【摘要】：空間數(shù)據(jù)的不確定性傳播是地理信息系統(tǒng)（GIS）中的關(guān)鍵問題之一，也是一個頗受關(guān)注的研究熱點。我們知道，不確定性一般可用誤差來描述，而誤差對空間數(shù)據(jù)而言是不可避免的，且隨著空間數(shù)據(jù)的運算與操作過程，誤差會不斷傳播形成累積，最終對決策分析結(jié)果可能產(chǎn)生重要影響。目前，關(guān)于這個問題的研究，雖然已有不少成果，但大都基于線性傳播過程的理論，對非線性情形考慮較少，而非線性過程又是大量存在的，因此，從理論上深入研究非線性傳播過程的誤差傳播方法具有重要的學(xué)術(shù)意義和應(yīng)用價值。 為提高不確定性傳播過程的理論精度，本文從提高傳播函數(shù)泰勒展式的逼近程度入手，著重研究基于高階泰勒展式的誤差傳播方法，并與Monte Carlo隨機模擬法和矩設(shè)計法比較分析，通過模擬實驗驗證方法的有效性，并應(yīng)用于地理實際問題的不確定性評價問題。本文的主要目的和研究內(nèi)容如下： (1)研究現(xiàn)有誤差傳播的基本理論與方法，通過模擬實驗對這些方法進行歸納、比較和總結(jié)，以便對實際應(yīng)用提供所需的方法指導(dǎo)； (2)基于誤差傳播函數(shù)的高階泰勒展式法，針對GIS中疊加操作提出線-線疊加、線-面疊加和面-面疊加中的不確定性傳播方法，并進行模擬實驗和實例分析，與現(xiàn)有MonteCarlo法和矩設(shè)計法進行比較，驗證所提方法的高精度和各種方法的優(yōu)劣性； (3)對多輸出變量模型提出相應(yīng)的基于高階泰勒展式的誤差傳播方法，擴展現(xiàn)有的單變量模型誤差傳播方法，有效利用地理變量空間相關(guān)的特點，，為GIS多邊形疊加操作中不確定性傳播研究提供更加嚴(yán)格的理論支持，并通過模擬實驗驗證所提方法的有效性。 (4)對于矩陣形式的泰勒展式法公式，針對GIS中面積計算導(dǎo)出相應(yīng)的計算公式，通過模擬實驗驗證公式的有效性與實用性。
[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.
【學(xué)位授予單位】：長安大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：P208

【引證文獻】

相關(guān)碩士學(xué)位論文 前1條

1 孟子健;區(qū)間不確定性傳播的快速算法[D];長安大學(xué);2014年

本文編號：2132473