Wiener-Hammerstein Systems Research Articles

Self-error learning framework-based algorithm for parameter recovery of extended Wiener–Hammerstein systems subject to quantised measurements

In this study, a novel estimation scheme is proposed for identifying extended Wiener–Hammerstein systems with hysteresis nonlinearity subject to quantised measurements. The proposed scheme is established in a self-error learning framework to achieve high-performance parameter estimation compared with classic error feedback learning estimation algorithms. Initially, the useful identification data can be extracted from contaminated system data by introducing an adaptive filter. Then, with the help of the filtered data, the identification error expression used to establish the estimator is derived. Subsequently, an online compensation estimation error variable is proposed to eliminate the effect of the regression vector on the convergence performance. A new adaptive law is designed with adaptive recursive gain, considering the compensation estimation error data and parameter initial error data. Under general persistent excitation (PE) condition, the PE condition of the regressor information is verified online, and the estimator convergence is strictly proven. Finally, the statistical results of two illustrated examples and a real-word example are provided to validate the positive features and effectiveness of the proposed estimation scheme.

An Error Learning Scenario-Based Scheme to Quantized Identification in Wiener-Hammerstein Systems Subject to Deadzone Nonlinearity

An Error Learning Scenario-Based Scheme to Quantized Identification in Wiener-Hammerstein Systems Subject to Deadzone Nonlinearity

Binary-Valued Identification of Nonlinear Wiener–Hammerstein Systems Using Adaptive Scheme

Binary-Valued Identification of Nonlinear Wiener–Hammerstein Systems Using Adaptive Scheme

Identification of fractional order Wiener-Hammerstein systems based on adaptively fuzzy PSO and data filtering technique

Identification of fractional order Wiener-Hammerstein systems based on adaptively fuzzy PSO and data filtering technique

Auxiliary model-based multi-innovation PSO identification for Wiener–Hammerstein systems with scarce measurements

In many actual systems, it is often difficult to obtain complete input and output data. Thus, the problem of scarce measurements usually appears in the identification of these systems. This article investigates the parameter estimation of Wiener–Hammerstein systems with scarce measurements. A Wiener–Hammerstein system comprises an input linear unit, a nonlinear unit, and an output linear unit. The nonlinear unit in this paper is described by the saturation and dead-zone characteristics respectively. To solve the incomplete data problem caused by scarce measurements, the auxiliary model is applied. Then the auxiliary model-based improved particle swarm optimization (PSO) algorithm is derived. Furthermore, the multi-innovation technology is introduced to improve the convergence speed and estimation accuracy, and the auxiliary model-based multi-innovation improved PSO is proposed. Finally, the simulations of two numerical examples and the application of the turntable servo system indicate that the proposed multi-innovation method is applicable to Wiener–Hammerstein models with scarce measurements, the estimation accuracy and convergence speed are greatly improved.

Identification of Wiener–Hammerstein systems by [formula omitted]–constrained Volterra series

In the paper the Wiener–Hammerstein (LNL) system is identified with the help of Volterra series and ℓ1-constrained least squares. The nonparametric approach to the problem ensures wide applicability of the proposed method, as it does not require an extensive a priori knowledge about the underlying system. In the main part of the paper, the convergence of the identification algorithm is shown for a general class of systems with smooth nonlinearities and stable dynamics, under the assumption that the input is a bounded i.i.d.random signal. The rate of convergence is examined as well. Moreover, the large error of the standard least squares-based models, inherently associated with high dimensional representations (such as those based on Volterra series expansion), is reduced by the imposed ℓ1-constraint and hence the method allows for a scarcer data set. In addition, the results of numerical simulations are provided to illustrate the superiority of the proposed method over the standard one.

Parameter Estimation of Parallel Wiener-Hammerstein Systems by Decoupling their Volterra Representations

Abstract Nonlinear dynamic systems are often approximated by a Volterra series, which is a generalization of the Taylor series for systems with memory. However, the Volterra series lacks physical interpretation. To take advantage of the Volterra representation while aiming for an interpretable block-oriented model, we establish a link between the Volterra representation and the parallel Wiener-Hammerstein model, based on decoupling of multivariate polynomials. The true link is through a constrained decoupling model with (block-)Toeplitz structure on the factors and sets of identical internal branches. The solution of the modified decoupling problem then reveals directly the parameters of the parallel Wiener-Hammerstein model of the system. However, due to the uniqueness properies of the plain decoupling algorithm, even if the structure is not imposed, the method still leads to the true solution (in the exact case).

Low-rank tensor recovery for Jacobian-based Volterra identification of parallel Wiener-Hammerstein systems

Abstract We consider the problem of identifying a parallel Wiener-Hammerstein structure from Volterra kernels. Methods based on Volterra kernels typically resort to coupled tensor decompositions of the kernels. However, in the case of parallel Wiener-Hammerstein systems, such methods require nontrivial constraints on the factors of the decompositions. In this paper, we propose an entirely different approach: by using special sampling (operating) points for the Jacobian of the nonlinear map from past inputs to the output, we can show that the Jacobian matrix becomes a linear projection of a tensor whose rank is equal to the number of branches. This representation allows us to solve the identification problem as a tensor recovery problem.

