A robust model determination algorithm for nonlinear system identification.

摘要

A complete nonlinear system identification algorithm, including model form determination as well as parameter identification, is presented in this dissertation. Compared with previous work, the present approach offers the most robust method yet for automatically determining the mathematical forms of the (unknown) model. By combining a proven nonlinear state estimation algorithm, known as “Minimum Model Error (MME)” estimation, with a new iterative correlation routine, it is possible to develop nonlinear models of state that accurately represent the system's dynamics.; Mathematical modeling of systems has numerous benefits, some of which include prediction and control. The trouble is physical systems are inherently nonlinear, and many systems cannot be approximated very well by linear modeling techniques. Now the task becomes how to develop nonlinear models, and therein lies the basis for this research.; A model determination algorithm is developed based on a forward-stepwise regression (FSR) routine where variables are added and removed from the model based on a hypothesis test and a statistical significance check using the F-distribution. For the complete nonlinear system identification algorithm a function library comprising of nonlinear (or linear) functions of the state estimate from MME replace variables from the FSR routine with the model correction (also from MME) being to-be-identified. A floating threshold significance is then imposed to make a more problem-dependent algorithm, with the modified stepwise regression algorithm (MSR) resulting. Finally, a dual MME/MSR algorithm is developed and shown to recreate “unknown” system models from complex higher-order, nonlinear systems.; The complete MME/MSR system identification algorithm is applied throughout to several different examples each nonlinear with zero a priori knowledge of the system model. In every case the new algorithm identifies the system dynamics correctly under a variety of conditions.