Hybrid Uncertainty Propagation Algorithm Based On Polynomial Chaos Expansion

In recent years,uncertainty theory has been constantly developed and improved,and various approaches for uncertainty representation and propagation have been proposed.Uncertainty is a broad term and involves measurement errors,natural variability,fuzziness and lack of knowledge.Multiple types of uncertainty often coexist in many practical problems.But the study of hybrid uncertainty is still in its infancy and many key issues remain to be solved.Therefore,it is of great academic significance and application value to study hybrid uncertainty and its propagation algorithm.In this thesis,we mainly study the hybrid uncertainty with aleatory uncertainty and epistemic uncertainty propagation algorithm.Firstly,the hybrid uncertainty system model is established which contains fuzzy variables with known possibility distribution and the random variables with known probability box form.The above system model is used as a research object to design an effective and fast hybrid uncertainty propagation algorithm.The main research contents are as follows:(1)The principle of polynomial chaos expansion is introduced and two key problems need to be considered: calculating the multidimensional Legendre polynomials and solving the coefficients of polynomial chaos expansion.This uncertainty analysis method is evaluated by calculating the statistical characteristics of the output response of the system.Then the polynomial chaos expansion is transformed into Bernstein form by using the Garloff method,and the output value is obtained according to the nature of Bernstein polynomials.(2)The mixed uncertainty model is set up based on the basic theory of fuzzy variables,fuzzy uncertainty processing method,the concept of probability boxes and uncertainty analysis.Equal probability transform is carried out for separate the distribution parameters from the distribution functions of the random variables.For aleatory uncertainty,Latin hypercube sampling is used for uncertainty simulation of random variables.The fuzzy uncertainty is reduced to the interval uncertainty by the ?-cut set.Then the polynomial chaos expansion method is used for interval uncertainty propagation.(3)As an application,the proposed method is utilitied to analyse the hybrid uncertainty of water level in the risk model of flood dam design.An analytical approximation system model is studied for calculating the maximum water level of a river.The hybrid uncertainty propagation algorithm is performed to this model according to second order and third order polynomial chaos expansions.The accuracy and validity of the new algorithm are verified by comparing with the traditional uncertainty analysis method.