Identification of Wiener models using optimal local linear models

The Wiener model is a versatile nonlinear block oriented model structure for miscellaneous applications. In this paper a method for identifying the parameters of such a model using optimal local linear models is presented. The linear model part is represented by a discretetime transfer function and the non-linear characteristic is represented by piece-wise linear functions. Parameter estimation as well as partitioning of the local linear models is simultaneously accomplished by the identification procedure. The optimality of the proposed algorithm is threefold: First, each local model is linear in the parameters and therefore optimal parameter estimation methods like Recursive Least-Squares can be applied, thus leading to a robust solution. Second, the region of validity of each local model is adaptively optimized using the Chi-squared distribution of the estimated residual. This approach not only enables an automatic choice of the model size but it also incorporates the measurement noise level of the output variable into the result. And third, the resulting global model has a minimum of local models while guaranteeing optimal performance. A simulation of the pharmacological Propofol model is included, which documents the ability of the algorithm to balance the output noise with the systems nonlinearity.