New perspective on reliability updating with equality information under line sampling

Abstract

The observations provided by monitoring and sensor can be used to reevaluate the important structure performance for deepening the understanding of structural model and the reliability. Thus it is necessary to perform the reliability updating and estimate the posterior failure probability based on the collected observations. The posterior failure probability can be viewed as a corrected failure probability based on the onsite observation information and the prior failure probability, and it is more practical to reflect the current structure safety level than the prior failure probability. Current methods for estimating the posterior failure probability with equality observation information are to transform it into an inequality one by introducing an auxiliary variable, which enables it to be estimated by the structural reliability analysis methods. However, this is a challenging task because directly estimating the rare posterior failure probability often requires large number of samples. A new line sampling-based perspective on reliability updating is proposed in this paper, on which the posterior failure probability can be expressed by a more concise mathematical form and completed in the original random input space without introducing the auxiliary variable. Benefit from the high sampling efficiency of line sampling, the number of required samples is greatly reduced compared with Monte Carlo simulation. Additionally, the adaptive Kriging model is employed to identify the failure samples in the proposed reliability updating model, which can further reduce the computational cost. The efficiency and accuracy of the proposed method are demonstrated on the numerical and engineering examples.