Treatment of Multiple Design Points in Reliability Methods

Abstract

Asymptotic approximations and importance sampling methods are developed for evaluating a class of probability integrals with multiple design points that may arise in the calculation of the reliability of uncertain systems. The asymptotic approximation is used as a first step to provide a computationally efficient estimate of the probability integral. The importance sampling method utilizes information available about the location of multiple design points and the asymptotic estimates for each design point in order to substantially accelerate the convergence of available importance sampling methods that use information from one design point only. Implementation issues related to the choice of importance sampling density and sample generation for reducing the variance of the estimate and accelerating convergence are addressed. The computational efficiency and improved accuracy of the proposed approximations are demonstrated by investigating the reliability of a ten story building equipped with a tuned mass damper for which multiple design points are encountered and the contribution from more than one design point to the value of the reliability integral is significant.

Additional details