Bayesian Updating of Time-Dependent Structural Reliability Using the Method of Moment

Bayesian updating of the reliability of deteriorating engineering structures based on inspection data has been attracting a lot of attention recently because it can provide more accurate estimates of the structural reliability as the number of inspection data increases. However, in the process of updating the reliability of deteriorating structures, it is not a trivial work to obtain the posterior distribution of the random variable of interest due to its multidimensional parameter integral space and complex integral function. This paper presents a new effective method for obtaining the explicit posterior distribution for the random variable of interest and evaluating time-variant reliability combined with all updated random variables. In the proposed method, the Smolyak-type quadrature formula is first applied to obtain the first three posterior moments of the uncertain parameters, and the three-parameter lognormal distribution is used to approximate their posterior probability distributions. Then, the two-layer Smolyak-type sparse grid is adopted to estimate the first three posterior moments of the random variable of interest, and its explicit posterior distribution can also be approximated by the three-parameter lognormal distribution. Finally, the time-variant reliability analysis considering Bayesian updating is conducted using all updated random variables. Numerical examples demonstrate that the proposed method requires less computational cost, but the results provided are almost the same as those of the Markov chain Monte Carlo simulation.