0
Research Papers: Design Automation

Variance-Based Sensitivity Analysis to Support Simulation-Based Design Under Uncertainty

[+] Author and Article Information
Max M. J. Opgenoord

Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: mopg@mit.edu

Douglas L. Allaire

Assistant Professor
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: dallaire@tamu.edu

Karen E. Willcox

Professor
Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: kwillcox@mit.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 5, 2016; final manuscript received June 30, 2016; published online September 12, 2016. Assoc. Editor: Samy Missoum.

J. Mech. Des 138(11), 111410 (Sep 12, 2016) (12 pages) Paper No: MD-16-1188; doi: 10.1115/1.4034224 History: Received March 05, 2016; Revised June 30, 2016

Sensitivity analysis plays a critical role in quantifying uncertainty in the design of engineering systems. A variance-based global sensitivity analysis is often used to rank the importance of input factors, based on their contribution to the variance of the output quantity of interest. However, this analysis assumes that all input variability can be reduced to zero, which is typically not the case in a design setting. Distributional sensitivity analysis (DSA) instead treats the uncertainty reduction in the inputs as a random variable, and defines a variance-based sensitivity index function that characterizes the relative contribution to the output variance as a function of the amount of uncertainty reduction. This paper develops a computationally efficient implementation for the DSA formulation and extends it to include distributions commonly used in engineering design under uncertainty. Application of the DSA method to the conceptual design of a commercial jetliner demonstrates how the sensitivity analysis provides valuable information to designers and decision-makers on where and how to target uncertainty reduction efforts.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Comparison of design process using global sensitivity analysis and distributional sensitivity analysis

Grahic Jump Location
Fig. 2

Flow chart for distributional sensitivity analysis

Grahic Jump Location
Fig. 3

Reasonable distributions for the normal distribution. In this example λi=0.5 : (a) lower bound for the updated distribution and (b) upper bound for the updated distribution.

Grahic Jump Location
Fig. 4

Reasonable distributions for different strategies for triangular distributions. In this example, λi=0.5 : (a) Lower bound for strategy where shape is kept fixed, (b) upper bound for strategy where shape is kept fixed, (c) lower bound for strategy where most-likely value is kept fixed, and (d) upper bound for strategy where most-likely value is kept fixed.

Grahic Jump Location
Fig. 5

Variance-based sensitivity index functions for X1, X2, and X3 for the Ishigami test function

Grahic Jump Location
Fig. 6

Convergence of δ(g,g̃) for the additive function in Eq. (19) for different numbers of quadrature points and basis functions using quasi Monte Carlo simulation with 65,536 samples

Grahic Jump Location
Fig. 7

Distributional sensitivity analysis results for the additive function with normal distributions: (a) variance-based sensitivity index functions for X1, X2, and X3 with λi = 0.0, 0.05, …, 1.0 and (b) comparison between main-effect sensitivity indices Si and average main effect sensitivity indices ηi

Grahic Jump Location
Fig. 8

Distributional sensitivity analysis results for the Boeing 737-800 (a) variance-based sensitivity index function and (b) average main effect sensitivity indices compared to global sensitivity indices

Grahic Jump Location
Fig. 9

Distributional sensitivity analysis results for the D8.6: (a) variance-based sensitivity index function and (b) average main effect sensitivity indices compared to global sensitivity indices

Grahic Jump Location
Fig. 10

Contour of PFEI as a function of OPR and M for both aircraft. The shaded contour is the TASOPT “truth” output, while the dashed lines represent the ANOVA-HDMR surrogate and the circles represent the quadrature points: (a) Boeing 737-800 and (b) D8.6.

Grahic Jump Location
Fig. 11

Average main effect sensitivity indices from DSA of all uncertain design input parameters according to the distributions for the Boeing 737-800 in Refs. [43] and [44]

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In