Two spatial association–considered mathematical models for diagnosing the long-term balanced relationship and short-term fluctuation of the deformation behaviour of high concrete arch dams

The safety of a high concrete arch dam should be rapidly diagnosed from different angles. Displacement is an actual comprehensive reflection of the arch dam, and it is very important to diagnose the overall deformation behaviour by displacement-based mathematical monitoring models. In this article, based on the spatial association validation of the measured displacement of two high arch dams by the empirical orthogonal function decomposition and the Pearson correlation analysis, two spatial association–considered mathematical models were proposed for the dam displacement of multimonitoring points: one model for the long-term balanced relationship and one model for the short_term fluctuation. To diagnose the abnormality of the dam long-term spatial association, each displacement time series of the multimonitoring points on the dam body with strong spatial associations was decomposed by wavelet multiresolution analysis, and the decomposed high-frequency components, which had the same periodicity as the causal factors of the reservoir water level or air temperature, were determined to establish the cointegration monitoring model. The second model was a combination prediction model, with two sub-models established from the modelling angles of the hydraulic, seasonal and time causal factors and the adjacent point displacement factors, and this second model was mainly used for identifying dam short_term local abnormal deformation behaviour. Engineering examples show that the deformation behaviour of an arch dam under normal conditions has strong spatial associations. The two proposed models have high accuracy and interpreting ability and can effectively reduce the number of needed monitoring models.