A novel reconstruction method for displacement missing data of arch dam via hierarchical clustering and deep learning

The absence of displacement monitoring data presents a challenge to real-time dam safety monitoring. This article introduces a novel method for reconstructing missing displacements, comprehensively taking into account the spatiotemporal correlation and causal effect mechanism of displacement. Firstly, adaptive weighted derivative dynamic time warping (AWDDTW) and adaptive weighted dynamic time warping (AWDTW), in conjunction with clustering algorithms, are proposed to extract spatiotemporal correlation among dam displacements. Secondly, by stacking residual blocks within the residual network and densifying the shortcut connections between residual blocks, the deep stacked residual network (DS-ResNet) is established to effectively capture the intricate mappings between displacements and various factors. Finally, using two arch dams, as examples, we simulated scenarios of continuous long-term and multiple short-term missing data to validate the new method proposed in this study. The results indicate that the proposed clustering algorithm can accurately compute the similarity between displacement sequences of different lengths and monitoring frequencies, thereby providing more precise displacement point partitioning results. Compared to models such as random forests, relevance vector machines, multilayer perceptron, ResNet and Transformer, the DS-ResNet demonstrates superior capability in identifying and extracting effective information from displacement sequences under both continuous long-term and multiple short-term missing data scenarios. Compared to methods that solely consider spatiotemporal correlation or causal effect mechanism of displacement, the proposed method can more comprehensively reflect the operating patterns of arch dams and more accurately reconstruct missing displacement values. The research presented herein offers new technical means and solution approaches for dam safety monitoring and operational management.