古塔的变形情况及趋势研究

依据2013年全国大学生数学建模竞赛C题所给的古塔各层中观测点坐标的信息,运用基于最小二乘法的椭圆拟合算法结合MATLAB软件,列表给出各次测量的古塔各层中心坐标。利用古塔各层中心坐标,并将问题进行转化,采用初等数学模型研究古塔的倾斜程度、弯曲程度、扭曲程度,最后建立灰色预测模型GM(1,1),对上述引起古塔变形的三个因素进行拟合、预测,分析古塔的变形趋势。

Study on Deformation and Tendency of Old Pagoda

According to coordinates of points observed for each layer of ancient pagoda in problem C of Chinese Undergraduate Mathematical Contest in Modeling（2013）, this article lists the measured coordinates of the center of each layer in old pagoda by using ellipse fitting method which based on least-square principle and MATLAB. The problem is transformed by using the coordinates of the center of old pagoda in each layer, when the tilting degree, bending degree, twisting degree of old pagoda can be studied through primary mathematics model. Finally, the paper establishes the gray prediction model GM （1,1）, summarizes and predicts the three factors which caused the deformation of old pagoda, and analyzes its trend.