Nonlinear system identification with regularized local FIR model networks

Abstract

An algorithm for the identification of nonlinear black-box systems is introduced utilizing recently proposed techniques for the regularized estimation of impulse responses for linear systems. Based on a comparison of the fundamental advantages and disadvantages of (N)FIR and (N)ARX model structures for the linear and nonlinear case it is outlined that the novel regularized FIR model estimation removes the major drawback of high parameter variances from the FIR model and makes it thus feasible and even advantageous as a local model structure in local model networks. The estimation of the local FIR models is performed with a special regularization matrix, which is derived from the concept of reproducing Kernel Hilbert spaces incorporating the knowledge of the exponential decay of the impulse response of a stable system. The algorithm is applied to a test system and is, in contrast to local ARX models, always able to achieve stability and a fairly good prediction accuracy. The proposed procedure is also applied for the identification of a Diesel engine. A validated simulation model is used to generate identification data and the described approach is used to construct a model that is able to represent the influence of the variable turbine geometry and the injected fuel mass on the predicted motor torque.