2011年高教社杯全国大学生数学建模竞赛优秀论文 - 图文

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is one of the practical form of values. The so-called values refers to the objective things are of no value and the value of fundamental perspective. Different values, people's behaviour, attitudes, ways are different. People-oriented focus on human value and reality, we need the broadest masses as values. Adhere to people-oriented values, is to make the economy more development, improve democracy, cultural prosperity, and live a happier; is deeply concerned that human development and human values, development of social and human development of rational unified, insisted in the material civilization, political civilization and spiritual civilization in the overall advancement of Socialist civilization to a higher level. Also want to see that person's value is not only meet your needs, also is to meet the needs of others and the community. Adhere to people-oriented, to strongly advocate every community member, serve others, beneficial to the community of people. The so-called Outlook, attitude is on the record, including who, how to create a record of achievements, how to evaluate performance, and so on. What values, what kind of Outlook. Adhere to people-oriented Outlook, is on the premise of respecting the interests and power of people, creating a popular, warm hearts, steady heart performance, creating \one officer, the benefit of\s, and overall construction of well-off society and promoting the all-round development of people's performance. Achievement evaluation in both economic accomplishments, take another look at the effectiveness of social progress; changes in both urban and rural change; both hard environment to strengthen and take another look at the soft environment improvement momentum of development at present, depending on the potential for sustainable development. Leave people to talk about \hless and leave people to talk about \ook\4. people responded to the starting point of the question, and replied to questions point. Man is the sum of social relationships. We cannot leave the chichuanyongdu, housing, tourism and entertainment, entertaining, and even certain political, economic, cultural and social environment, and so on. Due to human needs, all walks of life will come into being. People create for their survival, and continue enjoying the results of the construction. Colorful in the transformation of the people of the world, community vitality in the creation of man. Therefore, any work we do, the starting point is human, what are people. Us speed up development, the core of which is to meet the needs of people, including survival needs, emotional needs and self-actualization needs. It should be noted that people are not machines, not the slave of an object, not to be controlled. People have their own personality, has its own personality, has its own dignity. Person in need of care, you need to understand, need to meet. It is said that in the \society, people plant\society, man is an animal\on society, return 2011高教社杯全国大学生数学建模竞赛

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is one of the practical form of values. The so-called values refers to the objective things are of no value and the value of fundamental perspective. Different values, people's behaviour, attitudes, ways are different. People-oriented focus on human value and reality, we need the broadest masses as values. Adhere to people-oriented values, is to make the economy more development, improve democracy, cultural prosperity, and live a happier; is deeply concerned that human development and human values, development of social and human development of rational unified, insisted in the material civilization, political civilization and spiritual civilization in the overall advancement of Socialist civilization to a higher level. Also want to see that person's value is not only meet your needs, also is to meet the needs of others and the community. Adhere to people-oriented, to strongly advocate every community member, serve others, beneficial to the community of people. The so-called Outlook, attitude is on the record, including who, how to create a record of achievements, how to evaluate performance, and so on. What values, what kind of Outlook. Adhere to people-oriented Outlook, is on the premise of respecting the interests and power of people, creating a popular, warm hearts, steady heart performance, creating \one officer, the benefit of\s, and overall construction of well-off society and promoting the all-round development of people's performance. Achievement evaluation in both economic accomplishments, take another look at the effectiveness of social progress; changes in both urban and rural change; both hard environment to strengthen and take another look at the soft environment improvement momentum of development at present, depending on the potential for sustainable development. Leave people to talk about \hless and leave people to talk about \ook\4. people responded to the starting point of the question, and replied to questions point. Man is the sum of social relationships. We cannot leave the chichuanyongdu, housing, tourism and entertainment, entertaining, and even certain political, economic, cultural and social environment, and so on. Due to human needs, all walks of life will come into being. People create for their survival, and continue enjoying the results of the construction. Colorful in the transformation of the people of the world, community vitality in the creation of man. Therefore, any work we do, the starting point is human, what are people. Us speed up development, the core of which is to meet the needs of people, including survival needs, emotional needs and self-actualization needs. It should be noted that people are not machines, not the slave of an object, not to be controlled. People have their own personality, has its own personality, has its own dignity. Person in need of care, you need to understand, need to meet. It is said that in the \ety, people plant\ety, man ian animal\on society, return 2011高教社杯全国大学生数学建模竞赛

