Sequential sparse Bayesian learning of long-term thermomechanical performance of energy piles from limited multi-parameter monitoring data

Energy piles combine structural support with ground-source heat exchange, enabling effective seasonal thermal storage. However, long-term cyclic thermal loads on piles can induce complex thermo-mechanical interactions with surrounding soils. Predicting the long-term performance of energy piles is crucial for reliable foundation design but remains challenging due to limited monitoring data, significant parameter uncertainty, and the high computational cost of fully coupled numerical analyses. To address these challenges, this study proposes a multi-objective sparse ensemble learning (MO-SEL) framework that combines physics-informed load transfer functions with sequential sparse Bayesian learning to predict long-term pile performance. A physics-embedded feature library is first constructed from diverse finite difference models. The most informative bases are then automatically selected using multi-parameter monitoring data within a dimensionally consistent formulation, followed by joint prediction of displacement and axial strain with explicit uncertainty quantification. Applications to physical model tests and full-scale case studies demonstrate that MO-SEL yields accurate and uncertainty-aware predictions of long-term pile performance, with dynamic updating strategies further enhancing reliability as new data become available. More importantly, the framework enables both reconstruction and forward prediction of full-field strain distributions along the pile shaft, including unmonitored zones, an advantage not achievable with conventional black-box machine learning methods.