Mathematical Problems in Engineering

Volume 2016, Article ID 8702970, 7 pages

http://dx.doi.org/10.1155/2016/8702970

## A Hybrid Approach for Fault Diagnosis of Railway Rolling Bearings Using STWD-EMD-GA-LSSVM

^{1}School of Machine-Electricity and Automobile Engineering, Beijing University of Civil Engineering Architecture, Beijing 100044, China^{2}Beijing Key Laboratory of Performance Guarantee on Urban Rail Transit Vehicles, Beijing University of Civil Engineering Architecture, Beijing 100044, China^{3}Subway Operation Technology Centre, Mass Transit Railway Operation Corporation Ltd., Beijing 102208, China

Received 16 September 2015; Accepted 29 February 2016

Academic Editor: Yongjun Shen

Copyright © 2016 Dechen Yao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Vibration signals resulting from railway rolling bearings are nonstationary by nature; this paper proposes a hybrid approach for the fault diagnosis of railway rolling bearings using segment threshold wavelet denoising (STWD), empirical mode decomposition (EMD), genetic algorithm (GA), and least squares support vector machine (LSSVM). The original signal is first denoised using STWD as a prefilter, which improves the subsequent decomposition into a number of intrinsic mode functions (IMFs) using EMD. Secondly, the IMF energy-torques are extracted as feature parameters. Concurrently, a GA is employed to optimize the LSSVM to improve the classification accuracy. Finally, the extracted features are used as inputs for classification by the GA-LSSVM. Actual railway rolling bearing vibration signals are used to experimentally verify the effectiveness of the proposed method. The results show that the novel method is effective and accurate for fault diagnosis of railway rolling bearings.

#### 1. Introduction

Rolling bearings are one of the crucial components used in the railway sector, and bearing failure generally leads to serious damage for the railway. Hence, the fault diagnosis of railway rolling bearings is of great significance [1]. In fault diagnosis, the most important aspect is the feature extraction, which is employed to characterize the operating status of railway rolling bearings. Accurate and effective features can be easily used for automatic fault diagnosis in tandem with a neural network [2] or a relevance vector machine [3]. However, the nonlinear and nonstationary nature of acquired railway rolling bearing vibration signals and the existence of interferences caused by external factors both increase the difficulty of extracting features from the complex vibration signal. Over the last two decades, numerous fault diagnosis methods have been developed such as envelope analysis, short-time Fourier transform (STFT) [4], principal component analysis (PCA) [5], artificial neural network (ANN) [6], and genetic algorithm (GA) [7]. In this paper, a hybrid method for the fault diagnosis of railway rolling bearings is presented. The vibration signal from a bearing at an early stage of defect development is often masked by machine noise, making it difficult to detect the fault by vibration analysis techniques [8]; therefore, segment threshold wavelet denoising (STWD) is used as a prefilter for denoising. The vibration signal is then decomposed via empirical mode decomposition (EMD), which is a very reasonable approach for nonstationary signal analysis. EMD is used to extract the energy-torques of the intrinsic mode functions (IMFs) as feature parameters to be input into a least squares support vector machine (LSSVM) for classification. A GA is employed to search for optimal LSSVM parameters to ensure optimal adaptation in its global scope. Actual railway rolling bearing vibration signals are used to experimentally verify the effectiveness of the proposed method. The results show that the proposed method is effective and achieves a high recognition rate for fault diagnosis of railway rolling bearings.

The remainder of this paper is organized as follows. EMD and energy-torque feature extraction are discussed in Section 2. GA-LSSVM is described in Section 3. In Section 4, the method is validated experimentally. Finally, conclusions are drawn in Section 5.

#### 2. EMD and Energy-Torque Feature Extraction

##### 2.1. EMD

The EMD method proposed by Huang et al. [9] decomposes a signal into a number of IMFs and a single residue. Each IMF must satisfy the following conditions:(1)Over the entire dataset, the number of extrema and the number of zero-crossings must either be equal or differ at most by one.(2)At any point, the mean values of the envelopes defined by local maxima and by local minima are zero.

In accordance with this definition, any signal can be decomposed as follows [10].

*Step 1. *Define and .

*Step 2. *Define the maximum number of extracted IMFs.

*Step 3. *Identify all the local extrema of .

*Step 4. *Connect all local maxima and minima by a cubic spine as the upper envelope and the lower envelope , respectively.

*Step 5. *Construct the mean of the upper and lower envelopes .

*Step 6. *Define the detail (proto-IMF) as , and replace by .

*Step 7. *Repeat Steps 3–6 until meets IMF conditions (1) and (2) and the stoppage criterion of the sifting process is fulfilled; then derive the th IMF () from and replace by .

