A TAYLOR SERIES BASED INPUT VARIABLE SELECTION FOR NONLINEAR SYSTEM

Abstract

Input variable selection is always a significant problem in nonlinear system modeling. In this paper, we propose an effective and efficient input variable selection method based on Taylor series. We assume the nonlinear system as an at least 3 order derivative and continuous function f(x), and approximate it with 3 order Taylor series in the small proximities of the sample data. We define the average absolute values of first order partial derivates at the sample data as the importance indexes for the input variable candidates, and the average absolute values of second order partial derivatives as the correlation degrees between the input candidates. The importance indexes of the input variable candidates can be calculated by solving the linear equation at low computational cost. In this paper, we describe the nonlinear system as an Adaptive Network Based Fuzzy Inference System (ANFIS). Guided by the priori knowledge of input variables, importance indexes and correlation degrees, a fast input variable selection method is presented in which Regularity Criterion is adopted to evaluate the performance of the selected input variables. Experiment results and theoretical analysis both prove that this input variable selection method can speed up the selection process and is more powerful than the typical search tree method.