Research Papers: Design Automation

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

[+] Author and Article Information
Loïc Brevault

Research Engineer
Onera—The French Aerospace Lab,
Palaiseau F-91123, France
e-mail: loic.brevault@onera.fr

Sylvain Lacaze

Application Support Engineer
The Mathworks,
10 Cowley Park,
Cambridge CB4 0HH, UK
e-mail: sylvain.lacaze@mathworks.co.uk

Mathieu Balesdent

Research Engineer
Onera—The French Aerospace Lab,
Palaiseau F-91123, France
e-mail: mathieu.balesdent@onera.fr

Samy Missoum

Associate Professor
Aerospace and Mechanical
Engineering Department,
University of Arizona,
Tucson, AZ 85721
e-mail: smissoum@email.arizona.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 14, 2016; final manuscript received June 22, 2016; published online September 12, 2016. Assoc. Editor: Mian Li.

J. Mech. Des 138(11), 111401 (Sep 12, 2016) (11 pages) Paper No: MD-16-1123; doi: 10.1115/1.4034106 History: Received February 14, 2016; Revised June 22, 2016

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.

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Fig. 1

Flowchart of the proposed process for reliability analysis in the presence of mixed aleatory/epistemic uncertainties

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Fig. 4

Optimal epistemic realization leading to Pmax

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Fig. 5

Subset sampling samples for u* = 4.72

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Fig. 2

Reliability index and pseudo confidence bounds at 95%

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Fig. 3

Initial and final training set, exact limit state, and kriging approximation

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Fig. 9

Reliability index and pseudo confidence bounds at 95%

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Fig. 10

Optimal epistemic realization leading to Pmax

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Fig. 11

Impact points of the launch vehicle second stage with CMC and subset sampling impact point joint PDF

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Fig. 6

Second-stage separation with impact point in nominal conditions and disciplines involved in the stage fallout reliability problem

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Fig. 7

Subset simulation histogram flight path angle samples

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Fig. 8

Convergence criterion cv



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