Identification Of Wiener Systems Research Articles

Parameter estimation of multivariable Wiener nonlinear systems by the improved particle swarm optimization and coupling identification

This paper investigates the parameter estimation of multivariable Wiener nonlinear systems. To solve the inconsistency problem of the parameter vector and the parameter matrix, the coupling identification concept is applied. Combined with particle swarm optimization (PSO) and an auxiliary model, the partially coupled improved particle swarm optimization (PC-IPSO) method is proposed. In this algorithm, the adaptive feedback inertia weight is improved to accelerate the convergence speed, and the retirement update mechanism is introduced to improve the optimization ability of the basic PSO algorithm. To verify the performance of PC-IPSO, we also derive a multivariable improved PSO (M-IPSO) method for comparison. The computational complexity analysis shows that the PC-IPSO algorithm requires less computational resources than the M-IPSO algorithm. Then, the convergence of the improved PSO method is analyzed. The simulation results indicate that the PC-IPSO method has a faster convergence speed and higher identification accuracy than the M-IPSO and several existing state-of-the-art methods for multivariable Wiener system identification.

Identification of Wiener Systems with Recursive Gauss-Seidel Algorithm

The Recursive Gauss-Seidel (RGS) algorithm is presented that is implemented in a one-step Gauss-Seidel iteration for the identification of Wiener output error systems. The RGS algorithm has lower processing intensity than the popular Recursive Least Squares (RLS) algorithm due to its implementation using one-step Gauss-Seidel iteration in a sampling interval. The noise-free output samples in the data vector used for implementation of the RGS algorithm are estimated using an auxiliary model. Also, a stochastic convergence analysis is presented, and it is shown that the presented auxiliary model-based RGS algorithm gives unbiased parameter estimates even if the measurement noise is coloured. Finally, the effectiveness of the RGS algorithm is verified and compared with the equivalent RLS algorithm by computer simulations.

Nonparametric identification of Wiener system with a subclass of wide‐sense cyclostationary excitations

SummaryThe paper identifies a Wiener system, which is excited by a cyclostationary time series. To estimate the first subsystem's linear dynamic impulse response: this proposed algorithm first kernel‐windows the Wiener system's input measurements, then cross‐correlates with the output time series. To identify the second subsystem's static nonlinearity: this proposed algorithm first estimates the unobservable inter‐block internal signal (consistently in the statistical sense), and then kernel‐windows these estimates with the Wiener system output. This estimator provides the unusual capability to identify non‐invertible nonlinearities. This strategy removes any restrictive requirement for a Gaussian random excitation or a sinusoidal deterministic excitation. This paper further proves the estimator's asymptotic consistency and determines the kernel bandwidth for algorithmic convergence. The proposed algorithm's efficacy is verified in the context of two common applications: a servo mechanical system and a telecommunication channel.

Exponential excitations for effective identification of Wiener system

The paper considers the problem of nonparametric estimation of nonlinear characteristic in the FIR Wiener system. Methods proposed so far have suffered from the so-called ‘curse of dimensionality’ and their practical applications have been limited to the very short impulse responses of the linear component. In the proposed approach, the class of (stochastically initialised) repeated exponential input excitations is introduced, and a modified kernel-based estimator is presented. It is shown that the rate of convergence to the genuine system characteristic is significantly improved and does not depend on the length of the impulse response of the linear dynamic block.

Nonlinear Spline Versoria Prioritization Optimization Adaptive Filter for Alpha-Stable Clutter

The increasing demand for a better quality of service in radar and wireless communications has attracted research on interference suppression. Nonlinear filtering methods based on spline architecture have been widely utilized in signal processing due to their effectiveness against alpha-stable interference. However, existing nonlinear spline adaptive filter algorithms suffer from high steady-state misalignment. To achieve lower steady-state misalignment along with having comparable computational complexity, we propose a nonlinear spline Versoria prioritization optimization adaptive filter (SPOAF-MVC) for alpha-stable clutter in this article. Furthermore, we study the bound on learning rate and computational complexity for the proposed algorithm. Numerical simulations confirm the effectiveness and efficiency of the proposed SPOAF-MVC algorithm for alpha-stable clutter under the Wiener system identification.