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Now, we are in a new historical stage of all-round construction of a well-off society. In perform duties, and carried out work of process in the, we to put people as a guide principles, and a test standard, efforts from masses most hope do of things do up, from masses most care of hot problem grabbed, from masses most not satisfaction of place modified up, not make nominal of formalism, not do grandstanding of cosmetic, to seeking of style, help masses share, is people benefit. (C) the investee people is not only an idea, it is a job requirement. Philosophy through to the people-oriented thought in the work of the Office, must be clear work objectives. Party Office in the city this year remains: Advanced civil strife, local brand. The County (City) Party Committee offices and units directly under the Office to hold high the banner of first to excellence, people-oriented requirements, strengthen the construction and management of the Office towards the work \political participation based on conspiracy to adhere to people-oriented, will be around to promotcoordinationDevelopment events, great searchings. The 16 session of the party's scientific Outlook on development, is the new Central collective leadership to the development of connotation, development essentials, further deepen the essence of development and innovation, is our party's ruling idea a leap. At present, establishing and implementing the scientific concept of development has become the party's important work. As the Office of party Committee, working party should service center, initiative to claim leadership of the decision, the current focus is to focus on promoting comprehensive, coordinated and sustainable development with more suggestions, do more research, summarized the typical. One is drafted to raise the level of your presentation. Your presentation is the main Office of \sic carrier staff service, is important to measure service levels. The quality of your presentation, mainly depends on how much we drafted a document recognized by the leadership, how many are listening to the people in favour of the report, how many paid dividends in the practical work. Improve presentation drafting level, requirements we accurate grasp led intent, General led care of work are to as understand, General led consider of problem are to in-depth thinking; requirements we highlight place features, put superior approach policy and local actual combined up, put presentation of theme thrust and masses of by thought by wants to combined up; requirements we seeks to streamlined clear, with simple of language expression deep of thought, with short of length hosted rich of connotation. Second, the survey results more. Investigation of the base, the road to success is something, is our for the Party Committee's policy decision a good idea, an important part of a good staff. This year, to focus around industrial XING city, and farmers increase, and and manpower development, and seeking, major problem and foster advantage industry, and adjustment agricultural structure, and carriedis one of the practical form of values. The so-called values refers to the objective things are of no value and the value of fundamental perspective. Different values, people's behaviour, attitudes, ways are different. People-oriented focus on human value and reality, we need the broadest masses as values. Adhere to people-oriented values, is to make the economy more development, improve democracy, cultural prosperity, and live a happier; is deeply concerned that human development and human values, development of social and human development of rational unified, insisted in the material civilization, political civilization and spiritual civilization in the overall advancement of Socialist civilization to a higher level. Also want to see that person's value is not only meet your needs, also is to meet the needs of others and the community. Adhere to people-oriented, to strongly advocate every community member, serve others, beneficial to the community of people. The so-called Outlook, attitude is on the record, including who, how to create a record of achievements, how to evaluate performance, and so on. What values, what kind of Outlook. Adhere to people-oriented Outlook, is on the premise of respecting the interests and power of people, creating a popular, warm hearts, steady heart performance, creating \one officer, the benefit of\s, and overall construction of well-off society and promoting the all-round development of people's performance. Achievement evaluation in both economic accomplishments, take another look at the effectiveness of social progress; changes in both urban and rural change; both hard environment to strengthen and take another look at the soft environment improvement momentum of development at present, depending on the potential for sustainable development. Leave people to talk about \hless and leave people to talk about \ook\4. people responded to the starting point of the question, and replied to questions point. Man is the sum of social relationships. We cannot leave the chichuanyongdu, housing, tourism and entertainment, entertaining, and even certain political, economic, cultural and social environment, and so on. Due to human needs, all walks of life will come into being. People create for their survival, and continue enjoying the results of the construction. Colorful in the transformation of the people of the world, community vitality in the creation of man. Therefore, any work we do, the starting point is human, what are people. Us speed up development, the core of which is to meet the needs of people, including survival needs, emotional needs and self-actualization needs. It should be noted that people are not machines, not the slave of an object, not to be controlled. People have their own personality, has its own personality, has its own dignity. Person in need of care, you need to understand, need to meet. It is said that in the \society, people plant\society, man is an animal\on society, return

城市表层土壤重金属污染分析

摘要

本文利用克里格插值法，多因子综合指数评价法，相关分析，因子分析，聚类分析，Grid data插值模型分别进行了空间分析，污染程度分析，污染原因的分析以及确定污染源的位置。

