A new interpretation on structural reliability updating with adaptive batch sampling-based subset simulation

Reliability analysis aims at quantitatively assessing the risks of structures and infrastructure systems considering various sources of aleatory or epistemic uncertainties. This concept can be interpreted as reliability updating (RU) to track the change of risks, fusing new data emerged in the operation period. Optimal allocation of resources can be therefore prepared for reasonable maintenance and rehabilitation. In the state-of-the-art method for RU with equality information, auxiliary random variables are introduced to transform the problem into an inequality one. However, the joint events derived in aforementioned approach are typically very rare, which can be computationally cumbersome via simulation techniques. To enhance the performance of RU with equality information, this paper proposes a new reliability updating approach that decomposes the joint event term into two separate multipliers and subsequently computes conditional probability through subset simulation (SS). Moreover, this work analyzes the statistical properties for RU through SS. An adaptive manner is proposed to dynamically adjust the batch sample size for each subset so that the consistency of simulation results can be ensured. Compared to past SS-based reliability updating approaches, the proposed method is computationally easier to handle and substantially more robust. Three numerical examples together with a practical application of structural health monitoring are investigated to demonstrate the computational superiority of the proposed method.