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Model for Choosing the Shape Parameter in the Multiquadratic Radial Basis Function Interpolation of an Arbitrary Sine Wave and Its Application

Author

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  • Jian Sun

    (College of Science, North China University of Science and Technology, Tangshan 063210, China)

  • Ling Wang

    (College of Science, North China University of Science and Technology, Tangshan 063210, China)

  • Dianxuan Gong

    (College of Science, North China University of Science and Technology, Tangshan 063210, China)

Abstract

In multiquadratic radial basis function (MQ-RBF) interpolation, shape parameters have a direct effect on the interpolation accuracy. The paper presents an MQ-RBF interpolation technique with optimized shape parameters for estimating the parameters of sine wave signals. At first, we assessed the impact of basic sinusoidal parameters on the MQ-RBF interpolation outcomes through numerical experiments. The results indicated that the angular frequency of a sine wave is a crucial determinant of the corresponding MQ-RBF interpolation shape parameters. A linear regression method was then used to establish the optimal parameter selection formula for a single-frequency sine wave, based on a large volume of experimental data. For multi-frequency sinusoidal signals, appropriate interpolation shape parameters were selected using the random walk algorithm to create datasets. These datasets were subsequently used to train several regression models, which were then evaluated and compared. Based on its operational cost and prediction accuracy, the random forest algorithm was chosen to establish the shape parameter selection model for multi-frequency sinusoidal signals. The inclusion of the Bayesian optimizer resulted in a highly accurate model. The establishment of this model enabled the adaptive selection of the corresponding shape parameters for any sine wave signal, providing a convenient means of selecting MQ-RBF interpolation shape parameters. Furthermore, the paper proposes an MQ-RBF interpolation subdivision least squares method that significantly improves the estimation accuracy of sine wave parameters. The practicality of the method was validated by successfully applying it in the calibration of the clock delay mismatch of a time-interleaved analog-to-digital converter system.

Suggested Citation

  • Jian Sun & Ling Wang & Dianxuan Gong, 2023. "Model for Choosing the Shape Parameter in the Multiquadratic Radial Basis Function Interpolation of an Arbitrary Sine Wave and Its Application," Mathematics, MDPI, vol. 11(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1856-:d:1123097
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    References listed on IDEAS

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    1. Yusen Wang & Wenlong Liao & Yuqing Chang, 2018. "Gated Recurrent Unit Network-Based Short-Term Photovoltaic Forecasting," Energies, MDPI, vol. 11(8), pages 1-14, August.
    2. Lin-Tian Luh, 2022. "A Direct Prediction of the Shape Parameter in the Collocation Method of Solving Poisson Equation," Mathematics, MDPI, vol. 10(19), pages 1-18, October.
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    1. Jian Sun & Ling Wang & Dianxuan Gong, 2023. "A Joint Optimization Algorithm Based on the Optimal Shape Parameter–Gaussian Radial Basis Function Surrogate Model and Its Application," Mathematics, MDPI, vol. 11(14), pages 1-20, July.

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