Varying Coefficient Regression Model And Its Application In Deformation Modeling

By analyzing deformation monitoring data, finding the discipline of deformation and building model to predict deformation is one major work of deformation monitoring. Regression analysis, as a traditional method of deformation analysis, has the advantage of simple model and easy to explain. Regression analysis has a wide range of applications in the field of deformation analysis. The model building by general regression analysis is static model. However, in practical applications, the structure or physical properties of the monitoring object change with the passage of time, because of structural fatigue, corrosion and other factors. Therefore, the static model building by general regression analysis is difficult to predict. Therefore, this article will introduce varying coefficient method to the field of deformation analysis modeling, the main research contents and results are as follows:1) Comparing and analyzing parametric regression, nonparametric regression, semi-parametric regression, varying coefficients regression, temporal regression. Summarize the advantages and disadvantages of each method.2) Modeling in the use of varying coefficient regression.In the base of analyzing varying coefficient regression algorithm, local linear estimation is used to fit the varying coefficient. Simulation and the dam deformation modeling experiments show that:the coefficients of Varying coefficient model can reflect dam structure changes with the change of external factors, and the accuracy of model prediction is better than the normal linear regression model. Varying coefficient regression model is a dynamic model, is suitable for deformation analysis modeling.3) The traditional model of dam deformation analysis, often using a single measurement point modeling. Model is only suitable for a single measuring point, ignoring the correlation between the measuring points, is not conducive to judge the whole dam. This article proposes a spatial and temporal varying coefficient regression method based on PCA, and use this method to establish the spatial and temporal varying coefficient dam deformation model. Wu qiang xi deformation monitoring data modeling experiment shows that:it can acquire the displacement of the dam anywhere, anytime, and compared with a single measuring point model and static temporal deformation model has higher prediction accuracy.