Probabilistic machine learning-based forecasting of wind speed uncertainty using adaptive kernel density estimation

Rami Al-Hajj; Rami Al-Hajj

doi:10.3934/mbe.2025083

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 9: 2269-2299. doi: 10.3934/mbe.2025083

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Research article

Probabilistic machine learning-based forecasting of wind speed uncertainty using adaptive kernel density estimation

Rami Al-Hajj ^,

College of Engineering and Technology, American University of the Middle East, Kuwait

Received: 28 May 2025 Revised: 02 July 2025 Accepted: 09 July 2025 Published: 16 July 2025

Short-term wind speed forecasting is essential for enhancing the efficiency and dependability of wind renewable energy installations. Although often used, conventional point predictions generated by machine learning techniques frequently fail to accurately capture the natural uncertainty associated with wind speed variation. Modeling this type of uncertainty is crucial for providing credible information as the level of uncertainty increases. Prediction intervals (PIs) offer a probabilistic framework for quantifying forecast uncertainty. This paper presents a hybrid forecasting methodology that combines support vector regression (SVR) with adaptive kernel density estimation (AKDE) to estimate wind speed prediction intervals over various short-term horizons (10, 30, 60, and 120 minutes). In contrast to standard kernel density estimation (KDE), which employs a uniform bandwidth and may overlook local data attributes, the adaptive KDE approach adjusts the bandwidth in accordance with the local distribution of forecast errors, thereby facilitating more precise and locally tuned uncertainty quantification. The efficacy of the proposed SVR-AKDE model is evaluated against conventional KDE-based interval estimation. Outcomes are assessed by recognized PI quality indicators, including prediction interval coverage probability (PICP), prediction interval normalized average width (PINAW), and coverage width-based criterion (CWC). Simulation findings confirm the efficacy of our approach and demonstrate that the SVR-AKDE-based PI forecasting consistently provides enhanced coverage and narrower widths compared to traditional KDE. This approach provides a comprehensive solution for short-term wind speed forecasting with quantifiable uncertainty, therefore enhancing its application in operational wind energy control.
- wind speed forecasting,
- renewable energy,
- support vector regressors,
- prediction intervals,
- probabilistic energy forecasting,
- adaptive kernel density estimator,
- AKDE,
- SVR
Citation: Rami Al-Hajj. Probabilistic machine learning-based forecasting of wind speed uncertainty using adaptive kernel density estimation[J]. Mathematical Biosciences and Engineering, 2025, 22(9): 2269-2299. doi: 10.3934/mbe.2025083

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Abstract

Short-term wind speed forecasting is essential for enhancing the efficiency and dependability of wind renewable energy installations. Although often used, conventional point predictions generated by machine learning techniques frequently fail to accurately capture the natural uncertainty associated with wind speed variation. Modeling this type of uncertainty is crucial for providing credible information as the level of uncertainty increases. Prediction intervals (PIs) offer a probabilistic framework for quantifying forecast uncertainty. This paper presents a hybrid forecasting methodology that combines support vector regression (SVR) with adaptive kernel density estimation (AKDE) to estimate wind speed prediction intervals over various short-term horizons (10, 30, 60, and 120 minutes). In contrast to standard kernel density estimation (KDE), which employs a uniform bandwidth and may overlook local data attributes, the adaptive KDE approach adjusts the bandwidth in accordance with the local distribution of forecast errors, thereby facilitating more precise and locally tuned uncertainty quantification. The efficacy of the proposed SVR-AKDE model is evaluated against conventional KDE-based interval estimation. Outcomes are assessed by recognized PI quality indicators, including prediction interval coverage probability (PICP), prediction interval normalized average width (PINAW), and coverage width-based criterion (CWC). Simulation findings confirm the efficacy of our approach and demonstrate that the SVR-AKDE-based PI forecasting consistently provides enhanced coverage and narrower widths compared to traditional KDE. This approach provides a comprehensive solution for short-term wind speed forecasting with quantifiable uncertainty, therefore enhancing its application in operational wind energy control.

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