Estimation of Structural Failure Probability Based on a Quasi Ideal Importance Sampling Method: Construction of a Quasi Ideal Importance Sampling Marginal Density Function by a Repetitive Simulation

This paper is concerned with the estimation of structural failure probability based on a quasi ideal importance sampling combined with repetitive simulation procedure. A quasi ideal importance sampling joint probability density function combined in the conditional expectation is composed on the basis of the ideal importance sampling concept and the respective marginal p.d.f.s are constructed numerically by using small samples. The respective marginal p.d.f.s are renewed in every repetitive simulation procedure until they converge to a certain quasi ideal sampling distribution and by using the resultant marginal p.d.f.s the quasi ideal importance sampling simulation are executed to estimate the failure probability of structures with multiple failure modes. Numerical example shows that the proposed method gives accurate estimations with shorter processing time