Fast Algorithms For Interval Uncertainty Propagation

Interval uncertainty propagation problem involves multiple disciplines, from the floodforecasting, engineering structure safety monitoring to the risk analysis of investment project,is a popular research topic. It is well known that uncertainty can be described by error, whichis inevitable for measuring. It should be noted that error would be propagated andaccumulated along with the operations, lastly has an important effect on the results of decisionanalysis. At present, the research on error propagation has achieved great developments.However, most of them are based on the linear propagation theory, while the computationalefficiency problem is seldom considered. We know that in the interval uncertainty propagationproblems, computational efficiency can not be ignored, thus the deep study of methods ofinterval uncertainty propagation is theoretically of significant academic contributions andapplication values.In order to improve the calculation efficiency during the propagation of uncertainty, inthis paper, we start by the size of the uncertainty for input variables, present linear modeland monotonicity model for different situations, and focus on the study of fast algorithms withdifferent number of input variables based on different model. Finally, through the simulationexperiment to compare the different fast algorithms, and the validity of these methods ischecked. The main works of this thesis are as follows:(1) We study the basic knowledge, basic theory and basic propagation methods ofuncertainty propagation.(2) Under the premise of the uncertainty of the input variable of x is small, we presentthe fast propagation algorithms based on linear Taylor expansion, and then according tothe number of input variables x, respectively using numerical differential or Monte Carlomethod based on Cauchy distribution for fast computation of interval uncertainty.(3) Under the premise of the uncertainty of the input variable of x is not very small sothat the higher order of x should not be ignore any more, we present a fast propagationalgorithm based on monotonicity.(4) The experimental simulation is presented for different fast algorithms in differentconditions, and the validity and practicability of the models are verified.