针对问题一，本文利用Sufer软件，通过克里格插值法画出8种重金属元素的等值图，并利用单污染指数评价法和多因子综合指数评价法对分别对同功能区不同采集点和不同功能区重金属综合污染程度进行分析，得出1. 不同的人类活动造成城市土壤中不同类型的重金属积累2. 工业区，交通区，生活区，公园绿地区属于重污染区，山区属于轻度污染区3.不同功能区污染指数的排序为：工业区>交通区>生活区>公园绿地区>山区。

针对问题二，本文首先对8种重金属元素进行相关分析，得出Cd与Pb，Cr与Cu，Cr与Ni，Cu与Pb之间相关性显著，可能具有同源关系或复合关系。然后对8种重金属元素进行因子分析，得出Cr Ni Cu在因子1有较高的载荷，As Cd Pb Zn在因子2上有较高的载荷，可能主要来自类似的一个源，Hg在因子3上远远高于在其他元素在该因子的载荷，可能由单一污染源产生。最后通过对两个模型综合分析，得出Cr Cu Ni在两种分析方法中都具有很强的关联性，分析污染产生的原因可能与电镀，合金制造等重工业有关，As Cd Pb Zn Cu在两种分析方法中呈现出一些差异，因此其污染来源情况比较复杂，可能与尾气排放，人类活动丢弃物以及农用废物有关，Hg在两种分析方法中均表现出独立性，因此伴随Hg产生的其他重金属元素则相对较少，主要来源可能是科学仪器制造，医学仪器制造工厂等对Hg有特定需求的工厂。

针对问题三，本文通过对污染传播特征的研究，发现污染源的重金属浓度最高，并向周围呈递减趋势扩散。本文利用聚类分析找出8种重金属元素浓度的所有极大异常点，通过其传播特性可以预见这些极大异常点距离污染源是非常接近，从而对污染源的确定提供依据。然后我们又采用Grid data插值模型，运用局部搜索方法，成功地搜索出了每种重金属元素的污染源位置并与极大异常点坐标接近，证明了该方法的可行性。最后统一各元素污染源坐标得出综合污染源有8处，单一污染源有9处，并用逐步多元回归模型对部分点进行了检验，验证了解的准确性。

针对问题四，本文采用的Grid data插值法优点在于能够快速定位污染源，但是由于在搜索过程中考虑到计算量巨大，所以搜索步长为100，由此产生的误差较大。为更好地研究城市地质环境的演变模式，还应考虑土壤类型、土地利用、道路等因素对重金属的影响。

关键词：克里格插值；综合指数评价；相关分析；因子分析；GridData插值

dividends in the practical work. Improve presentation drafting level, requirements we accurate grasp led intent, General led care of work are to as understand, General led consider of problem are to in-depth thinking; requirements we highlight place features, put superior approach policy and local actual combined up, put presentation of theme thrust and masses of by thought by wants to combined up; requirements we seeks to streamlined clear, with simple of language expression deep of thought, with short of length hosted rich of connotation. Second, the survey results more. Investigation of the base, the road to success is something, is our for the Party Committee's policy decision a good idea, an important part of a good staff. This year, to focus around industrial XING city, and farmers increase, and and manpower development, and seeking, major problem and foster advantage industry, and adjustment agricultural structure, and carried0

