Hammerstein Nonlinear Systems Research Articles

Identification of Wiener–Hammerstein nonlinear systems with backlash operators

Identification of Wiener–Hammerstein nonlinear systems with backlash operators

Iterative parameter identification for Hammerstein systems with ARMA noises by using the filtering identification idea

SummaryIn practical applications, many processes have nonlinear characteristics that require nonlinear models for accurate description. However, constructing such models and determining their parameters are a challenging task. This article explores filtered identification methods for estimating the parameters of a particular type of nonlinear Hammerstein systems with ARMA noise. An auxiliary model‐based least squares algorithm is developed for such systems based on the auxiliary model identification idea. A hierarchical least squares algorithm that utilizes the hierarchical identification principle is proposed to enhance computational efficiency. Additionally, a key term separation technique is employed to express the system output as a linear combination of parameters, allowing the system to be decomposed into smaller subsystems for more efficient estimation of parameters. Simulation results demonstrate the effectiveness of these proposed algorithms.

Parameter learning of multi‐input multi‐output Hammerstein system with measurement noises utilizing combined signals

SummaryIn this article, the parameter learning scheme for the multi‐input multi‐output (MIMO) Hammerstein nonlinear systems under measurement noises is studied, which is derived by exploiting the correlation analysis and data filtering technique. The coupled MIMO Hammerstein system presented involves a static nonlinear subsystem modeled by neural fuzzy model (NFM), and a dynamic linear subsystem established by autoregressive moving average with extra input (ARMAX) model. To learn the unknown parameter of the MIMO Hammerstein system, the combined signals are designed to realize that identification of the nonlinear subsystem is separated from that of linear subsystem. First, the correlation properties of separable signals in a nonlinear system are analyzed, then the parameters of the linear subsystem are estimated utilizing correlation analysis, which can deal with the issue of unmeasured intermediate variable in the Hammerstein system. Second, the data filtering technique is introduced to derive the data filtering‐based recursive least squares technique for learning the nonlinear subsystem parameter, which can reduce the impact of the moving average noise and improve the precision of parameter estimation. Finally, the effectiveness and feasibility of the proposed identification scheme is proved by numerical simulation and nonlinear pH process.

Identification of the Hammerstein nonlinear system with noisy output measurements

Identification of the Hammerstein nonlinear system with noisy output measurements

Recursive Identification of Nonlinear Hammerstein Systems with FIR Linear Parts under Impulsive Noise with Model Selection and Order Determination

Recursive Identification of Nonlinear Hammerstein Systems with FIR Linear Parts under Impulsive Noise with Model Selection and Order Determination

基于滤波和递推的Hammerstein非线性系统估计与控制

基于滤波和递推的Hammerstein非线性系统估计与控制

An efficient conjugate gradient based Cholesky CMA‐ES estimation algorithm for nonlinear systems

AbstractThis article studies the parameter estimation problems of nonlinear systems with colored noise using the covariance matrix adaptation evolution strategy (CMA‐ES), which is one of the most competitive evolutionary algorithms available and has been applied in the area of reinforcement learning and process control. However, a major limitation that impedes the application of the CMA‐ES is the high computational complexity caused by matrix decomposition. To solve this problem, an efficient Cholesky CMA‐ES which uses the Cholesky factor instead of the covariance matrix to reduce the computational complexity, and updates the search direction and distribution mean based on the conjugate gradient method to improve the search accuracy is proposed. By using the auxiliary model identification idea, the Cholesky CMA‐ES can be applied to solve the parameter estimation problems of the Hammerstein nonlinear systems with colored noise. Two simulation examples are provided to demonstrate its effectiveness.

Two‐stage and three‐stage recursive gradient identification of Hammerstein nonlinear systems based on the key term separation

AbstractThis article explores recursive algorithms for parameter identification issues of Hammerstein output‐error systems. The proposed approach includes the key term separation auxiliary model recursive gradient algorithm, which utilizes the gradient search and the key term separation. To enhance computational efficiency, the system is decomposed into two or three subsystems through the hierarchical identification principle. Based on this, a key term separation based auxiliary model two‐stage recursive gradient algorithm and a key term separation based auxiliary model three‐stage recursive gradient algorithm are presented. The simulation results verify the validity of the obtained algorithms.

Bias-Correction Errors-in-Variables Hammerstein Model Identification

In this paper, a Bias-Correction Least-Squares (BCLS) algorithm is proposed for identifying block-oriented Errors-In-Variables nonlinear Hammerstein (EIV-Hammerstein) systems. Due to both the input and output of the EIV-Hammerstein system are observed with additive white noises, the estimation bias of traditional LS algorithm is introduced. The estimation bias is derived from a consistency point of view, which is a function about noises variances and monomial of noiseless system input-output measurements. A bias-estimation scheme based only on the available noisy measurements is then proposed for consistent identification of the monomial of noiseless system input-output measurements in a recursive form. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the unknown noise variances for practical applications. Such that the noise effect can be eliminated and the consistent estimated parameters are obtained. The effectiveness of the proposed method is demonstrated by a simulation example and an experimental prototype of wireless power transfer system.

