Efficient Algorithm of Real-Time Failure Probability Function Updating

To match the safety level of a structure in real time with the gradually collected observations, it is necessary to develop an efficient method for updating the failure probability function (FPF). Directly updating FPF requires a time-demanding double-loop framework, where repeated failure probability analysis is involved for the varied observations and distribution parameters. To address the issue, an efficient single-loop method is proposed to update FPF in real time. Firstly, the Bayesian approach is used to construct a single-loop framework, and it only requires one augment failure probability analysis to approximate the prior FPF. Secondly, by separating the observation-related part in FPF updating, the posterior FPF varying with the gradually collected observations can be estimated by sharing the sample of the performance function evaluation for prior FPF. Finally, the Kriging model is adaptively embedded to further enhance the efficiency of the proposed method, and the presented examples verify the high efficiency under acceptable accuracy.