Time-Dependent Uncertainty Analysis of Structures Based on Copula Functions

Abstract

Structural systems (e.g., building systems, bridge systems) are large and complex systems including many uncertain factors. Therefore, for structural reliability analysis, the effects of uncertain factors on the structural systems must be taken into account in order to make proper reliability analysis. The uncertainty in structural reliability analysis has caused more attention by the planners and designers; however, how to make reasonable uncertainty model is rarely studied in the analysis of structural reliability. This paper firstly describes the copula theory - especially the Gaussian copula theory - then, based on the time-dependent parameters of the Gaussian copula, the dynamic measure of time-variant correlation coefficients, with respect to Gaussian copula, is treated as a time series, and then a Bayesian dynamic linear model was introduced. Based on the time-variant monitored data of the structures, the correlation coefficients of the two monitored variables are solved and predicted. What is more, a framework for analyzing the time-dependent uncertainty parameters from Gaussian copula involved in the processes of structural reliability analysis is proposed. Finally, based on the predicted time-dependent uncertainty parameters, the first order reliability method (FORM) is adopted to solve the time-variant reliability indices, which are compared with the reliability indices solved with first-order, second-moment method (FOSM) without considering the correlation coefficients of two monitored variables. Finally, a numerical example is provided to illustrate the feasibility and accuracy of the solved reliability indices.