Optimal Design of Hierarchical B-Spline Networks for Nonlinear System Identification

Hierarchical B-spline networks consist of multiple B-spline networks assembled in different level or cascade architecture. To identify the hierarchical B-spline networks and select important input features for each sub-B-spline network automatically, a predefined instruction/operator set was used. The structures of hierarchical B-spline networks were created and evolved by using Probabilistic Incremental program Evolution (PIPE), and the parameters were optimized by using Differential Evolution (DE) algorithm. In this framework, the selection method of important input variables for each sub-B-spline network was also accomplished by PIPE. Empirical results on benchmark system identification problems indicate that the proposed method is effective and efficient.