Regressor Selection in System Identification using ANOVA

Abstract: The aim of this work is to nd a good method to select regressors for nonlinear system identification. A literature survey over possible methods to select the model structure for nonlinear systems, mainly autoregressive processes, is first given. The main ideas are:1. Compare estimated models, using different regressor vectors, with each other.2. Compare the variability of the output data, given one regressor vector, with the variability of the output data given other regressor vectors.The second idea is investigated further by applying a common statistical tool, analysis of variance, to system identification applications. This method differs from most of the suggested methods by treating the variability in a stochastic framework, instead of treating the problem from a geometrical point of view. An investigation of the properties of analysis of variance (ANOVA), practical considerations with its use and Monte-Carlo simulations covering several aspects of the use of ANOVA in system identication applications is performed. It is shown that ANOVA is reliable, useful for different types of input signals and not critically sensitive to the amount of measurement noise. Moreover, the computations are fast, without iterations or minimisations. The result of this work is a suggested procedure for selecting a model structure from input/output data, using analysis of variance.