Least squares support vector machines with tuning based on chaotic differential evolution approach applied to the identification of a thermal process

In the past decade, support vector machines (SVMs) have gained the attention of many researchers. SVMs are non-parametric supervised learning schemes that rely on statistical learning theory which enables learning machines to generalize well to unseen data. SVMs refer to kernel-based methods that have been introduced as a robust approach to classification and regression problems, lately has handled nonlinear identification problems, the so called support vector regression. In SVMs designs for nonlinear identification, a nonlinear model is represented by an expansion in terms of nonlinear mappings of the model input. The nonlinear mappings define a feature space, which may have infinite dimension. In this context, a relevant identification approach is the least squares support vector machines (LS-SVMs). Compared to the other identification method, LS-SVMs possess prominent advantages: its generalization performance (i.e. error rates on test sets) either matches or is significantly better than that of the competing methods, and more importantly, the performance does not depend on the dimensionality of the input data. Consider a constrained optimization problem of quadratic programing with a regularized cost function, the training process of LS-SVM involves the selection of kernel parameters and the regularization parameter of the objective function. A good choice of these parameters is crucial for the performance of the estimator. In this paper, the LS-SVMs design proposed is the combination of LS-SVM and a new chaotic differential evolution optimization approach based on Ikeda map (CDEK). The CDEK is adopted in tuning of regularization parameter and the radial basis function bandwith. Simulations using LS-SVMs on NARX (Nonlinear AutoRegressive with eXogenous inputs) for the identification of a thermal process show the effectiveness and practicality of the proposed CDEK algorithm when compared with the classical DE approach.