Fault Detection for Nonlinear Dynamic Systems With Consideration of Modeling Errors: A Data-Driven Approach.

This article is concerned with data-driven realization of fault detection (FD) for nonlinear dynamic systems. In order to identify and parameterize nonlinear Hammerstein models using dynamic input and output data, a stacked neural network-aided canonical variate analysis (SNNCVA) method is proposed, based on which a data-driven residual generator is formed. Then, the threshold used for FD purposes is obtained via quantiles-based learning, where both estimation errors and approximation errors are considered. Compared with the existing work, the main novelties of this study include: 1) SNNCVA provides a new parameterization strategy for nonlinear Hammerstein systems by utilizing input and output data only; 2) the associated residual generator can ensure FD performance where both the system model and its nonlinearity are unknown; and 3) with consideration of modeling-induced errors, the quantiles are invoked and used to provide a reliable FD threshold in situations where only limited samples are available. Studies on a nonlinear hot rolling mill process demonstrate the effectiveness of the proposed method.

Correlation analysis-based parameter learning of Hammerstein nonlinear systems with output noise

In this paper, a novel correlation analysis-based parameter learning scheme for Hammerstein nonlinear systems with output noise is presented. The developed Hammerstein system contains a static nonlinear block approximated by neural fuzzy network and a linear dynamic block modeled by transfer function, and parameter separation learning of the nonlinear block and linear block are realized by using combined signals. Firstly, based on the input and output of the separable signal, the correlation analysis algorithm is applied to estimate linear block parameters, thereby the interference of moving average noise is dramatically handled. Moreover, to improve parameter estimation precision of the learned Hammerstein system, multi-innovation theory and data filtering technology are introduced, and a data filtering-based multi-innovation stochastic gradient learning scheme is implemented for jointly estimating nonlinear block parameters and noise model using random signals. Studies with a numerical simulation and a practical nonlinear process demonstrate the efficiency. In the numerical simulation, when the noise to signal ratio is less than 33.37%, estimate error of the linear block parameters using least squares method is less than 0.0796. In contrast, estimate error of the proposed method is less than 0.0338. For the modeling ability of the nonlinear block, the proposed method has an improvement of 67.07% than the MI-ESG method with innovation length of six. With regard to practical nonlinear process, when the concentration set value is 0.1, the rise time of the proposed method is 0.021 h, while the rise time of MPC and traditional PI controller and is 0.055 h and 0.143 h, respectively.

Modeling and identification for practical nonlinear process using neural fuzzy network–based Hammerstein system

To address the strong nonlinearity and unknown disturbance in practical nonlinear process, an identification scheme of neural fuzzy network (NFN)–based Hammerstein nonlinear system using multi-signals is developed in this paper. The proposed Hammerstein system has a static nonlinear subsystem approximated by NFN and a dynamic linear subsystem described by autoregressive exogenous system (ARX). First, the nonlinear subsystem and the linear subsystem are separated and identified by the designed multi-signals, and then parameters of the linear subsystem and noise model are identified simultaneously by making use of recursive extended least squares approach, which is effective for compensating the error caused by output noise. Furthermore, in order to cope with unmeasurable variable issue of the identified system, auxiliary model technology is developed, and the nonlinear subsystem parameters are estimated by applying derived auxiliary model recursive extended least squares approach. Experimental results of three typical nonlinear processes verify the effectiveness and accuracy of the proposed method, and the simulation results show that the proposed method can obtain higher identification accuracy than other optimization algorithms.

Parameter identification for Hammerstein nonlinear system with polynomial and state space model

This study investigates a two-stage parameter identification algorithm for the Hammerstein nonlinear system based on special test signals. The studied Hammerstein nonlinear system has a static nonlinear subsystem represented by polynomial basis function and a dynamic linear subsystem described by canonical observable state space model, and special test signals composed of binary signals and random signals are applied to parameter identification separation of the nonlinear subsystem and linear subsystem. The detailed identification procedures consist of two main steps. Firstly, using the characteristics that binary signals do not excite the static nonlinear subsystem, the dynamic linear subsystem parameters are identified through recursive least squares algorithm based on input-output data of binary signals. Secondly, unmeasurable state variables of the identified system are replaced with estimated values, thus the nonlinear subsystem parameters are obtained using recursive least squares algorithm with the help of input-output data of random signals. The efficiency and accuracy of proposed identification scheme are confirmed on experiment results of a numerical simulation and a practical nonlinear process, and experimental simulation results show that the developed two-stage identification algorithm has excellent predictive performance for identifying the Hammerstein nonlinear state space systems.

A Simulation and Experimental Study on Identification of an Electromechanical System

The current applications in electromechanical energy conversion demand highly accurate speed and position control. For this purpose, a better understanding of the motion characteristics and dynamic behavior of electromechanical systems including nonlinear effects is needed. In this paper, a suitable model of Permanent Magnet Direct Current (PMDC) motor rotating in two directions is developed for identification purposes. Model is parameterized and identified via simulation and using real experimental data. Linear and nonlinear models for the system are built for identification, and the effective nonlinearities in the system, which are Coulomb friction and dead zone, are integrated into the nonlinear model. A Weiner- Hammerstein nonlinear system description is used for identification of the model. MATLAB is selected as the investigating tool, and a simulation model is used to observe the error between the simulated and estimated outputs. Identification of the linear and nonlinear system models using experimental data is performed using the least squares (LS) and recursive least squares (RLS) methods. Performance of the model and identification method with the real time experiments are presented numerically and graphically, revealing the advantages of the proposed nonlinear identification approach.

