Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the parameters of a wide range of block-oriented nonlinear models. One class of these approaches uses linear approximations to initialize the identification algorithm. The best linear approximation framework and the -approximation framework, or equivalent frameworks, allow the user to extract important information about the system, guide the user in selecting good candidate model structures and orders, and prove to be a good starting point for nonlinear system identification algorithms. This paper gives an overview of the different block-oriented nonlinear models that can be identified using linear approximations, and of the identification algorithms that have been developed in the past. A non-exhaustive overview of the most important other block-oriented nonlinear system identification approaches is also provided throughout this paper.
In this paper we show that it is possible to retrieve structural information about complex block-oriented nonlinear systems, starting from linear approximations of the nonlinear system around different setpoints. The key idea is to monitor the movements of the poles and zeros of the linearized models and to reduce the number of candidate models on the basis of these observations.Besides the well known open loop single branch Wiener-, Hammerstein-, and Wiener-Hammerstein systems, we also cover a number of more general structures like parallel (multi branch) Wiener-Hammerstein models, and closed loop block oriented models, including linear fractional representation (LFR) models.
A large variety of nonlinear systems can be approximated by parallel Wiener-Hammerstein models. These models consist of a multiple input multiple output (MIMO) nonlinear static block sandwiched between two linear dynamic blocks. One method is available for the identification of a general parallel Wiener-Hammerstein model. It represents the nonlinear block as a multivariate polynomial, which typically contains cross-terms. These make it harder to interpret and to invert the model. We want to eliminate the cross-terms, and thus come to a decoupled polynomial representation. In this paper, the simultaneous decoupling of quadratic and cubic polynomials is formulated as a standard tensor decomposition. A simulation example shows that the simultaneous decoupling can result in a model with less parallel branches than a decoupling of all polynomials separately.
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