Shock and Vibration

Volume 2018, Article ID 8174860, 13 pages

https://doi.org/10.1155/2018/8174860

## Comparison of Support Vector Machine-Based Techniques for Detection of Bearing Faults

School of Mechanical Engineering, North China University of Water Resources and Electric Power, Zhengzhou, China

Correspondence should be addressed to Lijun Wang; moc.361@bmjlw

Received 23 March 2018; Revised 19 October 2018; Accepted 13 November 2018; Published 20 December 2018

Academic Editor: Paola Forte

Copyright © 2018 Lijun Wang 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

This paper presents a method that combines Shuffled Frog Leaping Algorithm (SFLA) with Support Vector Machine (SVM) method in order to identify the fault types of rolling bearing in the gearbox. The proposed method improves the accuracy of fault diagnosis identification after processing the collected vibration signals through wavelet threshold denoising. The global optimization and high computational efficiency of SFLA are applied to the SVM model. Simulation results show that the SFLA-SVM algorithm is effective in fault diagnosis. Compared with SVM and Particle Swarm Optimization SVM (PSO-SVM) algorithms, it is demonstrated that the SFLA-SVM algorithm has the advantages of better global optimization, higher accuracy, and better reliability of diagnosis. Its accuracy is further improved through the integration of the wavelet threshold denoising method.

#### 1. Introduction

Rolling bearing is an important rotating mechanical part widely used in the fields of aerospace and metallurgy and in automotive, manufacturing, and chemical industry. Its working condition affects the entire equipment as well as the whole production. Its failure can cause economic losses and possible personal injury [1]. For example, a major derailment accident of Lanzhou Railway Branch 1479 train happened on November 30, 1991, due to poor-quality bearing and cage broken [2]. In June 1992, a 600 MW supercritical forming unit from Japan Kansai Electric Power Company Hainan Power Plant in the speeding test caused a strong unit vibration due to the unit bearing failure and the critical speed drop. It not only damaged the aircraft but also resulted in an economic loss of up to 5 billion yen [3]. Therefore, it is very important to detect and diagnose the rolling running bearings.

Around 60% of the mechanical equipment failures are caused by the gearbox, of which the failure caused by the bearings accounts for about 19% [4]. Many methods such as PSO, Genetic Algorithm, and Ant Colony Algorithm were developed for the bearings fault analysis. In this paper, a combined SFLA-SVM method is proposed to diagnose the fault of the gearbox through the determination of the type of failure of the rolling bearing in the gearbox for the first time. The performance of the new method is then compared with the SVM method and PSO-SVM method.

#### 2. Methods

##### 2.1. Shuffled Frog Leaping Algorithm (SFLA)

SFLA is a swarm intelligence optimization algorithm proposed by Eusuff and Lasey in 2001, which was refined in 2003 and 2006 [5]. The algorithm is inspired by the biological foraging behavior in nature, in which the methods of local search and information sharing in the population are combined to carry out the computation of the global optimization of randomness and certainty. SFLA has the advantages of Mimetic Algorithm (MA) and PSO with local search capacities. By using the components-mixing-division of each meme form, it can achieve global information sharing and find the global optimal solution rather than the local optimum. The advantageous characteristics of SFLA include ease of setting up, high precision, fast convergence, and global optimization [6].

The SFLA model is as follows:(1)Initialization of the SFLA parameters, including deciding the total number of frogs _{,} analyzing the experimental data, proposing frog heron number *m*, and setting the maximum distance that frog individuals can move to. Mimetic group evolution algebra is . Algorithm mixed sort iteration number is _{.} The frog individual biggest search range is .(2)Calculation of the fitness value: Assume the first frog population iswhere is a frog individual. The fitness value is calculated first, and then the data are stored according to the size of the value of the sort, which is recorded as . Finally, the best frog individual is recorded as .(3)Division of the population: The frog population is divided into memes , using the following equation, and the best frog individual and the worst frog individual in each group are recorded:(4)Local search: According to the rules of in the local search The frog jumping step is decided by Equation (4) is used to update the value and calculate its fitness value. If the updated frog is better than the original frog, it will replace the original frog. Otherwise, replace with . Equations (3) and (4) are used to iterate each mimetic group. If the optimization fails, a new frog individual will be randomly formed to replace the original . According to this process, there are times of mimetic group to gain a new mimetic group .(5)Mixing of populations: The evolved frog populations are mixed again to form , and the global best frog is updated and recorded. Then, the frogs in are grouped once again.(6)If the number of iterations of the algorithm satisfies the condition , go back to step (4); otherwise, output the best frog individual.

