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Timely and accurate condition monitoring and fault diagnosis of rotating machinery are very important to maintain a high degree of availability, reliability and operational safety. This paper presents a novel intelligent method based on local mean decomposition (LMD) and multiclass reproducing wavelet support vector machines (RWSVM), which is applied to diagnose rotating machinery faults. First, the sensorbased vibration signals measured from the rotating machinery are preprocessed by the LMD method and product functions (PFs) are produced. Second, statistic features are extracted to acquire more fault characteristic information from the sensitive PF. Finally, these features are fed into a multiclass RWSVM to identify the rotating machinery health conditions. The experimental results validate the effectiveness of the proposed RWSVM method in identifying rotating machinery fault patterns accurately and effectively and its superiority over that based on the general SVM.
Rotating machinery fault diagnosis is actually a pattern recognition process [
The purpose of extracting the features is to extract parameters representing the machine operation conditions to be used for machine condition identification. There are a number of feature extraction methods for vibration signals in the literature. A popular and noted example is the timefrequency analysis method of wavelet transform, which has obtained great success in machine fault diagnostics for its many distinct advantages [
Local mean decomposition (LMD) is a novel adaptive time–frequency analysis method proposed by Smith [
Final condition identification is another task in fault diagnosis of rotating machinery. Machine condition identification via artificial intelligence techniques can provide an automated fault diagnosis procedure [
The combination of wavelet analysis and SVM kernel function is a new idea and technology, which has the advantages of better accuracy, generalization capability and multiresolution [
To automatically and effectively diagnose rotating machinery faults, a novel fault diagnosis method based on LMD and RWSVM is proposed in this paper. In the proposed method, the sensorbased vibration signals captured from the rotating machinery are first decomposed by the LMD method. Second, the most sensitive PF that contains the main fault information is selected. Third, statistic features are extracted from the most sensitive PF. Finally, these features are input into the RWSVM to recognize the health conditions of the rotating machinery. The identification results validate the effectiveness of the proposed method.
LMD was originally developed to decompose modulated signals into a small set of product functions (PFs), each of which is the product of an amplitude envelope signal and a frequency modulated (FM) signal. Different from EMD, the essence of the LMD method is to isolate pure FM signals and envelope signals from the original signal by iteration, and then multiply the pure FM signals with envelope signals to get a PF component whose instantaneous frequency is physically meaningful.
A more detailed and comprehensive explanation of LMD is provided in references [
In order to verify the effectiveness of the proposed signal transient detection method, an application example for the detection of localized outerrace defects of rolling bearing (type ZA2115) is provided here. The rotating frequency
The LMD is employed to decompose the vibration acceleration signal and a total of six PFs and the residual item are obtained, as shown in
As shown in
The main idea in this proposed method is to construct a reproducing wavelet estimator by solving an empirical risk minimization problem. According to the learning theory [
In order to avoid illposed problems, we have to look for the function f that minimizes the regularized empirical risk functional instead of the empirical risk according to regularization theory [
By minimizing the regularized empirical risk in
In the case of RWSVM method,
Wavelet frames' finite set of
Consider the family
So far, we can construct a wavelet kernel in RKHS as follows:
For a common multidimensional wavelet function, the mother wavelet can be given as the product of onedimensional (1D) wavelet function according to the tensor products of RKHS [
Let ψ(
For practical kernel construction, we have to define a mother wavelet function ψ and select suitable parameters according to the problem at hand. Moreover, we can truncate the range of the scales and set coefficients in
In this study, we constructed RWSVM with different wavelet functions.
The initial SVM is an essentially binary classifier, and Lingras and Butz [
A novel intelligent fault diagnosis strategy is proposed in this study, which is based on LMD and multiclass RWSVM.
acquiring vibration acceleration signals when the rotating machinery operation state is normal or faulty.
preprocessing vibration signals by using LMD.
extracting seven statistic features [
constructing classification process for fault diagnosis by RWSVM using different reproducing wavelet kernel function.
