New Algorithm for Korenberg-Billings Model of Nonlinear System Identification

Abstract

A new algorithm is presented here for nonlinear system identification based on input and output relationship by a cascade structure of dynamic linear(L), static nonlinear(N), and dynamic linear(L) subsystems, or the Korenberg-Billings (K-B) Model. It uses a series of multilevel inputs to separate the Volterra components in the output signal and then uses Flethcer-Reeves method to minimize a cost function to separate the two linear subsystems from the nonliear subsystem. It does not employ any correlation functions as were used by both Korenberg and Billings. Therefore the input is not restricted to white Gaussian noise, the computation is simpler, and the result is much more accurate than the previous methods. Three computer programs, namely, Iden idet, Oddident, P_Lident, have been developed to identify systems with even, odd, and piece-wise types of nonlinearity. Numerical example is presented to show computation result. In addition, a nonlinear piecewise saturation model has been developed for the interfacial impedance of metallic bioelectrodes based on overpotential signals from several levels of current density input. The result shows remarkable similarity to the model developed previously by using fractal dimension study.