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    A new regularized method stabilizes parameter estimation for Radial Basis Function-Artificial Intelligence (RBF-AR(X)) models, improving nonlinear system modeling and forecasting accuracy.

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    Area of Science:

    • Engineering
    • Computer Science
    • Mathematics

    Background:

    • Radial Basis Function (RBF) network-style coefficients AutoRegressive (with exogenous inputs) [RBF-AR(X)] models are effective for nonlinear system modeling.
    • The Structured Nonlinear Parameter Optimization Method (SNPOM) is commonly used for RBF-AR(X) model identification.
    • A key challenge with SNPOM is potential parameter divergence during optimization.

    Purpose of the Study:

    • To present a regularized SNPOM to address parameter divergence in RBF-AR(X) model estimation.
    • To introduce a regularization parameter detection technique for improved parameter estimation.
    • To enhance the stability and accuracy of nonlinear system modeling using RBF-AR(X) models.

    Main Methods:

    • Separation of RBF-AR(X) model parameters into linear and nonlinear sets.
    • Application of a gradient-based nonlinear optimization algorithm for nonlinear parameters.
    • Utilizing the regularized least squares method for linear parameters estimation.
    • Integration of a regularization parameter detection technique.

    Main Results:

    • The proposed regularized SNPOM effectively handles parameter instability in the optimization process.
    • The method demonstrates comparable or superior multistep forecasting accuracy compared to previous approaches.
    • Improved robustness in parameter estimation and forecasting is observed.

    Conclusions:

    • The regularized SNPOM offers a stable and effective solution for RBF-AR(X) model parameter estimation.
    • This approach mitigates the issue of parameter divergence, a common problem in nonlinear system modeling.
    • The technique enhances the reliability and performance of RBF-AR(X) models for forecasting applications.