Discrete indirect adaptive sliding mode control for uncertain Hammerstein nonlinear systems

The robustness issue of uncertain nonlinear systems’ control has attracted the attention of numerous researchers. In this paper, we propose three techniques to deal with the uncertain Hammerstein nonlinear model. First, a discrete sliding mode control (SMC) is developed, which is based on converting the original nonlinear system into a linearized one in the vicinity of the operating region using Taylor series expansion. However, the presence of relatively high nonlinearities and parameter variations leads to the deterioration of the desired performances. In order to overcome these problems and to improve the performance of classical SMC, we propose two solutions. The first one is based on the synthesis of a discrete SMC, taking into account the presence of nonlinearity. The second solution is a new discrete adaptive SMC for input–output Hammerstein model. In order to show the effectiveness of the proposed controllers, a detailed robustness analysis is clearly developed. Simulation examples are reported at the end of the paper.

Improving the modelling efficiency of Hammerstein system using Kalman filter and its parameters optimised using social mimic algorithm: Application to heating and cascade water tanks

Identification of Hammerstein systems finds extensive applications in solving the stability and design issues of non-linear dynamic systems. Hence, in this paper, a first attempt is made to solve the parameter estimation problem of Hammerstein non-linear systems by using the evolutionary optimisation algorithm (EOA) coupled Kalman filter (KF). The standard KF produces the best possible optimal states for the particular state estimation problem based on its properly tuned parameters θ^0−, P0−, φ, Q and R termed as initial state, initial error covariance, state transition, process noise covariance and measurement noise covariance, respectively. These parameters must be concurrently tuned to achieve a stable filtering operation. The manual and existing adaptive tuning methods do not guarantee optimality, convergence and also require a large amount of data. Moreover, the adaptive methods tune only a few statistics (Q and R) simultaneously. To defeat these foreknown problems, in the proposed method, initially, a recently established EOA named social mimic optimisation (SMO) algorithm is employed to get the global optimised KF parameters along with an efficient cost function that has been derived based on the model output for the concurrent achievement of all the KF parameters. Finally, the standard KF technique identifies the estimated parameters of the Hammerstein model with those optimised KF parameters. Various numerical and experimental test results demonstrate that the proposed SMO-based KF approach offers high accuracy in estimating the parameters along with the good convergence speed compared to the standard KF, other presented EOA-based KF approaches and recently reported techniques.

Identification of fractional-order Hammerstein nonlinear ARMAX system with colored noise

Identification of fractional-order Hammerstein nonlinear ARMAX system with colored noise

Comments on “Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle model”

The purpose of this article is to discuss some aspects of the convergence analysis performed in the paper (Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle model, Eur Phys J Plus 134: 407, 2019). It is highlighted that the way the authors prove convergence suffers a lack of correct and valid mathematical justifications.

The data filtering based multiple‐stage Levenberg–Marquardt algorithm for Hammerstein nonlinear systems

AbstractThis article considers the parameter identification problem of multiple‐input single‐output Hammerstein nonlinear systems. Applying the data filtering technique, the input–output data are filtered. The filtered system is decomposed into multiple subsystems with fewer variables by using the hierarchical identification principle. The data filtering based multiple‐stage Levenberg–Marquardt algorithm is proposed for interactively identifying each subsystem. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.

Joint tracking coefficients and the time delay of a nonstationary linear system, preceded by a static nonlinearity

SummaryThe paper considers a block‐oriented nonlinear Hammerstein system that consists of a linear block with real‐valued time‐varying unknown coefficients and a pure time delay, preceded by the static nonlinearity. The joint tracking of linear block coefficients and the time delay while processing observation samples is under consideration. The difficulty of the tracking process consists in the initial nonconvexity of the objective function to be minimized, in respect of the time delay. To obtain current estimates of the true coefficients and the time delay it is necessary to overcome the multiextremality of the objective function. A global optimization problem could be solved by changing a form of the nonconvex objective function into a convex one. The optimization problem has been subdivided into two problems that are analyzed in this article, as well. The first one consists of removal of the objective function multiextremality in respect of the time delay, while hunting for the global extremum. Therefore, the well‐known approach based on the method of corrective operators, which is used to transform the multiextremal criterion into a unimodal function for the nonstationary Wiener system, is developed here for the Hammerstein one. The other problem consists of the applicability of unified adaptive algorithms, used for Wiener systems in the case of Hammerstein systems. The recursive parametric identification technique, based on the adaptive algorithm procedures, is developed here for the nonstationary block‐oriented Hammerstein systems, too. The applicability of algorithms is supported by various simulation tests solved by computer for distinct inputs and for two static nonlinearities.