Linear-wavelet networks

Roberto Galvão; Victor Becerra; João Calado; Pedro Silva

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 2, page 221-232
  • ISSN: 1641-876X

Abstract

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This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated fermentation process, it is shown that a linear-wavelet network yields a smaller approximation error when compared with a wavelet network with the same number of regressors. The proposed technique is also applied to the identification of a pressure plant from experimental data. In this case, the results show that the introduction of wavelets considerably improves the prediction ability of a linear model. Standard errors on the estimated model coefficients are also calculated to assess the numerical conditioning of the identification process.

How to cite

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Galvão, Roberto, et al. "Linear-wavelet networks." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 221-232. <http://eudml.org/doc/207693>.

@article{Galvão2004,
abstract = {This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated fermentation process, it is shown that a linear-wavelet network yields a smaller approximation error when compared with a wavelet network with the same number of regressors. The proposed technique is also applied to the identification of a pressure plant from experimental data. In this case, the results show that the introduction of wavelets considerably improves the prediction ability of a linear model. Standard errors on the estimated model coefficients are also calculated to assess the numerical conditioning of the identification process.},
author = {Galvão, Roberto, Becerra, Victor, Calado, João, Silva, Pedro},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {regression analysis; wavelet networks; nonlinear models; system identification},
language = {eng},
number = {2},
pages = {221-232},
title = {Linear-wavelet networks},
url = {http://eudml.org/doc/207693},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Galvão, Roberto
AU - Becerra, Victor
AU - Calado, João
AU - Silva, Pedro
TI - Linear-wavelet networks
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 2
SP - 221
EP - 232
AB - This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated fermentation process, it is shown that a linear-wavelet network yields a smaller approximation error when compared with a wavelet network with the same number of regressors. The proposed technique is also applied to the identification of a pressure plant from experimental data. In this case, the results show that the introduction of wavelets considerably improves the prediction ability of a linear model. Standard errors on the estimated model coefficients are also calculated to assess the numerical conditioning of the identification process.
LA - eng
KW - regression analysis; wavelet networks; nonlinear models; system identification
UR - http://eudml.org/doc/207693
ER -

References

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