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

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.

An Adaptive Selection Method for Shape Parameters in MQ-RBF Interpolation for Two-Dimensional Scattered Data and Its Application to Integral Equation Solving

“…These parameters determine the basic shape of the trigonometric curve. As stated by [7], the basic shape of the MQ-RBF is determined by its parameter c. Our numerous experimental results indicate that A, B, and ϕ have negligible influence on the copt, while ω exerts a profound impact on the copt [32]. Consequently, the IRW algorithm is employed to explore the relationship between ω and the c opt .…”

A Joint Optimization Algorithm Based on the Optimal Shape Parameter–Gaussian Radial Basis Function Surrogate Model and Its Application

“…In conclusion, the PSO algorithm outputs the optimal shape parameter c opt of the G-RBF based on the calculated results. Following experimental research by numerous researchers [19][20][21][22][23][24][25][26], it has been confirmed that the method proposed in [27] demonstrates high accuracy in selecting the shape parameters of radial basis function interpolation. Therefore, it has been widely utilized.…”

Research on a Coal Seam Modeling Construction Method Based on Improved Kriging Interpolation

“…Jia et al proposed using hierarchical regional labels such as geological elements as covariates in the machine learning model to predict the spatial distribution of selenium elements, further expanding the service application dimension of geochemical data and making the application of soil geochemical data more accurate and science [21] . Sun et al proposed an MQ-RBF interpolation technology with optimized shape parameters, which significantly improved the estimation accuracy of sine wave parameters and achieved clock delay mismatch calibration for time-interleaved analog-to-digital converter systems [22] . Wu proposed a seismic data interpolation scheme with diversified objectives to provide theoretical foundation and technical support to solve the problem of missing seismic data with non-stationary characteristics [23] .…”