Efficient method for updating the failure probability of a deteriorating structure without repeated reliability analyses

Bayesian updating is widely applied to evaluate the failure probability of a deteriorating structure; however, it requires considerable computational effort. This is because reliability analysis based on posterior distributions must be repeated each time the inspection data are updated. To overcome this problem, this study proposes an efficient method to directly update the failure probability of a deteriorating structure. In the proposed method, an updating factor is proposed to quantify the updated information by separating the components to be updated from the reliability analysis with the direct prior distribution. Thus, both the need to repeat the structural reliability analysis and reacquire posterior distributions/samples each time the inspection data are updated can be avoided. The point-estimate method combined with the bivariate dimension-reduction method is introduced to directly update the failure probability, from which only the updating factor at the fixed estimation points, that is, the components that have no relationship with the structural analysis, needs to be updated, thus considerably reducing the computation time. The efficacy and accuracy of the proposed method were verified through four numerical examples, wherein commonly used methods were employed for comparison.