Orthogonal least squares methods and their application to non-linear system identification
TLDR
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram- Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed.Abstract:
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram-Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed. The classical Gram-Schmidt, modified Gram-Schmidt, and Householder transformation algorithms are then extended to combine structure determination, or which terms to include in the model, and parameter estimation in a very simple and efficient manner for a class of multivariate discrete-time non-linear stochastic systems which are linear in the parameters.read more
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References
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Journal ArticleDOI
The Practical Identification of Systems with Nonlinearities
Stephen A. Billings,M.B. Fadzil +1 more
TL;DR: In this article, the NARMAX model is used to identify nonlinear heat exchanger models and the application of model validity tests to detect the existence of unmodelled linear or nonlinear terms in the residuals is discussed.
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Experiments on error growth associated with some linear least-squares procedures.
TL;DR: In this article, the authors compared the performance of the first three procedures and a procedure based on Gaussian elimination for solving an n X n system of equations and concluded that the modified Gram-Schmidt procedure is best for the linear least-squares problem.
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On determining the structure of a non-linear system
Alan A. Desrochers,S. Mohseni +1 more
TL;DR: The essential feature of the technique is that it generates a sequence of projection matrices such that the original vector-valued functions become conjugate directions and allows the structure for the optimal n-term model to be assembled in n selections from the library.
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Identification of a non-linear difference equation model of an industrial diesel generator
TL;DR: In this article, the authors presented methods of analysing data from nonlinear systems and estimating non-linear models from noisy input-output measurements using a NARMAX model relating rack position to engine torque.
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Prediction-error estimation algorithm for non-linear output-affine systems
Sheng Chen,Stephen A. Billings +1 more
TL;DR: A prediction-error estimation algorithm is developed for non-linear discrete-time systems which can be represented by the output-affine difference equation model and a comparison with the NARMAX (nonlinear ARMAX) model is given.