Details
| Original language | English |
|---|---|
| Title of host publication | e-proceedings of the 30th European Safety and Reliability Conference and 15th Probabilistic Safety Assessment and Management Conference (ESREL2020 PSAM15) |
| Subtitle of host publication | 01-05 November 2020, Venice, Italy |
| Editors | Piero Baraldi, Francesco Di Maio, Enrico Zio |
| Place of Publication | Singapore |
| Pages | 4957-4963 |
| Number of pages | 7 |
| ISBN (electronic) | 9789811485930 |
| Publication status | Published - 2020 |
| Event | 30th European Safety and Reliability Conference, ESREL 2020 and 15th Probabilistic Safety Assessment and Management Conference, PSAM15 2020 - Venice, Italy Duration: 1 Nov 2020 → 5 Nov 2020 |
Abstract
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.
Keywords
- Hybrid uncertainty, Imprecise probability, Operator norm theory, Uncertainty quantification
ASJC Scopus subject areas
- Engineering(all)
- Safety, Risk, Reliability and Quality
- Social Sciences(all)
- Safety Research
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e-proceedings of the 30th European Safety and Reliability Conference and 15th Probabilistic Safety Assessment and Management Conference (ESREL2020 PSAM15): 01-05 November 2020, Venice, Italy. ed. / Piero Baraldi; Francesco Di Maio; Enrico Zio. Singapore, 2020. p. 4957-4963.
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Breaking the double loop
T2 - 30th European Safety and Reliability Conference, ESREL 2020 and 15th Probabilistic Safety Assessment and Management Conference, PSAM15 2020
AU - Faes, Matthias G.R.
AU - Valdebenito, Marcos A.
AU - Moens, David
AU - Beer, Michael
N1 - Funding Information: Matthias Faes acknowledges the financial support of the Research Foundation Flanders (FWO) in the context of his post-doctoral grant under grant number 12P3519N as well as the Humboldt Foundation. Marcos Valdebenito acknowledges the support of ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Hybrid uncertainty
KW - Imprecise probability
KW - Operator norm theory
KW - Uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=85110311370&partnerID=8YFLogxK
U2 - 10.3850/978-981-14-8593-0_5707-cd
DO - 10.3850/978-981-14-8593-0_5707-cd
M3 - Conference contribution
AN - SCOPUS:85110311370
SP - 4957
EP - 4963
BT - e-proceedings of the 30th European Safety and Reliability Conference and 15th Probabilistic Safety Assessment and Management Conference (ESREL2020 PSAM15)
A2 - Baraldi, Piero
A2 - Di Maio, Francesco
A2 - Zio, Enrico
CY - Singapore
Y2 - 1 November 2020 through 5 November 2020
ER -