0
RESEARCH PAPERS

Relative Entropy Based Method for Probabilistic Sensitivity Analysis in Engineering Design

[+] Author and Article Information
Huibin Liu

Integrated DEsign Automation Laboratory (IDEAL), Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Tech B224, Evanston, IL 60208-3111

Wei Chen1

Integrated DEsign Automation Laboratory (IDEAL), Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Tech B224, Evanston, IL 60208-3111

Agus Sudjianto

Risk Quality and Productivity Executive,Bank of America

1

Corresponding author. E-mail: weichen@northwestern.edu

J. Mech. Des 128(2), 326-336 (Apr 24, 2005) (11 pages) doi:10.1115/1.2159025 History: Received October 15, 2004; Revised April 24, 2005

In this paper, a new Probabilistic Sensitivity Analysis (PSA) approach based on the concept of relative entropy is proposed for design under uncertainty. The relative entropy based method evaluates the impact of a random variable on a design performance by measuring the divergence between two probability density functions of the performance response, obtained before and after the variation reduction of the random variable. The method can be applied both over the whole distribution of a performance response [called global response probabilistic sensitivity analysis (GRPSA)] and in any interested partial range of a response distribution [called regional response probabilistic sensitivity analysis (RRPSA)]. Such flexibility of our approach facilitates its use under various scenarios of design under uncertainty, for instance in robust design, reliability-based design, and utility optimization. The proposed method is applicable to both the prior-design stage for variable screening when a design solution is yet identified and the post-design stage for uncertainty reduction after an optimal design has been determined. The saddlepoint approximation approach is introduced for improving the computational efficiency of applying our proposed method. The proposed method is illustrated and verified by numerical examples and industrial design cases.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Examples of probabilistic design formulations

Grahic Jump Location
Figure 2

Whole vs partial range of a response distribution

Grahic Jump Location
Figure 3

Absolute divergence in RRPSA

Grahic Jump Location
Figure 4

p0 as weighting factor in RRPSA

Grahic Jump Location
Figure 5

Comparison of impacts of uncertainty in inputs

Grahic Jump Location
Figure 6

Distributions of random inputs

Grahic Jump Location
Figure 7

Comparison of impacts of inputs

Grahic Jump Location
Figure 8

PDF of Y and the enlargement of the left tail (failure range)

Grahic Jump Location
Figure 9

Importance rankings of engine design

Grahic Jump Location
Figure 10

Robust design formulation for the engine assembly design

Grahic Jump Location
Figure 11

Limit state functions of active constraints

Grahic Jump Location
Figure 12

Importance rankings based on total effects

Grahic Jump Location
Figure 13

Reliability improvement by variation reduction in inputs, g2

Grahic Jump Location
Figure 14

Reliability improvement by variation reduction in inputs, g8

Grahic Jump Location
Figure 15

Reliability improvement by variation reduction in random inputs, g10

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