is one of the practical form of values. The so-called values refers to the objective things are of no value and the value of fundamental perspective. Different values, people's behaviour, attitudes, ways are different. People-oriented focus on human value and reality, we need the broadest masses as values. Adhere to people-oriented values, is to make the economy more development, improve democracy, cultural prosperity, and live a happier; is deeply concerned that human development and human values, development of social and human development of rational unified, insisted in the material civilization, political civilization and spiritual civilization in the overall advancement of Socialist civilization to a higher level. Also want to see that person's value is not only meet your needs, also is to meet the needs of others and the community. Adhere to people-oriented, to strongly advocate every community member, serve others, beneficial to the community of people. The so-called Outlook, attitude is on the record, including who, how to create a record of achievements, how to evaluate performance, and so on. What values, what kind of Outlook. Adhere to people-oriented Outlook, is on the premise of respecting the interests and power of people, creating a popular, warm hearts, steady heart performance, creating \one officer, the benefit of\s, and overall construction of well-off society and promoting the all-round development of people's performance. Achievement evaluation in both economic accomplishments, take another look at the effectiveness of social progress; changes in both urban and rural change; both hard environment to strengthen and take another look at the soft environment improvement momentum of development at present, depending on the potential for sustainable development. Leave people to talk about \hless and leave people to talk about \ook\4. people responded to the starting point of the question, and replied to questions point. Man is the sum of social relationships. We cannot leave the chichuanyongdu, housing, tourism and entertainment, entertaining, and even certain political, economic, cultural and social environment, and so on. Due to human needs, all walks of life will come into being. People create for their survival, and continue enjoying the results of the construction. Colorful in the transformation of the people of the world, community vitality in the creation of man. Therefore, any work we do, the starting point is human, what are people. Us speed up development, the core of which is to meet the needs of people, including survival needs, emotional needs and self-actualization needs. It should be noted that people are not machines, not the slave of an object, not to be controlled. People have their own personality, has its own personality, has its own dignity. Person in need of care, you need to understand, need to meet. It is said that in the \ety, people plant\ety, man ian animal\on society, return 目录

一、问题的重述与分析 ............................................... 2 二、模型的假设 ..................................................... 3 三、符号说明 ....................................................... 4 四、模型的建立与求解 ............................................... 4

4.1重金属元素的空间分布及污染程度 .............................. 4

4.1.1 重金属元素的空间分布 .................................. 4 4.1.2 不同区域重金属的污染程度的分析 ........................ 5 4.2 重金属污染的原因分析 ....................................... 7

4.2.1 Pearson相关系数 ...................................... 7 4.2.2 相关系数的求解与分析 .................................. 8 4.2.3 因子分析 .............................................. 8 4.2.4 因子分析的求解与结论 .................................. 9 4.3 污染源位置的确定 .......................................... 10

4.3.1 聚类分析 ............................................. 10 4.3.2 Grid data插值模型 ................................... 11 4.3.3 插值模型的建立与求解 ................................. 11 4.4 模型的检验 ................................................ 13 4.5 模型优缺点分析及讨论 ...................................... 14 五、结论 .......................................................... 14 六、参考文献 ...................................................... 15

一、问题的重述与分析

1.问题的重述

随着城市经济的快速发展和城市人口的不断增加，人类活动对城市环境质量的影响日显突出。对城市土壤地质环境异常的查证，以及如何应用查证获得的海量数据资料开展城市环境质量评价，研究人类活动影响下城市地质环境的演变模式，日益成为人们关注的焦点。

按照功能划分，城区一般可分为生活区、工业区、山区、主干道路区及公园绿地区等，分别记为1类区、2类区、……、5类区，不同的区域环境受人类活动影响的程度不同。

现对某城市城区土壤地质环境进行调查。为此，将所考察的城区划分为间距1公里左右的网格子区域，按照每平方公里1个采样点对表层土（0~10 厘米深度）进行取样、编号，并用GPS记录采样点的位置。应用专门仪器测试分析，获得了每个样本所含的多种化学元素的浓度数据。另一方面，按照2公里的间距在那些远离人群及工业活动的自然区取样，将其作为该城区表层土壤中元素的背景值。

附件1列出了采样点的位置、海拔高度及其所属功能区等信息，附件2列出了8种主要重金属元素在采样点处的浓度，附件3列出了8种主要重金属元素的背景值。

现要求你们通过数学建模来完成以下任务：

(1) 给出8种主要重金属元素在该城区的空间分布，并分析该城区内不同区域重金属的污染程度。

(2) 通过数据分析，说明重金属污染的主要原因。

(3) 分析重金属污染物的传播特征，由此建立模型，确定污染源的位置。 (4) 分析你所建立模型的优缺点，为更好地研究城市地质环境的演变模式，还应收集什么信息？有了这些信息，如何建立模型解决问题？

2.问题的分析

本文将所有问题细化为一下几个步骤：

(1)利用软件画出8种重金属污染元素的空间分布图； (2)建立综合评价指标对污染程度进行评价；

(3)对数据进行统计分析，研究各元素之间的相关性，从而分析污染原因； (4)运用插值法解出污染源坐标，并用逐步回归进行检验；

二、模型的假设

1.提供的数据真实有效；

2.8种重金属元素能够全面反映某一区域污染程度，不受其他元素影响； 3.插值方法所产生的模型误差在可承受范围之内。