期刊名称：International Journal of Applied Mathematics and Computer Science
电子版ISSN：2083-8492
出版年度：2019
卷号：29
期号：3
页码：1-10
DOI：10.2478/amcs-2019-0042
出版社：De Gruyter Open
摘要：A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear
dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse
nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the
Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are
estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates
are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one.
Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed
Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the
inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy
removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the
practical effectiveness of the proposed approach.
