Bayesian approach to identify Hammerstein–Wiener non‐linear model in presence of noise and disturbance

Esmaeilani, Leili; Ghaisari, Jafar; Bagherzadeh, Mohammad Ali

doi:10.1049/iet-cta.2018.5562

Cited by 14 publications

(11 citation statements)

References 38 publications

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“…Notice that (kT) contains the unmeasured terms y 0 (kT − iT), u(kT − iT), and u(kT + h − iT), it is impossible to compute the estimatê(kT) by using ( 11)- (12). The solution here is based on the auxiliary model identification idea: 53 letŷ 0 (kT − iT),û(kT − iT), andû(kT + h − iT) be the estimates of y 0 (kT − iT), u(kT − iT), and u(kT + h − iT), respectively, and use y i (kT), f i [u(kT − T)],ŷ 0 (kT − iT), andû(kT + jh − iT) to define the estimate of (kT) aŝ (kT) ∶= [−y 2 (kT), −y 3 (kT), … , −y l (kT), −ŷ 0 (kT − T), −ŷ 0 (kT − 2T), … , −ŷ 0 (kT − nT),…”

Section: The Kt-ffsg Algorithmmentioning

confidence: 99%

“…Nonlinear systems have attracted numerous attention of researchers owing to their simple structures and effectual reflections to nonlinear plants, [1][2][3][4] for example, the Hammerstein systems, [5][6][7] the Wiener systems, [8][9][10] the Hammerstein-Wiener (H-W) systems, 11,12 and the Wiener-Hammerstein (W-H) systems. 13,14 A Hammerstein system consists of a static input nonlinear element in series with a dynamic linear subsystem.…”

Section: Introductionmentioning

confidence: 99%

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Gradient‐based recursive parameter estimation for a periodically nonuniformly sampled‐data Hammerstein–Wiener system based on the key‐term separation

Liu

Ding

2021

Adaptive Control & Signal

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The identification of the Hammerstein-Wiener (H-W) systems based on the nonuniform input-output dataset remains a challenging problem. This article studies the identification problem of a periodically nonuniformly sampled-data H-W system. In addition, the product terms of the parameters in the H-W system are inevitable. In order to solve the problem, the key-term separation is applied and two algorithms are proposed. One is the key-term-based forgetting factor stochastic gradient (KT-FFSG) algorithm based on the gradient search. The other is the key-term-based hierarchical forgetting factor stochastic gradient (KT-HFFSG) algorithm. Compared with the KT-FFSG algorithm, the KT-HFFSG algorithm gives more accurate estimates. The simulation results indicate that the proposed algorithms are effective.

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Section: The Kt-ffsg Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gradient‐based recursive parameter estimation for a periodically nonuniformly sampled‐data Hammerstein–Wiener system based on the key‐term separation

Liu

Ding

2021

Adaptive Control & Signal

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“…The Hammerstein‐Wiener system is a nonlinear system with three blocks where a dynamic linear part is sandwiched between two static nonlinear parts 7,8 . Due to the effectual reflections to nonlinear plants, the Hammerstein‐Wiener systems are involved in a wide range of applications such as the pressure swing adsorption process 9 .…”

Section: Introductionmentioning

confidence: 99%

Recursive least squares estimation methods for a class of nonlinear systems based on non‐uniform sampling

Liu

Chen

Ding

et al. 2021

Adaptive Control & Signal

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Summary Many dynamic processes in practice have nonlinear characteristics and must be described by using nonlinear models. It remains to be a challenging problem to build the models of such nonlinear systems and to estimate their parameters. This article studies the parameter estimation problem for a class of Hammerstein‐Wiener nonlinear systems based on non‐uniform sampling. By means of the auxiliary model identification idea, an auxiliary model‐based recursive least squares algorithm is derived for the systems. In order to enhance the computational efficiency, an auxiliary model‐based hierarchical least squares algorithm is proposed by utilizing the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms.

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“…For H-W with process noise, some papers were proposed in [49][50][51][52][53]. Esmaeilani et al and Wills et al [54][55][56] have proposed identification methods for an H-W system's class presenting measurement and process noises.…”

Section: Introductionmentioning

confidence: 99%

An Improved Method for Stochastic Nonlinear System’s Identification Using Fuzzy-Type Output-Error Autoregressive Hammerstein–Wiener Model Based on Gradient Algorithm, Multi-Innovation, and Data Filtering Techniques

et al. 2021

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This paper proposes an innovative identification approach of nonlinear stochastic systems using Hammerstein–Wiener (HW) model with output-error autoregressive (OEA) noise. Two fuzzy systems are suggested for the identification of the input and output nonlinear blocks of a proposed model from given input-output data measurements. In this work, the need for the commonly used assumptions including well-known structure of input and/or output nonlinearities and/or reversible nonlinear output is eliminated by replacing the intermediate variables and noise with their estimates. Four parametric estimation algorithms to identify the proposed fuzzy-type stochastic output-error autoregressive HW (FSOEAHW) model are derived based on backpropagation algorithm and multi-innovation and data filtering identification techniques. The proposed algorithms are improved backpropagation gradient (IBPG) algorithm, multi-innovation IBPG (MIIBPG) algorithm, a data filtering IBPG (FIBPG) algorithm, and a multi-innovation-based FIBPG (MIFIBPG) algorithm. The convergence of the parameter estimation algorithms is studied. The effectiveness of the proposed algorithms is shown by a given simulation example.

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Bayesian approach to identify Hammerstein–Wiener non‐linear model in presence of noise and disturbance

Cited by 14 publications

References 38 publications

Gradient‐based recursive parameter estimation for a periodically nonuniformly sampled‐data Hammerstein–Wiener system based on the key‐term separation

Gradient‐based recursive parameter estimation for a periodically nonuniformly sampled‐data Hammerstein–Wiener system based on the key‐term separation

Recursive least squares estimation methods for a class of nonlinear systems based on non‐uniform sampling

An Improved Method for Stochastic Nonlinear System’s Identification Using Fuzzy-Type Output-Error Autoregressive Hammerstein–Wiener Model Based on Gradient Algorithm, Multi-Innovation, and Data Filtering Techniques

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