Efficient Bayesian multilevel uncertainty quantification for enhanced reliability assessment and decision support

• Applicants: Privatdozent Dr.-Ing. Iason Papaioannou; Professor Dr. Daniel Straub
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: from 2020 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 449529210

• Final Report Year: 2024

Final Report Abstract

Uncertainty quantification plays a central role in modern engineering practice. It supports judging the adequacy of modelling choices, the description of naturally random phenomena and — ultimately — making optimal decisions in an imperfect, partially known world. Uncertainty quantification in engineering is carried out with a computational model that describes the physical processes underlying an engineering application. Within uncertainty quantification, two types of uncertainty are commonly discerned. This distinction is based on whether uncertainty arises due to an inherently random phenomenon — known as aleatory uncertainty — or whether it stems from a lack of knowledge that can be potentially reduced with more information — known as epistemic uncertainty. The separate treatment of such polymorphic uncertainty types can be of paramount importance, yet is currently often neglected in practice. Within this project, in a first step, we focussed on developing original methods for the subdisciplines of classic uncertainty quantification and extending existing methods developed in the predecessor of this project that was part of the SPP1886. This includes methods for probabilistic sensitivity analysis, reliability analysis as well as the Bayesian inference of computational models. In a second step, methods for polymorphic uncertainty quantification, in particular for polymorphic reliablity analysis were developed. These methods are based on formulating polymorphic quantities of interest as conditional expectations. The developed methods are capable of efficiently computing such expectations conditioned on a subset of the model uncertainties, e.g., the conditional failure probability of a system. In a further paper, a novel reliability sensitivity measure based on decision theory that requires the computation of such conditional failure probabilities is presented. These sensitivity measures express how much any model uncertainty affects the expected utility in the context of a predefined decision problem and can be used to guide decisions regarding the reduction of individual model uncertainties.

Publications

• Decision-theoretic reliability sensitivity. Reliability Engineering & System Safety, 221, 108215.
  Straub, Daniel; Ehre, Max & Papaioannou, Iason
  
• Certified Dimension Reduction for Bayesian Updating with the Cross-Entropy Method. SIAM/ASA Journal on Uncertainty Quantification, 11(1), 358-388.
  Ehre, Max; Flock, Rafael; Fußeder, Martin; Papaioannou, Iason & Straub, Daniel
  
• Stein Variational Rare Event Simulation
  Max Ehre, Iason Papaioannou & Daniel Straub
  
• Variance-based reliability sensitivity with dependent inputs using failure samples. Structural Safety, 106, 102396.
  Ehre, Max; Papaioannou, Iason & Straub, Daniel