Predicting Pelton turbine bucket free-surface flow with an attention-based temporal convolutional network: A data-driven surrogate model

Accurately resolving free-surface flow over Pelton turbine buckets is essential for efficiency optimization but remains prohibitively expensive when using conventional computational fluid dynamics (CFD) or smoothed particle hydrodynamics. To overcome this bottleneck, we proposed a data-driven deep learning model, the attention-enhanced temporal convolutional network (TCN), for predicting transient free-surface flow on buckets through convolutions in temporal and spatial dimensions. A surface-point-cloud sampling (SPCS) strategy was applied to the CFD results of a micro-Pelton turbine prototype, yielding 30 complete free-surface flow patterns that mirror the off-design operating condition. Extended dynamic mode decomposition (EDMD) was applied to free-surface flows under both design and off-design operating conditions, revealing modal similarities across flow patterns. Attention-enhanced TCN model was subsequently trained on 30 complete flow patterns under off-design condition. Model parameters including input and prediction horizons and channel configuration were evaluated to ensure model reliability and generalization. Ablation studies show that the temporal layer delivers the bulk of the error reduction, while the attention layer supplies the remaining improvement margin. The attention-enhanced TCN model attains mean squared error (MSE) below 2%, mean absolute error (MAE) below 7%, and coefficient of determination (R2) exceeding 0.9 on untrained flow patterns, delivering a 58% improvement in MAE over Bayesian-optimized four baselines models. Compared with full CFD strategy, the attention-enhanced TCN model compresses the flow data in ratio 1005 and successfully enables learns the evolution of the free-surface flow with high accuracy, which offers a practical pathway for integrating data-driven models into digital-twin frameworks for hydropower optimization.