Identification of Parallel-Cascade Wiener System using Tensor Decomposition of an associated Volterra kernel

In this paper, we propose tensorbased methods for identifying nonlinear Parallel- Cascade Wiener (PCW) systems. Parameters of linear subsystems are first estimated using an approach based on the PARAFAC decomposition of the associated pth-order Volterra kernel. This approach consists in applying the Alternating Least Squares (ALS) algorithm. Then the coefficients of nonlinear subsystems approximated as polynomials are estimated by mean the least square sense from the reconstructed output of the linear subsystems. The proposed parameter estimation method and its performance are illustrated by means of simulation results.

Identification of Wiener systems based on the variable forgetting factor multierror stochastic gradient and the key term separation

SummaryThe identification of Wiener systems is very difficult because of the output nonlinearity and the parameter product term. To identify the Wiener system, a novel stochastic gradient algorithm based on the multierror and the key term separation is proposed. Firstly, the Wiener system is parameterized as a pseudo‐linear model to avoid the products of the parameters. Secondly, a parzen window is used to estimate the probability density function of the error. Thirdly, a stochastic information gradient algorithm with the multierror is adopted to estimate the parameters. The multierror takes the place of the scalar error by the stacked error, which accelerates the algorithm greatly. Fourthly, a variable forgetting factor considering errors is integrated to further speed the algorithm up. Finally, the proposed algorithm is validated by a numerical example and an industrial case. The estimation results indicate that the proposed algorithm can obtain accurate estimates with fast convergence speed.

NONLINEAR SYSTEM IDENTIFICATION OF WPC TERRACE WALL WITH HAMMERSTEIN-WIENER MODEL USING AMBIENT VIBRATION

Today, many advances in engineering field have been and are being made. Especially the predictions of the strengths and behavior of the models designed against external factors are of great importance. Elimination of negative effects and necessary updates on the model or in other words, strengthening works play the biggest role in the design stages. In addition to all these, the dynamically influenced situations of existing structures should be revealed. New methods have been developed for this and similar reasons. System identification is one of these methods. System identification is simply the estimation of the mathematical model of the building from the input and output vibration data obtained through the structures. Thanks to the predicted mathematical model, the reactions of the building to dynamic effects can be predicted. The aim of this study is to reveal the mathematical model of the WPC terrace wall with the nonlinear system identification method. Finally, nonlinear system identification of the WPC terrace wall results demonstrated that fit to estimation data was nearly 100 % and it can be concluded that Hammerstein–Wiener system identification method is efficient and accurate in identifying mathematical model of the WPC terrace wall.

Nonlinear Double-Capacitor Model for Rechargeable Batteries: Modeling, Identification, and Validation

This paper proposes a new equivalent circuit model for rechargeable batteries by modifying a double-capacitor model proposed in [1]. It is known that the original model can address the rate capacity effect and energy recovery effect inherent to batteries better than other models. However, it is a purely linear model and includes no representation of a battery's nonlinear phenomena. Hence, this work transforms the original model by introducing a nonlinear-mapping-based voltage source and a serial RC circuit. The modification is justified by an analogy with the single-particle model. Two parameter estimation approaches, termed 1.0 and 2.0, are designed for the new model to deal with the scenarios of constant-current and variable-current charging/discharging, respectively. In particular, the 2.0 approach proposes the notion of Wiener system identification based on maximum a posteriori estimation, which allows all the parameters to be estimated in one shot while overcoming the nonconvexity or local minima issue to obtain physically reasonable estimates. An extensive experimental evaluation shows that the proposed model offers excellent accuracy and predictive capability. A comparison against the Rint and Thevenin models further points to its superiority. With high fidelity and low mathematical complexity, this model is beneficial for various real-time battery management applications.

