Structural reliability analysis for p-boxes using multi-level meta-models

Abstract

In modern engineering, computer simulations are a popular tool to analyse, design, and optimize systems. Furthermore, concepts of uncertainty and the related reliability analysis and robust design are of increasing importance. Hence, an efficient quantification of uncertainty is an important aspect of the engineer's workflow. In this context, the characterization of uncertainty in the input variables is crucial. In this paper, input variables are modelled by probability-boxes, which account for both aleatory and epistemic uncertainty. Two types of probability-boxes are distinguished: free and parametric (also called distributional) p-boxes. The use of probability-boxes generally increases the complexity of structural reliability analyses compared to traditional probabilistic input models. In this paper, the complexity is handled by two-level approaches which use Kriging meta-models with adaptive experimental designs at different levels of the structural reliability analysis. For both types of probability-boxes, the extensive use of meta-models allows for an efficient estimation of the failure probability at a limited number of runs of the performance function. The capabilities of the proposed approaches are illustrated through a benchmark analytical function and two realistic engineering problems.

Robust propagation of probability boxes by interval predictor models

“…1. In contrast to the random set approach applied to the propagation of distribution free probability boxes in the multi-level metamodel algorithm [27], the approach proposed in this paper does not require multiple levels of metamodeling, since one IPM is sufficient to obtain both the upper and lower bound of the performance function. Therefore the algorithm proposed in this paper is effectively a single loop approach, as the optimisation takes place during the creation of the metamodel.…”

“…In the literature, some metamodeling techniques have been proposed to reduce the computational demands of the analysis, which would allow the objective function to be evaluated with less computational expense [32,26,27,16]. However, these techniques are usually dependent on the assumptions required to construct the metamodel, which may be implicit or explicit.…”

Modeling of structures with polymorphic uncertainties at different length scales

“…Each distribution inside the p-box is valid, which is also denoted as free p-box. [9] In contrast to a free p-box, a parametric p-box [9] is obtained, if all distributions inside the p-box are defined as a bunch of CDFs of the same type with interval distribution parameters, for example, a Gaussian distribution with an interval mean value. A parametric p-box is similar to a fuzzy stochastic variable, that is, it is obtained as an -cut of a fuzzy stochastic variable, and therefore it is also denoted as interval stochastic number by Freitag et al [10] Imprecise stochastic quantities may also be incorporated by solely prescribing bounds on specific statistical moments as constraints to global optimization problems to identify the sharpest bounds on, for example, the probability of failure.…”

Efficient structural reliability analysis by using a PGD model in an adaptive importance sampling schema

“…The second group are the so-called variance-reducing sampling strategies, e.g. importance sampling [4][5][6], directional sampling [7][8][9], asymptotic sampling [1,10,11] or subset simulation methods [12][13][14], to name a few. In the importance sampling method, an additional sampling density or weighting function is used to concentrate the samples in the most important region, i.e.…”