Accurately identifying faults in rolling bearing systems by analyzing vibration signals, which are often nonstationary, is challenging. To address this issue, a new approach based on complementary ensemble empirical mode decomposition (CEEMD) and time series modeling is proposed in this paper. This approach seeks to identify faults appearing in a rolling bearing system using proper autoregressive (AR) model established from the nonstationary vibration signal. First, vibration signals measured from a rolling bearing test system with different defect conditions are decomposed into a set of intrinsic mode functions (IMFs) by means of the CEEMD method. Second, vibration signals are filtered with calculated filtering parameters. Third, the IMF which is closely correlated to the filtered signal is selected according to the correlation coefficient between the filtered signal and each IMF, and then the AR model of the selected IMF is established. Subsequently, the AR model parameters are considered as the input feature vectors, and the hidden Markov model (HMM) is used to identify the fault pattern of a rolling bearing. Experimental study performed on a bearing test system has shown that the presented approach can accurately identify faults in rolling bearings.
Rolling element bearing failure is one of the foremost causes of failures in rotating machinery, and such failure may result in costly production loss and catastrophic accidents. Early detection and diagnosis of bearing faults while the machine is still in operation can help to avoid abnormal event progression and to reduce productivity loss [
In order to overcome limitations of the traditional techniques, autoregressive (AR) model has been successfully applied to extracting features from vibration signals for fault diagnosis in recent years [
Empirical mode decomposition (EMD) is an adaptive timefrequency signal processing method [
In this paper, we combine the advantages of CEEMD and time series model and propose a new method based on CEEMD and AR model for rolling bearing fault diagnosis. The CEEMD is used as the pretreatment to filter the signal and extract the IMF which is closely correlated to the filtered signal, and then the AR model of the selected IMF is established. The AR model parameters are used as the feature vectors to a classifier, where the hidden Markov model (HMM) is used to identify the fault pattern of a rolling bearing. The rest of this paper is organized as follows. In Section
Autoregressive moving average (ARMA) model is the representative time series model, which can be expressed in linear difference equation form as
It is critical to determine the order number of the AR model, because the accuracy of the order not only affects the accuracy of identification of the system, but also influences the stability of the system. In order to estimate the order of the AR model correctly, FPE criterion, BIC criterion, and AIC criterion are usually used [
FPE criterion
BIC criterion
AIC criterion
Complementary ensemble empirical mode decomposition (CEEMD) is an improved algorithm based on empirical mode decomposition (EMD). Through EMD process, any complex time series can be decomposed into finite numbers of intrinsic mode functions (IMFs), and each IMF reflects the dynamic characteristic of the original signal. The IMF component must satisfy two conditions: (a) the number of poles and zeros is either equal to each other or differs at most by one; (b) the upper and lower envelopes must be locally symmetric about the timeline. The basic principle of EMD method is to decompose the original signal
The EMD method is a kind of adaptive local analysis method, with each IMF highlighting the local features of the data. However, EMD decomposition results often suffer from mode mixing, which is defined as either a single IMF consisting of widely disparate scales or a signal residing in different IMF components [
The waveform of the simulated signal is shown in Figure
Signal waveforms.
The decomposition result by EMD.
To overcome the problem of mode mixing, the ensemble empirical mode decomposition (EEMD) was proposed [
The decomposition result by EEMD.
It should be noted that, during the EEMD process, each individual trial may produce noisy results, but the effect of the added noise can be suppressed by large number of ensemble mean computations. This would be too time consuming to implement. An improved algorithm, named complementary ensemble mode decomposition (CEEMD), is suggested to improve the computation efficiency. In this algorithm, the residue of the added white noises can be extracted from the mixtures of data and white noises via pairs of complementary ensemble IMFs with positive and negative added white noises. Although this new approach yields IMF with a similar RMS noise to EEMD, it eliminates residue noise in the IMFs and overcomes the problem of mode mixing with much more efficiency [
the average of corresponding component in
Decomposition flow chart of CEEMD.
Figure
The decomposition result by CEEMD.
Based on CEEMD and time series model, a hybrid fault diagnosis approach can be designed. The hybrid approach combines the advantages of CEEMD method in the nonstationary signal decomposition with the ability of time series modeling in feature extraction. The flow chart of the developed approach is shown in Figure
The flow chart of the proposed method.
The main steps are as follows.
To demonstrate the validity of the method proposed in this study, three signals
Signal waveforms of
Figure
Correlation coefficients between filtered signal and each IMF.
Signal  Correlation coefficient  

IMF1  IMF2  IMF3  IMF4  IMF5  IMF6  IMF7  IMF8  

−0.0031  −0.0009  0.0371  0.4096  0.9668  0.2428  0.1273  −0.0448 

0.0051  0.0004  0.0435  0.2111  0.4695  0.8887  0.7214  −0.0201 

−0.0234  −0.0154  0.0286  0.5900  0.8953  0.1649  0.1887  −0.0210 
The decomposition results by CEEMD.
It can be seen in Table
Model parameter estimation results.
Signal  Model parameter  






 

