Interval importance sampling method for finite element-based structural reliability assessment under parameter uncertainties

Parameters of a probabilistic model often cannot be determined precisely on the basis of limited data. In this case the unknown parameters can be introduced as intervals, and the imprecise probability can be modeled using a probability bounding approach. Common methods for bounding imprecise probability involve interval analysis to compute bounds of the limit state probability. A large number of interval finite element (FE) analyses have to be performed if the structural response defined as the limit state is determined implicitly through FE analysis. A new interval importance sampling method is developed in this paper which applies importance sampling technique to the imprecise probability. The proposed methodology has a desirable feature that expensive interval analyses are not required. Point samples are generated according to the importance sampling function. The limit states are computed using deterministic FE analyses. The bounds of the imprecise probability density function are introduced in the formulation at a later stage to incorporate the effects of the imprecision in the probability functions on the reliability results. Examples are given to illustrate the accuracy and efficiency of the interval importance sampling method. The second example also compares the proposed method with the conventional Bayesian approach.