Realistic and efficient reliability estimation for aerospace structures

Abstract

In this paper an efficient procedure for calculating non-exceedance probabilities of the structural response is presented, with emphasis on structures modeled by large finite element systems with many uncertain parameters. This is a problem which receives considerable attention in numerous applications of engineering mechanics, such as space and aerospace engineering. For this purpose, a novel sampling procedure is introduced, which allows a significant reduction of the variance of the estimator of the probability of failure when compared to that of direct Monte Carlo simulation. This improvement in the computational efficiency is most important, as the computational efforts are much higher when uncertainties are considered.The only prerequisite for the application of this sampling procedure is an estimate of the gradient of the performance function of the structure. The calculation of the gradient is carried out efficiently, by exploiting the correlation between a randomly chosen input and the corresponding output of the system. The proposed concept is especially suited for high-dimensional problems in reliability engineering, e.g. for a rather large number n of random variables, say n>100.To demonstrate the practical value of the methodology a reliability analysis of the INTEGRAL-satellite of the European Space Agency (ESA) has been performed. The results show that both for the frequency response analysis and the structural reliability analysis a substantial number of parameters of the finite element model play an important role.