Reliability Analysis in the Presence of Aleatory and Epistemic Uncertainties, Application to the Prediction of a Launch Vehicle Fallout Zone

Abstract

The design of complex systems often requires reliability assessments involving a large number of uncertainties and low probability of failure estimations (in the order of 10−4). Estimating such rare event probabilities with crude Monte Carlo (CMC) is computationally intractable. Specific numerical methods to reduce the computational cost and the variance estimate have been developed such as importance sampling or subset simulation. However, these methods assume that the uncertainties are defined within the probability formalism. Regarding epistemic uncertainties, the interval formalism is particularly adapted when only their definition domain is known. In this paper, a method is derived to assess the reliability of a system with uncertainties described by both probability and interval frameworks. It allows one to determine the bounds of the failure probability and involves a sequential approach using subset simulation, kriging, and an optimization process. To reduce the simulation cost, a refinement strategy of the surrogate model is proposed taking into account the presence of both aleatory and epistemic uncertainties. The method is compared to existing approaches on an analytical example as well as on a launch vehicle fallout zone estimation problem.

Bounds approximation of limit‐state surface based on active learning Kriging model with truncated candidate region for random‐interval hybrid reliability analysis

“…In Reference , we have proved that the upper bound in References will always be smaller than that of Equation (1) and the lower bound is always larger than that of Equation (2). This means References cannot obtain the true maximum or minimum failure probability. In fuzzy sets and evidence theory which are closely related to interval sets theory, the bounds of P f were defined similarly as Equations (1) and (2) .…”

“…Note that in References , the bounds of P f were defined differently from Equations (1) and (2). In Reference , we have proved that the upper bound in References will always be smaller than that of Equation (1) and the lower bound is always larger than that of Equation (2). This means References cannot obtain the true maximum or minimum failure probability.…”

“…The performance function is constructed as. 38 G(x, y) = 9.3 − Δ 2 (x, y), (44) where Δ 2 is the vertical deflection of node 2, which is obtained by the FE method coded in Matlab. The uncertain variables are shown in Table 6.…”

Probabilistic Analysis for Structures with Hybrid Uncertain Parameters

“…For the models of the first type, uncertain model parameters with sufficient experimental data are represented by the probability model, and uncertain parameters with limited information are quantified by intervals. Several analysis techniques for this model have been developed [15][16][17][18][19]. Hybrid models of the second type are also called probability-box or interval random variable models in the literature [20][21][22][23].…”

Probability and interval hybrid reliability analysis based on adaptive local approximation of projection outlines using support vector machine

“…Yang et al (2015) propose an expected risk function for kriging to search for the training points located around the limitstate surface, where kriging is an interpolation technique for the construction of metamodels (Matheron, 1973). Brevault, Lacaze, Balesdent, and Missoum (2016) employ the modification of the generalized max-min to refine the limit-state surface approximated by the kriging metamodel.…”