数值积分方法改进的灰色模型对建筑沉降预测的精度分析  

Accuracy Analysis of Building Settlement Prediction Based on Grey Model Improved by Numerical Integration Method

作　　者：陈富胜 CHEN Fusheng(Yangjiang Surveying and Mapping Geographic Information Center,Yangjiang Guangdong 529500,China)

机构地区：[1]阳江市测绘地理信息中心,广东阳江529500

出　　处：《北京测绘》2021年第6期786-789,共4页Beijing Surveying and Mapping

摘　　要：灰色模型以其对原始数据需求量较少的优势,成为建筑沉降预测中常用的数学模型。灰色模型的灰微分方程实际上是白化方程的梯形积分形式,由于梯形公式的代替精度有限,导致灰色模型预测精度不足。本文提出使用牛顿柯达斯系数为基础的数值积分公式,将牛顿柯达斯系数中n=1~4的数值积分公式用于灰色模型背景值优化,讨论精度提升与计算效率兼顾的背景值优化方案。结果表明,n=4时的牛顿柯达斯公式预测效果较好,相对误差为6.15%,更适合用于实际沉降预测。Because of its less demand for original data,grey model has become a commonly used mathematical model in building settlement prediction.The differential equation of grey model is actually the trapezoidal integral form of albino equation.Due to the limited replacement precision of trapezoidal formula,the prediction accuracy of grey model is insufficient.In this paper,the numerical integration formula based on Newton Kodak coefficient was proposed,and the numerical integral formula with n=1 to 4 in Newton Kodak coefficient wasapplied to optimize the background value of grey model,and the accuracy improvement and calculation werediscussed.with the background value optimization scheme with consideration of efficiency.The results showed that the prediction effect of Newton Kodak formula asbetter when n=4,and the relative error was 6.15%,which was more suitable for the actual settlement prediction.

关 键 词：数值积分 灰色模型 沉降预测 牛顿-柯达斯系数 

分 类 号：P258[天文地球—测绘科学与技术]