Uncertainty Propagation Analysis Of Mechanical Structures Considering The Correlation

Uncertainties of structure sizes, material properties and loads widely exist in mechanical structures. These uncertainties are the most important factors in the mechanical structure analysis. The propagation of these uncertainties can lead to the uncertainty of mechanical structures’ performance. Therefore, it is an inevitable procedure in mechanical structure design to develop an efficient uncertainty propagation analysis method and obtain accurate evaluation of uncertainty factors.The current uncertainty propagation analysis methods typically assume that all the random variables are independent to each other. However, under most circumstances,there are correlations among random variables, and these correlations probably have significant effect on the uncertainty propagation analysis results. Theoretically,Rosenblatt transformation is a precise correlation processing method. However,Rosenblatt transformation is based on the accurate joint probability distribution functions(PDFs), whereas in real application, because of the existence of many constraints only part of probability information can be obtained such as marginal distribution and correlation coefficient, with which the accurate joint PDFs are hardly constructed. Thus, Rosenblatt transformation can’t be utilized in real application easily. Therefore, a new method which is capable of overcoming aforementioned shortcomings is needed and will have significant influence on uncertainty propagation analysis and reliability design.Based on the current uncertainty propagation analysis methods, this thesis conducts a series of studies on the uncertainty propagation considering the complex correlation among random variables by introducing in a new mathematical tool in uncertainty analysis area named Copula function. The main contributions of this thesis are as follows:(1) A bivariate Copula based structural uncertainty propagation method is proposed to deal with uncertainty propagation problem considering the complex nonlinear correlation among random variables. The correlations among random variables are expressed by an optimal bivariate Copula, which is identified by AIC criterion. The joint PDFs are constructed by optimal Copula function and the first four order moments are calculated with direct integration. This method provides a general solution to the uncertainty propagation problem considering complex correlationamong random variables.(2) A Vine Copula based structural uncertainty propagation analysis method is proposed, which is an effective approach to conduct an uncertainty propagation analysis on complex multi-dimensional correlation problems. A joint PDF among multi-dimensional random variables is established using a Vine Copula function,based on which an uncertainty propagation analysis model is constructed. Two solution algorithms are proposed to solve this uncertainty propagation analysis model:Monte Carlo Simulation method based on Vine Copula(VC-MCS) and Dimension Reduction Integration method based on Vine Copula(VC-DRI). Although VC-MCS has low efficiency, it can provide a generalized solution approach and provide an important reference solution for the development of other high-efficiency algorithms.VC-DRI has high efficiency, and can be used to solve actual engineering problems.