Application of Total Probability Theorem in Proposing a Novel Simulation-Based Structural Reliability Method
摘要
A significant challenge in structural reliability analysis is finding accurate and efficient approaches to estimate the probability of failure in structures. Monte Carlo simulation is an accurate technique to compute the probability of failure. However, its low efficiency is a notable disadvantage. In this paper, an effective approach is presented to greatly enhance the efficiency of Monte Carlo simulation using the total probability theorem. In this method, the sample space is divided into distinct regions, and the probability of failure in each region is evaluated independently. Then the total probability of failure is computed using the total probability theorem. The number of generated samples in each region could be determined differently depending on the specifications of the problem. Therefore, the generated samples can be more concentrated on the failure domain, resulting in a notable reduction in the number of required samples. By employing this method, significant efficiency improvements are achieved maintaining the accuracy of the Monte Carlo simulation. The performance of the proposed method is evaluated using various problems.