Parameter identification based on prescribed estimation error performance for extended Wiener–Hammerstein systems

Most identification algorithms do not consider the prescribed error bound on the parameter estimation error information, which may result in the poor transient performance of parameter estimation during the identification process. In this study, a novel identification scheme is presented for the extended Wiener–Hammerstein systems with backlash non-linearity, which is implemented by using prescribed performance function and error transformation technique. To improve the transient performance of parameter estimation, the prescribed performance function is designed to prescribe estimation error bound. Then, the error transformation technique is applied to transform the prescribed estimation error problem into an equivalent generalised error problem, which can simplify the design of identification algorithm. By developing the parameter updating law, the convergence of generalised error problem can be guaranteed, and the parameter estimation of considered system can be achieved. The numerical example and experiment results validate that the proposed scheme can provide more accurate parameter estimation and better transient performance than the available identification approaches.

Adaptive filtering scheme for parameter identification of nonlinear Wiener–Hammerstein systems and its application

ABSTRACT In this paper, a novel adaptive filtering scheme is first proposed to estimate the parameters of the nonlinear Wiener–Hammerstein systems with hysteresis, which is derived by exploiting the filtering technique and cost function framework. Different from the conventional cost function, the cost function of this paper involves estimation error information term and initial estimate term. In this scheme, the filtering technique is utilised to produce the estimation error information by using a group of auxiliary variables. The estimation error information term can improve the estimation accuracy. Based on developed cost function framework, the parameter update law is derived. Furthermore, the convergence of the proposed scheme is proved under the persistent excitation condition (PE). The efficiency and applicability of the proposed scheme are validated through the simulation and experiment.

Identification of nonlinear Wiener-Hammerstein systems by a novel adaptive algorithm based on cost function framework

This paper investigates parameter identification of nonlinear Wiener-Hammerstein systems by using filter gain and novel cost function. Taking into account the system information is corrupted by noise, the filter gain is exploited to extract the system data. By using several auxiliary filtered variables, an extended estimation error vector is developed. Then, based on the discount term of the extended estimation error and the penalty term on the initial estimate, a novel cost function is developed to obtain the optimal parameter adaptive law. Compared with the conventional cost function which is composed of the square sum of output error, the proposed algorithm based on the cost function of this paper can provide faster convergence rate and higher estimation accuracy. Furthermore, the convergence analysis of the proposed scheme indicates that the parameter estimation error can converge to zero. The effectiveness and practicality of the proposed scheme are validated through the simulation example and experiment on the turntable servo system.

Modified multi-innovation stochastic gradient algorithm for Wiener–Hammerstein systems with backlash

In this paper, the identification of the Wiener–Hammerstein systems with unknown orders linear subsystems and backlash is investigated by using the modified multi-innovation stochastic gradient identification algorithm. In this scheme, in order to facilitate subsequent parameter identification, the orders of linear subsystems are firstly determined by using the determinant ratio approach. To address the multi-innovation length problem in the conventional multi-innovation least squares algorithm, the innovation updating is decomposed into sub-innovations updating through the usage of multi-step updating technique. In the identification procedure, by reframing two auxiliary models, the unknown internal variables are replaced by using the outputs of the corresponding auxiliary model. Furthermore, the convergence analysis of the proposed algorithm has shown that the parameter estimation error can converge to zero. Simulation examples are provided to validate the efficiency of the proposed algorithm.

WH-EA: An Evolutionary Algorithm for Wiener-Hammerstein System Identification

Current methods to identify Wiener-Hammerstein systems using Best Linear Approximation (BLA) involve at least two steps. First, BLA is divided into obtaining front and back linear dynamics of the Wiener-Hammerstein model. Second, a refitting procedure of all parameters is carried out to reduce modelling errors. In this paper, a novel approach to identify Wiener-Hammerstein systems in a single step is proposed. This approach is based on a customized evolutionary algorithm (WH-EA) able to look for the best BLA split, capturing at the same time the process static nonlinearity with high precision. Furthermore, to correct possible errors in BLA estimation, the locations of poles and zeros are subtly modified within an adequate search space to allow a fine-tuning of the model. The performance of the proposed approach is analysed by using a demonstration example and a nonlinear system identification benchmark.

Fast proportional integral phasor extremum seeking control for a class of nonlinear system

In this paper, we present a modification of the phasor extremum-seeking control for the fast optimization of a class of Wiener-Hammerstein nonlinear dynamical systems with a general strict unimodal nonlinearity. Based on the prior knowledge of the system’s relative order and number of non-minimum phase zeros, the proposed approach uses a high frequency perturbation signal and the phasor of the plant output to enable fast convergence of the overall system without the need for filters of the plant’s input and output. The extremum-seeking controller has two modes. In addition to the integral term, a proportional term is used to enable the application to very slow and integrating systems. Semi-global practical asymptotic stability analysis of the overall system to the unknown optimum is achieved. The effectiveness of the proposed approach is illustrated using numerical examples for different types of Wiener-Hammerstein systems.

