Displacement is the most intuitive reflection of the structural behaviour of concrete dams, and it is of great significance to predict future displacement for dam health diagnosis. The mathematical models used to predict displacement are mostly established with the only regression objective of minimizing the mean square error between the measured and fitted displacements, whereas the spatial associations between the displacements of multiple monitoring points of an arch dam are ignored. To increase the prediction accuracy of machine learning technique-based mathematical models, a spatial association-coupled support vector machine model is proposed in this article to predict the displacement of high arch dams. This approach is conducted by performing an incremental distance-based spatial clustering for dam displacement field in the first step. The displacement spatial association is quantified by the integrated shape similarity index between the measured time series of multiple monitoring points and is then coupled with the fitting mean square error to optimize the parameters of the support vector machine model. A case study of an engineering example indicates that the prediction accuracy and generalization ability of the proposed double objective support vector machine model have been greatly improved compared to the traditional single objective support vector machine model. For the total 34 plumb line monitoring points on the dam body of the Jinping-I arch dam, when using the hydraulic, seasonal and time- and hydraulic, hysteretic, seasonal and time-based double objective support vector machine models, the prediction accuracy of 25 and 21 monitoring points increases with an average rate of 50.8% and 47.4%, and the degrees of overfitting are evenly reduced by 44.3% and 70.9%, respectively.

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.

Displacement is the most intuitive reflection of the comprehensive behavior of concrete dams, especially the time effect displacement, which is a key index for the evaluation of the structural behavior and health status of a dam in long-term service. The main purpose of this paper is to establish a state space model for separating causal components from the measured dam displacement. This approach is conducted by initially proposing two equations, which are the state and observation equations, and model parameters are then optimized by the Kalman filter algorithm. The state equation is derived according to the creep deformation of dam concrete and foundation rock and is used to preliminarily predict the dam time effect displacement. Considering the generally recognized three components of dam displacement, the hydraulic-seasonal-time (HST) model is used to establish the observation equation, which is used to update the time effect displacement. The efficiency and rationality of the established state space model is verified by an engineering example. The results show that the hydraulic component separated by the state space model only contains the instantaneous elastic hydraulic deformation, while the hysteretic elastic hydraulic deformation is divided into the time effect component. The inverted elastic modulus of dam body concrete is an instantaneous value for the state space model but a comprehensive reflection of the instantaneous and hysteretic elastic deformation ability for the HST model, where the hysteretic elastic deformation is a part of the hydraulic component. For the Xiaowan arch dam, the inverted values are 42.9 and 36.7 GPa for the state space model and HST model, respectively. The proposed state space model is useful to improve the interpretation ability of the separated displacement components of concrete dams.