关于GIS不确定性传播问题的若干研究
发布时间：2018-07-18 16:22
【摘要】：空间数据的不确定性传播是地理信息系统（GIS）中的关键问题之一，也是一个颇受关注的研究热点。我们知道，不确定性一般可用误差来描述，而误差对空间数据而言是不可避免的，且随着空间数据的运算与操作过程，误差会不断传播形成累积，最终对决策分析结果可能产生重要影响。目前，关于这个问题的研究，虽然已有不少成果，但大都基于线性传播过程的理论，对非线性情形考虑较少，而非线性过程又是大量存在的，因此，从理论上深入研究非线性传播过程的误差传播方法具有重要的学术意义和应用价值。 为提高不确定性传播过程的理论精度，本文从提高传播函数泰勒展式的逼近程度入手，着重研究基于高阶泰勒展式的误差传播方法，并与Monte Carlo随机模拟法和矩设计法比较分析，通过模拟实验验证方法的有效性，并应用于地理实际问题的不确定性评价问题。本文的主要目的和研究内容如下： (1)研究现有误差传播的基本理论与方法，通过模拟实验对这些方法进行归纳、比较和总结，以便对实际应用提供所需的方法指导； (2)基于误差传播函数的高阶泰勒展式法，针对GIS中叠加操作提出线-线叠加、线-面叠加和面-面叠加中的不确定性传播方法，并进行模拟实验和实例分析，与现有MonteCarlo法和矩设计法进行比较，验证所提方法的高精度和各种方法的优劣性； (3)对多输出变量模型提出相应的基于高阶泰勒展式的误差传播方法，扩展现有的单变量模型误差传播方法，有效利用地理变量空间相关的特点，，为GIS多边形叠加操作中不确定性传播研究提供更加严格的理论支持，并通过模拟实验验证所提方法的有效性。 (4)对于矩阵形式的泰勒展式法公式，针对GIS中面积计算导出相应的计算公式，通过模拟实验验证公式的有效性与实用性。
[Abstract]:Uncertainty propagation of spatial data is one of the key problems in geographic information system (GIS), and it is also a hot research topic. We know that uncertainty can generally be described by errors, which are inevitable to spatial data, and they are propagated and accumulated as the spatial data is calculated and operated. Finally, it may have an important influence on the results of decision analysis. At present, although there have been a lot of achievements in the study of this problem, most of them are based on the theory of linear propagation process. It is of great academic significance and practical value to study the error propagation method of nonlinear propagation process in theory. In order to improve the theoretical accuracy of the uncertain propagation process, this paper begins with the improvement of the approximation degree of the Taylor expansion of the propagation function, focuses on the error propagation method based on the higher-order Taylor expansion, and compares it with the Monte Carlo stochastic simulation method and the moment design method. The effectiveness of the method is verified by simulation experiments and applied to the uncertainty evaluation of geographical practical problems. The main purposes and contents of this paper are as follows: (1) the basic theories and methods of error propagation are studied, and these methods are summarized, compared and summarized through simulation experiments, in order to provide the necessary guidance for practical application. (2) based on the higher-order Taylor expansion method of error propagation function, the uncertain propagation methods of line-line superposition, line-surface superposition and surface-surface superposition in GIS are proposed, and the simulation experiments and examples are carried out. Compared with the existing Monte Carlo method and moment design method, the high accuracy and superiority of the methods are verified. (3) the corresponding error propagation method based on higher-order Taylor expansion is proposed for the multi-output variable model. By extending the existing single variable model error propagation methods and effectively utilizing the spatial characteristics of geographical variables, this paper provides a more rigorous theoretical support for the research of uncertainty propagation in GIS polygon superposition operation. The effectiveness of the proposed method is verified by simulation experiments. (4) for the Taylor expansion formula in matrix form, the corresponding calculation formula is derived for the area calculation in GIS, and the validity and practicability of the formula are verified by simulation experiments.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P208
本文编号：2132473
[Abstract]:Uncertainty propagation of spatial data is one of the key problems in geographic information system (GIS), and it is also a hot research topic. We know that uncertainty can generally be described by errors, which are inevitable to spatial data, and they are propagated and accumulated as the spatial data is calculated and operated. Finally, it may have an important influence on the results of decision analysis. At present, although there have been a lot of achievements in the study of this problem, most of them are based on the theory of linear propagation process. It is of great academic significance and practical value to study the error propagation method of nonlinear propagation process in theory. In order to improve the theoretical accuracy of the uncertain propagation process, this paper begins with the improvement of the approximation degree of the Taylor expansion of the propagation function, focuses on the error propagation method based on the higher-order Taylor expansion, and compares it with the Monte Carlo stochastic simulation method and the moment design method. The effectiveness of the method is verified by simulation experiments and applied to the uncertainty evaluation of geographical practical problems. The main purposes and contents of this paper are as follows: (1) the basic theories and methods of error propagation are studied, and these methods are summarized, compared and summarized through simulation experiments, in order to provide the necessary guidance for practical application. (2) based on the higher-order Taylor expansion method of error propagation function, the uncertain propagation methods of line-line superposition, line-surface superposition and surface-surface superposition in GIS are proposed, and the simulation experiments and examples are carried out. Compared with the existing Monte Carlo method and moment design method, the high accuracy and superiority of the methods are verified. (3) the corresponding error propagation method based on higher-order Taylor expansion is proposed for the multi-output variable model. By extending the existing single variable model error propagation methods and effectively utilizing the spatial characteristics of geographical variables, this paper provides a more rigorous theoretical support for the research of uncertainty propagation in GIS polygon superposition operation. The effectiveness of the proposed method is verified by simulation experiments. (4) for the Taylor expansion formula in matrix form, the corresponding calculation formula is derived for the area calculation in GIS, and the validity and practicability of the formula are verified by simulation experiments.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P208
【引证文献】
相关硕士学位论文 前1条
1 孟子健;区间不确定性传播的快速算法[D];长安大学;2014年
本文编号：2132473
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