Abstract
The geographically and temporally weighted regression (GTWR) model is a dynamic model which considers the spatiotemporal correlation and the spatiotemporal nonstationarity. Taking into account these advantages, we proposed a spatiotemporal deformation modelling method based on GTWR. In order to further improve the modelling accuracy and efficiency and considering the application characteristics of deformation modelling, the inverse window transformation method is used to search the optimal fitting window width and furthermore the local linear estimation method is used in the fitting coefficient function. Moreover, a comprehensive model for the statistical tests method is proposed in GTWR. The results of a dam deformation modelling application show that the GTWR model can establish a unified spatiotemporal model which can represent the whole deformation trend of the dam and furthermore can predict the deformation of any point in time and space, with stronger flexibility and applicability. Finally, the GTWR model improves the overall temporal prediction accuracy by 43.6% compared to the single-point time-weighted regression (TWR) model.
Highlights
Regression analysis is a commonly used deformation modelling method
In order to take into account the temporal nonstationarity, Lu et al [5] used the time-weighted regression (TWR) method to model dam deformation. e TWR model assumes that the linear regression coefficient is a function of time to adapt the temporal nonstationarity, and the prediction accuracy of the model is higher than that of the linear regression model
To Mathematical Problems in Engineering avoid the boundary effect of the model regression coefficient fitting in geographically and temporally weighted regression (GTWR), the local linear estimation method is used in the fitting coefficient function. e statistical test is very important in GTWR modelling to ensure the reliability of the model
Summary
Regression analysis is a commonly used deformation modelling method. It can establish a functional model between deformation and influence factors and carry out physical interpretation and prediction of deformation. In order to take into account the temporal nonstationarity, Lu et al [5] used the time-weighted regression (TWR) method to model dam deformation. Li et al [6] and Dai et al [7] applied the space-time autoregressive (STAR) model and the spatiotemporal independent component regression (STICR) model to build a deformation model. Both consider the spatiotemporal correlation and can establish an overall spatiotemporal deformation model for all points. In order to take both the spatiotemporal correlation and the spatiotemporal nonstationarity of the deformation data into consideration, a spatiotemporal deformation modelling method based on the GTWR model was proposed and applied for dam deformation modelling. We combine the existing statistical test theory of the GTWR model, including the regression coefficients test of the GTWR model proposed by Xiao et al [8] and establish a five-step test method to conduct a comprehensive statistical test on the GTWR model
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