A Novel Fast Orthogonal Search Method for design of functional link networks and their use in system identification

In this paper, a functional link neural net (FLN) capable of performing sparse nonlinear system identification is proposed. Korenberg´s fast orthogonal search (FOS) is adopted 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, members in lower pins are tried first. If a solution is not found, next pins join the candidates pool until the identification process completes within prespecified accuracy. The modified Gram Schmidt orthogonalization and Choleskey decomposition are applied to create orthogonal functionals that can linearly fit the identified system. The proposed architecture is tested on noise-free and noisy nonlinear systems and shown to find sparse models that can approximate the experimented systems with acceptable accuracy.