{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T19:54:53Z","timestamp":1769284493502,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T00:00:00Z","timestamp":1769040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JSAN"],"abstract":"<jats:p>Accurate global irradiance (GI) forecasting is essential for improving photovoltaic (PV) energy management, stabilizing renewable power systems, and enabling intelligent control in solar-powered applications, including electric vehicles and smart grids. The highly stochastic and non-stationary nature of solar radiation, influenced by rapid atmospheric fluctuations and seasonal variability, makes short-term GI prediction a challenging task. To overcome these limitations, this work introduces a new hybrid forecasting architecture referred to as WTX\u2013CBO, which integrates a Wavelet Transform (WT)-based decomposition module, an encoder\u2013decoder Transformer model, and an XGBoost regressor, optimized using the Chaotic Billiards Optimizer (CBO) combined with the Adam optimization algorithm. In the proposed architecture, WT decomposes solar irradiance data into multi-scale components, capturing both high-frequency transients and long-term seasonal patterns. The Transformer module effectively models complex temporal and spatio-temporal dependencies, while XGBoost enhances nonlinear learning capability and mitigates overfitting. The CBO ensures efficient hyperparameter tuning and accelerated convergence, outperforming traditional meta-heuristics such as Particle Swarm Optimization (PSO) and Genetic Algorithms (GA). Comprehensive experiments conducted on real-world GI datasets from diverse climatic conditions demonstrate the outperformance of the proposed model. The WTX\u2013CBO ensemble consistently outperformed benchmark models, including LSTM, SVR, standalone Transformer, and XGBoost, achieving improved accuracy, stability, and generalization capability. The proposed WTX\u2013CBO framework is designed as a high-accuracy decision-support forecasting tool that provides short-term global irradiance predictions to enable intelligent energy management, predictive charging, and adaptive control strategies in solar-powered applications, including solar electric vehicles (SEVs), rather than performing end-to-end vehicle or photovoltaic power simulations. Overall, the proposed hybrid framework provides a robust and scalable solution for short-term global irradiance forecasting, supporting reliable PV integration, smart charging control, and sustainable energy management in next-generation solar systems.<\/jats:p>","DOI":"10.3390\/jsan15010012","type":"journal-article","created":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T09:16:59Z","timestamp":1769159819000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid Wavelet\u2013Transformer\u2013XGBoost Model Optimized by Chaotic Billiards for Global Irradiance Forecasting"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-9759-7814","authenticated-orcid":false,"given":"Walid","family":"Mchara","sequence":"first","affiliation":[{"name":"Laboratory of Robotics, Informatics and Complex Systems (RISC), National Engineering School of Tunis (ENIT), University of Tunis El Manar (UTM), BP N\u00b0 37, Le Belvedere, Tunis 1002, Tunisia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1498-2215","authenticated-orcid":false,"given":"Giovanni","family":"Cicceri","sequence":"additional","affiliation":[{"name":"Department of Biomedicine, Neuroscience, and Advanced Diagnostics (BiND), University of Palermo, 90127 Palermo, Italy"},{"name":"Department of Engineering, University of Messina, 98166 Messina, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3942-720X","authenticated-orcid":false,"given":"Lazhar","family":"Manai","sequence":"additional","affiliation":[{"name":"Laboratory of Robotics, Informatics and Complex Systems (RISC), National Engineering School of Tunis (ENIT), University of Tunis El Manar (UTM), BP N\u00b0 37, Le Belvedere, Tunis 1002, Tunisia"},{"name":"Higher Institute of Informations and Communication Technology (ISTIC), University of Carthage, BP N\u00b0 123, Hammam Chatt 1164, Tunisia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8289-2449","authenticated-orcid":false,"given":"Monia","family":"Raissi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Shaqra University, Dawadmi 11911, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4404-9204","authenticated-orcid":false,"given":"Hezam","family":"Albaqami","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Artificial Intelligence, College of Computer Science and Engineering, University of Jeddah, Jeddah 21493, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Oluwalana, O.J., and Grzesik, K. 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