##### 2.2. Support Vector Machine

In 1995, Vapnik proposed a machine learning method, Support Vector Machine (SVM). SVM is a learning method based on statistical theory and risk minimization [7]. Its core idea is to transform the problem of linear inseparability through the kernel formula, and then find the best classification surface in the space and the solution to the problem using convex quadratic programming [8]. It successfully solved over learning and the local minimum problem. It also has the better generalization ability.

The SVM algorithm model is as follows:(1)Give sample and the matching .(2)Select the proper kernel formula and related parameters.(3)Solve the maximum value of the formula under constraints and to gain the best value .(4)Calculate , where the first ingredient of represents the best bias . Then, the best decision plane is .(5)Classify the vector and calculate as +1 or −1 to decide .

##### 2.3. SFLA-SVM Model

Fu found that there are mainly two features that affect SVM’s learning ability: penalty and Gaussian kernel coefficient [9]. These two limits directly affect the SVM’s classification accuracy and generalization ability. If is too large, the training accuracy is high while the generalization ability is poor. If is too small, the training accuracy is poor. When is too large, the classification accuracy of SVM will be reduced. When is too small, the reasoning ability of SVM will be worsened. Therefore, the proper parameters can enable the model to have better generalization ability and classification accuracy.

Although there is no unified method to decide the best features and , the methods of network search and cross-validation are normally selected [10]. In this paper, SFLA-SVM model is proposed, whose process is outlined below:(1)Initialize the frog to form vectors randomly. The ingredient is a random number between . The total number of iterations of the frog is . The number of subpopulations is , and the number of subpopulation iterations is .(2)Calculate the fitness value of each frog individual. If the constraint does not satisfy, set the fitness value of the frog individual as an infinite positive number. Otherwise, keep the fitness value and divide the subpopulation.(3)Perform iterative optimization on each subpopulation and then mix all the subpopulations to form a new population and return to step (2). Repeat the steps (2) and (3) until the number of iterations of the total population is reached and returns .(4)Calculate the best bias from .(5)Compute the decision formula and then decide the classification vector .

##### 2.4. Wavelet Threshold Denoising

A significant problem in wavelet threshold denoising is how to choose the threshold. If the chosen threshold is too small, the noise will largely remain in the signal. However, if the threshold is too large, it will remove useful and important characteristic information from the signal resulting in deviation. Therefore, the threshold will directly affect the denoising effect [11].

Another problem in wavelet threshold denoising is how to choose the threshold formula. Wavelet threshold denoising includes hard threshold denoising, soft threshold denoising, and default threshold denoising [12]. Hard threshold formula and soft threshold formula are the two most commonly used threshold formulas.

The expression for a hard threshold formula is

The expression of a soft threshold formula is

In Equations (5) and (6), is a wavelet coefficient, is the denoised wavelet coefficient, and is a threshold value, whose formula iswhere is the standard deviation of the noise and is the strength of the signal.

After breaking up the noisy signal by wavelet, the signal has a larger amplitude than that the noise does. Therefore, choosing the wavelet coefficients is achieved by setting the threshold.

The basic steps of the wavelet threshold denoising using (6) are as follows:(1)Use wavelet transform to break up the noisy signal and to obtain a set of wavelet coefficients .(2)Threshold the wavelet coefficient to decide the estimated value of the wavelet coefficient , so that is minimum.(3)Use wavelet inverse transform to remake to gain the estimated signal , which is the signal after denoising.

There is a difference between the wavelet coefficient gained by the soft threshold formula and that of the original signal. The hard threshold formula is not continuous at the threshold point. These defects affect the effect of denoising. Therefore, in order to overcome the shortcomings of the traditional wavelet threshold, soft threshold and hard threshold, it is necessary to improve the selection of the threshold.

The improved threshold iswhere is the resolution scale. As the scale increases, the threshold decreases. Compared with the original method, the new threshold is more adaptive to separate noise at all levels.

The improved threshold formula iswhere is the wavelet coefficient, is the denoised wavelet coefficient, is the threshold, and is the adjustment parameter. The improved threshold formula has the advantages of both the soft and hard threshold formulas.

#### 3. Application of SFLA-SVM Algorithm in Gearbox Bearing Fault Diagnosis

##### 3.1. Experimental Platform

Figure 1 shows the experimental platform, a gearbox equipment of Beijing Capital Airlines. It consists of a frequency controller, motors, brakes, gear boxes, and other parts. The performance of the gearbox equipment is stable, and it can withstand certain load impact. There is enough space for gear replacement and installation. It can simulate various types of fault conditions for gearbox analysis, noise characteristic analysis, vibration characteristic analysis, health/condition monitoring, and fault diagnosis.