Applying polynomial decoupling methods to the polynomial NARX model

System identification uses measurements of a dynamic system’s input and output to reconstruct a mathematical model for that system. These can be mechanical, electrical, physiological, among others. Since most of the systems around us exhibit some form of nonlinearbehavior, nonlinear system identification techniques are the tools that will help us gain abetter understanding of our surroundings and potentially let us improve their performance. One model that is often used to represent nonlinear systems is the polynomial NARX model, an equation error model where the output is a polynomial function of thepast inputs and outputs. That said, a major disadvantage with the polynomial NARX modelis that the number of parameters increases rapidly with increasing polynomial order.Furthermore, the polynomial NARX model is a black-box model, and is therefore difficultto interpret. This paper discusses a decoupling algorithm for the polynomial NARX modelthat substitutes the multivariate polynomial with a transformation matrix followed by abank of univariate polynomials. This decreases the number of model parameters significantly and also imposes structure on the black-box NARX model. Since a non-convex opti-mization is required for this identification technique, initialization is an important factor toconsider. In this paper the decoupling algorithm is developed in conjunction with severaldifferent initialization techniques. The resulting algorithms are applied to two nonlinear benchmark problems: measurement data from the Silver-Box and simulation data fromthe Bouc-Wen friction model, and the performance is evaluated for different validation signals in both simulation and prediction.

Jaar van publicatie:2021

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:6

Auteurs:International

Authors from:Higher Education

Toegankelijkheid:Closed