摘要
2011年"高教社杯"全国大学生数学建模竞赛A题"城市表层土壤重金属污染分析"提出了一个从稀疏的污染元素抽样数据估测污染源的问题。本文通过数学建模给出了一个可行的方法。首先,通过建立重金属载体的可压缩流体欧拉连续性方程,并结合问题实际,得到了简化的可压缩流体欧拉连续性方程,建立了沿特征线估测孤立污染源的数学模型;其次,利用稀疏的检测值建立了更切合实际的修正的Shepard插值,设计了沿流线估测可孤立区域污染源的算法;最后,基于所提出的模型和算法,应用赛题数据给出了重金属铜的3个孤立污染源。
The part A of CUMCM-2011 for college students,entitled 'The Analysis of Heavy Metals Pollution in Urban Topsoil',proposed a problem for estimating the pollution sources based on some sparse sampled data.This paper presents a feasible method for solving this problem by a mathematical model.We first present a condensable and continuous formula of heavy metals carrier.Combined with the actual problems,the formula is simplified,and the mathematical model for estimating the isolated pollution sources by the characteristic line is proposed.Then we use the amendment Shepard interpolation method to do the realistic interpolation based on the sparse data,and present a corresponding algorithm.At last we give three isolated pollution sources of Cu based on the given data.
出处
《数学建模及其应用》
2012年第1期57-61,共5页
Mathematical Modeling and Its Applications
基金
山东科技大学"群星计划"项目(qx0902089)
关键词
重金属污染
Shepard插值
特征线
孤立污染源
heavy metal pollution
Shepard interpolation
characteristic line
isolated pollution source
