Error Estimation and Error Reduction in Separable Monte–Carlo Method

摘要

Reliability-based design often uses theMonte–Carlo method as a sampling procedure for predicting failure. Thencombination of designing for very small failure probabilities (u000110u00028nu0002 10u00026n) and using computationally expensivenfinite element models, makes Monte–Carlo simulations very expensive. This paper uses an improved samplingnprocedure for calculating the probability of failure, called separable Monte–Carlo method. The separable Monte–nCarlo method can improve the accuracy of the traditional crude Monte–Carlo when response and capacity arenindependent. In previous research, accuracy of separable Monte–Carlo for a simple limit state was estimated vianexpectation calculus for a simple form of the limit state. In this paper, error estimates for a general limit state arendeveloped through bootstrapping, and it is demonstrated that the estimates are reasonably accurate. SeparablenMonte–Carlo allows us to choose different sample sizes of the response and capacity in the limit state, and the paperndemonstrates that bootstrapping may be used to estimate the contribution of the response and capacity to the totalnerror.When the accuracy of the probability of failure is not good enough, the paper proposes reformulation of thenlimit state as another way to reduce uncertainty associated with the expensive random variable (usually thenresponse). The accuracy of the bootstrapping estimates and the effectiveness of regrouping is demonstrated with annexample of prediction of failure in a composite laminate with the Tsai–Wu failure criterion.