变系数回归模型及其在变形建模中的应用

发布时间：2018-04-14 22:36

本文选题：变形监测 + 回归分析　；参考：《中南大学》2014年硕士论文

【摘要】：通过对变形监测数据进行分析,发现变形规律并建立模型对变形进行预报预测,是变形监测的一项主要工作。其中,回归分析作为一种传统的变形分析方法,具有建模简单,易于解释等优点,在变形分析与建模领域有着广泛的应用。然而,普通线性回归分析所建立的模型是一种静态模型,在实际应用中,受结构疲劳、材料腐蚀等因素的影响,变形体的结构或物理性质将随着时间的推移或周边环境的变化而发生改变,因此,利用普通线性回归而建立的静态模型难以进行准确的预报预测。为此,本文将变系数方法引入变形分析建模领域,主要研究内容与成果如下： 1)对比分析了参数回归分析、非参数回归分析、半参数回归分析、变系数回归、时空回归分析等回归分析方法,并总结归纳了各方法的优缺点。 2)利用变系数回归分析方法进行变形分析建模。在对变系数回归算法进行了深入分析的基础上,采用局部线性估计的方法对变系数回归中的系数进行拟合。仿真和大坝变形建模实验表明：变系数模型中的系数可反映大坝结构对外界影响因素响应的变化,模型预测精度也明显优于普通的线性回归模型。说明变系数回归模型是一种动态模型,适用于变形分析建模。 3)传统的大坝变形分析建模中,常采用单测点模型建模。即模型仅对单一测点进行建模分析,忽略了各测点之间的相关性,不利于对大坝整体性能状态进行判断。本文提出了一种基于PCA(主成分分析)的时空变系数回归方法,并利用该方法建立了时空变系数大坝变形模型。通过五强溪大坝上一条引张线上的变形监测数据建模实验可知：该模型能够准确得出大坝上任意位置、任意时刻的变形位移量,并较之单测点模型及静态时空变形模型具有更高的预测精度。图24幅,表3个,参考文献60篇。
[Abstract]:Through the analysis of deformation monitoring data, it is a main work of deformation monitoring to find out the deformation law and establish a model to forecast and forecast the deformation.Among them, regression analysis, as a traditional deformation analysis method, has the advantages of simple modeling and easy interpretation, and is widely used in the field of deformation analysis and modeling.However, the model established by ordinary linear regression analysis is a static model, which is affected by structural fatigue, material corrosion and other factors in practical application.The structure or physical properties of deformable bodies will change with the passage of time or the change of surrounding environment. Therefore, it is difficult to predict accurately by the static model established by ordinary linear regression.Therefore, the variable coefficient method is introduced into the field of deformation analysis and modeling. The main research contents and results are as follows:1) the methods of regression analysis, such as parametric regression, non-parametric regression, semi-parametric regression, variable coefficient regression and space-time regression, are compared and analyzed, and the advantages and disadvantages of each method are summarized.2) the method of variable coefficient regression analysis is used to model the deformation analysis.Based on the deep analysis of variable coefficient regression algorithm, the local linear estimation method is used to fit the coefficients in variable coefficient regression.Simulation and dam deformation modeling experiments show that the coefficients in the variable coefficient model can reflect the response of the dam structure to the external factors, and the prediction accuracy of the model is obviously better than that of the ordinary linear regression model.It shows that the variable coefficient regression model is a kind of dynamic model, which is suitable for deformation analysis.3) in traditional dam deformation analysis modeling, single point model is often used.That is to say, the model can only model and analyze a single measuring point, neglecting the correlation between the measured points, which is not conducive to judging the overall performance state of the dam.In this paper, a spatio-temporal variable coefficient regression method based on PCA (principal component analysis) is proposed, and a dam deformation model with time-space variable coefficient is established by using this method.Through the modeling experiment of deformation monitoring data on a stretch line on the Wuqiangxi dam, it can be seen that the model can accurately obtain the deformation displacement at any position and at any time on the dam.Compared with the single point model and the static space-time deformation model, the prediction accuracy is higher.There are 24 figures, 3 tables and 60 references.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU196.1;TV698.11

【参考文献】