4.7183  −9.1103  9.2034  −5.1408  1.5207  −0.1914 

4.8894  −9.8269  10.3945  −6.1194  1.9153  −0.2531 

4.8718  −9.9955  11.1616  −7.2529  2.6430  −0.4282 
A total of 90 feature vectors were collected from three groups of signals using the proposed approach. Onethird of the feature vectors in each condition were used for training the classifier and others were used for testing. The results of the signal classification are listed in Table
Signal classification results.
Signal type  Test sample  Classification results  Classification rate [%]  Overall classification rate [%]  






20  19  1  0  95  96.7 

20  0  19  1  95  

20  0  0  20  100 
Results in Table
In order to illustrate the practicability and effectiveness of the proposed method, a bearing fault data set from the electrical engineering laboratory of Case Western Reserve University is analyzed [
Bearing test stand.
Figure
Vibration signal waveforms of different conditions.
The decomposition results by CEEMD under different conditions.
No defect
Inner ring defect
Rolling element defect
Outer ring defect
Correlation coefficients calculated between the filtered signal and each IMF are shown in Table
Correlation coefficients between filtered signals and each IMF.
Signal  Correlation coefficient  

IMF1  IMF2  IMF3  IMF4  IMF5  IMF6  IMF7  IMF8  
(a)  0.4135  0.7538  0.4381  0.4880  0.4356  0.1792  0.0971  −0.0056 
(b)  0.8794  0.4275  0.2583  0.1337  0.0421  0.0285  −0.0009  −0.0074 
(c)  0.9509  0.2180  0.2325  0.1337  0.0821  0.0350  −0.0017  0.0009 
(d)  0.9878  0.1267  0.0636  0.0509  0.0136  0.0060  −0.0008  −0.0068 
The IMF which is closely correlated to the filtered signal is IMF2 for signal (a) and IMF1 for signals (b), (c), and (d), respectively. These IMFs are used for AR model construction. The model order estimation curves of the four conditions based on the principle of FPE criterion are shown in Figure
Model parameter estimation results.
Signal  Model parameter  






 
(a)  3.1280  −4.7797  4.2245  −2.1489  0.4241  0.0356 
(b)  0.2084  −1.3585  0.5142  −0.6356  0.3471  −0.0422 
(c)  0.1335  −1.6472  0.3941  −0.8473  0.2142  −0.1011 
(d)  −0.1172  −1.2159  0.1178  −0.1283  0.1467  0.2533 
The model order estimation curves.
No defect
Inner ring defect
Rolling element defect
Outer ring defect
The parameters in Table
The results of quantization.
No defect
Inner ring defect
Rolling element defect
Outer ring defect
A total of 160 feature vectors were collected from the four conditions, half of the feature vectors were used for training the classifier and others for signal classification, and the classification results are listed in Table
Fault diagnosis using CEEMD and time series model.
Fault type  Test sample  Classification results  Classification rate [%]  Overall classification rate [%]  

No defect  Inner ring defect  Rolling element defect  Outer ring defect  
No defect  20  20  0  0  0  100  97.5 
Inner ring defect  20  0  19  1  0  95  
Rolling element defect  20  0  1  19  0  95  
Outer ring defect  20  0  0  0  20  100 
For comparison, Tables
Fault diagnosis using time series model only.
Fault type  Test sample  Classification results  Classification rate [%]  Overall classification rate [%]  

No defect  Inner ring defect  Rolling element defect  Outer ring defect  
No defect  20  19  1  0  0  95  90.0 
Inner ring defect  20  1  17  2  0  85  
Rolling element defect  20  0  2  17  1  85  
Outer ring defect  20  0  0  1  19  95 
Fault diagnosis using EMD and time series model.
Fault type  Test sample  Classification results  Classification rate [%]  Overall classification rate [%]  

No defect  Inner ring defect  Rolling element defect  Outer ring defect  
No defect  20  19  1  0  0  95  93.75 
Inner ring defect  20  0  18  2  0  90  
Rolling element defect  20  0  1  19  0  95  
Outer ring defect  20  0  0  1  19  95 
Aiming at diagnosing rolling bearing faults, a hybrid approach based on CEEMD and time series modeling is proposed in this paper. The CEEMD method can decompose the nonstationary signal into a series of IMFs with low computation. AR model is an effective approach to extract the fault feature of the vibration signals and the fault pattern can be identified directly by the extracted fault features without establishing the mathematical model and studying the fault mechanism of the system. In this paper, the CEEMD method is used as a pretreatment, which can increase the accuracy of the AR model for the measured signal, and the AR model of the IMF which is closely correlated to the filtered signal is established to extract the fault feature parameters. Comparing to the EMDAR approach and the direct modeling approach where raw signals are directly used as input for AR modeling, a higher classification rate was shown to be achieved by using the new approach (e.g., 96.7% for simulated signals and 97.5% for experimental data). Meanwhile we anticipate that the proposed method can also be used for incipient fault diagnosis in rolling bearing, where further experiments are needed to verify the accuracy. Since the approach presented in this study is generic in nature, it can be readily adapted to a broad range of applications for machine fault diagnosis.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work has been supported in part by the National Natural Science Foundation of China (no. 61101163 and no. 51175080) and the Nature Science Foundation of Jiangsu Province of China (no. BK2012739).