Pump energy consumption forecasting in long-distance water supply systems based on enhanced variational mode decomposition and deep learning

Accurate pump energy consumption forecasting in long-distance water supply systems (LWSS) is crucial for operational scheduling optimisation and demand response. However, nonlinear variations in pump parameters during long-term operation often degrade the forecasting accuracy. To address this, this study proposes a novel hybrid framework, CV-CBiLSTM-Att, which integrates Chaos Particle Swarm Optimization (CPSO)-tuned Variational Mode Decomposition (VMD) with a deep learning network, utilising hydraulic flow rate as the primary predictor to capture the intrinsic nonlinear relationship between flow dynamics and pump energy consumption. Specifically, the CPSO algorithm is employed to minimise envelope entropy, globally searching for the optimal decomposition mode number (K) and penalty factor (α). This adaptive decomposition effectively disentangles the non-stationary flow rate signal into band-limited Intrinsic Mode Functions (IMFs), avoiding mode mixing and residual noise. Subsequently, a Convolutional Neural Network (CNN) extracts local invariant features from the multiscale IMFs, while a Bidirectional Long Short-Term Memory (BiLSTM) network captures long-range temporal dependencies. Crucially, an Attention mechanism is integrated to assign adaptive weights to pivotal hidden states, thereby enhancing the model's sensitivity to peak-valley transitions. Validated against 11 benchmark models using real-world LWSS operational data, the proposed framework demonstrates superior robustness. Experimental results indicate that the CV-CBiLSTM-Att model reduces the Root Mean Square Error (RMSE) by 68.06% compared to the baseline LSTM. Further, the model exhibits exceptional distributional consistency, achieving a Nash-Sutcliffe Efficiency (NSE) of 0.972, a Kling-Gupta Efficiency (KGE) of 0.976, and a negligible systematic bias (PBIAS < 0.1%), confirming its stability in capturing peak-to-valley energy dynamics. These findings verify that the proposed framework offers a highly accurate and reliable approach for energy management in LWSS.