New Approaches For Interval Uncertainty Propagation And Application In GIS

Uncertainty exists in all aspects of life.Two types of uncertainties are mainly considered in the literature: aleatory uncertainty and epistemic uncertainty.The theory and method of dealing with aleatory uncertainty have been well developed and mainly based on probability theory,while the research on epistemic uncertainty is still at a stage of development.What is studied more less is interval uncertainty which is a kind of epistemic uncertainty resulting from interval data.There are many sources of interval data and interval data almost presents in all of disciplines.Interval uncertainty analysis plays an important role in prediction,optimization,decision making,risk assessment,structural reliability analysis,system security,stability design and so on.Therefore,it is of great theoretical and practical value to deeply study the interval uncertainty and its propagation method.In this thesis,we mainly focuses on interval uncertainty and introduces three existing interval uncertainty theory.For the interval uncertainty problem of calculating the range of output,we then propose a fast propagation approach based on subinterval and sampling.And for the interval uncertainty problem of calculating the distribution function of output,we propose a Monte Carlo interval uncertainty propagation method based on kernel density estimation,generalized Latin hypercube sampling and cubic spline interpolation.Finally,the proposed method is applied to solve the problem of interval uncertainty in GIS.Our main work is as follows:1.We give a detailed report on three uncertainty propagation methods: Interval calculation,Taylor expansion method and Monte Carlo method,and propose a fast algorithm to calculate the range of output based on subinterval,sampling and Taylor expansion method.It is subinterval-sampling-uncertainty propagation algorithm.Then the proposed algorithm is applied to solve the issues of interval uncertainty in the famous “Sandia challenge problem” which is raised in the Sandia workshop.The obtained results are compared with the results of other methods in the literatures to verify the advantages of the new algorithm.2.A new method is presented to calculate the range and distribution of the output based on the interval sampling technique,nonparametric estimation methods-kernel density estimation and cubic spline interpolation of fitting curves.This method is called interval kernel density estimation-Monte Carlo propagation method.Then we conduct examples to discuss and summarize the accuracy and advantages of the method.3.The issues of interval uncertainty in GIS are investigated and discussed in detail.The subinterval-sampling-uncertainty propagation algorithm is applied in basic operations of GIS such as the length of line segment,polygon area and polygon overlay analysis.The advantages and disadvantages of different methods are compared.