A Probabilistic Prediction Model for Displacement of Super High Arch Dams Considering Deformation Spatial Association

  Objectives  Machine learning language has become an ideal modeling tool in the field of dam health monitoring with its powerful nonlinear data mining ability. However, the minimum fitting mean square error (MSE) is determined as the only optimization objective in the traditional modeling process, which is likely to cause over-fitting problems.

  Methods  To overcome this problem, based on the relevance vector machine (RVM), a probabilistic prediction model is established under the constraint of double optimization objectives, which integrates the deformation spatial association and MSE. The deformation spatial association is quantified by the shape similarity index (SSI) at first. The double objective is then established with the combination of the MSE and SSI, and is achieved by making the MSE as small as possible, while the SSI is as large as possible.

  Results  Engineering example of the Jinping-I arch dam shows that the average decrease proportion of the root mean square error and maximum absolute error of the proposed double objective RVM model is 31.2% and 24.8%, respectively, and the prediction performance can be further improved by using the multi-kernel function. The prediction confidence bandwidth of the RVM model is significantly smaller than that of the traditional multiple linear regression model, with an average decrease proportion of 75.1%.

  Conclusions  Therefore, the multi-kernel double objective RVM model established for the displacement of super high arch dams can effectively improve the prediction performance and reduce the uncertainty.