the testing samples can be in put into the trained RWSVM classifier and then the operating conditions can be identified by the output of the RWSVM classifiers.
In order to evaluate the effectiveness of the proposed method, two kinds of experimental setups are constructed to offer the vibration signals from various fault conditions.
In this experiment, a gear data set in axle II shown in
The present study chooses SVM with Gaussian radial basis function (RBF) kernel as a reference which is commonly preferred to other kernel function types [
For the SVM using RBF kernel in
As
From
In
Furthermore,
The tested aeroengine rotor system is a dismountable diskdrum type rotor whose structure sketch is shown in
The rotor structure is excited by utilizing a shaker with a constant excitation frequency of 1 Hz and the excitation position is on the shaft, as shown in
Each data subset consists of 50 samples and therefore the whole data set corresponding to the four bearing health conditions includes 200 samples. Each sample is a section of vibration signal containing 2,048 sampling points. Each subsample data set is split into two sets: 30 subsamples for training and 20 subsamples for testing.
The abovementioned intelligent method is employed again and the corresponding identification results are given in
In the two experiments, test results verify that the proposed RWSVM method obviously outperforms the SVM method in diagnosing different categories of gear and aeroengine rotor faults. In two experimental results, the proposed reproducing wavelet kernels function with multiresolution structure have a better performance and generalization ability than the traditional RBF kernel, and the best classification accuracy was obtained using the Coiflet kernel function. The main reasons are as follows:
The RBF is a kind of kernel function which is generally used. It shows the good generalization ability. However, With the RBF kernel functions, the SVM can not approach any curve in
The kernel functions of Haar wavelet, the Daubechies wavelet and the Coiflet wavelet are the orthonormal base of
The Coiflet kernel function has some interesting properties that make it useful in signal processing. It possesses maximal number of vanishing shifted scaling moments for the given number of scaling coefficients. Coiflet are separable filters in the sense that spatial frequencies in
The present study proposes a novel hybrid intelligent multifault classification method based on LMD and multiclass RWSVM. In the proposed method, LMD can select frequency bands adaptively according to the characteristics of the vibration signal and determine signal resolutions of different frequency bands. It can optimize the signal analysis and increase the accuracy of useful information extraction. RWSVM is effective in handling uncertain data and small samples, the experiment results demonstrate that RWSVM produces an obvious improvement in recognition accuracy and provides a good diagnosis capability. Compared with the general RBFSVM method, the proposed RWSVM has better generalization ability and strong robustness.
In addition, it should be noted that although the proposed method is only demonstrated by using the gearbox and the rotor examples in this work, it can be easily applied to other classification problems in mechanical fault diagnosis. The proposed RWSVM might provide a new opportunity for other condition monitoring and fault diagnosis which still needs to be further explored in the future.
This work was supported by the National Natural Science Foundation of China (Nos. 51225501 and 51175401), the Research Fund for the Doctoral Program of Higher Education of China (No. 20120201110028) and the Program for Changjiang Scholars and University Innovative Research Teams.
The authors declare no conflict of interest.
The time domain waveform and spectrum of the vibration acceleration signal of the rolling bearing with localized defects on the outer race: (
The decomposed results and residue by LMD of a bearing outer race fault signal.
Frequency spectrum of PF1.
Examples of wavelet kernel: (
‘Oneversusrest’ multiclass RWSVM.
Architecture of the proposed fault diagnosis system.
Structure sketch of the test bench for the experimental gearbox.
Gears defect in the shaft 2.
Vibration signals of time and frequency domain.
Results of the SVM classification for the experimental gear.
The structure of the aeroengine rotor and locations of the sensors:
Vibration signals of time and frequency domain.
Results of the SVM classification for the aeroengine rotor.
Parameters of gear transmission system.

 

Modules (mm)  The number of teeth  Modules (mm)  The number of teeth  
5.23  2  Z1  26  2  Z1  40 
Z2  64  Z2  85 
The classified result of gear transmission system test data.
 

SVM  RWSVM  

 



 
Normal state  90  95  100  100 
Pitting fault  80  85  90  95 
Spalling fault  95  100  100  100 
Eccentric fault  85  90  95  100 
 
Average accuracy (%)  87.5  92.5  96.25  98.75 
The classified result of aeroengine rotor test data.
 

SVM  RWSVM  

 



 
Normal state  95  100  100  100 
Pitting fault  90  90  95  100 
Spalling fault  90  90  95  100 
Eccentric fault  90  95  100  95 
 
Average accuracy (%)  91.25  95  97.5  98.75 