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Reliability-based design optimization under sampling uncertainty: shifting design versus shaping uncertainty

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Abstract

The objective of this paper is a tradeoff between changing design and controlling sampling uncertainty in reliability-based design optimization (RBDO). The former is referred to as ‘living with uncertainty’, while the latter is called ‘shaping uncertainty’. In RBDO, a conservative estimate of the failure probability is defined using the mean and the upper confidence limit, which are obtained from samples and from the normality assumption. Then, the sensitivity of the conservative probability of failure is derived with respect to design variables as well as the number of samples. It is shown that the proposed sensitivity is much more accurate than that of the finite difference method and close to the analytical sensitivity. A simple RBDO example showed that once the design variables reach near the optimum point, the number of samples is adjusted to satisfy the conservative reliability constraints. This example showed that not only shifting design but also shaping uncertainty plays a critical role in the optimization process.

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Abbreviations

d :

design point

G(·):

limit state function

z 1 − α :

1 − αlevel z-score

σ(·):

standard deviation

V(·):

variance

P T :

target probability of failure

y th :

threshold value of y

P F :

probability of failure

f x (·):

probability density function

s(·):

score function

I F :

indicator function

Ω F :

failure domain

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Acknowledgments

This research was also supported by the research grant of Agency for Defense Development and Defense Acquisition Program Administration of the Korean government.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32611, USA

    Sangjune Bae & Nam H. Kim

  2. Agency for Defense Development, Daejeon, Republic of Korea

    Seung-gyo Jang

Authors
  1. Sangjune Bae
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  2. Nam H. Kim
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  3. Seung-gyo Jang
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Correspondence to Nam H. Kim.

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Bae, S., Kim, N.H. & Jang, Sg. Reliability-based design optimization under sampling uncertainty: shifting design versus shaping uncertainty. Struct Multidisc Optim 57, 1845–1855 (2018). https://doi.org/10.1007/s00158-018-1936-0

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  • DOI: https://doi.org/10.1007/s00158-018-1936-0

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