基于分形插值的改进趋势面拟合法在地面沉降中的应用

摘要

According to the limited number and uneven distribution of monitoring points in regional land subsidence , generally , a surface fitting model is built by spatial interpolation to solve these problems . Based on the fractal interpolation , the thought of randomly selected iterated function is used to improve the traditional trend surface fitting method .After the improvement , the goodness coefficient of fitting is increased by 0.03, and up to 0.995, and the fitting results before and after improvement all meet the re-quirement of significance testing .The experimental results show that the fitting results by trend surface fit-ting method before and after improvement all meet the precision requirements of land subsidence monito -ring.But the fitting goodness is higher and the description for land subsidence changing is more ture after the improvement .The method can offer a more precise basis for subsidence disaster evaluation .%针对区域地面沉降监测点数量有限、分布不均的情况，一般采用空间插值的手段建立表面拟合模型来解决。基于分形插值，采用随机选择迭代函数的思想对传统的趋势面拟合法作出改进，改进后拟合优度系数提高0．03，达到0．995，且改进前后的拟合结果符合显著性检验的要求。实验结果表明：改进前后趋势面拟合法拟合结果满足地面沉降监测的精度要求，改进后方法的拟合优度更高，对现实地面沉降量变化的描绘更加真实，可为沉降灾害评价工作提供更准确的依据。