Parametric Identification of Nonlinear Systems by Haar Wavelets: Theory and Experimental Validation

Abstract

This study addresses the identification of nonlinear systems. It is assumed that the function form in the nonlinear system is known, leaving some unknown parameters to be estimated. Since Haar wavelets can form a complete orthogonal basis for the appropriate function space, they are used to expand all signals. In doing so, the state equation can be transformed into a set of algebraic equations in unknown parameters. The technique of Kronecker product is utilized to simplify the expressions of the associated algebraic equations. Together with the least square method, the unknown system parameters are estimated. The proposed method is applied to the identification of an experimental two-well chaotic system known as the Moon beam. The identified model is validated by comparing the chaotic characteristics, such as the largest Lyapunov exponent and the correlation dimension, of the experimental data with that of the numerical results. The simple least square approach is also performed for comparison. The results indicate that the proposed method can reliably identify the characteristics of the nonlinear chaotic system.