Multi-Scale ICEEMDAN–VMD Decomposition and Optimization-Enhanced CNN–BiGRU-MHA Model for ECT Accuracy Forecasting

To improve the prediction accuracy of electronic current transformer (ECT) errors, this study proposes a hybrid prediction model integrating ICEEMDAN decomposition, variational mode decomposition (VMD), and a deep learning framework. First, ICEEMDAN is employed to decompose the measurement data into multi-scale modal components. These components are then screened and reconstructed using multiscale permutation entropy (MPE) and probability density function (PDF) analysis. For complex components, VMD is applied for secondary decomposition with the objective of minimizing MPE, thereby reducing data complexity and providing cleaner, more informative input sequences for the hybrid model. Subsequently, a hybrid prediction model is constructed by combining convolutional neural networks (CNN), bidirectional gated recurrent units (BiGRU), and an attention mechanism. The network parameters of the sub-models are optimized <i>via</i> Snow Ablation Optimization (SAO) to overcome the randomness of traditional subjective parameter selection. The final prediction results are obtained by aggregating the outputs of all sub-models. Experimental results demonstrate that, compared to direct prediction and single-decomposition methods, the proposed model reduces RMSE, MAE, and MAPE by 32.7%, 32.2%, and 31.4%, and 23.8%, 22.2%, and 24.5%, respectively. This method significantly enhances ECT error prediction accuracy, providing an effective solution for real-time monitoring and smart grid operation and maintenance.