Reliability Sensitivity Estimation of Linear Systems under Stochastic Excitation M.A. Valdebenito a , H.A. Jensen a,* , G.I. Schu¨ eller b , F.E. Caro a a Universidad Tecnica Federico Santa Maria, Dept. de Obras Civiles, Av. Espa˜ na 1680, Valparaiso, Chile b Chair of Engineering Mechanics, University of Innsbruck, Technikerstraße 13, A-6020 Innsbruck, Austria, EU Abstract The objective of this paper is presenting an approach for reliability sensitivity estimation of linear structural systems subject to dynamical excitation characterized as a Gaussian process. The paper represents an extension of some ideas proposed previously in the context of sensitivity analysis. Novel aspects include the use of the Bootstrap method for assessing the error associated with the estimator of the reliability sensitivity and the application of the proposed approach to a more involved structural model Keywords: Stochastic Linear Dynamics, Importance Sampling, High dimensional reliability problems, Reliability Sensitivity Analysis, Gaussian Loading, Bootstrap 1. Introduction Structural reliability offers the possibility of accounting for the unavoidable effects of uncertainty over the per- formance of a structure [1, 2]. In particular, the level of safety of a structure can be measured in terms of reliability, which is a metric of the probability that a structure fulfills certain performance requirements during its lifetime. The complement of the reliability is the probability of failure (P F ), i.e. the probability that a structure violates prescribed performance criteria. Although reliability is an important metric, it is not the only metric that should be taken into account when designing a system. In fact, it is also of interest analyzing the sensitivity of the reliability with respect to variations in the properties of the structure [3, 4, 5, 6, 7, 8]. For example, determination of the variation in the reliability due to a change in the size of a structural member can provide useful information to increase the safety level or to identify the most influential design parameters. Thus, this contribution presents an approach for estimating reliability sensitivity for a particular class of structural systems, namely linear structures subject to dynamic loading modeled as a Gaussian stochastic process. This sensitivity is computed with respect to variables affecting structural performance (such as mass, stiffness, cross section of structural members, etc.). The approach reported herein is a revised and extended version of the work presented in [9]. Salient features of the proposed approach when compared to similar approaches introduced in the literature are the capability of considering problems involving a large number of random variables (in the order of thousands), the possibility of estimating sensitivity with respect to several variables simultaneously (scalability) and a high numerical efficiency * E-mail: hector.jensen@usm.cl Preprint submitted to Computers & Structures September 14, 2011