Wiener system identification by input injection method

SummaryThe article addresses the problem of nonlinear system identification with particular focusing on Wiener models. The proposed input injection methodology allows for identification of a working system—without stopping its usual operation, production processes, and so on. The only interferences are the slight random injections added to the input signal, which—by assumption—do not disturb the overall system's functionality. Such input injections allow to limit the curse of dimensionality issues, particularly troublesome in many approaches proposed in the literature for the Wiener system identification. Furthermore, all the requirements concerning the applicability of the method are rather mild. In particular, it is assumed that the static nonlinear characteristic is of nonparametric form and the existence of its two derivatives is needed for the consistency of the proposed estimate. The class of admissible output noises is also rather wide and does not exclude processes correlated with inputs signals.

Robust hierarchical identification of Wiener systems in the presence of dynamic disturbances

This paper is concerned with robust identification of Wiener systems in the presence of dynamic disturbances and stochastic noises. Since conventional statistical method cannot eliminate the dynamic disturbance. To solve this problem, the dynamic disturbance signal is modelled as a self-excitation time-varying parameters to be estimated by tracking strategy. Using the multi-innovation and auxiliary model scheme, a hierarchical recursive least squares algorithm with forgetting factors is designed in discrete-time domain. To improve the parameter estimation accuracy and decrease the error variance, the multi-innovation strategy is used to estimate the time-invariant system parameters. The dynamic disturbance still uses the single innovation method for quick tracking. The estimation error upper bound with finite sample data and asymptotic convergence properties are analyzed. Some guidelines are suggested to help the choice of multi-innovation length. The proposed parameterized identification facilitates controller design and system performance analysis. The effectiveness and superiority of the proposed algorithm are confirmed by utilizing theoretical analysis and numerical examples.

Identification of a deterministic Wiener system based on input least squares algorithm and direct residual method

The Wiener system is a type of block-oriented system that consists of a linear model followed in series with a static nonlinear element. In this work, two novel identification methods are proposed to estimate the order and parameters of a class of Wiener systems whose linear part is a finite impulse response function and whose nonlinear inverse function is a polynomial. First, a direct order identification method using the input-output data rather than an unknown intermediate variable is designed to estimate the order of the linear part. The method decreases the computational cost and improves the accuracy of order estimation, because it does not require calculating the intermediate variable. Second, an identification algorithm minimising the input prediction error is developed to obtain parameters of the Wiener system. Third, a numerical simulation and a case study verify the proposed algorithm. The proposed methods, with a little modification, can be applied to identify other block-oriented systems.

Identification of a deterministic Wiener system based on input least squares algorithm and direct residual method

Identification of a deterministic Wiener system based on input least squares algorithm and direct residual method

On the behavior of autonomous Wiener systems

Wiener systems are nonlinear dynamical systems, consisting of a linear dynamical system and a static nonlinear system in a series connection. Existing results for analysis and identification of Wiener systems assume zero initial conditions. In this paper, we consider the response of a Wiener system to initial conditions only, i.e., we consider autonomous Wiener systems. Our main result is a proof that the behavior of an autonomous Wiener system with a polynomial nonlinearity is included in the behavior of a finite-dimensional linear system. The order of the embedding linear system is at most n+dd – the number of combinations with repetitions of d elements out of n elements – where n is the order of the linear subsystem and d is the degree of the nonlinearity. The relation between the eigenvalues of the embedding linear system and the linear subsystem is given by a rank-1 factorization of a symmetric d-way tensor. As an application of the result, we outline a procedure for exact (deterministic) identification of autonomous Wiener systems.

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

Abstract A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.

