A multi-output prediction model for the high arch dam displacement utilizing the VMD-DTW partitioning technique and long-term temperature

The displacement evolutionary process reflects the structural safety status of the arch dam effectively. Establishing an effective predictive model for arch dam displacements is significant for dam monitoring. However, most existing data-driven methods predominantly rely on single-point prediction and neglect the spatial correlations and variations of displacements in different directions across the arch dam. Consequently, we propose the MC-TCN model, which integrates the multi-output (M) regression model with convolutional block attention mechanisms (C) and a temporal convolutional network (TCN) to forecast the arch dam's displacement trends while taking multiple points and zones into account. First, the Hydrostatic Long-term Temperature Time (HLTT) model, incorporating long-term temperature monitoring data, is developed to generate displacement components. Subsequently, displacements from various places and directions are decomposed into three models by variational model decomposition (VMD) and divided using a shape-based technique named dynamic time warping (DTW). Finally, The MC-TCN model is adopted to predict the displacement of the arch dam. The proposed approach is illustrated in detail using a nearly long-term dataset from a high arch dam in northwest China. Comparative assessments with seven advanced benchmark models attest to the accuracy and superiority of the MC-TCN model. Results indicate that the proposed approach achieves a coefficient of determination (R-2) above 0.992 in predicting displacements at various points and directions. It shows a high predictive capability. This approach presents a novel and effective predictive method for safety monitoring analysis in high arch dams.