*Step 8. *If the stoppage criterion of the signal’s decomposition is fulfilled, then finish the decomposition process; otherwise, go to Step 3.

##### 2.2. Energy-Torque Feature Extraction

The steps for energy-torque feature extraction are as follows.

*Step 1. *STWD is used to filter the railway rolling bearing signals.

*Step 2. *The denoised vibration signals are decomposed into some number of IMFs via EMD, and the first IMFs, that is, , , which include the most dominant fault energy, are chosen to extract the features.

*Step 3. *Calculate the energy-torque of every small time block, which, for a discrete signal, is given aswhere is the total number of sampling points and is the sampling period. Calculate the energy-torques for all respective , , based on (1).

*Step 4. *Construct the feature vector from : When become large, normalize as follows:whereThe th IMF energy-torque is then calculated as follows [11]:

#### 3. GA-LSSVM Algorithm

##### 3.1. GA

GA is a method proposed by Holland [12] for providing solutions to optimization and learning problems and is based freely on several features of biological evolution [13]. The algorithm begins with the initialization of a population of candidate solutions of which each is comprised of alterable properties denoted as chromosomes or a genotype. The initialized population is then evolved using genetic operators, giving, as in nature, more reproductive opportunities to the most highly fit chromosomes (i.e., those providing the best solution to the problem considered based on a fitness function) [14]. The GA applies selection, crossover, and mutation operators to construct fitter solutions and further processes the population by replacing unsuitable candidates according to the fitness function.

*(**1) Initialization of Population*. Set the population scale and generate initial population including individuals with the number . Set the range of data and select linear interpolation function [15] to generate real vectors as the individuals of GA.

*(**2) Determination of Fitness Function.* Fitness function is a good standard which will effectively evaluate the adaptability to environment of individuals in population.

*(**3) Selection*. The paper uses roulette wheel selection [16] to determine the probability by which the individual will be selected. The roulette wheel selection is a kind of selecting strategy for individual based on the fitness proportion. The formula of selection probability is shown as follows:where is the population scale and is the reciprocal of individual fitness.

*(**4) Crossover and Mutation*. To generate new population, GA takes the operations of crossover and mutation to deal with current population. As a consequence, probabilities of crossover and mutation are two important parameters which will have a great effect on the performance and property of convergence of GA. Different from traditional algorithm, this paper proposes the adaptive genetic algorithm [17], in which probabilities of crossover and mutation can change adaptively according to individual fitness. The adaptive change will maintain the diversity of population, improve the capability of global search, and avoid individual being mature earlier,where is the crossover probability, is the mutation probability, is the maximum fitness of population, is the average fitness, is the larger fitness of two individuals in crossover, and is the fitness of individual in mutation. Based on repeated experiments and former experience, the paper chooses , , , and .

##### 3.2. LSSVM Algorithm

LSSVM was proposed by Suykens et al. [18] to train an SVM by solving a set of linear equations. The primary differences between LSSVM and SVM are that LSSVM transforms the inequality constraints into equality constraints and employs a square instead of the empirical risk quadratic. LSSVM can be written as follows [19]:Here, is the linear classifier in the feature space, is the bias parameter, is the error of the th training example, such that is the empirical risk, and represents the penalty factor. We can then acquire the Lagrange functionwhere is the Lagrange multipliers.

The following are established according to the Karush-Kuhn-Tucker (KKT) condition:By eliminating the parameters and in (10), the equation can be rewritten asThe kernel function in this paper adopts the radial basis functionwhere is the kernel width.

##### 3.3. Selection of LSSVM Parameters by GA

After building the LSSVM model, GA is carefully designed to optimize the penalty factor and kernel parameters of LSSVM, avoiding premature convergence and permutation problems. The GA-LSSVM involves several steps as follows.

*Step 1 (encoding and initialization). *Free parameters and are represented by a chromosome comprised of two genes.

*Step 2 (calculating fitness function). *A fitness function is used to assess the quality of a solution.

*Step 3 (parent selection). *Two chromosomes with higher fitness values are selected from the parent population.

*Step 4 (crossover and mutation). *Crossover randomly exchanges genes between two chromosomes, and the mutation operator occasionally converts a “1” bit into a “0” bit or vice versa within a candidate solution’s genes.

Based on the algorithm elements described above, a flowchart of the proposed method for railway rolling bearing fault diagnosis using STWD-EMD-GA-LSSVM is presented in Figure 1. As shown in the flowchart, the raw vibration signal is denoised by STWD, EMD is used to decompose the denoised signal into a number of IMFs, and the IMF energy-torques are calculated. The GA is then used to optimize the LSSVM, and, finally, the GA-LSSVM is used for classification of the feature parameters.