A novel LOO based two-stage method for automatic model identification of a class of nonlinear dynamic systems

Abstract

This paper investigates the construction of models for a class of nonlinear systems that can be represented by linear in parameter models. This is not a trivial problem, as there are many possible combinations of model terms and exhaustive search is not an option when the number of possible model terms is large. Most existing fast approaches such as orthogonal least squares (OLS), fast recursive algorithm (FRA) and their variants serve the purpose of fast selection. However, these stepwise forward methods are greedy approaches in general and the resultant models are not optimal. Further, they do not control the model complexity (i.e. automatically stop the model selection). The two stage algorithm may improve the compactness of models obtained from forward algorithms, again, it does not determine how many model terms are necessary. Recently, some cross validation based methods have been proposed for automatic model construction, based on leave-one-out (LOO) criteria and OLS or FRA, however the issues related to the forward selection algorithms still exist. Further, LOO based methods are computationally expensive as the model often has to be trained N times (N is the number of samples) for just only one evaluation of the LOO criterion. In this paper, a novel and fast two stage algorithm is proposed for automatic construction of linear in parameter models for a class of nonlinear systems using LOO criterion, overcoming the disadvantages of stepwise model selection algorithms and reducing the computational complexity in applying the LOO criteria. Two numerical examples are presented to confirm its effectiveness.