Car assembly line fault diagnosis based on triangular fuzzy support vector classifier machine and particle swarm optimization

Abstract

This paper presents a new version of fuzzy support vector classifier machine to diagnose the nonlinear fuzzy fault system with multi-dimensional input variables. Since there exist problems of finite samples and uncertain data in complex fuzzy fault system modeling, the input and output variables are described as fuzzy numbers. Then by integrating the fuzzy theory and v-support vector classifier machine, the triangular fuzzy v-support vector regression machine (TF v-SVCM) is proposed. To seek the optimal parameters of TF v-SVCM, particle swarm optimization (PSO) is also applied to optimize parameters of TF v-SVCM. A diagnosing method based on TF v-SVCM and PSO are put forward. The results of the application in fault system diagnosis confirm the feasibility and the validity of the diagnosing method. The results of application in fault diagnosis of car assembly line show the hybrid diagnosis model based on TF v-SVCM and PSO is feasible and effective, and the comparison between the method proposed in this paper and other ones is also given, which proves this method is better than standard v-SVCM.

Introduction

Fault detection and diagnosis problem have been studied intensively in industries. Exact detection and diagnosis of faults is essential for the reliable, safe, and efficient operation of the plant and for maintaining quality of the products in manufacturing system. However, for lacking of available expert experience, it is very difficult in some applications such as car assembly process to obtain important state parameters on line that are good indicators of fault. So fault diagnosis of car assembly process is not an easy task and relevant researches are in need of further development.

It is the key for fault diagnosis of car assembly process that how to estimate the states accurately. Two kinds of estimation methods have therefore been developed including the model based approach and the neural network approach. During the study of the model of fermentation process, many kinetic models have been built, which can reflect the fault pattern of assembly process effectively. With the change of workshop environment, the faults and the noise can make the model parameters variable, while these parameters are often treated as constants in the previous models. Obviously, it is not accordant with the real practice and induces the invalidation of the estimation methods. On the other hand, neural networks have been utilized widely to estimate the parameters. But in most of the results, processes are dealt with “black-boxes”. That is to say, without regard to the known knowledge of the assembly process, neural networks are only used to describe their relationship between input and output.

In fault diagnosis practice of recent years, many effective approaches appear. The traditional neural network (NN) method obtains many harvests in application research of fault diagnosis, but it has a lot of questions in network structure selecting, network training and enhancing network spread ability (Demetgul et al., 2009, Wu and Liu, 2009). The support vector machine (SVM) is a new machine study method which was established by Vapnik (1995) in base of statistical learning theory (SLT). The SVM stresses to study statistical learning rules under small sample. via structural risk minimization principle to enhance extensive ability, the SVM preferably solves many practical problems, such as small sample, nonlinear, high dimension number and local minimum points. It excludes the problem of local mining encountered in training neural networks. It is a promising theory for the application to fault diagnosis (Abbasion et al., 2007, Camci and Chinnam, 2008, Falco et al., 2007, Fei et al., 2009, Liang and Du, 2007, Saravanan et al., 2008, Widodo and Yang, 2007a, Widodo and Yang, 2007b, Widodo and Yang, 2008, Wu et al., 2009, Xiang et al., 2008, Yang et al., 2007, Yélamos et al., 2009, Yuan and Chu, 2007, Wu and Rob, 2010).

In SVM approach, the parameter ε controls the sparseness of the solution in an indirect way. However, it is difficult to come up with a reasonable value of ε without the prior information about the accuracy of output values. Schölkopf, Smola, Williamson, and Bartlett (2000) and Chalimourda, Schölkopf, and Smola (2004) modify the original ε-SVM and introduce v-SVM, where a new parameter v controls the number of support vectors and the points that lie outside of the ε-insensitive tube. Then, the value of ε in the v-SVM is traded off between model complexity and slack variables via the constant v.

In many real applications, the observed input data cannot be measured precisely and usually described in linguistic levels or ambiguous metrics. However, traditional support vector classifier machine (SVCM) method cannot cope with qualitative information. It is well known that fuzzy logic is a powerful tool to handle fuzzy and uncertain data. Some scholars have explored the fuzzy support vector machine (FSVM). For pattern classification problems, Shieh and Yang (2008) apply a fuzzy SVM to construct a classification model of product form design based on consumer preferences by allocating continuous and discrete attributes to the product form. Each product sample was assigned a class label, and a fuzzy membership, which is used to describe the semantic differential score corresponding to this label. To better handle uncertainties existing in real classification data and in the membership functions in the traditional type-1 fuzzy logic system, Chen, Li, Harrison, and Zhang (2008) apply interval type-2 fuzzy sets to construct a type-2 SVMs fusion FLS. This type-2 fusion architecture takes consideration of the classification results from individual SVC and generates the combined classification decision as the output. Yang, Jin, and Chuang (2006) propose system uses both fuzzy support vector machines and the variable-degree variable-step-size least-mean-square algorithm to achieve these objectives. They apply fuzzy memberships to each point, and provide different contributions to the decision learning function for support vector machines. However, the fuzzy support vector classifier machines mentioned in the above literatures are not suitable for the input and output variables described as triangular fuzzy numbers. Then, this paper focuses on the modeling of the optimal problem on triangular fuzzy numbers space.

It is obvious that the left and right parts of triangular fuzzy number can represent the uncertain information of expert judgement. For ordinary fuzzy SVCM, all fuzzy information is transformed into a crisp number via membership or a mapping (Wu et al., 2009), the classifier analysis is based on the dealt sample set with crisp numbers. However, the paper suggests a novel fuzzy v-SVCM. The major novelty of the present work is that the inputs and outputs are described by triangular fuzzy numbers, and hence it allows a more effective description of fault system involving uncertainties. Additionally, the parameters pertaining in formulation are determined via PSO-based search. Compared with ordinary SVCM, the fuzzy SVCM model in triangular fuzzy number space, whose constraint conditions of are three times that of standard SVCM, establishes the optimal problem based on the left, middle and right of triangular fuzzy number respectively. In a word, the uncertain information is considered into the establishment of the novel fuzzy v-SVCM, as is suitable to complex nonlinear fuzzy fault system problems with uncertain influencing factors.

Based on the TF v-SVCM, an intelligence diagnosis approach for car assembly line with multi-dimension, nonlinearity, fuzzy feature and uncertain characteristics is proposed in this paper. TF v-SVCM is arranged in Section 2. Section 3 construct an intelligent diagnosing model based on the proposed TF v-SVCM and particle swarm optimization algorithm (PSO). Section 4 gives an application of the intelligence diagnosing system based on the TF v-SVCM model optimized by PSO algorithm. Section 5 draws the conclusions.