Reliability measure approach for confidence-based design optimization under insufficient input data

Jung, Yongsu; Cho, Hyunkyoo; Lee, Ikjin

doi:10.1007/s00158-019-02299-3

Cited by 25 publications

(10 citation statements)

References 53 publications

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“…In practice, however, it is often difficult to obtain statistical information with sufficient accuracy. This incents recent intensive study of RBDO with incomplete statistical information [9,10,16,21,22,24,25,35,37,38,46,50,51,53].…”

Section: Introductionmentioning

confidence: 90%

Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

Kanno

2021

Preprint

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This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the input distribution belong to a given convex set, we require that, for any realization of the input distribution, the failure probability of a structure should be no greater than a specified target value. We show that this distributionally-robust reliability constraint can be reduced equivalently to deterministic constraints. By using this reduction, we can treat a reliabilitybased design optimization problem under the distributionally-robust reliability constraint within the framework of deterministic optimization, specifically, nonlinear semidefinite programming. Two numerical examples are solved to show relation between the optimal value and either the target reliability or the uncertainty magnitude.

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Section: Introductionmentioning

confidence: 90%

Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

Kanno

2021

Preprint

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“…However, it is often difficult to obtain statistical information with sufficient accuracy in practice. This has incented recent intensive studies on RBDO with incomplete statistical information [12,13,19,25,26,28,29,43,47,48,57,61,62,64].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the failure probability is a random variable, and the confidence level of a reliability constraint, i.e., the probability that the failure probability is no greater than a target value, is specified. To reduce the computational cost of this method, Jung et al [29] proposed the so-called reliability measure approach, which was inspired by the performance measure approach [39,41]. Subsequently, to the reduce computational cost further, Wang et al [57] proposed the use of the second-order reliability method for computing the failure probability.…”

Section: Introductionmentioning

confidence: 99%

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Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

Kanno

2021

Japan J. Indust. Appl. Math.

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This study considers structural optimization under a reliability constraint, in which the input distribution is only partially known. Specifically, when it is only known that the expected value vector and the variance-covariance matrix of the input distribution belong to a given convex set, it is required that the failure probability of a structure should be no greater than a specified target value for any realization of the input distribution. We demonstrate that this distributionally-robust reliability constraint can be reduced equivalently to deterministic constraints. By using this reduction, we can handle a reliability-based design optimization problem under the distributionally-robust reliability constraint within the framework of deterministic optimization; in particular, nonlinear semidefinite programming. Two numerical examples are solved to demonstrate the relation between the optimal value and either the target reliability or the uncertainty magnitude.

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“…information (Jung et al 2019). In practice, design data are limited and obtaining information about the governing probabilistic distributions of the random variables is not feasible.…”

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confidence: 99%

Chebyshev inequality–based inflated convex hull for uncertainty quantification and optimization with scarce samples

Ayyasamy

Ramu

Elishakoff

2021

Struct Multidisc Optim

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Dealing with the unknown-but-bounded uncertainty and insufficient or scarce data is an often-encountered challenge in real life engineering. In this study, we develop an efficient convexity approach to construct the uncertainty model in the form of bounds to address such a challenge. Approaches that use probabilistic models require comprehensive information about the uncertainty, which is often difficult or expensive to obtain, whereas the convex models that approximate the uncertain region using different bounding geometries can operate with scarce data or parameter bounds. The novelty of the current work is to use (i) convex hull as the bounding geometry in the uncertain design space (ii) Chebyshev inequality to inflate the convex hull that can include future data points which will then be used in design. Convex hull provides the least volume compared to other geometries reported in literature, such as interval, ellipse, super ellipse, and parallelepiped that are used in convexity approaches. In addition, to obtain the bounds of linear limit states, it is sufficient to evaluate the limit states only at the vertices of the convex hull, thereby saving on expensive simulations at nonvertex points. The proposed method is demonstrated on engineering examples with different coefficient of variation and random variables following different distributions. Results reveal the superiority of the proposed approach over the existing convexity approaches for uncertainty quantification. Also, the optima obtained by proposed method are always conservative to ones from a large sample Monte Carlo simulation and thus avoids under-or over-design associated with safety factor approach. KeywordsSafety factor • Convex hull • Chebyshev inequality • Limit state bounds IntroductionMethods that are widely used for uncertainty quantification include probabilistic and convexity approaches (Wang et al. 2011). Probabilistic approaches usually require information such as the type of distribution and its parameters or require numerous data points to be able to generate these

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Reliability measure approach for confidence-based design optimization under insufficient input data

Cited by 25 publications

References 53 publications

Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

Chebyshev inequality–based inflated convex hull for uncertainty quantification and optimization with scarce samples

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