Parameter Estimation of Wiener Systems Based on the Particle Swarm Iteration and Gradient Search Principle
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Parameter Estimation of Wiener Systems Based on the Particle Swarm Iteration and Gradient Search Principle Junhong Li1 · Tiancheng Zong1 · Juping Gu1 · Liang Hua1 Received: 21 January 2019 / Revised: 17 December 2019 / Accepted: 19 December 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The Wiener nonlinear system is composed of a linear dynamic subsystem in series with a static nonlinear subsystem. This type of system is widely found in the petroleum, chemistry, thermal and other process industries. It is of great significance to obtain the parameter estimates of the Wiener systems. This paper studies the identification problem of the Wiener time delay nonlinear system. Based on the gradient search principle, a stochastic gradient identification algorithm and a gradient-based iterative identification algorithm are derived. Furthermore, a linearly decreasing weight particle swarm iterative identification algorithm is also proposed for the discussed Wiener time delay systems. Finally, a numerical example and two application cases are given for validating the feasibility of the three identification methods. The results demonstrate that the three algorithms can identify the unknown parameters of the Wiener model effectively. Moreover, the linearly decreasing weight particle swarm iterative identification algorithm behaves much better than the stochastic gradient and the gradient-based iterative algorithms in accuracy and convergence speed. Keywords Wiener system · Time delay · Parameter estimation · Particle swarm iterative identification · Gradient search principle
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Junhong Li [email protected] Tiancheng Zong [email protected] Juping Gu [email protected] Liang Hua [email protected]
1
School of Electrical Engineering, Nantong University, Nantong 226019, People’s Republic of China
Circuits, Systems, and Signal Processing
1 Introduction System identification has become an important research topic in the area of engineering and some other fields [15,30]. Nonlinear systems are widely exist in industry processes, and the identification of nonlinear systems has received much attention [18]. Much research has been performed on exploring new methods for nonlinear system identification and control [9,10]. There are different kinds of nonlinear models, such as bilinear system models [24], Hammerstein models [17], Wiener models [7] and output affine models [2]. A Wiener model is made up by a linear dynamic block along with a nonlinear memoryless block; this is a typical structure of the block-oriented nonlinear models [31]. Moreover, many nonlinear characteristics of industrial processes can be described by the Wiener model, such as continuous stirred tank reactors [5], heat exchange systems [14] and polymerization reactors [8]. Recently, De la Sen et al. have studied the SEIR epidemic model with stochastic Wiener-type perturbations around the equilibrium points [3,11]. The identification of Wiener nonlinear systems has received great attention over the last years. Different iden
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