Conservative reliability index for epistemic uncertainty in reliability-based design optimization

Ito, Makoto; Kim, Nam Ho; Kogiso, Nozomu

doi:10.1007/s00158-018-1903-9

Cited by 20 publications

(37 citation statements)

References 14 publications

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“…Our approach is more general, in the sense that we work directly in the original probability space of the posed random variable model. The work of Ito et al is closely related to what we suggest, though similarly assumes a transform to standard normal space, and does not guarantee the C2 property. We draw a close comparison between their CRI and our proposed MIP approach.…”

Section: Introductionmentioning

confidence: 92%

“…Here, we draw a comparison with the CRI of Ito et al, which is closely related to our proposed MIP approach. In nomenclature consistent with our presentation, they recommend solving

\begin{matrix} right min & left C (d), & right \\ right s.t. & left R^{α} \geq R, \\ right & left P_{\hat{θ}} [R (\hat{θ}) > R^{α}] = α . \end{matrix}

We note that the CRI approach is a form of PM, as it encourages conservatism based on the variability in the estimated reliability and indeed recovers the true reliability with perfect information (Appendix A.3).…”

Section: Precision Marginmentioning

confidence: 99%

“…Regardless, we will use the manipulations arising from in the same fashion as the approximations presented above, in order to provide some comparison against existing approaches. Note that we cannot use the approximation technique of Ito et al, as our design problem does not take the form of design variables perturbed by noise. One designs with the PRI via the constraint

\overset{β}{true} \geq {normalΦ}^{- 1} false(scriptR false)

; we present results from this approach in Figure .…”

Section: Enabling Estimationmentioning

confidence: 99%

“…To control effective reliability, we introduce minimum conditions that define precision margin (PM). To show the concept's generality, we formally prove that the conservative reliability index (CRI) of Ito et al is a PM. We also present two implementations of PM, both carrying unique advantages and challenges.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, in reviewing the literature, it was unclear to us how to measure the effects of parameter uncertainties in RBDO, let alone how to control realized design reliability. 3,6,7 The aforementioned works introduce approaches that are distinct in how they introduce engineering conservatism but are similar in that they recover the "true" reliability in the case of perfect information. This is in contrast with other design practices outside the framework of RBDO, such as those utilizing basis values (BVs).…”

Section: Introductionmentioning

confidence: 99%

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Cutting the double loop: Theory and algorithms for reliability‐based design optimization with parametric uncertainty

Rosario

Fenrich

Iaccarino

2019

Numerical Meth Engineering

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Summary Parametric uncertainties complicate engineering design—confounding regulated design approaches and degrading the performance of reliability efforts. The simplest means to tackle this uncertainty is double‐loop simulation, a nested Monte Carlo method that, for practical problems, is intractable. In this work, we introduce a flexible, general approximation technique that obviates the double loop. This approximation is constructed in the context of a novel theory of reliability design under parametric uncertainty: we introduce metrics for measuring the efficacy of reliability‐based design optimization strategies (epistemic design gap and effective reliability), minimal conditions for controlling uncertain reliability (precision margin), and stricter conditions that guarantee the desired reliability at a designed confidence level. We provide a number of examples with open‐source code to demonstrate our approaches in a reproducible fashion.

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Section: Introductionmentioning

confidence: 92%

“…Here, we draw a comparison with the CRI of Ito et al, which is closely related to our proposed MIP approach. In nomenclature consistent with our presentation, they recommend solving

\begin{matrix} right min & left C (d), & right \\ right s.t. & left R^{α} \geq R, \\ right & left P_{\hat{θ}} [R (\hat{θ}) > R^{α}] = α . \end{matrix}

Section: Precision Marginmentioning

confidence: 99%

\overset{β}{true} \geq {normalΦ}^{- 1} false(scriptR false)

; we present results from this approach in Figure .…”

Section: Enabling Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Cutting the double loop: Theory and algorithms for reliability‐based design optimization with parametric uncertainty

Rosario

Fenrich

Iaccarino

2019

Numerical Meth Engineering

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Robust geometry and topology optimization of plane frames using order statistics and force density method with global stability constraint

Shen

Ohsaki

Yamakawa

2021

Numerical Meth Engineering

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This paper presents a worst case approach for robust geometry and topology optimization of plane frames with global stability constraint. Uncertainty is assumed to exist in the nodal locations and cross‐sectional areas, and the worst values of the objective and stability constraint functions are relaxed to the quantile structural responses represented by the order statistics with given robustness and confidence levels. In order to alleviate the difficulty caused by melting nodes to some extent, the force density method is applied to an auxiliary truss model for geometry optimization of the frame, and the closely spaced nodes are merged. A method is presented for generating correlated imperfections for the nodal locations along each member, and a penalization approach is proposed for geometrical stiffness matrix to exclude superficial local buckling. It is demonstrated in the numerical examples that the result of robust optimization obtained by the proposed method is less sensitive to the uncertainty, and the stability constraint is also satisfied under uncertainty with the specified robustness and confidence levels.

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Computation‐with‐confidence for static elasticity: Data‐driven approach with order statistics

Kanno

2023

Z Angew Math Mech

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This paper presents a data‐driven method to identify a bound for the structural response of interest when a data set of elastic material responses is available. The obtained bound is probable in the sense that, at least with a certain confidence level, the probability that the structural response is within the bound is no smaller than a certain target value of reliability. The confidence level is ensured by considering the order statistics of the given data points. In this manner, this paper introduces the concept of reliability to the framework of data‐driven computational elasticity to address uncertainty in the data set. The method does not require any statistical information of the data points. Two numerical examples demonstrate the use of the proposed method to analyze static responses of structures by using only given material data sets.

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Conservative reliability index for epistemic uncertainty in reliability-based design optimization

Cited by 20 publications

References 14 publications

Cutting the double loop: Theory and algorithms for reliability‐based design optimization with parametric uncertainty

Cutting the double loop: Theory and algorithms for reliability‐based design optimization with parametric uncertainty

Robust geometry and topology optimization of plane frames using order statistics and force density method with global stability constraint

Computation‐with‐confidence for static elasticity: Data‐driven approach with order statistics

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