System Identification Using Optimally Designed Functional Link Networks via a Fast Orthogonal Search Technique

Abstract

In this paper, a sparse nonlinear system identification method is proposed. Functional link neural nets (FLN) with their high orders polynomial basis functions are capable of performing complex nonlinear mapping. However, a large number of inputs and accurate modeling will require a huge number of basis functions that need to be explored. The Fast Orthogonal Search (FOS) introduced by Korenberg [1] is adopted here to detect the proper model and its associated parameters. The FOS algorithm is modified by first sorting all possible nonlinear functional expansion of the input pattern according to their correlation with the system output. The sorted functions are divided into equal size groups, pins, where functions with the highest correlation with the output are assigned to the first pin. Lower correlation members go the following pin and so forth. During the identification process, candidates in lower pins are tried first. If a solution is not found, next pins join the candidates pool for further modeling until the identification process completes within a prespecified accuracy. The proposed architecture is tested on noisefree and noisy nonlinear systems and shown to find sparse models that can approximate the experimented systems with acceptable accuracy.