A roller bearing fault diagnosis method based on hierarchical entropy and support vector machine with particle swarm optimization algorithm
Introduction
Roller bearings are a critical and widely used component in the rotating machines. In order to keep bearings running with high reliability and maintain a low downtime of machinery, it is significant to develop a reliable technique to detect faults in bearings. Among various bearing fault diagnosis techniques, the most frequently used one is vibration signal processing [1], because vibration signals are closely related with the structural dynamics of the machine under monitoring. So it is possible to obtain dominant diagnostic information from faulty bearing vibration signals by using proper processing techniques.
As it is known, because of the non-liner factors such as clearance, friction and stiffness, while the roller bearing with faults is running, its vibration signals will present non-liner characteristics [2]. For this reason, the traditional time and frequency domain signal processing techniques based on the linear systems, even the advance signal processing techniques such as wavelet transforms, cannot make an accurate evaluation of the working conditions of roller bearing. The development of non-linear dynamic parameter estimation provides a good alternative for recognizing and predicting the complex non-linear dynamic behavior. Entropy-based parameters can describe the non-linear dynamical characteristics of vibration signal in time domain, and have been investigated and applied to the field of fault diagnosis [3], [4], [5]. Pincus [6], [7], [8] introduced approximate entropy (ApEn), a measure of signal complexity, which can be applied to clinical cardiovascular time series. Although ApEn has been introduced and selected as a tool for bearing vibration signal processing, due to its self-matching problem, ApEn is heavily dependent on the record length and its value is uniformly lower than expected for short records, and lacks relative coherence as well [9]. In order to overcome shortcomings of ApEn, Richman and Moorman [9] developed a new measurement of signal complexity, viz. sample entropy (SampEn), which is less dependent on data length and applied to the analysis of neonatal heart rate variability [10]. However, an increase in the entropy may not always be associated with an increase in dynamical complexity [11]. In order to address this problem, Costa et al. proposed multi-scale entropy (MSE) method which analyzes signals on multiple time scales rather than on a single scale, and applied MSE analysis to complex physiologic signals [11], [12]. Considering a machine composed of gears, bearings, shafts and other mechanical components, and the interaction and coupling effects between these components will introduce multiple intrinsic oscillatory modes in measure vibration signals, Zhang et al. [5] used the MSE method to analyze the faulty bearing vibration signals.
Recently, Jiang et al. [13] developed a hierarchical entropy (HE) method to quantify the complexity of a time series based on hierarchical decomposition and entropy analysis. They have applied the HE method to the cardiac interval time series to identify different heart failures. Compared with MSE, the superiority of HE lies that, for each time scale, it considers not only the lower frequency components which are generated by averaging the components in the previous scale but also the higher frequency component which is generated by taking the difference of two consecutive scales [13]. Considering the aforementioned complexity of the bearing vibration signal which is induced by the interaction and coupling effects of different components, the fault information may be hidden in the lower frequency component or in both. Therefore, MSE based on only low frequency components of the multiple scales of a time series may be not sufficient for extracting fault features from faulty bearing vibration signals. Based on this consideration, the HE method is introduced in the present study to the field of roller bearing fault diagnosis.
Normally, the process of roller bearing fault diagnosis includes data acquisition, feature extraction and pattern recognition, and the later two are the priority [14]. Hence, after feature extraction with HE, another point of roller bearing fault diagnosis is pattern recognition. Conventional statistical pattern recognition methods and artificial neural networks (ANN) are studied that the sufficient samples are available, which is not always true in practices [15]. Support vector machines (SVM) based on statistical learning theory that are of specialties for a smaller number of samples have better generalization than ANN and guarantee the local and global optimal solution are exactly the same [16]. Meantime, SVM can solve the learning problem with a smaller number of samples. In practical applications, it is hard or even impossible to obtain sufficient fault samples. For this reason, SVM is introduced into machines fault diagnosis due to their high accuracy and good generalization for a smaller sample number. Many researchers [17], [18], [19] have made their attempts using SVM to identify the rotating machine conditions.
In this paper, a new approach for roller bearing fault diagnosis is proposed through the combination of HE and SVM. First, SampEns of 8 nodes of hierarchical decomposition, viz. HEs are calculated to form fault feature vectors including rich fault information. Then, the fault features are input to the multi-class classifier of SVM and the fault types of roller bearings as well as different levels of severity are identified. The paper is organized as follows. In Section 2, SampEn and MSE are briefly introduced. Section 3 is dedicated to hierarchical decomposition and HE analysis. In Section 4, the multi-class SVM and the process of its parameters selection with particle swarm optimization (PSO) are given. In Section 5, the roller bearing fault diagnosis method based on HE and SVM is applied to the identification of bearing conditions and is compared with the MSE method. Finally, the conclusion of this paper is given in Section 6.
Section snippets
Review of sample entropy and multi-scale entropy
Given a time series of N points, {x(1), … , x(i), … , x(N)}, SampEn can be defined as follows [9]:
- (1)
Form the m-length vectors Xm(i)
- (2)
The distance between two such vectors is defined as
- (3)
For each Xm(i) and the fixed tolerance r, let Ai be the number of vector that satisfy d [Xm(i), Xm(j)] ⩽ r, then denote as
- (4)
The average of the is designated as
- (5)
By increasing the dimension
The hierarchical entropy method
The MSE measures the complexity very well for those time series whose information is only stored in its lower frequency components, but it will miss the information stored in a high frequency component. For this reason, literature [13] introduced the hierarchical entropy method as follows.
First, an averaging operator Q0 for the time series x = {x(1), … , x(i), … , x(N)} is defined byThe time series Q0(x) with length 2n−1 is the low frequency component of x at scale 2. A
Multi-class SVM
Considering different fault types as well as various levels of severity, the roller bearing fault recognition is a multi-class classification. The widely used strategies for multi-class classification are ’one-against-all’ and ’one-against-one’. Hsu and Lin gave a detailed comparison and concluded that ’one-against-one’ is a competitive approach [20]. Therefore, ’one-against-one’ method is adopted in this study. If k is the number of classes, it constructs k(k − 1)/2 classifiers and each one is
Experimental setup
All the vibration data of roller bearings analyzed in this paper comes from Case Western Reserve University (CWRU) bearing data center [26]. As shown in Fig. 2, the test stand consists of a 2 hp, three-phase induction motor (left), a torque transducer (middle), and a dynamometer (right). The transducer is used to collect speed and horsepower data. The dynamometer is controlled so that the desired torque load levels could be achieved. The test bearing supports the motor shaft at the drive end.
Conclusion
A new approach based on HE and SVM for fault diagnosis of roller bearings is put forward in this study. Due to the non-linear dynamic characteristics as well as interaction and coupling effects between mechanical components, the HEs of vibration signals under various conditions at scale 4 are calculated to form fault feature vectors. These feature vectors are then input into SVM for fault classification. During the training process of SVM prediction model, PSO is utilized to optimize the
Acknowledgment
The authors wound like to thank the Case Western University Bearing Data Center for kindly providing the experimental data.
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