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Interpretable wind speed forecasting through two-stage decomposition with comprehensive relative importance analysis

Author

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  • Zeng, Huanze
  • Wu, Binrong
  • Fang, Haoyu
  • Lin, Jiacheng

Abstract

Crucial decision support for the efficient scheduling and operation of wind farms is provided by accurate wind speed forecasting, thereby ensuring the smart power grid’s stable operation. However, the inherent volatility and non-stationarity of wind speed sequences represent a challenge to enhancing forecasting accuracy. Current research indicates a close correlation between wind speed and various meteorological factors; effectively utilizing these meteorological data can significantly improve the precision of wind speed predictions. This study introduces a novel short-term multivariate interpretable method for predicting wind speeds, aimed at enhancing both the accuracy and the interpretability of the forecasts. The proposed model integrates a two-stage decomposition process, comprehensive relative importance analysis (CRIA), a Newton–Raphson-based optimizer (NRBO), and interpretable deep learning model, temporal fusion transformers (TFT). The methodology begins with the multivariate variational mode decomposition (MVMD) of wind speed data and nine meteorological variables, resulting in multiple nonlinear subsequences. These subsequences are further decomposed into sub-modes using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). A novel feature selection method based on CRIA is then employed to identify the most informative subsequences in order to reduce the computational complexity of the model, prevent overfitting, and enhance the model’s generalization ability. Subsequently, the NRBO algorithm is used to optimize the hyperparameters of TFT. Experimental results demonstrate that the MVMD-CEEMDAN-CRIA-NRBO-TFT model proposed in this paper possesses superior predictive accuracy compared to seventeen other benchmark forecasting models. Additionally, the interpretable outcomes of the model provide an enriched perspective of relevant data and analytical insights for decision-making processes.

Suggested Citation

  • Zeng, Huanze & Wu, Binrong & Fang, Haoyu & Lin, Jiacheng, 2025. "Interpretable wind speed forecasting through two-stage decomposition with comprehensive relative importance analysis," Applied Energy, Elsevier, vol. 392(C).
  • Handle: RePEc:eee:appene:v:392:y:2025:i:c:s0306261925007457
    DOI: 10.1016/j.apenergy.2025.126015
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    References listed on IDEAS

