An iterative method for the identification of nonlinear systems using a Hammerstein model
TL;DR: In this article, an iterative method is proposed for the identification of nonlinear systems from samples of inputs and outputs in the presence of noise, which consists of a no-memory gain (of an assumed polynomial form) followed by a linear discrete system.
Abstract: An iterative method is proposed for the identification of nonlinear systems from samples of inputs and outputs in the presence of noise. The model used for the identification consists of a no-memory gain (of an assumed polynomial form) followed by a linear discrete system. The parameters of the pulse transfer function of the linear system and the coefficients of the polynomial non-linearity are alternately adjusted to minimize a mean square error criterion. Digital computer simulations are included to demonstrate the feasibility of the technique.
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TL;DR: The survey explains the least squares method and several of its variants which may solve the problem of correlated residuals, viz. repeated and generalized least squares, maximum likelihood method, instrumental variable method, tally principle.
1,479 citations
TL;DR: In this article, an optimal two-stage identification algorithm is presented for Hammerstein-Wiener systems, where two static nonlinear elements surround a linear block, and the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise.
519 citations
DOI•
01 Nov 1980TL;DR: A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way as discussed by the authors, where the limitations, relationships and applicability of the methods are discussed throughout.
Abstract: A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way. Algorithms based on the functional expansions of Wiener and Volterra, the identification of block-oriented and bilinear systems, the selection of input signals, structure detection, parameter estimation and recent results from catastrophe theory and included. The limitations, relationships and applicability of the methods are discussed throughout.
491 citations
TL;DR: It is shown that systems composed of cascade, feedforward, feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only.
446 citations
Journal Article•
TL;DR: An optimal two-stage identification algorithm is presented for Hammerstein–Wiener systems where two static nonlinear elements surround a linear block and is shown to be convergent in the absence of noise and convergence with probability one in the presence of white noise.
Abstract: An optimal two-stage identification algorithm is presented for Hammerstein–Wiener systems where two static nonlinear elements surround a linear block. The proposed algorithm consists of two steps: The first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases. Moreover, the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise.
398 citations
References
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TL;DR: In this paper, an iterative technique is proposed to identify a linear system from samples of its input and output in the presence of noise by minimizing the mean-square error between system and model outputs.
Abstract: An iterative technique is proposed to identify a linear system from samples of its input and output in the presence of noise by minimizing the mean-square error between system and model outputs. The model chosen has a transfer function which is a ratio of polynomials in z-1. Although the regression equations for the optimal set of coefficients are highly nonlinear and intractable, it is shown that the problem can be reduced to the repeated solution of a related linear problem. Computer simulation of a number of typical discrete systems is used to demonstrate the considerable improvement over the Kalman estimate which can be obtained in a few iterations. The procedure is found to be effective at signal-to-noise ratios less than unity, and with as few as 200 samples of the input and output records.
660 citations
TL;DR: In this paper, the identification of zero-memory multipoles and two-poles of class n_1 was studied, where the test signals are sine waves of different amplitudes and frequencies, and the measured quanity is the describing function of the device.
Abstract: The identification problem involves the determination of the identity of a black box from the observation of its responses to a set of input signals. In this paper attention is focused on the identification of zero-memory multipoles and two-poles of class n_1 . The test signals are sine waves of different amplitudes and frequencies, and the measured quanity is the describing function of the device. In the case of two-poles of class n_1 , it is found that the describing function is related to the characteristic function by an integral equation of second order which can be solved explicitly by the use of the Fourier-Hankel transformation.
107 citations