Entropy-guided iTransformer for multi-point deformation prediction of high arch dams considering near-dam mountain effects

Accurate deformation prediction of high arch dams is essential for ensuring long-term structural safety and operational reliability. However, conventional deformation models are predominantly developed based on individual monitoring points, which neglect the spatial correlations embedded in dam monitoring networks. Moreover, the predictive performance of these models is highly dependent on the selection of informative influencing factors, limiting their generalization capability under complex operating conditions. To address these limitations, this study proposes an entropy-guided multi-point deformation prediction framework for high arch dams that integrates Copula Entropy-based feature selection with an optimized inverted Transformer (iTransformer) model. First, the influence of near-dam mountain mass on dam deformation is explicitly considered, and mountain-enhanced hydrostatic-seasonal-time (MHST) factors are constructed using near-dam mountain residuals after least-squares removal of conventional hydrostatic, seasonal, and time-dependent components. Subsequently, a Copula Entropy-based partial mutual information (PMI) strategy is developed to quantify nonlinear dependencies between candidate influencing factors and multi-point deformation responses, enabling the construction of a compact and low-redundancy feature set. Furthermore, an iTransformer-based multi-output prediction model is established to capture spatially coordinated deformation patterns among multiple monitoring locations. An artificial ecosystem-based optimization algorithm (AEO) is introduced to optimize model hyperparameters and improve prediction robustness. The proposed framework enables synchronous deformation prediction across multiple monitoring points using physically interpretable input factors. Long-term field monitoring data from a large-scale high arch dam are employed to validate the effectiveness of the proposed method. Results demonstrate that the proposed model attains the lowest average root mean square error (RMSE) of 1.043 among the compared learning-based models. Although point-specific factor selection performs slightly better at TCN10 and TCN11, the proposed model provides the best aggregate performance across the three monitoring points, indicating its potential for dam health monitoring and safety assessment.