An introduction to models based on Laguerre, Kautz and other related orthonormal functions – Part II: non-linear models

Abstract

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and limitations are discussed within the contexts of non-linear system identification. The discussions comprise a broad bibliographical survey of the subject and a comparative analysis involving some specific model realisations, namely, Volterra, fuzzy, and neural models within the orthonormal basis functions framework. Theoretical and practical issues regarding the identification of these non-linear models are presented and illustrated by means of two case studies.

A Novel Developed Linear and Nonlinear System Identification for an Industrial Dryer

“…The filtered output for dryer is shown in figure 6. In comparison to [4], the results depicted in figure 6 are more satisfactory for implementation [33].…”

“…At the first time, some input and output data were collected by using two general sensors at input and output and tried to follow the methods which were done by other researchers [4,7], but no reasonable results obtained. Continuing research to overcome this problem, first, some precise sensors were located at system input and output for data acquisition, second, tried to do a novelty and formulize the fundamental identification techniques based on dryer system configuration, behavior, its initial delay and operation which achieved via some consultant and meetings with some engineers operating with this systems during recent years.…”

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

“…Details about Kautz functions are given in Section 2.2. The reader is also encouraged to see [42,43,37].…”

Damage detection in an uncertain nonlinear beam based on stochastic Volterra series: An experimental application

“…where k ∈ Z + → l η,ij (k) is a simple filtering of the input signal u(k) by the Kautz function ψ η,ij . More information about the nonlinear system identification method based on Volterra series, Kautz functions and the process of Volterra kernels estimation can be found in [27,28,29,16,17].…”