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Article

Wavelet Multiresolution Analysis-Based Takagi–Sugeno–Kang Model, with a Projection Step and Surrogate Feature Selection for Spectral Wave Height Prediction

by
Panagiotis Korkidis
* and
Anastasios Dounis
Department of Biomedical Engineering, University of West Attica, 12243 Athens, Greece
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(15), 2517; https://doi.org/10.3390/math13152517
Submission received: 6 July 2025 / Revised: 31 July 2025 / Accepted: 3 August 2025 / Published: 5 August 2025
(This article belongs to the Special Issue Applications of Mathematics in Neural Networks and Machine Learning)

Abstract

The accurate prediction of significant wave height presents a complex yet vital challenge in the fields of ocean engineering. This capability is essential for disaster prevention, fostering sustainable development and deepening our understanding of various scientific phenomena. We explore the development of a comprehensive predictive methodology for wave height prediction by integrating novel Takagi–Sugeno–Kang fuzzy models within a multiresolution analysis framework. The multiresolution analysis emerges via wavelets, since they are prominent models characterised by their inherent multiresolution nature. The maximal overlap discrete wavelet transform is utilised to generate the detail and resolution components of the time series, resulting from this multiresolution analysis. The novelty of the proposed model lies on its hybrid training approach, which combines least squares with AdaBound, a gradient-based algorithm derived from the deep learning literature. Significant wave height prediction is studied as a time series problem, hence, the appropriate inputs to the model are selected by developing a surrogate-based wrapped algorithm. The developed wrapper-based algorithm, employs Bayesian optimisation to deliver a fast and accurate method for feature selection. In addition, we introduce a projection step, to further refine the approximation capabilities of the resulting predictive system. The proposed methodology is applied to a real-world time series pertaining to spectral wave height and obtained from the Poseidon operational oceanography system at the Institute of Oceanography, part of the Hellenic Center for Marine Research. Numerical studies showcase a high degree of approximation performance. The predictive scheme with the projection step yields a coefficient of determination of 0.9991, indicating a high level of accuracy. Furthermore, it outperforms the second-best comparative model by approximately 49% in terms of root mean squared error. Comparative evaluations against powerful artificial intelligence models, using regression metrics and hypothesis test, underscore the effectiveness of the proposed methodology.
Keywords: wave height prediction; Takagi–Sugeno–Kang model; wavelets multiresolution analysis; Bayesian optimisation; feature selection wave height prediction; Takagi–Sugeno–Kang model; wavelets multiresolution analysis; Bayesian optimisation; feature selection

Share and Cite

MDPI and ACS Style

Korkidis, P.; Dounis, A. Wavelet Multiresolution Analysis-Based Takagi–Sugeno–Kang Model, with a Projection Step and Surrogate Feature Selection for Spectral Wave Height Prediction. Mathematics 2025, 13, 2517. https://doi.org/10.3390/math13152517

AMA Style

Korkidis P, Dounis A. Wavelet Multiresolution Analysis-Based Takagi–Sugeno–Kang Model, with a Projection Step and Surrogate Feature Selection for Spectral Wave Height Prediction. Mathematics. 2025; 13(15):2517. https://doi.org/10.3390/math13152517

Chicago/Turabian Style

Korkidis, Panagiotis, and Anastasios Dounis. 2025. "Wavelet Multiresolution Analysis-Based Takagi–Sugeno–Kang Model, with a Projection Step and Surrogate Feature Selection for Spectral Wave Height Prediction" Mathematics 13, no. 15: 2517. https://doi.org/10.3390/math13152517

APA Style

Korkidis, P., & Dounis, A. (2025). Wavelet Multiresolution Analysis-Based Takagi–Sugeno–Kang Model, with a Projection Step and Surrogate Feature Selection for Spectral Wave Height Prediction. Mathematics, 13(15), 2517. https://doi.org/10.3390/math13152517

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