A multivariate load forecasting framework for integrated energy systems based on multi-band decomposition and combined correlation analysis

Short-term integrated energy load forecasting is important for real-time operational adjustment and energy management, but seasonal variations, nonlinear meteorological effects, and interactions among multiple load types often reduce forecasting accuracy. To address limitations in feature selection, frequency-specific modeling, and cross-load information interaction, this paper proposes a multivariate load forecasting framework integrating combined correlation analysis, multi-band decomposition, and a cross-attention mechanism (CAM). Spearman correlation, mutual information, and random forest importance are first fused using an entropy-weighting strategy to construct season-specific input feature sets and reduce bias from any single correlation metric. Complete ensemble empirical mode decomposition with adaptive noise is then applied to decompose each load series into intrinsic mode functions, which are grouped into low-frequency, mid-frequency, and high-frequency components according to sample entropy and zero-crossing rate. Based on their temporal characteristics, Gated recurrent unit, multi-resolution time-series transformer, and convolutional neural network transformer models are assigned to the three frequency bands, respectively. The CAM further enhances information exchange among electricity, cooling, and heating loads. The predicted components are reconstructed to obtain the final forecasts, while Shapley additive explanations are used to assess the consistency between feature selection and model behavior. Case studies using data from Arizona State University and an industrial park in Gansu province show that, across the two datasets, the proposed method achieves average mean absolute percentage errors of 0.642%, 2.421%, and 1.384% for electricity, cooling, and heating loads, respectively, outperforming the benchmark models.