A Multi-Channel Δ-BiLSTM Framework for Short-Term Bus Load Forecasting Based on VMD and LOWESS

Short-term bus load forecasting in distribution networks faces severe challenges of non-stationarity, high-frequency disturbances, and multi-scale coupling arising from renewable integration and emerging loads such as centralized EV charging. Conventional statistical and deep learning approaches often exhibit instability under abrupt fluctuations, whereas decomposition-based frameworks risk redundancy and information leakage. This study develops a hybrid forecasting framework that integrates variational mode decomposition (VMD), locally weighted scatterplot smoothing (LOWESS), and a multi-channel differential bidirectional long short-term memory network (Δ-BiLSTM). VMD decomposes the bus load sequence into intrinsic mode functions (IMFs), residuals are adaptively smoothed using LOWESS, and effective channels are selected through correlation-based redundancy control. The Δ-target learning strategy enhances the modeling of ramping dynamics and abrupt transitions, while Bayesian optimization and time-sequenced validation ensure reproducibility and stable training. Case studies on coastal-grid bus load data demonstrate substantial improvements in accuracy. In single-step forecasting, RMSE is reduced by 65.5% relative to ARIMA, and R² remains above 0.98 for horizons h = 1–3, with slower error growth than LSTM, RNN, and SVM. Segment-wise analysis further shows that, for h=1, the RMSE on the fluctuation, stable, and peak segments is reduced by 69.4%, 62.5%, and 62.4%, respectively, compared with ARIMA. The proposed Δ-BiLSTM exhibits compact error distributions and narrow interquartile ranges, confirming its robustness under peak-load and highly volatile conditions. Furthermore, the framework’s design ensures both transparency and reliable training, contributing to its robustness and practical applicability. Overall, the VMD–LOWESS–Δ-BiLSTM framework achieves superior accuracy, calibration, and robustness in complex, noisy, and non-stationary environments. Its interpretable structure and reproducible training protocol make it a reliable and practical solution for short-term bus load forecasting in modern distribution networks.