A Physically Decoupled Deformation Monitoring Framework Incorporating Beta-Distributed Thermal Lag Modeling for Hydraulic Structures

Hydraulic structures in navigation–hydropower hubs exhibit complex deformation governed by coupled hydraulic, thermal, and long-term effects, making reliable deformation monitoring challenging. Conventional statistical models are prone to multicollinearity-induced overfitting and elevated false alarm rates, while existing temperature components inadequately characterize delayed thermal responses under large reservoir-level fluctuations. To address these issues, this study proposes an SMT-β deformation monitoring model that integrates separated modeling technology (SMT) with a beta distribution-based temperature formulation. Within a physics-guided sequential modeling framework, long-term deformation trends are first extracted using ICEEMDAN, followed by the development of a beta distribution-based temperature component to characterize lagged thermal effects during stable reservoir-level periods. The hydraulic load component is subsequently identified from the residual deformation, and the total deformation is reconstructed through linear superposition of physically interpretable components. Validation using monitoring data from a 300 m-class super-high arch dam demonstrates that the proposed model achieved the highest prediction accuracy (RMSE = 0.318 mm), reduced the overfitting coefficient to 0.48, and eliminated false alarms. The proposed framework effectively mitigates multicollinearity-induced overfitting while improving the physical interpretability of deformation monitoring, offering a robust and extensible approach for hydraulic structures subjected to complex environmental loads.