First excursion probabilities for linear systems by very efficient importance sampling

An analytical study of the failure region of the first excursion reliabilit y problem for linear dynamical systems subjected to Gaussian white noise ex citation is carried out with a view to constructing a suitable importance s ampling density for computing the first excursion failure probability. Cent ral to the study are 'elementary failure regions', which are defined as the failure region in the load space corresponding to the failure of a particu lar output response at a particular instant. Each elementary failure region is completely characterized by its design point, which can be computed rea dily using impulse response functions of the system. It is noted that the c omplexity of the first excursion problem stems from the structure of the un ion of the elementary failure regions. One important consequence of this un ion structure is that, in addition to the global design point, a large numb er of neighboring design points are important in accounting for the failure probability. Using information from the analytical study, an importance sa mpling density is proposed. Numerical examples are presented, which demonst rate that the efficiency of using the proposed importance sampling density to calculate system reliability is remarkable. (C) 2001 Elsevier Science Lt d. All rights reserved.