This paper discusses a novel initialization algorithm for the estimation of nonlinear state-space models. Good initial values for the model parameters are obtained by identifying separately the linear dynamics and the nonlinear terms in the model. In particular, the nonlinear dynamic problem is transformed into an approximate static formulation, and simple regression methods are applied to obtain the solution in a fast and efficient way. The proposed method is validated by means of two measurement examples: the Wiener-Hammerstein benchmark problem and the identification of a crystal detector.
The use of KCCA is suggested also in @cite_19 for the identification of nonlinear MIMO Hammerstein-Wiener systems. A subspace identification technique is used to estimate the nonlinearities separately from system dynamics.
@cite_19
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In this paper we present a novel algorithm to identify MIMO Hammerstein-Wiener systems under open and closed-loop conditions.We reformulate a linear regression problem, commonly used as the first step in closed loop subspace identification, as an intersection problem which can be solved by using canonical correlation analysis (CCA). This makes it possible to utilize ideas from machine learning to estimate the static nonlinearities of Hammerstein-Wiener systems, using kernel canonical correlation analysis (KCCA). In the second step the state sequence is estimated and consequently the dynamic part can be identified. The effectiveness of the approach is illustrated with a closed-loop simulation example.