Reliability assessment of civil structures with incomplete probability distribution information

Abstract

The probability distribution of random variables is usually incomplete owing to a limited amount of data, making it a challenging problem for structural reliability assessments. This paper presents a novel reliability analysis method for civil structures with incomplete data. The probability distributions of the random variables were estimated using an improved Bayesian inference method. In the proposed inference method, the frequencies and mode shapes were selected as the observation data. The likelihood function is replaced by homogeneous chaos, and the computational efficiency of Bayesian inference is improved. The affine invariant ensemble algorithm was used to generate samplers for the posterior distribution. After estimating the probability distribution of the incomplete random variables, a reliability analysis was performed, and the failure probability of the structure was estimated. Numerical studies on a two-span, two-story reinforced concrete building and a five-span bridge are presented. Experimental studies were also performed on an eight-story steel frame structure. The results show that the probability distributions of random variables can be significantly updated using the proposed technique and modal properties. The proposed technique was more efficient than the Gibbs sampling method. The failure probabilities of the structures were estimated using the estimated probability distributions.