Fault diagnosis of car assembly line based on fuzzy wavelet kernel support vector classifier machine and modified genetic algorithm

Abstract

This paper presents a new version of fuzzy wavelet support vector classifier machine to diagnosing 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, the input and output variables are described as fuzzy numbers. Then by integrating the fuzzy theory, wavelet analysis theory and v-support vector classifier machine, fuzzy wavelet v-support vector classifier machine (FWv-SVCM) is proposed. To seek the optimal parameters of FWv-SVCM, genetic algorithm (GA) is also applied to optimize unknown parameters of FWv-SVCM. A diagnosing method based on FWv-SVCM and GA is put forward. The results of the application in car assembly line diagnosis confirm the feasibility and the validity of the diagnosing method. Compared with the traditional model and other SVCM methods, FWv-SVCM method requires fewer samples and has better diagnosing precision.

Introduction

Recently, a novel machine learning technique, called support vector machine (SVM), has drawn much attention in the fields of pattern classification and regression estimation. SVM was first introduced by Vapnik, 2000, Vapnik, 1999. It is an approximate implementation to the structure risk minimization (SRM) principle in statistical learning theory, rather than the empirical risk minimization (ERM) method. This SRM principle is based on the fact that the generalization error is bounded by the sum of the empirical error and a confidence interval term depending on the Vapnik–Chervonenkis (VC) dimension (Vapnik, 2000). By minimizing this bound, good generalization performance can be achieved. Compared with traditional neural networks, SVM can obtain a unique global optimal solution and avoid the curse of dimensionality. These attractive properties make SVM become a promising technique. SVM was initially designed to solve pattern recognition problems (Cevikalp et al., 2007, Doumpos et al., 2007, Guo and Li, 2003, Huysmans et al., 2008, Jayadeva and Chandra, 2007, Juang et al., 2007, Peng et al., 2008, Ratsch et al., 2002, Wang et al., 2008, Widodo and Yang, 2008, Zhang et al., 2004, Wu and Law, 2010). With the introduction of Vapnik’s ε-insensitive loss function, SVM has been extended to function approximation and regression estimation problems (Hu et al., 2007, Lin et al., 2001, Rueda et al., 2004, Wu, 2009, Wu and Law, 2011, Wu et al., 2010, Zhang et al., 2004, Zhu et al., 2008) before 2001.

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 et al., 2000, Chalimourda et al., 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-SVRM 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 (SVC) method cannot cope with qualitative information. It is well known that fuzzy logic is a powerful tool to deal with 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 from the triangular fuzzy number space of which the input variables in classification problem of SVM may come from. Moreover, the kernel function of the published fuzzy SVCM pays less attention to wavelet support vector kernel.

It is obvious that the left and right parts of triangular fuzzy number can represent the uncertain information of expert judgement. For ordinary fuzzy SVRM, all fuzzy information is transformed into a crisp number via membership or a mapping, the regression analysis is based on the dealt sample set with crisp numbers. However, the paper suggests a novel fuzzy v-SVCM with wavelet kernels. 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 system involving uncertainties. Additionally, the parameters pertaining in formulation are determined via GA-based search. Compared with ordinary SVCM, the fuzzy SVCM model in triangular fuzzy number space, the proposed model, 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 with wavelet kernels, as is suitable to complex nonlinear fuzzy system diagnosing problem with uncertain influencing factors.

To overcome this disadvantage that the solution to the optimal parameter b of fuzzy v-SVCM with wavelet kernel model is difficult, the influencing of parameter b is taken into account confidence interval of fuzzy v-SVCM with wavelet kernel model. Finally, parameter b will be not come out in the classifier output function of the modified fuzzy v-SVCM with wavelet kernel model. The modified fuzzy v-SVCM with wavelet kernels model according to the structure risk minimization (SRM) is a new version of v-SVCM, named FWv-SVCM.

In this paper, we put forward a new FSVCM, called FWv-SVCM. Based on the FWv-SVCM, a diagnosing method for nonlinear fuzzy fault system is proposed. The rest of this paper is organized as follows. The FWv-SVCM is described in Section 2. In Section 3, a GA is used to optimize the unknown parameters of FWv-SVCM. In Section 4, a diagnosing method based on FWv-SVCM and GA is proposed. Section 5 gives an application in car assembly line diagnosis. FWv-SVCM is also compared with other SVCMs. Section 6 draws the conclusions.