Subspace-based identification algorithms for hammerstein and wiener models. Discussion (original) (raw)
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Subspace-based Identification Algorithms for Hammerstein and Wiener Models
European Journal of Control, 2005
Subspace-based algorithms for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein and Wiener models are presented in this paper. The proposed algorithms consist basically of two steps. The first one is a standard subspace-based identification algorithm applied to an auxiliary multivariable linear system whose inputs (respectively outputs) are filtered versions of the original inputs (respectively outputs). The filters are the nonlinear functions describing the static nonlinearities for the Hammerstein case and its inverses for the Wiener case. The second step consists of a 2-norm minimization problem which is solved via Singular Value Decomposition. Consistency of the estimates can be guaranteed under weak assumptions. The performance of the proposed identification algorithms is illustrated through simulation examples.
Subspace identification of multivariable Hammerstein and Wiener models
Proceedings of the 15th IFAC World Congress, 2002, 2002
In this paper, subspace-based algorithms for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein and Wiener models are presented. The proposed algorithms consist basically of two steps. The first one is a standard (linear) subspace algorithm applied to an equivalent linear system whose inputs (respectively outputs) are filtered (by the nonlinear functions describing the static nonlinearities) versions of the original inputs (respectively outputs). The second step consists of a 2-norm minimization problem which is solved via Singular Value Decomposition. Under weak assumptions, consistency of the estimates can be guaranteed. The performance of the proposed identification algorithms is illustrated through simulation examples.
Identification of a Benchmark Wiener–Hammerstein: A bilinear and Hammerstein–Bilinear model approach
Control Engineering Practice, 2012
In this paper the Wiener-Hammerstein system proposed as a benchmark for the SYSID 2009 benchmark session is identified as a bilinear discrete system. The bilinear approximation relies on both facts that the Wiener-Hammerstein system can be described by a Volterra series which can be approximated by bilinear systems. The identification is performed with an iterative bilinear subspace identification algorithm previously proposed by the authors. In order to increase accuracy, polynomial static nonlinearities are added to the bilinear model input. These Hammerstein type bilinear models are then identified using the same iterative subspace identification algorithm.
International Journal of Modelling, Identification and Control, 2019
This paper proposes two iterative procedures based on over-parameterisation and optimisation approaches for the identification of nonlinear systems which can be described by Hammerstein-Wiener stochastic models. In this case, the dynamic linear part of the considered system is described by ARMAX mathematical model. The static nonlinear block is approximated by polynomial functions. The first procedure is based on a combination of the prediction error method by using the recursive approximated maximum likelihood estimator (RAML), the singular value decomposition (SVD) approach and the fuzzy techniques in order to estimate the parameters of the considered process. As for the second procedure, it includes an appropriate representation named as generalised orthonormal basis filters (GOBF) in order to reduce the complexity of the considered system. The parametric estimation problem is formulated using the recursive extended least squares (RELS) algorithm incorporated with the singular value decomposition (SVD) and fuzzy techniques in order to segregate the coupled parameters and improve the estimation quality. The validity of the developed approaches is proved by considering a nonlinear hydraulic process simulation.
Kernel-based identification of Wiener–Hammerstein system
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.
Identification of MIMO Hammerstein models using Singular Value Decomposition approach
International Journal of Computer Applications, 2012
In this paper, we present a new approach to identify multivariable Hammerstein systems based on the Singular Value Decomposition (SVD) method. The technique allows for the determination of the memoryless static nonlinearity as well as the estimation of the model parameters of the dynamic Auto-Regressive model with eXogenous input (ARX) part. First of all, an iteration procedure is proposed to identify the parameters of Multi-Input Multi-Output (MIMO) Hammerstein models by using the Recursive Least Squares (RLS) algorithm. Secondly, the obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. So, to separate these parameters of the original parameters from the product terms, the singular value decomposition method is discussed. Finally, a simulation study is performed to demonstrate the effectiveness of the proposed method compared with the existing approaches.
Subspace based approaches for Wiener system 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.
A Refined Instrumental Variable Method for Hammerstein-Wiener Continuous-Time Model Identification
IFAC Proceedings Volumes, 2012
This study presents the first attempt of direct continuous-time model identification using instrumental variable method for Hammerstein-Wiener systems from sampled data. Under the assumption of monotonic function for the Wiener part, the whole non-linear model is first estimated as an augmented multiple-input single-output linear model, from which the model parameters are then extracted by singular value decomposition. A refined instrumental variable method is proposed to consistently identify this non-linear system acting in a coloured noisy environment. Monte Carlo simulation analysis is presented to illustrate the effectiveness of the proposed method.
Refined instrumental variable method for Hammerstein–Wiener continuous‐time model identification
IET Control Theory & Applications, 2013
This study presents the first attempt of direct continuous-time model identification using instrumental variable method for Hammerstein-Wiener systems from sampled data. Under the assumption of monotonic function for the Wiener part, the whole non-linear model is first estimated as an augmented multiple-input single-output linear model, from which the model parameters are then extracted by singular value decomposition. A refined instrumental variable method is proposed to consistently identify this non-linear system acting in a coloured noisy environment. Monte Carlo simulation analysis is presented to illustrate the effectiveness of the proposed method.
Subspace identification of Hammerstein systems using least squares support vector machines
IEEE Transactions on Automatic Control, 2000
In this paper, a method for the identification of multi-input/multi-output Hammerstein systems is presented. The method extends the N4SID linear subspace identification algorithm, mainly by rewriting the oblique projection in the N4SID algorithm as a set of componentwise LS-SVM regression problems. The linear model and static nonlinearities are obtained from a rank 1 approximation of a matrix produced by this regression problem.