Nonlinear System Identification Based on Reduced Complexity Volterra Models

Conventional Volterra series model is hardly applied to engineering practice due to its parametric complexity and estimation difficulty. To solve this problem, nonlinear system identification using reduced complexity Volterra models is proposed. Since the nonlinear components often play a secondary role compared to the dominant, linear component of the system, they spend the most of identification cost. So it is worth establishing a balance between identification cost and model accuracy by reducing the complexity of nonlinear components. Refer to the idea of nonlinear output frequency response function, conventional Volterra model is simplified. And then a minimum mean square error criterion based method to identify the simplified model is proposed. The distinguishing feature of this method is high accuracy, good robustness, and significant reduction in the computational requirements compare to the identification of conventional Volterra models. The simulation show that the proposed method is effective, and the reduced complexity Volterra model is of good generalization ability in general. So this nonlinear system identification approach is quite applicable to engineering practice. Introduction The Volterra series model provides an intuitive and relatively general framework for analyzing the behavior of non-linear systems [1]. Most real world systems are nonlinear in nature so thatnonlinear models are often preferable for representing systems under study. This is evidenced by the wild spread applications of Volterra models in fields including control [2], identification [3], damage detection [4] and assessment [5]. The objective of present study is to develop an efficient and practical approach for identification of quadratic nonlinear systems. A simplified nonparametric model identification method is presented. This method leads to significant reductions in both the computational requirements and the mathematical tractability comparing to traditional Volterra model. Simulations show present algorithm has excellent ability of model generalization and is still effective with output measurement noises, even in low signal-noise-ratio (SNR) condition. Preliminaries For a weakly nonlinear system up to second order Volterra series representation, the discrete time Volterra model can be expressed as 1 1 1 1 ( ) ( , , ) ( )