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Article

An Adaptive Multi-Scale Heterogeneous Ensemble Framework for Interpretable Wind Power Forecasting in Sustainable Grids

1
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 102488, China
2
School of Economics and Management, Shanghai Maritime University, Shanghai 201306, China
3
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
4
School of Chemical Engineering, Sichuan University, Chengdu 610065, China
*
Author to whom correspondence should be addressed.
Symmetry 2026, 18(6), 921; https://doi.org/10.3390/sym18060921
Submission received: 29 April 2026 / Revised: 21 May 2026 / Accepted: 22 May 2026 / Published: 27 May 2026

Abstract

Reliable short-term wind power forecasting is crucial for smart grid stability. However, high-dimensional noise and stochastic fluctuations in wind sequences often degrade the accuracy of traditional forecasting models. Moreover, wind power time series typically exhibit asymmetric rising and decaying patterns, which further complicate accurate modeling. To address these challenges, this study proposes a hybrid intelligent system that integrates three components: data preprocessing, heterogeneous ensemble learning, and probabilistic interval forecasting. First, we build a multi-stage preprocessing workflow. Adaptive DBSCAN and Local Outlier Factor (LOF) remove spatial and density anomalies. Then multivariate variational mode decomposition (MVMD) synchronously separates multi-scale oscillatory patterns while preserving cross-channel correlations and frequency-domain symmetry across input variables. SHAP analysis quantifies feature importance, ensuring interpretability. The selected features are fed into a heterogeneous ensemble model consisting of Transformer, BPNN, ELM, XGBoost, and QRLSTM, which collectively capture multi-scale temporal dependencies and diverse data patterns. The ensemble weights are dynamically optimized by a modified multi-objective dragonfly algorithm (MMODA) that balances forecast accuracy and stability. Based on this ensemble, we apply MMODA to tune kernel density estimation for generating high-quality forecast intervals, maximizing coverage while minimizing interval width. Experiments on two wind farms in Shandong show that our MMODA-optimized ensemble reduces mean absolute percentage error by about 44.7% compared to single models, and ablations confirm that MVMD preprocessing adds a further 10.7% reduction. The proposed system provides an interpretable and reliable decision-support tool for sustainable grid operations.
Keywords: wind power forecasting; heterogeneous ensemble learning; multivariate variational mode decomposition; interpretability; multi-objective optimization; deterministic and interval forecasting wind power forecasting; heterogeneous ensemble learning; multivariate variational mode decomposition; interpretability; multi-objective optimization; deterministic and interval forecasting

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MDPI and ACS Style

Gao, J.; Zhang, H.; Sun, Z.; Xu, H.; Li, J.; Heng, J. An Adaptive Multi-Scale Heterogeneous Ensemble Framework for Interpretable Wind Power Forecasting in Sustainable Grids. Symmetry 2026, 18, 921. https://doi.org/10.3390/sym18060921

AMA Style

Gao J, Zhang H, Sun Z, Xu H, Li J, Heng J. An Adaptive Multi-Scale Heterogeneous Ensemble Framework for Interpretable Wind Power Forecasting in Sustainable Grids. Symmetry. 2026; 18(6):921. https://doi.org/10.3390/sym18060921

Chicago/Turabian Style

Gao, Jiaoyang, Hui Zhang, Zhongmiao Sun, Hui Xu, Jiahe Li, and Jiani Heng. 2026. "An Adaptive Multi-Scale Heterogeneous Ensemble Framework for Interpretable Wind Power Forecasting in Sustainable Grids" Symmetry 18, no. 6: 921. https://doi.org/10.3390/sym18060921

APA Style

Gao, J., Zhang, H., Sun, Z., Xu, H., Li, J., & Heng, J. (2026). An Adaptive Multi-Scale Heterogeneous Ensemble Framework for Interpretable Wind Power Forecasting in Sustainable Grids. Symmetry, 18(6), 921. https://doi.org/10.3390/sym18060921

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