Data-driven models for the steady thermal performance prediction of energy piles optimized by metaheuristic algorithms

This study presents a comprehensive approach for predicting the steady heat performance of energy piles via hybrid models optimized by using four metaheuristic algorithms: the African vultures optimization algorithm (AVOA), the Teaching-learning-based optimization (TLBO), the Sparrow search algorithm (SSA), and the Grey wolf optimization algorithm (GWO). A robust database was compiled that incorporates field, laboratory, and numerical data. The optimized hybrid models demonstrated high prediction accuracy for both the outlet temperature (T-out) and heat flux (q), with R-2 > 0.9. The prediction error distribution for T-out was generally more concentrated than that for q. However, T-out predictions were slightly underestimated overall. Among the algorithms, the SSA and TLBO exhibited superior convergence speed and accuracy, whereas AVOA showed slower convergence but faster computation times. A sensitivity analysis revealed that the inlet temperature (T-in), the most influential factor, significantly influenced both T-out and q, with other factors, such as the mass flow rate (V-m) and pile length (L-p), being more critical for heat flux predictions. The findings emphasize the effectiveness of metaheuristic-optimized models in accurately predicting energy pile performance, providing a valuable tool for enhancing the efficiency and digitization of ground source heat pump systems.