Abstract
Current methods to identify Wiener-Hammerstein systems using Best Linear Approximation (BLA) involve at least two steps. First, BLA is divided into obtaining front and back linear dynamics of the Wiener-Hammerstein model. Second, a refitting procedure of all parameters is carried out to reduce modelling errors. In this paper, a novel approach to identify Wiener-Hammerstein systems in a single step is proposed. This approach is based on a customized evolutionary algorithm (WH-EA) able to look for the best BLA split, capturing at the same time the process static nonlinearity with high precision. Furthermore, to correct possible errors in BLA estimation, the locations of poles and zeros are subtly modified within an adequate search space to allow a fine-tuning of the model. The performance of the proposed approach is analysed by using a demonstration example and a nonlinear system identification benchmark.
Highlights
Nonlinearities are present to a greater or lesser extent in all real processes
The binary code used for the classification of the poles and zeros of the Best Linear Approximation (BLA) can be changed without user interaction as the false positions of the poles and zeros are corrected. This is an important advantage of WH-EA, since it is very likely that the BLA estimate is subject to errors due to noise and nonlinearity effects; this has been experimentally demonstrated; for this reason, many proposals carry out a final readjustment of the parameters of the Wiener-Hammerstein model
WH-EA is able to look for the best BLA split capturing at the same time the process static nonlinearity with high precision, solving a single optimization problem
Summary
Nonlinearities are present to a greater or lesser extent in all real processes. When nonlinearities are weak, linear models can be successfully used to forecast the evolution of variables or to design control schemes. On the same context of QBLA/ CBLA and in line with “brute-force” method, Westwick and Schoukens [46] propose a scanning technique for a rapid evaluation of all possible BLA partitions between both LTI blocks of the Wiener-Hammerstein system. With this evaluation, the vast majority of possible partitions are discarded. Once the front and the back dynamics of the Wiener-Hammerstein model have been identified, a parameterization of both LTI blocks is required in an additional step This step can be complicated because a linear phase shift can be present in the nonparametric estimate.
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