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 (Tout) and heat flux (q), with R2 > 0.9. The prediction error distribution for Tout was generally more concentrated than that for q. However, Tout 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 (Tin), the most influential factor, significantly influenced both Tout and q, with other factors, such as the mass flow rate (Vm) and pile length (Lp), 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.