Nonlinear Inertia Classification Model and Application

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2014, Article ID 987686, 9 pages http://dx.doi.org/10.1155/2014/987686 Research Article Nonlinear Inertia Classification Model and Application Mei Wang,1 Pai Wang,1 Jzau-Sheng Lin,2 Xiaowei Li,1 and Xuebin Qin1 1 2 College of Electric and Control Engineering, Xi’an University of Science and Technology, Xi’an 710054, China Department of Computer Science and Information Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan Correspondence should be addressed to Jzau-Sheng Lin; Received 26 February 2014; Accepted 24 April 2014; Published 22 May 2014 Academic Editor: Her-Terng Yau Copyright © 2014 Mei 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. Classification model of support vector machine (SVM) overcomes the problem of a big number of samples. But the kernel parameter and the punishment factor have great influence on the quality of SVM model. Particle swarm optimization (PSO) is an evolutionary search algorithm based on the swarm intelligence, which is suitable for parameter optimization. Accordingly, a nonlinear inertia convergence classification model (NICCM) is proposed after the nonlinear inertia convergence (NICPSO) is developed in this paper. The velocity of NICPSO is firstly defined as the weighted velocity of the inertia PSO, and the inertia factor is selected to be a nonlinear function. NICPSO is used to optimize the kernel parameter and a punishment factor of SVM. Then, NICCM classifier is trained by using the optical punishment factor and the optical kernel parameter that comes from the optimal particle. Finally, NICCM is applied to the classification of the normal state and fault states of online power cable. It is experimentally proved that the iteration number for the proposed NICPSO to reach the optimal position decreases from 15 to 5 compared with PSO; the training duration is decreased by 0.0052 s and the recognition precision is increased by 4.12% compared with SVM. 1. Introduction Power cables play an extremely important role in industrial production and modern life. At present, it is difficult for people to accept a bank system chaos or a wrong airport management system because of the power cable faults. In order to decrease and avoid the economic loss, the correct state classification of the online power cable is very necessary. Nowadays, the commonly used fault diagnosis methods of power cable are electrical bridge method and electrical impulse method. Both of these methods are offline methods [1]. Obviously, these offline methods cannot satisfy the requirement. In theory, the entropy of the zero-sequence components [2] of 3-phase voltages and 3-phase currents of the online power cable was used to extract the fault feature. In addition, wavelet transform is useful for the feature extraction of the early fault of the online cable, and then the voltages and currents are detected to get the subtle singular points by utilizing wavelet transform [3]. Furthermore, the artificial neural network [4] was also used to build the state classification model of the power cable because it can realize any nonlinear mapping. But artificial neural network needs a large number of samples and the training process may go to the local minimum point. The classification model of support vector machine (SVM) overcomes the disadvantage of big samples by obeying the rule of the minimum structural risk [5]. But the kernel parameter and the punishment factor have great influence on the quality of SVM model. Particle swarm optimization (PSO) is an evolutionary search algorithm [6] based on the swarm intelligence, which is suitable for parameter optimization. Therefore, the combination of PSO and SVM can find the optimal kernel parameter and the punishment factor of SVM and obtain a high quality of SVM classification model. This paper is organized as follows. After the introduction in Section 1, SVM and PSO related to this study are given in Section 2. It includes the conventional SVM and the traditional PSO as well as the specific PSO with a convergence factor and an inertia factor. Then, the nonlinear inertia convergence PSO (NICPSO) and the nonlinear inertia convergence classification model (NICCM) are proposed in Section 3. The experiments are implemented using NICPSO and NICCM to classify the normal state and several fault states of online power cable in Section 4. Finally, the conclusion is obtained in Section 5. 2 Mathematical Problems in Engineering 2. SVM and PSO The basic idea of NICCM is that SVM is taken as the classification model and PSO is taken to optimize the important parameters of the punishment factor and the kernel parameter of SVM. The principles of SVM and PSO are reviewed below. 2.1. SVM. The principle of SVM is to find an optimal classification hyperplane which separates as much as possible patterns of two classes to the correct classes. Meanwhile, the hyperplane ensures the maximum distance between the two classes of separable samples [7]. If 𝑑+ is the minimum distance from the classification hyperplane to the positive sample set, and 𝑑− is the minimum distance from the classification hyperplane to the negative sample set, then the margin of the classification hyperplane is “𝑑+ +𝑑− ”. The linear SVM is to find the separation hyperplane with maximum margin. Namely, all the training samples should satisfy the following constraints of |𝑑+ | = |𝑑− | = 1: 𝑥𝑖𝑇 𝑤 + 𝑏 ≥ +1, 𝑦𝑖 = +1, 𝑖 = 1, 2, . . . , 𝑁, 𝑥𝑖𝑇 𝑤 + 𝑏 ≤ −1, 𝑦𝑖 = −1, 𝑖 = 1, 2, . . . , 𝑁, ∀𝑖, 1 [2 ∗ ‖𝑤‖2 ] (4) where sgn is the sign function. The class of pattern 𝑥 is determined by the sign of the brackets. For the case of imperfect separable linear samples, the loss introduced by classification error should be considered. The relax factor 𝜀𝑖 ≥ 0, 𝑖 = 1, . . . , 𝑁, is used to (2). There is 𝑦𝑖 (𝑥𝑖𝑇 𝑤 + 𝑏) − 1 + 𝜀𝑖 ≥ 0, (2) } s.t. 𝑦𝑖 (𝑥𝑖𝑇 𝑤 + 𝑏) − 1 ≥ 0, 𝑖=1 ∀𝑖. (5) Then the classification hyperplane with a soft margin is determined by the optimization problem where 𝑥𝑖 is the 𝑖th training sample and 𝑦𝑖 is the class label of the training sample 𝑥𝑖 ; 𝑤 and 𝑏 are the parameters of the classification hyperplane; 𝑇 represents the transposition of a vector; 𝑁 is the number of samples. If a training sample satisfies (2), then it is a support vector. The change of a support vector impacts the change of the margin and the solution of problem. Linear support vector machine is a maximization problem in the view of (2). Equivalently, it is a minimum problem of ‖𝑤‖2 in the condition of (2); namely, it is an optimization problem with the constraint 𝐽 = min { 𝑙 𝑓 (𝑥) = sgn (𝑤∗ ⋅ 𝑥 + 𝑏∗ ) = sgn {∑ 𝑦𝑖 𝛼𝑖∗ (𝑥 ⋅ 𝑥𝑖 ) + 𝑏∗ } , (1) or the equivalent constraint 𝑦𝑖 (𝑥𝑖𝑇 𝑤 + 𝑏) − 1 ≥ 0, expansion theorem, a sample space (...truncated)