Decomposition-based recursive least-squares parameter estimation algorithm for Wiener-Hammerstein systems with dead-zone nonlinearity

ABSTRACTIn this paper, a decomposition-based recursive least-squares algorithm is proposed for the parameter estimation of Wiener-Hammerstein systems with dead-zone. Based on a smooth parameterisation of the dead-zone nonlinearity, the Wiener-Hammerstein systems with dead-zone can be transformed into a particular model where the parameter vector involves the least number of parameters needed for the identification model description by using the key-term separation principle. On the basis of the particular model, the hierarchical identification principle is presented to decompose the particular model into two identification subsystems, whose parameters are estimated by using a recursive least squares and the auxiliary model method. Furthermore, the convergence analysis of the proposed algorithm ensures that the estimated parameters convergence to their true values. Compared with recursive least squares algorithm and multi-innovation least-squares, the proposed algorithm can avoid the redundant parameters estimation, and meanwhile reduce the computational burden. Numerical examples and experiment are carried out to illustrate the validity of the proposed algorithm.

Structure Detection of Wiener–Hammerstein Systems With Process Noise

Identification of nonlinear block-oriented models has been extensively studied. The presence of the process noise, more precisely its location in the block-oriented model influences essentially the development of a consistent identification algorithm. The present work is proposed with the aim to localize the process noise in the block-oriented model for accurate nonlinear modeling. To this end, the response of a Wiener-Hammerstein system is theoretically analyzed, the disturbance component in the output, caused by the process noise preceding the static nonlinearity, is shown to be dependent on the input signal. Inspired by such theoretical observation, a simple and new protocol is developed to determine the location of the process noise with respect to the static nonlinearity by using an input signal that is periodic, but nonstationary within one period. In addition, the proposed technique is promising to detect the type of certain static nonlinearity (e.g., dead-zone, saturation). Finally, it is validated on a simulated example and a real-life benchmark.

Linear approximation and identification of MIMO Wiener–Hammerstein systems

This paper considers the linear approximation and identification of multi-input multi-output (MIMO) Wiener–Hammerstein systems, or LNL systems. Evaluating the input–output cross-covariance matrix of the MIMO LNL system for Gaussian inputs, we show that the best linear approximation of the MIMO LNL system in the mean square sense can be obtained by the orthogonal projection (ORT) subspace identification method. For each allocation of the poles of the best linear approximation between the two linear subsystems, the unknown parameters in the numerators of the linear subsystems and the coefficients of a basis function expansion of the nonlinearity are estimated by applying the separable least-squares. The best LNL system is the one that gives the minimum mean square output error. A numerical example is included to show the feasibility of the present approach.

Structure discrimination in block-oriented models using linear approximations: A theoretic framework

In this paper we show that it is possible to retrieve structural information about complex block-oriented nonlinear systems, starting from linear approximations of the nonlinear system around different setpoints. The key idea is to monitor the movements of the poles and zeros of the linearized models and to reduce the number of candidate models on the basis of these observations. Besides the well known open loop single branch Wiener-, Hammerstein-, and Wiener–Hammerstein systems, we also cover a number of more general structures like parallel (multi branch) Wiener–Hammerstein models, and closed loop block oriented models, including linear fractional representation (LFR) models.

Challenges in the Identification of Discrete Time Block Oriented Models for Continuous Time Nonlinear Systems

Block oriented nonlinear models capture the dynamics of a nonlinear system with linear dynamic sub-systems (L), the nonlinear behavior is modeled using static nonlinear subblocks (N). In this paper we focus on three important theoretical and practical challenges that need to be addressed when the class of systems is generalized from the simple but very popular Wiener, Hammerstein, Hammerstein-Wiener or Wiener-Hammerstein systems to more complex nonlinear systems, including nonlinear feedback loops: 1) Dealing with complex blockoriented models: initial (structure revealing) tests; 2) Testing of candidate semi-physical blockoriented models; and 3) Approximating continuous time nonlinear systems by a discrete time recursive model. Experimental illustrations and verifications are shown.

Recovering Wiener-Hammerstein nonlinear state-space models using linear algebra

This paper considers Wiener-Hammerstein systems consisting of a cascade of a linear dynamical system, a static nonlinearity and another linear dynamical system. We start from a black-box nonlinear state-space description of the system and develop a method to reconstruct the parameters of the underlying Wiener-Hammerstein block structure by means of linear algebra operations. First, the static nonlinearity is retrieved by decoupling the nonlinear part of the state-space equations into a single-branch nonlinear function. From there on, a canonical Wiener-Hammerstein nonlinear state-space model is recovered by using linear algebraic and geometric tools. The method is validated on a simulation example.