一种同时优化背景值和初始条件的GM(1,1)建模方法  

A GM(1,1) Modeling Method of Optimization Integrated Background Values with Initial Conditions

作　　者：邹进贵[1,2] 聂海滨[1] 邱国庆 ZOU J ingui;NIE Haibin;QIU Guoqing(School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;Key Laboratory of Precise Engineering and Industry Surveying, National Administration of Surveying, Mapping and Geoinformation Wuhan 430079, China)

机构地区：[1]武汉大学测绘学院,湖北武汉430079 [2]精密工程与工业测量国家测绘地理信息局重点实验室,湖北武汉430079

出　　处：《测绘地理信息》2018年第2期79-82,共4页Journal of Geomatics

基　　金：国家自然科学基金资助项目(41074025)

摘　　要：针对传统灰色GM（1,1）模型中由背景值构造和初值选取不准确引起的固有模型误差问题,基于GM（1,1）建模机理和累加生成序列非齐次指数规律的特性,结合积分几何意义和函数逼近的思想,提出了一种同时优化背景值和初始条件的GM（1,1）建模方法。该方法通过构建区间动态序列模型,利用复化Simpson求积公式重构背景值,以一次累加数列各分量的加权平均值作为模型的初始条件,并根据误差平方和最小原则确定初始条件的时间参数。通过对深基坑围护结构变形监测数据进行分析,表明所提优化模型具有较高的建模精度。Based on GM（1,1）modeling mechanism and accumulated generating sequence inhomogeneous exponential characteristics,combined with integral geometry meaning and function approximation thinking,a GM（1,1）modeling simultaneous optimization of background values and initial conditions has been proposed.By constructing dynamic series models in range,this method combines compound Simpson formula to reconstruct the background values,takes a weighted average of the cumulative number of columns as the initial condition of each component of the model and determines the initial conditions time parameters based on the rule of minimum squared error.Through deformation monitoring data of deep excavation retaining structure,experimental results show that the optimization model has higher modeling accuracy.

关 键 词：GM(1 1) 动态序列模型 复化Simpson公式 初始条件 时间参数 

分 类 号：P258[天文地球—测绘科学与技术]