On the Identification of Wiener Systems Having Saturation-like Functions with Positive Slopes

摘要

Straipsnyje nagrinejamas Vinerio sistemu laipsniškas tiesines dalies, aprašomos skirtumine lygtimi su nežinomais koeficientais ir dalimis tiesiško netiesiškumo su nežinomais nuožulnumais bei nežinomu slenksčiu, junginys. Parodyta, kad pertvarkius išejimo signalo stebejimus pagal didejančias ju reikšmes, galima išskirti vidurine stebejimu dali, atitinkančia nestebimo tarpinio signalo stebejimus. Pasiulytas pilno tarpinio signalo atstatymo budas pagal iejimo signalo ir išejimo signalo vidurines dalies stebejimus. Nežinomu tiesines Vinerio sistemos dalies koeficientu ir dalimis tiesiško netiesiškumo parametru bei slenksčio iverčiai gaunami mažiausiuju kvadratu metodo algoritmais, apdorojant stebimu iejimo, pertvarkyto išejimo bei atkurto tarpinio signalu duomenis. Pateikti modeliavimo rezultatai.%The aim of the given paper is the development of an approach for parametric identification of Wiener systems with piecewise linear nonlinearities, i.e., when the linear part with unknown parameters is followed by a saturation-like function with unknown slopes. It is shown here that by a simple data reordering and by a following data partition the problem of identification of a nonlinear Wiener system could be reduced to a linear parametric estimation problem. Afterwards, estimates of the unknown parameters of linear regression models are calculated by processing respective particles of input-output data. A technique based on ordinary least squares (LS) is proposed here for the estimation of parameters of linear and nonlinear parts of the Wiener system, including the unknown threshold of piecewise nonlinearity, too. The results of numerical simulation and identification obtained by processing observations of input-output signals of a discrete-time Wiener system with a piecewise nonlinearity by computer are given.