Abstract
The substantial cooling demand required to maintain ice surfaces in indoor ice rinks results in considerable energy consumption, making the optimization of refrigeration system performance both necessary and urgent. To address the current lack of research on cooling load prediction in ice rinks, this study proposes a cooling load prediction method based on Grey Relational Analysis (GRA) and an improved Long Short-Term Memory (LSTM) network, combined with the Whale Optimization Algorithm (WOA) to achieve dynamic load allocation for multiple chillers, using a standard indoor ice rink in Beijing as a case study. First, GRA is employed to identify feature variables highly correlated with cooling load, including skater flow, outdoor humidity, solar diffuse radiation, and dry-bulb temperature. Subsequently, an improved LSTM model is constructed by incorporating stacked structures, time-enhanced features, and batch normalization modules, and its superior performance is verified through ablation experiments. The results show that stacked structures and time-feature embedding significantly improve prediction capability, with the model integrating both modules reducing prediction errors by up to 12.94% in MAPE and a maximum decrease of 9.77 in RMSE. In contrast, batch normalization was found to weaken the LSTM’s ability to model sequential dependencies. In the load allocation model, the WOA strategy demonstrated optimal energy consumption control under low-, medium-, and high-load conditions, clearly outperforming conventional Chiller Sequencing and Average Load Method, with energy savings achieving 6.8%. Moreover, WOA exhibits superior performance compared with both the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). This study provides a feasible intelligent optimization pathway for energy-efficient scheduling of refrigeration systems in indoor ice rink, offering substantial engineering application value and broad prospects for promotion. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1038/s41598-026-38121-6.