Tensor Analysis-Based Model Structure Determination and Parameter Estimation for Block-Oriented Nonlinear Systems

Abstract

A block-oriented nonlinear system is composed of a concatenation of blocks representing either memoryless nonlinearities or linear dynamic subsystems. Wiener, Hammerstein, and Wiener-Hammerstein (WH) models are the most commonly used ones for modeling such block-oriented nonlinear systems. In this paper, we develop a tensor analysis-based approach for determining both the structure and the parameters of the most appropriate model among the three above listed models. The structure is deduced from the rank of a tensor obtained by convolving a random finite impulse response (FIR) linear filter with a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> th-order Volterra kernel ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> > 2), associated with the block-oriented nonlinear system to be identified. The parameters of the linear subsystems are obtained from the PARAllel FACtor analysis (PARAFAC) decomposition of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> th-order Volterra kernel associated with the original nonlinear system and/or an extended WH system, whereas those of the nonlinear subsystem are estimated using the least squares method. The performance of the proposed identification scheme is illustrated by means of some simulation results.