Fault diagnosis based on dependent feature vector and probability neural network for rolling element bearings
Introduction
Rolling element bearings (REB) are frequently used in rotary machinery, and they are also crucial mechanical parts. REB faults not only affect the normal operation of the machine, but may also cause consequences such as production disruptions, economic loss, and even life casualties [1], [2]. Therefore, the exact condition monitoring and fault diagnosis for REB play an important role in ensuring the reliable running of machinery [3], [4], and the researches on REB fault diagnosis are very necessary to be developed and continuously improved [5], [6].
Signal processing is a significant procedure of fault diagnosis systems, and time–frequency analysis [7], envelope analysis [8], cyclostationary analysis [9] and the combinations of them [10], [11] are commonly adopted in fault diagnosis. In recent years, an advanced time–frequency analysis method called empirical mode decomposition (EMD) has become widely used in signal analysis. EMD is self-adaptive in nature and decomposes a signal on the basis of its frequency content and variation [12], [13]. EMD is a powerful method for nonlinear and non-stationary signal processing [14], and the IMF components produced by this method usually possess physical meanings. EMD has been proved quite versatile in a broad range of applications in the fault diagnosis of machinery, such as gear fault diagnosis [15], [16], rotor fault diagnosis [5] and REB fault diagnosis [16], [17].
Feature selection is a critical processing step designed to find the most informative feature subset, and it is an effective method to improve the classification accuracy and reduce the computational burden of the classifier [18], [19]. The commonly used feature selection methods include distance evaluation technique [20], local learning-based feature selection [21], mutual information algorithm [22], [23], F-score feature selection [24] and Laplacian based feature selection [25]. All of them could eliminate redundant features, and find an informative feature subset. Therefore, they could effectively improve the diagnostic accuracy and reduce the computing complexity. Feature weighting technique is another significant procedure to improve the classification accuracy, which could emphasize the contribution of the sensitive features to classification and weaken the interference of irrelevant features [26], [27]. Therefore, Feature weighting is widely used in forecasting [28], classification [29] and fault diagnosis [30], [31].
On the basis of feature selection methods and feature weighting techniques, this paper pays more attention to the different description ability of each feature about different samples and its different influence on the correct recognition of different samples. In order to achieve this purpose, dependent feature vector (DFV) is proposed in this paper to denote the fault symptom attributes. DFV selects the informative feature subset for each sample according to its own characteristics, and uses different feature subsets to describe different samples. So, it not only retains the most effective information for each sample, but also could reduce the differences among the samples of the same class. Then, through selecting appropriate value (DV) for the invalid DF, DFV significantly enlarges the difference among the different classes. Therefore, DFV could effectively enhance the compactness of the samples in the same class and the separability among different classes, achieving the accurate fault description. Moreover, the redundant information of each sample is removed to the hilt via DFV. Hence, the computing complexity and burden of feature extraction and fault identification are greatly reduced, while the fault diagnosis accuracy is also improved.
Fault classification is another key procedure. In the past few decades, support vector machine [24], [28], [29], artificial neural network [10] and fuzzy inference [18], [30], [31] are widely used and developed to identify mechanical failures. Probability neural network (PNN) [32], which needs one epoch of training and could accomplish training and classifying in an extremely short time, is proved to be very suitable for identification problems with simple feature vector [33]. In accordance with the simplicity of DFV, PNN is introduced as the classifier to realize automatic fault classification.
The purpose of this paper is to establish a fault diagnosis method based on DFV and PNN (DFV–PNN) for REB fault diagnosis. It is structured as follows: Section 2 puts forward the basic concept of DFV. The establishing method, computing method and effectiveness evaluation of DFV are described in Section 3. And in Section 4, the classifier is discussed. The experiment of REB fault diagnosis is introduced in Section 5. Finally, the conclusions of this work are summarized in Section 6.
Section snippets
The proposition of DFV
For classification problems, almost all of the traditional intelligent classification methods use the same feature vector to represent all samples. They ignore the different description ability of one feature to different samples, as well as its different influence on the correct recognition of different samples. However, humans usually deal with the same problems through another way, and they describe samples of a certain class using a unique feature vector. For example, for the classification
The structure establishing of DFV
The feature vector establishing is a key step for fault diagnosis. According to the peculiarity of DFV, a nested method for establishing DFV is proposed in this paper, and the specific operation process is showed in Fig. 5. First, the LF is chosen for the sample space, and the different value intervals of LF are obtained. And then, in accordance with the value intervals of the LF, the sample space is divided into several subspaces. For the subspaces which include samples of only one class, the
The classifier
Classifier is one of the most important factors which directly determines the efficiency and accuracy of fault diagnosis, so it is very significant to choose an appropriate classifier according to the specific diagnosis object.
PNN is a feed-forward four-layer neural network introduced by Specht in 1988 based on Parzen probabilistic density function and Bayesian classification rule [32]. It was proved that PNN is easy to train and it can be used in real-time applications [33], [36]. Moreover,
The experimental data
The experiment and engineering application based on the above theory are introduced in this section. The rolling bearing fault data used in this paper comes from the dataset of the rolling element bearings [38], [39], which is obtained by installing deep groove ball bearings manufactured by SKF in a motor-driven mechanical system. In this paper, the signals are collected at 24,000 samples/s under 2 hp load, and the defect sizes are 0.007 or 0.014 in, as showed in Fig. 10. Each original signal was
Conclusions
A novel fault diagnosis method (DFV–PNN) for REB based on DFV and PNN is presented and discussed in this paper. In this method, DFV is proposed to denote the fault symptom attributes of the six faults.
DFV is a self-adapting sample representation method. And it uses a unique feature selection technique which selects the most effective features for each sample according to its own characteristics. It also has a unique structure: The LF of all samples are the same, the effective DF is decided by
Acknowledgements
We would like to thank Kenneth A. Loparo, Ph.D., Case Western Reserve University, for his experimental data provided. Thanks to the anonymous referees for their helpful comments and suggestion to improve the presentation of this study.
This work was supported by the National Natural Science Foundation of China (No. 51239004), the National Natural Science Foundation of China (No. 51079057), and the research funds of University and college PhD discipline of China (No. 20100142110012).
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