System identification: theory for the user
System identification: theory for the user
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
An introduction to wavelets
Neurofuzzy adaptive modelling and control
Neurofuzzy adaptive modelling and control
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Using wavelet network in nonparametric estimation
IEEE Transactions on Neural Networks
Nonlinear model structure detection using optimum experimental design and orthogonal least squares
IEEE Transactions on Neural Networks
Model selection approaches for non-linear system identification: a review
International Journal of Systems Science
A new RBF neural network with boundary value constraints
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on human computing
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
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A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory and have been extensively used in linear and non-linear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilize the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least-squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model.