Real-time high-fidelity reliability updating with equality information using adaptive Kriging

Current state-of-the-art methods for reliability updating with equality information transform this challenging problem into an inequality one by introducing an auxiliary random variable. However, the joint event of information and failure in the derived conditional probabilities is typically very rare, and therefore, very challenging to estimate. Moreover, updating the reliability as new information arrives requires reevaluation of the probability of the joint event, which involves large numbers of calls to performance functions. We address these limitations by proposing a new approach to reliability updating called RUAK. One of the important contributions is the decomposition of the rare joint event of the failure and observed information into two events both with relatively high probabilities. Moreover, an adaptive Kriging-based reliability analysis method is proposed for the estimation of the prior failure probability and the conditional probability of information. This way, reliability updating for new information is conducted using the efficient Kriging meta-model, which significantly enhances the computational efficiency. Results for four examples indicate that the computational demand using RUAK is decreased by two orders of magnitude compared to the state-of-the-art methods, while achieving higher accuracy. This approach facilitates real-time reliability updating for various applications such as health monitoring and warning systems.