An interpretable attention model for multipoint dam deformation prediction using sensor data-based spatiotemporal features

Dam deformation prediction is a vital indicator for structural safety assessment. Although existing prediction models effectively extract temporal features from environmental variable sensor data, they inadequately capture the critical spatiotemporal coupling effects among hydraulic, thermal, and aging variables, which are primary influences on dam deformation behavior. To address this limitation, this study proposes a novel deep learning network named SAO-STformer, which integrates the Spatiotemporal-Transformer with the snow ablation optimizer. Specifically, the Spatiotemporal-Transformer model incorporates three significant enhancements over the traditional Transformer architecture. First, a multivariate patch embedding method is introduced to segment the sensor data of each variable into fixed-length temporal patches with positional encoding, forming a two-dimensional vector array that effectively preserves essential spatiotemporal information. Second, a spatiotemporal attention mechanism is implemented, consisting of: (1) a temporal attention layer that employs multihead self-attention to extract intravariable temporal dependencies and (2) a spatial attention layer incorporating a routing mechanism with dual multihead self-attention layers to establish comprehensive intervariable spatial connectivity. Third, a hierarchical scale fusion mechanism is introduced, whereby each encoder layer integrates adjacent variable patch representations to generate multiscale representations. Furthermore, the snow ablation optimizer is used for hyperparameter tuning of the Spatiotemporal-Transformer, and its dual-population mechanism helps balance global exploration and local exploitation, thereby reducing the risk of premature convergence and improving the reliability of the optimized model configuration. Upon validation using sensor data from a high arch dam, the proposed model outperforms traditional machine learning methods and existing Transformer variants across all evaluated metrics. The observed residuals, which are near zero and uniformly distributed, indicate an excellent model fit. Notably, the visualized spatiotemporal attention weights provide quantitative insights into the primary environmental variables and their dynamic coupling mechanisms that influence dam deformation. These findings offer significant theoretical contributions and practical guidance for dam safety monitoring and reinforcement strategies.