IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i8p1856-d1123097.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/8/1856/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/8/1856/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jessica Wojtkiewicz & Matin Hosseini & Raju Gottumukkala & Terrence Lynn Chambers, 2019. "Hour-Ahead Solar Irradiance Forecasting Using Multivariate Gated Recurrent Units," Energies, MDPI, vol. 12(21), pages 1-13, October.
    2. Ruijin Zhu & Xuejiao Gong & Shifeng Hu & Yusen Wang, 2019. "Power Quality Disturbances Classification via Fully-Convolutional Siamese Network and k-Nearest Neighbor," Energies, MDPI, vol. 12(24), pages 1-12, December.
    3. Khan, Zulfiqar Ahmad & Khan, Shabbir Ahmad & Hussain, Tanveer & Baik, Sung Wook, 2024. "DSPM: Dual sequence prediction model for efficient energy management in micro-grid," Applied Energy, Elsevier, vol. 356(C).
    4. Leijiao Ge & Tianshuo Du & Changlu Li & Yuanliang Li & Jun Yan & Muhammad Umer Rafiq, 2022. "Virtual Collection for Distributed Photovoltaic Data: Challenges, Methodologies, and Applications," Energies, MDPI, vol. 15(23), pages 1-24, November.
    5. Andi A. H. Lateko & Hong-Tzer Yang & Chao-Ming Huang, 2022. "Short-Term PV Power Forecasting Using a Regression-Based Ensemble Method," Energies, MDPI, vol. 15(11), pages 1-21, June.
    6. Ying Cao & Xi Wang & Li Zhu & Hongwei Wang & Xiaoning Wang, 2023. "A Meta-Learning-Based Train Dynamic Modeling Method for Accurately Predicting Speed and Position," Sustainability, MDPI, vol. 15(11), pages 1-20, May.
    7. Yuan-Kang Wu & Cheng-Liang Huang & Quoc-Thang Phan & Yuan-Yao Li, 2022. "Completed Review of Various Solar Power Forecasting Techniques Considering Different Viewpoints," Energies, MDPI, vol. 15(9), pages 1-22, May.
    8. Seung Chan Jo & Young Gyu Jin & Yong Tae Yoon & Ho Chan Kim, 2021. "Methods for Integrating Extraterrestrial Radiation into Neural Network Models for Day-Ahead PV Generation Forecasting," Energies, MDPI, vol. 14(9), pages 1-18, May.
    9. Mohammad Taghi Sattari & Halit Apaydin & Shahaboddin Shamshirband, 2020. "Performance Evaluation of Deep Learning-Based Gated Recurrent Units (GRUs) and Tree-Based Models for Estimating ETo by Using Limited Meteorological Variables," Mathematics, MDPI, vol. 8(6), pages 1-18, June.
    10. Ruijin Zhu & Weilin Guo & Xuejiao Gong, 2019. "Short-Term Photovoltaic Power Output Prediction Based on k -Fold Cross-Validation and an Ensemble Model," Energies, MDPI, vol. 12(7), pages 1-15, March.
    11. Huu Khoa Minh Nguyen & Quoc-Dung Phan & Yuan-Kang Wu & Quoc-Thang Phan, 2023. "Multi-Step Wind Power Forecasting with Stacked Temporal Convolutional Network (S-TCN)," Energies, MDPI, vol. 16(9), pages 1-20, April.
    12. Ze Wu & Feifan Pan & Dandan Li & Hao He & Tiancheng Zhang & Shuyun Yang, 2022. "Prediction of Photovoltaic Power by the Informer Model Based on Convolutional Neural Network," Sustainability, MDPI, vol. 14(20), pages 1-16, October.
    13. Alabi, Tobi Michael & Lu, Lin & Yang, Zaiyue, 2022. "Data-driven optimal scheduling of multi-energy system virtual power plant (MEVPP) incorporating carbon capture system (CCS), electric vehicle flexibility, and clean energy marketer (CEM) strategy," Applied Energy, Elsevier, vol. 314(C).
    14. Ramadhan, Raden A.A. & Heatubun, Yosca R.J. & Tan, Sek F. & Lee, Hyun-Jin, 2021. "Comparison of physical and machine learning models for estimating solar irradiance and photovoltaic power," Renewable Energy, Elsevier, vol. 178(C), pages 1006-1019.
    15. Shangfu Wei & Xiaoqing Bai, 2022. "Multi-Step Short-Term Building Energy Consumption Forecasting Based on Singular Spectrum Analysis and Hybrid Neural Network," Energies, MDPI, vol. 15(5), pages 1-21, February.
    16. Sarmas, Elissaios & Spiliotis, Evangelos & Stamatopoulos, Efstathios & Marinakis, Vangelis & Doukas, Haris, 2023. "Short-term photovoltaic power forecasting using meta-learning and numerical weather prediction independent Long Short-Term Memory models," Renewable Energy, Elsevier, vol. 216(C).
    17. Hu, Zehuan & Gao, Yuan & Ji, Siyu & Mae, Masayuki & Imaizumi, Taiji, 2024. "Improved multistep ahead photovoltaic power prediction model based on LSTM and self-attention with weather forecast data," Applied Energy, Elsevier, vol. 359(C).
    18. Xue-Bo Jin & Wei-Zhen Zheng & Jian-Lei Kong & Xiao-Yi Wang & Yu-Ting Bai & Ting-Li Su & Seng Lin, 2021. "Deep-Learning Forecasting Method for Electric Power Load via Attention-Based Encoder-Decoder with Bayesian Optimization," Energies, MDPI, vol. 14(6), pages 1-18, March.
    19. Rongsheng Liu & Minfang Peng & Xianghui Xiao, 2018. "Ultra-Short-Term Wind Power Prediction Based on Multivariate Phase Space Reconstruction and Multivariate Linear Regression," Energies, MDPI, vol. 11(10), pages 1-17, October.
    20. Stefano Massucco & Gabriele Mosaico & Matteo Saviozzi & Federico Silvestro, 2019. "A Hybrid Technique for Day-Ahead PV Generation Forecasting Using Clear-Sky Models or Ensemble of Artificial Neural Networks According to a Decision Tree Approach," Energies, MDPI, vol. 12(7), pages 1-21, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1856-:d:1123097. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.