    as
    1. Jiang, Wenjun & Liu, Bo & Liang, Yang & Gao, Huanxiang & Lin, Pengfei & Zhang, Dongqin & Hu, Gang, 2024. "Applicability analysis of transformer to wind speed forecasting by a novel deep learning framework with multiple atmospheric variables," Applied Energy, Elsevier, vol. 353(PB).
    2. Liu, Hui & Mi, Xiwei & Li, Yanfei, 2018. "An experimental investigation of three new hybrid wind speed forecasting models using multi-decomposing strategy and ELM algorithm," Renewable Energy, Elsevier, vol. 123(C), pages 694-705.
    3. Wu, Tangjie & Ling, Qiang, 2024. "STELLM: Spatio-temporal enhanced pre-trained large language model for wind speed forecasting," Applied Energy, Elsevier, vol. 375(C).
    4. Liu, Hui & Chen, Chao, 2019. "Data processing strategies in wind energy forecasting models and applications: A comprehensive review," Applied Energy, Elsevier, vol. 249(C), pages 392-408.
    5. Serra, Adrià & Ortiz, Alberto & Cortés, Pau Joan & Canals, Vincent, 2025. "Explainable district heating load forecasting by means of a reservoir computing deep learning architecture," Energy, Elsevier, vol. 318(C).
    6. Kavasseri, Rajesh G. & Seetharaman, Krithika, 2009. "Day-ahead wind speed forecasting using f-ARIMA models," Renewable Energy, Elsevier, vol. 34(5), pages 1388-1393.
    7. Niu, Zhewen & Han, Xiaoqing & Zhang, Dongxia & Wu, Yuxiang & Lan, Songyan, 2024. "Interpretable wind power forecasting combining seasonal-trend representations learning with temporal fusion transformers architecture," Energy, Elsevier, vol. 306(C).
    8. Zhang, Zongwei & Lin, Lianlei & Gao, Sheng & Wang, Junkai & Zhao, Hanqing, 2024. "Wind speed prediction in China with fully-convolutional deep neural network," Renewable and Sustainable Energy Reviews, Elsevier, vol. 201(C).
    9. Sun, Xiaoying & Liu, Haizhong, 2024. "Multivariate short-term wind speed prediction based on PSO-VMD-SE-ICEEMDAN two-stage decomposition and Att-S2S," Energy, Elsevier, vol. 305(C).
    10. Zhang, Dongqin & Hu, Gang & Song, Jie & Gao, Huanxiang & Ren, Hehe & Chen, Wenli, 2024. "A novel spatio-temporal wind speed forecasting method based on the microscale meteorological model and a hybrid deep learning model," Energy, Elsevier, vol. 288(C).
    11. Cai, Yizhuo & Li, Yanting, 2024. "Short-term wind speed forecast based on dynamic spatio-temporal directed graph attention network," Applied Energy, Elsevier, vol. 375(C).
    12. Jiang, Ping & Liu, Zhenkun & Niu, Xinsong & Zhang, Lifang, 2021. "A combined forecasting system based on statistical method, artificial neural networks, and deep learning methods for short-term wind speed forecasting," Energy, Elsevier, vol. 217(C).
    13. Yang, Wendong & Zang, Xinyi & Wu, Chunying & Hao, Yan, 2024. "A new multi-objective ensemble wind speed forecasting system: Mixed-frequency interval-valued modeling paradigm," Energy, Elsevier, vol. 304(C).
    14. Zheng, Peijun & Zhou, Heng & Liu, Jiang & Nakanishi, Yosuke, 2023. "Interpretable building energy consumption forecasting using spectral clustering algorithm and temporal fusion transformers architecture," Applied Energy, Elsevier, vol. 349(C).
    15. Du, Pei & Yang, Dongchuan & Li, Yanzhao & Wang, Jianzhou, 2024. "An innovative interpretable combined learning model for wind speed forecasting," Applied Energy, Elsevier, vol. 358(C).
    16. Ait Maatallah, Othman & Achuthan, Ajit & Janoyan, Kerop & Marzocca, Pier, 2015. "Recursive wind speed forecasting based on Hammerstein Auto-Regressive model," Applied Energy, Elsevier, vol. 145(C), pages 191-197.
    17. Bommidi, Bala Saibabu & Teeparthi, Kiran & Kosana, Vishalteja, 2023. "Hybrid wind speed forecasting using ICEEMDAN and transformer model with novel loss function," Energy, Elsevier, vol. 265(C).
    18. Jiang, Zheyong & Che, Jinxing & He, Mingjun & Yuan, Fang, 2023. "A CGRU multi-step wind speed forecasting model based on multi-label specific XGBoost feature selection and secondary decomposition," Renewable Energy, Elsevier, vol. 203(C), pages 802-827.
    19. Cai, Chenhao & Zhang, Leyao & Zhou, Jianguo, 2024. "DMPR: A novel wind speed forecasting model based on optimized decomposition, multi-objective feature selection, and patch-based RNN," Energy, Elsevier, vol. 310(C).
    20. Fu, Wenlong & Zhang, Kai & Wang, Kai & Wen, Bin & Fang, Ping & Zou, Feng, 2021. "A hybrid approach for multi-step wind speed forecasting based on two-layer decomposition, improved hybrid DE-HHO optimization and KELM," Renewable Energy, Elsevier, vol. 164(C), pages 211-229.
    21. Zhao, Jing & Guo, Yiyi & Lin, Yihua & Zhao, Zhiyuan & Guo, Zhenhai, 2024. "A novel dynamic ensemble of numerical weather prediction for multi-step wind speed forecasting with deep reinforcement learning and error sequence modeling," Energy, Elsevier, vol. 302(C).
    22. Fu, Jiaqian & Sun, Yuying & Li, Yunhe & Wang, Wei & Wei, Wenzhe & Ren, Jinyang & Han, Shulun & Di, Haoran, 2025. "An investigation of photovoltaic power forecasting in buildings considering shadow effects: Modeling approach and SHAP analysis," Renewable Energy, Elsevier, vol. 245(C).
    23. Joseph, Lionel P. & Deo, Ravinesh C. & Casillas-Pérez, David & Prasad, Ramendra & Raj, Nawin & Salcedo-Sanz, Sancho, 2024. "Short-term wind speed forecasting using an optimized three-phase convolutional neural network fused with bidirectional long short-term memory network model," Applied Energy, Elsevier, vol. 359(C).
    24. Yang, Dongchuan & Li, Mingzhu & Guo, Ju-e & Du, Pei, 2024. "An attention-based multi-input LSTM with sliding window-based two-stage decomposition for wind speed forecasting," Applied Energy, Elsevier, vol. 375(C).
    25. Wu, Binrong & Yu, Sihao & Peng, Lu & Wang, Lin, 2024. "Interpretable wind speed forecasting with meteorological feature exploring and two-stage decomposition," Energy, Elsevier, vol. 294(C).
    26. Li, Qingyang & Wang, Guosong & Wu, Xinrong & Gao, Zhigang & Dan, Bo, 2024. "Arctic short-term wind speed forecasting based on CNN-LSTM model with CEEMDAN," Energy, Elsevier, vol. 299(C).
    27. Wu, Huijuan & Meng, Keqilao & Fan, Daoerji & Zhang, Zhanqiang & Liu, Qing, 2022. "Multistep short-term wind speed forecasting using transformer," Energy, Elsevier, vol. 261(PA).
    28. Liang, Yang & Zhang, Dongqin & Zhang, Jize & Hu, Gang, 2024. "A state-of-the-art analysis on decomposition method for short-term wind speed forecasting using LSTM and a novel hybrid deep learning model," Energy, Elsevier, vol. 313(C).
    29. Han, Yan & Mi, Lihua & Shen, Lian & Cai, C.S. & Liu, Yuchen & Li, Kai & Xu, Guoji, 2022. "A short-term wind speed prediction method utilizing novel hybrid deep learning algorithms to correct numerical weather forecasting," Applied Energy, Elsevier, vol. 312(C).
    30. Lim, Bryan & Arık, Sercan Ö. & Loeff, Nicolas & Pfister, Tomas, 2021. "Temporal Fusion Transformers for interpretable multi-horizon time series forecasting," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1748-1764.
    31. Zhang, Shuai & Chen, Yong & Xiao, Jiuhong & Zhang, Wenyu & Feng, Ruijun, 2021. "Hybrid wind speed forecasting model based on multivariate data secondary decomposition approach and deep learning algorithm with attention mechanism," Renewable Energy, Elsevier, vol. 174(C), pages 688-704.
    32. Wu, Binrong & Wang, Lin, 2024. "Two-stage decomposition and temporal fusion transformers for interpretable wind speed forecasting," Energy, Elsevier, vol. 288(C).
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