Nonlinear System Identification Using Wavelet based SDP Models

System identi…cation has played an increasingly dominant role in a wide range of engineering applications. While linear system’s theory is mature, nonlinear system identi…cation remains an open research area in recent years. This thesis develops a new, e¢ cient and systematic approach to the identi…cation of nonlinear dynamic systems using wavelet based State Dependent Parameter (SDP) models, from structure determination to parameter estimation. In this approach, the system’s nonlinearities are analysed and e¤ectively represented by a SDP model structure in the form of wavelets. This provides a computationally e¢ cient tool to open up the ‘black-box’, o¤ering valuable insights into the system’s dynamics. In this thesis, 1-dimensional (1-D) approach is …rst developed based on a conventional SDP model structure which relies on a single state variable dependency. It is then extended into a multi-dimensional approach in order to solve the identi…cation problem of systems with signi…cant multi-variable dependence nonlinear dynamics. Here, parametrically e¢ cient nonlinear model is obtained by the application of an e¤ective model structure selection algorithm based on the Predicted Residual Sums of Squares (PRESS) criterion in conjunction with Orthogonal Decomposition (OD) to avoid any ill-conditioning problems associated with the parameter estimation. This thesis also investigates the aspects of noise, stability and other engineering application of the proposed approaches. More speci…cally, this includes: (1) nonlinear identi…cation in the presence of noise, (2) development of bounded characteristics of the estimated models and (3) application studies where the developed approaches have been used in various engineering applications. Particularly, the modelling and forecast of daily peak power demand in the state of Victoria, Australia have been e¤ectively studied using the proposed approaches. This strongly motivates a great deal of potential future research to be carried out in the area of power system modelling.