Fast Numerical Algorithms for Wiener Systems Identification

IEEE Transactions on Automatic Control, 2000

We consider the problem of Wiener system identification in this note. A Wiener system consists of a linear time invariant block followed by a memoryless nonlinearity. By modeling the inverse of the memoryless nonlinearity as a linear combination of known nonlinear basis functions, we develop two subspace based approaches, namely an alternating projection algorithm and a minimum norm method, to solve for the Wiener system parameters. Based on computer simulations, the algorithms are shown to be robust in the presence of modeling error and noise.

ISA Transactions, 2017

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used.

Automatica, 2008

In this paper, we investigate what constitutes the least amount of a priori information on the nonlinearity so that the FIR linear part is identifiable in the non-Gaussian input case. Three types of a priori information are considered including quadrant information, point information and locally monotonous information. In all three cases, identifiability has been established and corresponding identification algorithms are developed with their convergence proofs. ᭧

Applied Sciences

Efficiently solving a system identification problem represents an important step in numerous important applications. In this framework, some of the most popular solutions rely on the Wiener filter, which is widely used in practice. Moreover, it also represents a benchmark for other related optimization problems. In this paper, new insights into the regularization of the Wiener filter are provided, which is a must in real-world scenarios. A proper regularization technique is of great importance, especially in challenging conditions, e.g., when operating in noisy environments and/or when only a low quantity of data is available for the estimation of the statistics. Different regularization methods are investigated in this paper, including several new solutions that fit very well for the identification of sparse and low-rank systems. Experimental results support the theoretical developments and indicate the efficiency of the proposed techniques.

International Journal of Adaptive Control and Signal Processing, 2018

In this article, a real-time block-oriented identification method for nonlinear multiple-input-multiple-output systems with input time delay is proposed. The proposed method uses the Wiener structure, which consists of a linear dynamic block (LDB) followed by a nonlinear static block (NSB). The LDB is described by the Laguerre filter lattice, whereas the NSB is characterized using the neural networks. Due to the online adaptation of the parameters, the proposed method can cope with the changes in the system parameters. Moreover, the convergence and bounded modeling error are shown using the Lyapunov direct method. Four practical case studies show the effectiveness of the proposed algorithm in the open-loop and closed-loop identification scenarios. The proposed method is compared with the recently published methods in the literature in terms of the modeling accuracy, parameter initialization, and required information from the system.

Lecture Notes in Control and Information Sciences, 2010

Automatica, 2017

This paper addresses the problem of Wiener-Hammerstein (LNL) system identification. We present two estimates, which recover the static nonlinear characteristic and the linear dynamic blocks separately. Both algorithms are based on kernel preselection of data and application of local least squares and crosscorrelation techniques. Formal proofs of consistency are derived under very mild a priori restrictions imposed on the input excitation and system characteristics. In particular, the input need not be Gausssian, and a wide (nonparametric) class of nonlinear characteristics is admitted. Finally, we propose a universal multi-stage identification strategy which allows to split the resulting linear model into two separate blocks. We also present a simple simulation example to illustrate the behavior of the method in practice.

In this work, a non-iterative identification approach is presented for estimating a Single Input Single Output (SISO) Wiener model, comprising an Infinite Impulse Response (IIR) discrete transfer function followed by static non-linearity. Global Orthogonal Basis Functions and orthogonal Hermite polynomials are used as expansion bases for the linear subsystem and the non-linearity, respectively. A multi-index based method is used to transform the non-convex optimization over the parameter values into an over-parametrized linear regression. A Singular Value Decomposition based method is then used to project the result of the over-parametrized linear regression onto the class of Linear Non-linear (LN) models. The advantages obtained by using orthogonal polynomials are illustrated using a series of simulation examples.

Control Engineering Practice, 2012

This paper considers the identification of Wiener-Hammerstein systems using Least-Squares Support Vector Machines based models. The power of fully black box NARX-type models is evaluated and compared with models including information about the structure of the systems. For the NARX models it is shown how to extend the kernel based estimator to large data sets. For the structured model the emphasis is on preserving the convexity of the estimation problem through a suitable relaxation of the original problem. To develop an empirical understanding of the implications of the different model design choices, all considered models are compared on an artificial system under a number of different experimental conditions. The obtained results are then validated on the Wiener-Hammerstein benchmark data set and the final models are presented. It is illustrated that black box models are a suitable technique for the identification of Wiener-Hammerstein systems. The incorporation of structural information as well as using large data sets give rise to significant improvements in modeling performance.

2001

In this paper, non iterative algorithms for the identification of (multivariable) nonlinear systems consisting of the interconnection of LTI systems and static nonlinearities are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and singular value decomposition. Three different block-oriented nonlinear models are considered in this paper, viz., the Hammerstein model, the Wiener model, and the Feedback Block-Oriented model. For the Hammerstein model, the algorithm provides consistent estimates even in the presence of coloured output noise, under weak assumptions on the persistency of excitation of the inputs. For the Wiener model and the Feedback Block-Oriented model, consistency of the estimates can only be guaranteed in the noise free case. Key in the derivation of the results is the use of rational orthonormal bases for the representation of the linear part of the systems. An additional advantage of this is the possibility of incorporating prior information about the system in a typically black-box identification scheme.