Effect of Penalty Function Parameter in Objective Function of System Identification

Abstract

The evaluation of an objective function for a particular model allows one to determine the optimality of a model structure with the aim of selecting an adequate model in system identification. Recently, an objective function was introduced that, besides evaluating predictive accuracy, includes a logarithmic penalty function to achieve a suitable balance between the former model’s characteristics and model parsimony. However, the parameter value in the penalty function was made arbitrarily. This paper presents a study on the effect of the penalty function parameter in model structure selection in system identification on a number of simulated models. The search was done using genetic algorithms. A representation of the sensitivity of the penalty function parameter value in model structure selection is given, along with a proposed mathematical function that defines it. A recommendation is made regarding how a suitable penalty function parameter value can be determined.