1. Introduction
Rotating machinery plays a significant role in modern industrial fields, and its health status greatly influences the production efficiency and product quality. Besides, once an unexpected or sudden fault occurs, it could result in large economic losses. Hence, it is of great practical significance to diagnose rotating machine faults [
1]. During the running process of various kinds of rotating machines, rolling element bearings are the most widely used parts. However, owing to their structural properties and operating environment, rolling bearing damage is inevitable and will affect the mechanical properties of the equipment to some extent [
2]. Therefore, some diagnostic measures need to be carried out for rolling element bearings, thus promoting the stable and efficient operation of rotating machines [
3,
4]. Generally, when a fault occurs in a rolling element, it is accompanied by a certain amount of vibration and sound. Thus, potential faults can be well detected with appropriate techniques for processing the collected vibration or acoustic signals [
5,
6]. Due to the fact that vibration signals carry rich information about potential faults, vibration analysis has been widely applied to diagnose the faults of rolling element bearings, which always includes two procedures: one is the feature extraction of vibration signals with signal processing techniques, and the other is the fault pattern recognition for the extracted features [
7,
8].
After collecting the vibration signals, the extraction of representative features is the main mission. However, the signals are always non-stationary and non-linear, which makes it difficult to extract the pivotal features effectively. To solve this problem, many time-frequency signal processing methods have been proposed in previous studies, such as wavelet transform (WT, [
9]), empirical mode decomposition (EMD, [
10]), ensemble empirical mode decomposition (EEMD, [
11]) and variational mode decomposition (VMD, [
12]). Among the above methods, WT [
9] is an adaptive signal analysis method proposed based on the localization idea of the Fourier transform, possessing strong recognition ability for transient signals, and has been widely used to analyze non-stationary signals [
13,
14]. However, once the wavelet basis is designated, the generalization will be poor. EMD, originally proposed by Huang [
10], decomposes a given signal into components with different scales through loop iteration, and possesses better adaptability since the decomposition only depends on the local characteristics of the signal. Though EMD has attracted great attention due to its ability to deal with non-stationary signals [
15,
16], its performance is severely affected by mode mixing and end effects. To solve these problems, an improved version-EEMD was put forward with noise assistance [
11] and has become a focus in the field of signal processing [
17,
18]. Unlike EMD/EEMD that lack a mathematical theory foundation, the newly proposed VMD [
12] is a quasi-orthogonal signal processing method which decomposes the given signal by solving a constrained variational problem. Besides, the effectiveness and superiority of VMD have been verified in previous studies [
19,
20].
With the non-stationarity of the vibration signals weakened by the aforementioned methods, it is necessary to extract fault features from the components. As it is known that information entropy is an effective indicator for measuring the uncertainty degree of signals, combining entropy theory with signal processing methods is expected to represent the fault characteristics well. For this reason, different entropy methods, including energy entropy [
21], sample entropy [
22,
23], approximate entropy [
24,
25], permutation entropy [
26,
27] and so on, have been utilized to solve feature extraction and fault diagnosis problems. For example, Xiao et al. [
21] extracted the energy entropy of sub-band signals decomposed from the stator current of doubly-fed wind turbine with dual-tree complex wavelet transform. Zhang et al. [
23] calculated the sample entropy of sub-bands of rolling bearings decomposed by lifting wavelet packet transform. An et al. [
25] calculated the approximate entropy of the selected components of vibration signals from a wind turbine rolling bearing decomposed by adaptive local iterative filtering. Shi et al. [
27] combined the improved local mean decomposition with permutation entropy to extract features. Among the above entropy methods, permutation entropy proposed by Bandt et al. [
28] is a time series method, which can detect the dynamic catastrophic behavior. Due to the simple and fast calculation as well as strong anti-noise ability, permutation entropy was introduced to measure the status characterization of rotary machines [
29]. Subsequently, it has been widely applied to extract features for fault diagnosis and shown outstanding performance [
26,
27].
