Using polynomial chaos expansion for uncertainty and sensitivity analysis of bridge structures

Abstract

The quantification of the uncertainty effect of random system parameters, such as the loading conditions, material and geometric properties, on the system output response has gained significant attention in recent years. One of the well-known methods is the first-order second-moment (FOSM) method, which can be used to determine the mean value and variance of the system output. However, this method needs to derive the formulas for calculating the local sensitivity and it can only be used for systems with low-level uncertainties. Polynomial Chaos (PC) expansion is a new non-sampling-based method to evaluate the uncertainty evolution and quantification of a dynamical system. In this paper, PC expansion is used to represent the stochastic system output responses of civil bridge structures, which could be the natural frequencies, linear and nonlinear dynamic responses. The PC coefficients are obtained from the non-intrusive regression based method, and the statistical characteristic can be evaluated from these coefficients. The results from the proposed approach are compared with those calculated with commonly used methods, such as Monte Carlo Simulation (MCS) and FOSM. The accuracy and efficiency of the presented PC based method for uncertainty quantification and global sensitivity analysis are investigated. Global sensitivity analysis is performed to quantify the effect of uncertainty in each random system parameter on the variance of the stochastic system output response, which can be obtained directly from the PC coefficients. The results demonstrate that PC expansion can be a powerful and efficient tool for uncertainty quantification and sensitivity analysis in linear and nonlinear structure analysis.