Equivalent target probability of failure to convert high-reliability model to low-reliability model for efficiency of sampling-based RBDO

This study presents a methodology to convert an RBDO problem requiring very high reliability to an RBDO problem requiring relatively low reliability by appropriately increasing the input standard deviations for efficient computation in sampling-based RBDO. First, for linear performance functions with independent normal random inputs, an exact probability of failure is derived in terms of the ratio of the input standard deviation, which is denoted by \(\boldsymbol {\delta } \). Then, the probability of failure estimation is generalized for other types of random inputs and performance functions. For the generalization of the probability of failure estimation, two types of coefficients need to be determined by equating the probability of failure and its sensitivities with respect to the input standard deviation at the given design point. The sensitivities of the probability of failure with respect to the standard deviation are obtained using the first-order score function for the standard deviation. To apply the proposed method to an RBDO problem, a concept of an equivalent target probability of failure, which is an increased target probability of failure corresponding to the increased input standard deviations, is also introduced. Numerical results indicate that the proposed method can estimate the probability of failure accurately as a function of the input standard deviation compared to the Monte Carlo simulation results. As anticipated, the sampling-based RBDO using equivalent target probability of failure helps find the optimum design very efficiently while yielding reasonably accurate optimum design, which is close to the one obtained using the original target probability of failure.