During the fault pattern recognition stage, many machine learning methods have been proposed in the previous literatures, including
k-nearest neighbor [
30], Bayesian decision [
31], artificial neural network (ANN, [
32,
33]), support vector machine (SVM, [
34]) and so on. Among these recognition techniques,
k-nearest neighbor is simple in theory and susceptible to sample distribution. Bayesian decision can acquire well performance with the consideration of priori probabilities. ANN has strong recognition ability when the number of samples is large. However, all three methods mentioned above are based on empirical risk minimization, i.e., abundant samples are needed to achieve high accuracy. In contrast, SVM, proposed by Vapnik [
35] based on structural risk minimization, has certain advantages in dealing with small samples and linearly inseparable problems. However, the pattern recognition performance of SVM is influenced by the parameters. To solve the problem, different optimization methods, such as particle swarm optimization [
36], antlion algorithm [
37], fruit fly algorithm [
38] and ant colony algorithm [
39] were proposed and employed to choose the best parameters for SVM.
Sine cosine algorithm (SCA) is a newly developed optimization algorithm proposed by Mirjalili [
40] that has shown good performance in many studies [
41,
42]. To achieve accurate fault diagnosis for rotating machinery, a hybrid fault diagnosis model with entropy-based feature extraction and SVM optimized by chaos quantum sine cosine algorithm (CQSCA) is developed in this research. Firstly, the adaptive VMD is employed to decompose the vibration signals into a set of components, during which stage the preset parameter
K of VMD is ascertained with central frequency observation method. Then, the permutation entropy values of all the sub-signals are calculated, thus to construct the feature vector of the given fault sample. Subsequently, an improved SVM model with full fusion of chaotic initialization, quantum technique and SCA for parameter selection, whose effectiveness has been proved in pattern recognition experiments, is presented to classify different fault types. Finally, the superiority of the proposed method was confirmed through engineering applications as well as comparative analysis.
The remainder of this paper is organized as follows:
Section 2 presents the base theory of VMD and permutation entropy.
Section 3 introduces the improved pattern recognition method based on SVM optimized with chaos quantum sine cosine algorithm and validates the effectiveness with pattern recognition experiment.
Section 4 delineates the procedures of the proposed hybrid fault diagnosis model with entropy-based feature extraction and SVM optimized by CQSCA.
Section 5 illustrates the superiority of the proposed method with engineering application and comparative analysis. The conclusions are summarized in
Section 6.
6. Conclusions
In order to enhance the fault diagnosis precision for rotating machinery, a hybrid approach with the fusion of entropy-based feature extraction and SVM optimized by a chaos quantum sine cosine algorithm is proposed in this paper. Firstly, the preset parameter K of VMD is chosen using the central frequency observation method, after which the signals collected under different states are decomposed into series of intrinsic mode functions (IMFs). Subsequently, the permutation entropy values of all IMFs are calculated to assemble the feature vectors of different fault samples. Finally, an optimized SVM model based on chaotic initialization, quantum technique and SCA (CQSCA) for parameter selection, whose availability has been ascertained with recognizing experiment, is proposed to achieve the pattern recognition for different kind of faults. In the engineering applications, the proposed VMD-PE-CQSCA-SVM method was successfully employed to recognize different fault samples and compared with some other relevant methods, including EMD-PE-PSO-SVM, EMD-PE-SCA-SVM, EMD-PE-CQSCA-SVM, EEMD-PE-PSO-SVM, EEMD-PE-SCA-SVM, EEMD-PE-CQSCA-SVM, VMD-PE-PSO-SVM, VMD-PE-SCA-SVM. The application results indicate that the proposed method achieves the best performance during both the training stage and testing stage in terms of the average accuracy of ten times randomized experiments. Particularly, the test accuracy of the proposed method is 22.70% and 14.88% higher than that of EMD-PE-CQSCA-SVM and EEMD-PE-CQSCA-SVM, and also 0.52% and 1.57% higher than VMD-PE-PSO-SVM and VMD-PE-SCA-SVM. Furthermore, the boxplots of different diagnosis methods show that the stability and precision of the proposed method is superior to those of other methods. Thus, the proposed method is a reliable and effective tool for fault diagnosis of rotating machinery.