Identification in the delta domain: a unified approach via GWOCFA

The identification of linear dynamic systems in the delta domain has been proposed in this paper with the help of a hybrid metaheuristic algorithm combining chaotic firefly algorithm (CFA) and grey wolf optimiser (GWO). GWO performs the global search, while CFA fine-tunes the solutions through its local search abilities, thereby balancing exploration and exploitation features. Linear systems with static nonlinearities at the input are termed as the Hammerstein model, whereas linear systems with static nonlinearities at the output are known as the Wiener model. A test case with continuous polynomial nonlinearities has been taken up for Hammerstein and Wiener system identification in the delta domain. Delta operator parameterisation unifies identification of continuous-time systems with the discrete domain at a higher sampling rate. Pseudo-random binary sequence (PRBS), polluted with white Gaussian noise of fixed signal-to-noise ratio (SNR), has been considered as the input signal to estimate the unknown model parameters as well as static nonlinear coefficients. The hybrid algorithm not only supersedes the parent heuristics of which it is constituted but also proves better in comparison with some standard and latest heuristic approaches reported in the literature. Nonparametric statistical tests are performed to validate the results. The plots of fitness function (normalised value) against the number of iterations also support the convergence speed and accuracy of the results.

Bayesian nonparametric identification of Wiener systems

We propose a nonparametric approach for the identification of Wiener systems. We model the impulse response of the linear block and the static nonlinearity using Gaussian processes. The hyperparameters of the Gaussian processes are estimated using an iterative algorithm based on stochastic approximation expectation–maximization. In the iterations, we use elliptical slice sampling to approximate the posterior distribution of the impulse response and update the hyperparameter estimates. The same sampling is finally used to sample the posterior distribution and to compute point estimates. We compare the proposed approach with a parametric approach and a semi-parametric approach. In particular, we show that the proposed method has an advantage when a parametric model for the system is not readily available.

A nonlinear Wiener system identification based on improved adaptive step-size glowworm swarm optimization algorithm for three-dimensional elliptical vibration cutting

Three-dimensional elliptical vibratory cutting (3D EVC) is a precision machining technology that has been extensively used in the aerospace, military, and civil industries. However, if the best processing performance and precise control are required, system identification is the primary prerequisite. Therefore, a 3D EVC nonlinear Wiener model system identification is studied, and an improved adaptive step-size glowworm swarm optimization algorithm (IASGSO) is proposed to identify and optimize the nonlinear Wiener system model parameters. The step-size value of the IASGSO algorithm is adjusted by the distance based on the global best point, which overcomes the shortcomings of the traditional glowworm swarm optimization (GSO) algorithm that is easy to be premature and generate oscillation near the global optimal solution in the later period. The results show that the IASGSO algorithm has the advantage of effectively searching the global optimum value over the traditional GSO algorithm by using two standard test functions to test the performance of both the GSO algorithm and IASGSO algorithm. Based on the system identification experiment, the fitting rate of the proposed method can reach the accuracy of 98.46%, proving the proposed IASGSO algorithm feasibility and accuracy to a large extent. It is expected that both the proposed IASGSO algorithm and the findings in this work will not only solve the local convergence problem of traditional algorithms but also make sense for the precision machining of processing systems.

Fractional Wiener system identification using heuristic optimization technique based on key_term principle

Abstract In this work, identification of fractional Wiener system is considered; this nonlinear class is defined by the separation of the nonlinear static behavior and the linear invariant time behavior into different blocks. For this purpose, the parameters of the linear and the nonlinear part of the Wiener system as well as the fractional order are estimated, using the heuristic particle swarm optimization (PSO). It is combined with the key_term principle to determine the unmeasurable internal variable. In order to confirm the performance of this approach, a simulation example is considered for different signal to noise ratios.

Multi–Level Identification of Hammerstein-Wiener Systems

The paper addresses the problem of Hammerstein–Wiener (N–L–N) system identification. The system is identified in so-called two-experiment approach. In passive experiment the system is excited with random noise, whereas in active experiment binary sequences are used. We present an algorithm with four consecutive stages, in which static nonlinear characteristics are recovered separately from the linear dynamic block. The proposed method uses both parametric and nonparametric identification tools. The estimates are based on kernel preselection of data and application of local least squares. Identification of output nonlinearity is processed under active experiment. We analyze the consistency of the proposed estimates under some a priori restrictions imposed on the excitation signal and system characteristics. Finally, we present a simple simulation example to demonstrate the behaviour of the algorithm.