Interpretable GBDT model-based multi-objective optimization analysis for the lateral inlet/outlet design in pumped-storage power stations

The uneven velocity distribution formed at the lateral inlet/outlet poses a significant risk of damaging the trash racks. Reasonable design of the inlet/outlet structures requires the consideration of two major aspects: the average velocity (V-m) and the coefficient of unevenness (U-c). This paper developed an optimization framework that combines an interpretable Gradient Boosting Decision Tree (SOBOL-GBDT) with a Non-dominated Sorting Genetic Algorithm (NSGA-II). 125 conditions are simulated by performing CFD simulations to generate the dataset, followed by GBDT implemented to establish a nonlinear mapping between the input parameters including vertical (alpha) and horizontal (beta) diffusion angles, diffusion segment length (L-D), channel area (C-A), and the objectives U-c and V-m. The SOBOL analysis reveals that in U-c prediction, C-A and alpha play more significant roles in the model development compared to beta and L-D. Besides, GBDT is observed to better capture interactive effects of the input parameters compared with other machine learning models. Subsequently, a multi-objective optimization framework using GBDT-NSGA-II is developed. The framework calculates the optimal Pareto front and determines the best solution using a pseudo-weight method. The results demonstrate that this framework leads to significant improvements in flow separation reduction in the diffusion segment and the normalized velocity distribution. The SOBOL-GBDT-NSGA-II framework facilitates a rational and effective design of the inlet/outlet.