Breaking the double loop: Operator norm theory as a tool to compute with imprecise probabilities

Matthias G.R. Faes, Marcos A. Valdebenito, David Moens, Michael Beer

Resultado de la investigación: Capítulo del libro/informe/acta de congresoContribución a la conferenciarevisión exhaustiva

Resumen

In engineering analysis, numerical models are being increasingly used for the approximation of the real-life behavior of components and structures. In this context, a designer is often faced with uncertain and inherently variable model quantities, which are respectively represented by epistemic and aleatory uncertainties. To ensure interpretability, and hence, correct engineering decisions, these sources of uncertainty must remain strictly separated during the analysis. In case an analyst is faced with combinations of epistemic and aleatory uncertainty, which can take the form of imprecise probabilities (e.g., stochastic quantities with imprecisely defined hyper-parameters) or hybrid uncertainties (combinations of stochastic quantities, intervals and/or imprecise probabilities), the computation of the bounds on the reliability involves solving a set of nested optimization problems (a.k.a., “the double loop”), where the calculation of the reliability of the structure has to be performed for each realisation of the epistemic uncertainty. In this paper, a method is presented to break this double loop by virtue of the operator norm theorem. Indeed, in case linear models are considered, the paper shows that the computational efficiency of propagating these uncertainties can be reduced to solving two optimization problems and two calculations of the structural reliability. A case study involving a finite element model of a clamped plate is included to illustrate the application, efficiency and effectivity of the developed technique.

Idioma originalInglés
Título de la publicación alojada30th European Safety and Reliability Conference, ESREL 2020 and 15th Probabilistic Safety Assessment and Management Conference, PSAM 2020
EditoresPiero Baraldi, Francesco Di Maio, Enrico Zio
EditorialResearch Publishing Services
Páginas4957-4963
Número de páginas7
ISBN (versión digital)9789811485930
EstadoPublicada - 2020
Evento30th European Safety and Reliability Conference, ESREL 2020 and 15th Probabilistic Safety Assessment and Management Conference, PSAM 2020 - Venice, Virtual, Italia
Duración: 1 nov. 20205 nov. 2020

Serie de la publicación

Nombre30th European Safety and Reliability Conference, ESREL 2020 and 15th Probabilistic Safety Assessment and Management Conference, PSAM 2020

Conferencia

Conferencia30th European Safety and Reliability Conference, ESREL 2020 and 15th Probabilistic Safety Assessment and Management Conference, PSAM 2020
País/TerritorioItalia
CiudadVenice, Virtual
Período1/11/205/11/20

Huella

Profundice en los temas de investigación de 'Breaking the double loop: Operator norm theory as a tool to compute with imprecise probabilities'. En conjunto forman una huella única.

Citar esto