Study of the effective number of parameters in nonlinear identification benchmarks

This paper discusses the importance of the notion of effective number of parameters as a measure of model complexity. Exploiting this concept allows a fair comparison of models obtained from different model classes. Several illustrative examples of linear and nonlinear models are presented to provide more insight in the problem. As one possible way of showing that model complexity can be reduced without having to pull any parameters to zero, an approach for rank reduced estimation based on the truncated SVD is also discussed. These ideas are then applied to two nonlinear real world problems: the Wiener-Hammerstein and the Silverbox benchmarks.