Research Papers

Reliability Based Design Optimization Modeling Future Redesign With Different Epistemic Uncertainty Treatments

[+] Author and Article Information
Taiki Matsumura

e-mail: taiki.matsumura@ufl.edu

Raphael T. Haftka

e-mail: haftka@ufl.edu
Department of Mechanical
and Aerospace Engineering,
University of Florida,
Gainesville, FL 32611

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received December 20, 2012; final manuscript received May 8, 2013; published online July 2, 2013. Assoc. Editor: David Gorsich.

J. Mech. Des 135(9), 091006 (Jul 02, 2013) (9 pages) Paper No: MD-12-1616; doi: 10.1115/1.4024726 History: Received December 20, 2012; Received May 08, 2013

Design under uncertainty needs to account for aleatory uncertainty, such as variability in material properties, and epistemic uncertainty including errors due to imperfect analysis tools. While there is a consensus that aleatory uncertainty be described by probability distributions, for epistemic uncertainty there is a tendency to be more conservative by taking worst case scenarios or 95th percentiles. This conservativeness may result in substantial performance penalties. Epistemic uncertainty, however, is usually reduced by additional knowledge typically provided by tests. Then, redesign may take place if tests show that the design is not acceptable. This paper proposes a reliability based design optimization (RBDO) method that takes into account the effects of future tests possibly followed by redesign. We consider each realization of epistemic uncertainty to correspond to a different design outcome. Then, the future scenario, i.e., test and redesign, of each possible design outcome is simulated. For an integrated thermal protection system (ITPS) design, we show that the proposed method reduces the mass penalty associated with a 95th percentile of the epistemic uncertainty from 2.7% to 1.2% compared to standard RBDO, which does not account for the future. We also show that the proposed approach allows trading off mass against development costs as measured by probability of needing redesign. Finally, we demonstrate that the tradeoff can be achieved even with the traditional safety factor based design.

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Fig. 1

Probability of failure estimation: Epistemic and aleatory uncertainties are treated equally

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Fig. 2

Probability of failure estimation: Epistemic and aleatory uncertainties are treated differently

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Fig. 3

Illustration of Bayesian updating, describing an initial distribution and likelihood (top) and updated distributions of two of many possible futures (bottom). It is assumed that the measurement error is ±2%.

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Fig. 4

Illustration of redesign decision by an updated distribution of probability of failure after test

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Fig. 5

Possible effects of redesign on the distribution of probability of failure and objective function

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Fig. 6

Flowchart of simulating future scenarios

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Fig. 7

(a) ITPS and (b) a unit cell of the ITPS

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Fig. 8

(a) Possible true probability of failure before test (PPtrue,i) and (b) updated probability of failure after test (P95,iup) of the optimal solution from the standard RBDO using P95ini

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Fig. 9

Optimal designs from RBDO with simulated future using the mean of probability of failure. Note that the target probability of redesign was always a multiple of 10%, so the slight deviations from these values in the symbols reflect errors due to the use of surrogates.

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Fig. 10

Mass penalty for conservative design (comparison between the 95th percentile design and the mean design). Note that, for 95th percentile design, the deviation of the optimal solution of the standard RBDO from the Pareto front reflects the error of the surrogate models.

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Fig. 11

Mass and probability of redesign tradeoff (using safety factor vs. using the mean of probability of failure). Note that the target probability of redesign was always a multiple of 10%, so the slight deviations from these values in the symbols reflect errors due to the use of surrogates.

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Fig. 12

Difference in error calibration between Bayesian approach and safety factor approach




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