Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

Abstract

Summary In this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener‐FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener‐FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.

Robust identification for input non‐uniformly sampled Wiener model by the expectation‐maximisation algorithm

“…(4) The assumptions of heavy-tailed distribution include Laplace distribution, Gaussian mixture distribution and flat-topped tdistribution [23]. (5) The case of missing data and time delay in Wiener model is studied in literature [58].…”

Identification of series–parallel systems composed of linear and nonlinear blocks

“…Several studies have been focused on the identification of nonlinear systems constituted by the series connection of linear and nonlinear blocks 4,5 . Most papers on nonlinear system identification have addressed the problem of Wiener and Hammerstein models 6–11 . The problem has been addressed following several approaches and methods, for example, stochastic methods, 12–14 deterministic recursive techniques, 15 frequency methods 16,17 …”

“…Parallel block‐oriented models have gained renewed interest lately 19 . In Schoukens et al 20,21 and Schoukens et al 22 The identification problem for those block‐structured systems has been approached on the basis of several assumptions, for example, the system nonlinearity is invertible, the linear block is parametric 23 or finite impulse response (FIR) 7 …”

“…4,5 Most papers on nonlinear system identification have addressed the problem of Wiener and Hammerstein models. [6][7][8][9][10][11] The problem has been addressed following several approaches and methods, for example, stochastic methods, [12][13][14] deterministic recursive techniques, 15 frequency methods. 16,17 To increase modeling capability, more complex models have been proposed involving parallel connections.…”

“…19 In Schoukens et al 20,21 and Schoukens et al 22 The identification problem for those block-structured systems has been approached on the basis of several assumptions, for example, the system nonlinearity is invertible, the linear block is parametric 23 or finite impulse response (FIR). 7 Considering both series and parallel coupling of linear and nonlinear blocks improves modeling capability but also increases model complexity. 24 This article presents an identification approach for a nonlinear system that consists of a series connection of two systems, each one of them is constituted of the parallel connection of linear and nonlinear F I G U R E 1 The studied nonlinear system consisting of the series connection of two sets of linear and nonlinear blocks coupled in parallel.…”