Probability Density Function Control-Based Deep Ensemble Learning for Wind Energy System Power Forecasting

Jianfang Li

doi:10.1002/acs.4050

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Probability Density Function Control-Based Deep Ensemble Learning for Wind Energy System Power Forecasting

2025-07-16

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DOI：10.1002/acs.4050

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Abstract

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Accurate and reliable wind power forecasting plays a crucial role in the utilization of wind energy. However, the complexity of the nonlinear process of converting wind energy into power alters the statistical distributions of errors (known as concept drift), making the accomplishment of this task greatly challenging. For this purpose, we devise an innovative approach for predicting wind power based on the “decomposition-prediction-ensemble” framework. First, the raw wind power data is broken down into multiple intrinsic mode functions (IMFs) via improved variational mode decomposition, and the dimensionality of these IMFs is reduced by adopting kernel principal component analysis, thus significantly simplifying the intricacies of the multidimensional IMF data. Then, considering the asymmetric characteristic of modeling error, a probability density function control- based temporal convolutional network is developed for each subseries, where the modeling error PDF is controlled to close to an ideal Gaussian distribution, so that the prediction model parameters are adjusted. Finally, the multiple subseries forecasting models are integrated by a PDF-based differential evolution ensemble strategy. And the convergence of ensemble strategy is analyzed from a mathematical point of view. As a result, the proposed method can break through the limitation of symmetric loss capturing merely the second moment information, alleviating distribution shift of error to make an unbiased estimate. Real-world wind farm data are utilized for empirical analysis, and the simulation outcomes verify the high accuracy and generalization ability of the proposed model.

Keywords:

hybrid ensemble learning

nonlinear system identification

probability density function control

wind energy system

wind power prediction