Nonlinear system identification for cascaded block model: an application to electrode polarization impedance.

A new algorithm has been developed to identify a system divided into cascaded blocks of dynamic linear (L), static nonlinear (N), and dynamic linear (L) subsystems based strictly on the input-output relationship. The nonlinear element is assumed to be equicontinuous, or must be satisfied by the Weierstrass criterion. Therefore, it could either be continuous type as represented by polynomial approximation or abrupt type as represented by piecewise-linear segments. The process uses a series of multilevel input to decouple the two linear subsystems from the nonlinear subsystem and then applies the predictor-corrector algorithm to minimize a cost function to obtain the parameter of the subsystem. The method does not restrict the type of input signal and no prior knowledge of the subsystems is necessary. Numerical example for a prescribed system is given and the results show almost identical values by any one of the three types of input, namely: step, sinusoidal, or white noise. Three computer programs have been developed for the identification of the system with odd, even, and piecewise abrupt types of nonlinearity. The method is applied to model the interfacial phenomenon of noble metal electrode (Pt) at the nonlinear range and the algorithm is verified by comparison with the result developed previously.