Bayesian Calibration and Probability Bounds Analysis Solution to the Nasa 2020 UQ Challenge on Optimization Under Uncertainty

Alexander Wimbush, Ander Gray, Roberto Rocchetta, Marco de Angelis, Peter Hristov, Enirque Miralles-Dolz, Dominic Calleja

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Abstract

Uncertainty quantification is a vital part of all engineering and scientific pursuits. Some of the current most challenging tasks in UQ involve accurately calibrating, propagating and performing optimisation under aleatory and epistemic uncertainty in high dimensional models with very few data; like the challenge proposed by Nasa Langley this year. In this paper we propose a solution which clearly separates aleatory from epistemic uncertainty. A multidimensional 2nd-order distribution was calibrated with Bayesian updating and used as an inner approximation to a p-box. A sliced normal distribution was fit to the posterior, and used to produce cheap samples while keeping the posterior dependence structure. The remaining tasks, such as sensitivity and reliability optimisation, are completed with probability bounds analysis. These tasks were repeated a number of times as designs were improved and more data gathered.
Original languageEnglish
Title of host publicationProceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference
EditorsPietro Baraldi, Francesco di Maio, Enrico Zio
ISBN (Electronic)978-981-14-8593-0
Publication statusPublished - 1 Nov 2020

Keywords

  • Bayesian calibration
  • 2nd-order distribution
  • probability bounds analysis
  • uncertainty propagation
  • uncertainty reduction
  • epistemic uncertainty
  • optimization under uncertainty

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