A new class of wavelet networks for nonlinear system identification

Area of Science:

• Signal Processing
• Machine Learning
• System Identification

Background:

• Nonlinear system identification in high dimensions presents significant challenges.
• Traditional neural networks struggle with the complexity of multivariate functions.
• Wavelet decompositions offer multiscale analysis capabilities beneficial for complex systems.

Purpose of the Study:

• To propose a new class of wavelet networks (WNs) for effective nonlinear system identification.
• To convert high-dimensional nonlinear models into linear-in-the-parameter regressions.
• To leverage the strengths of wavelet analysis and neural networks for complex systems.

Main Methods:

• Utilizing a superimposition of functions with fewer variables for model structure.
• Employing truncated wavelet decompositions to expand individual functions.
• Applying forward orthogonal least squares (OLS) algorithm with error reduction ratio (ERR) for model term selection.

Main Results:

• The proposed WNs successfully handle nonlinear identification problems in high dimensions.
• Multivariate nonlinear networks are effectively converted into linear regressions.
• The method efficiently identifies relevant model terms using OLS and ERR.

Conclusions:

• The new wavelet networks offer a powerful tool for high-dimensional nonlinear system identification.
• This approach combines the benefits of multiscale wavelet analysis and neural network capabilities.
• The integration of analysis of variance (ANOVA) expansion enables handling of complex nonlinearities.