4 Hz). Although there is a difference of 8 Hz between Accelerometer 5.2.. Diagnosis of the bearing with an outer race defect According to the correlation coefficients between the IMFs and the filtered signal from the bearing with an outer race defect, which are listed in Table 3, IMF has the largest correlation coefficient of.8994. This IMF was thus selected for the fault diagnosis. The envelope spectrum of IMF is shown in Fig. 8a. To clearly display the CDFs of the tested bearings installed in the DC motor, the frequency spectra were limited to the range of Hz. As Fig. 8a shows, higher impacts can clearly be seen at the frequency of 36 Hz (BPFO) and its harmonics (around 2, 3, 4 of BPFO, etc.). The identified characteristic defect frequency of 36 Hz is only slightly different to the (a) A traction motor, the tested bearing and an accelerometer Y Horizontal Z Vertical Top View X Axial Traction Motor Ball bearing SKF 625 (b) Schematic diagram of the traction motor Fig. 9. A traction motor and its bearing (SKF 625).
32 W. Guo et al. / Measurement 45 (22) 38 322 the theoretical value (BPFI = 92 Hz listed in Table 5) and the identified value (2 Hz), the defect on the inner race of the tested bearing was still located. 5.2.3. Diagnosis of the bearing with a ball defect Once a defect occurs in the rolling element(s) of a bearing, it will ideally strike the outer race and the inner race each time. However, the ball does not always contact both races and the corresponding impulse may be lost. Such a defect is normally difficult to detect. In the experiment, most of the impulses related to the ball defect were successfully extracted from the raw vibration signal and resided in IMF that is shown in the first diagram of Fig. 7c. The envelope spectrum of this IMF is shown in Fig. 8c, and the identified CDF for the ball defect and its harmonics are also marked in the figure. The CDF (27 Hz) identified from the IMF is very close to the theoretical value (29 Hz), indicating that at least one of the rolling balls in the tested bearing has a defect. This result matches the experimental setup, which is shown in Fig. 3e. 5.2.4. Diagnosis of the bearing with multiple defect (i.e. outer and inner race defects) A bearing with multiple defects, in this case defects on the outer and the inner races, was also considered in the experiments. Generally, as the distance between the mounted accelerometer and the defect increases, the vibration picked up by the accelerometer is attenuated. As Fig. 3a shows, the accelerometer mounted on the DC motor was closer to the outer race than the inner race. (a) 3 A raw bearing signal collected from the traction motor (Kurtosis = 2.7) (b) -3 The filtered signal (Kurtosis = 6.33) (c) -.6 IMF (Kurtosis = 7.49) (d) -.6.2 (e) -.2. (f) -..2.4.6.8. Hz BPFO The envelope spectrum of IMF.4 3x 2x 4 8 2 6 2 Frequency (Hz) Fig.. A raw vibration signal collected from the bearing in the traction motor, the filtered signal, and main decomposition results obtained using the hybrid signal processing method, along with the envelope spectrum of IMF. The signal generated by the faulty bearing was recovered and distributed in IMF, and its CDF was accordingly identified from the envelope spectrum of this IMF.
W. Guo et al. / Measurement 45 (22) 38 322 32 The impulses generated by the inner race defect were thus rather weak and easily concealed by the impulses of the outer race defect and the noise. This was also observed in the experimental results. The hybrid signal processing method successfully extracted most of the impulses and distributed to. The envelope spectrum of is shown in Fig. 8d and reveals the detected BPFO (39 Hz) and its harmonics (2 and 3 BPFO) along with the BPFI (2 Hz). Although the amplitude at BPFI is relatively small, this CDF can be clearly observed in the frequency spectrum. Therefore, the tested bearing has defects on the outer and the inner races. 5.2.5. Diagnosis of the bearing installed in the traction motor Envelope spectral analysis was also performed on the resultant signal (IMF) obtained by applying the hybrid signal processing method to the vibration signal from the traction motor. The displayed frequency range of the spectrum is 2 Hz to display the CDF clearly. The detected frequency in the envelope spectrum shown in Fig. f is Hz, which approximately matches the BPFO (4 Hz) listed in Table 6. Meanwhile, the harmonics (2,3) of the BPFO can also be observed in Fig. f. Hence, the impact is confirmed as being generated on the outer race of the tested bearing. The faulty element in the tested bearing also supports this conclusion. The fault diagnoses of the resultant signals obtained from the experiments and the application demonstrate the effectiveness of our hybrid method in recovering important faulty features hidden in raw vibration signals with strong noise. The resultant signals remove most of the noise in the raw signals. The proposed hybrid signal processing method also reveals the temporal impacts from the raw signal while preserving the important features of single or multiple defects of bearings. 6. Conclusions This paper presents a hybrid signal processing method based on spectral kurtosis (SK) and ensemble empirical mode decomposition (EEMD) that can recover faulty bearing signals from large noise. The hybrid signal processing method involves two steps. First, the raw vibration signal embedded with large noise is filtered using an optimal band-pass filter based on SK. The extracted impulsive part from the noisy signal provided the necessary extremes for the signal decomposition. The filtered signal was then decomposed using EEMD method. The transient faulty signal was then separated from the noise by distributing them into different IMFs. For each faulty bearing, the IMF with the largest correlation coefficient was selected as the resultant signal that contains the main impulses related to the bearing defect. Vibration signals collected from faulty bearings installed in an experimental motor and a real traction motor were used to prove the efficiency of the proposed hybrid signal processing method. To further validate the faulty features in the resultant signals, the envelope spectral analysis method was used. Regardless of the type of defect occurred in the tested bearings, whether a single defect (on the outer or the inner race, or in the ball) or multiple defects (on the outer and the inner races), the characteristic defect frequencies of the rolling bearings were easily identified in the respective envelope spectra of the resultant signals. As a result, the defect types of the tested bearings could be determined. In summary, the results demonstrate that the proposed hybrid signal processing method can recover faulty bearing signals from large noise and increase the kurtosis of the analyzed signal to a remarkable degree. 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