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Research Papers: Design Automation

Deciding Degree of Conservativeness in Initial Design Considering Risk of Future Redesign

[+] Author and Article Information
Nathaniel B. Price

Mem. ASME
Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611;
ONERA—The French Aerospace Lab,
Palaiseau 91123, France;
École des Mines de Saint-Étienne,
Saint-E′ tienne 42023, France
e-mail: natprice@ufl.edu

Nam-Ho Kim

Mem. ASME
Associate Professor
Department of Mechanical
and Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: nkim@ufl.edu

Raphael T. Haftka

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

Mathieu Balesdent

ONERA—The French Aerospace Lab,
Palaiseau 91123, France
e-mail: mathieu.balesdent@onera.fr

Sébastien Defoort

ONERA—The French Aerospace Lab,
Palaiseau 91123, France
e-mail: sebastien.defoort@onera.fr

Rodolphe Le Riche

CNRS Permanent Research Associate
École des Mines de Saint-Étienne,
Saint-Étienne 42023, France
e-mail: leriche@emse.fr

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 3, 2016; final manuscript received July 17, 2016; published online September 12, 2016. Editor: Shapour Azarm.

J. Mech. Des 138(11), 111409 (Sep 12, 2016) (13 pages) Paper No: MD-16-1181; doi: 10.1115/1.4034347 History: Received March 03, 2016; Revised July 17, 2016

Early in the design process, there is often mixed epistemic model uncertainty and aleatory parameter uncertainty. Later in the design process, the results of high-fidelity simulations or experiments will reduce epistemic model uncertainty and may trigger a redesign process. Redesign is undesirable because it is associated with costs and delays; however, it is also an opportunity to correct a dangerous design or possibly improve design performance. In this study, we propose a margin-based design/redesign method where the design is optimized deterministically, but the margins are selected probabilistically. The final design is an epistemic random variable (i.e., it is unknown at the initial design stage) and the margins are optimized to control the epistemic uncertainty in the final design, design performance, and probability of failure. The method allows for the tradeoff between expected final design performance and probability of redesign while ensuring reliability with respect to mixed uncertainties. The method is demonstrated on a simple bar problem and then on an engine design problem. The examples are used to investigate the dilemma of whether to start with a higher margin and redesign if the test later in the design process reveals the design to be too conservative, or to start with a lower margin and redesign if the test reveals the design to be unsafe. In the examples in this study, it is found that this decision is related to the variance of the uncertainty in the high-fidelity model relative to the variance of the uncertainty in the low-fidelity model.

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Figures

Grahic Jump Location
Fig. 1

The overall design process consists of optimization of the margins based on an MCS of the deterministic design/redesign process

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Fig. 2

Flowchart showing the steps in the two-stage deterministic design/redesign process (lower box from Fig. 1). Margins n={nini,nlb,nub,nre} are shown as inputs at relevant steps.

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Fig. 3

Uniaxial tension test—comparison of expected cross-sectional area after possible redesign as a function of probability of redesign for redesign for performance (conservative initial design) versus redesign for safety (ambitious initial design)

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Fig. 4

Uniaxial tension test—epistemic uncertainty in cross-sectional area for 20% probability of redesign

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Fig. 5

Uniaxial tension test—epistemic uncertainty in margin with respect to high-fidelity model for 20% probability of redesign. Plots show overlapping transparent histograms.

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Fig. 6

Uniaxial tension test—epistemic uncertainty in margin with respect to true model for 20% probability of redesign. Plots show overlapping transparent histograms.

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Fig. 7

Uniaxial tension test—epistemic uncertainty in reliability index for 20% probability of redesign. Plots show overlapping transparent histograms.

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Fig. 8

Uniaxial tension test—epistemic uncertainty in failure for 20% probability of redesign. The figures are plotted with different scales to show the change in the tail of the distribution. Plots show overlapping transparent histograms.

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Fig. 9

Uniaxial tension test—redesign for safety is preferred when high-fidelity model error is low, but redesign for performance is preferred when high-fidelity model error is high. Plot is for fixed probability of redesign of 20%.

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Fig. 10

A response surface of the engine performance map calculates maximum available thrust at a given Mach number, M, and altitude, h. The throttle setting is normalized to one at an altitude of approximately 32,000 ft and Mach 1.9.

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Fig. 11

SSBJ Engine—comparison of expected engine weight after possible redesign as a function of probability of redesign for redesign for performance (conservative initial design) versus redesign for safety (ambitious initial design)

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Fig. 12

SSBJ Engine—epistemic uncertainty in throttle setting for 20% probability of redesign

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Fig. 13

SSBJ Engine—epistemic uncertainty in engine weight for 20% probability of redesign

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Fig. 14

SSBJ Engine—epistemic uncertainty in margin with respect to high-fidelity model for 20% probability of redesign. Plots show overlapping transparent histograms.

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Fig. 15

SSBJ Engine—epistemic uncertainty in probability of failure for 20% probability of redesign. The figures are plotted with different scales to show the change in the tail of the distribution. Plots show overlapping transparent histograms.

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Fig. 16

SSBJ Engine—redesign for safety is preferred when high-fidelity model error is low, but redesign for performance is preferred when high-fidelity model error is high. Plot is for fixed probability of redesign of 20%.

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