Uncertainty quantification and reduction using sensitivity analysis and Hessian derivatives

Josefina Sánchez, Kevin Otto

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

1 Citation (Scopus)
6 Downloads (Pure)

Abstract

We study the use of Hessian interaction terms to quickly identify design variables that reduce variability of system performance. To start we quantify the uncertainty and compute the variance decomposition to determine noise variables that contribute most, all at an initial design. Minimizing the uncertainty is next sought, though probabilistic optimization becomes computationally difficult, whether by including distribution parameters as an objective function or through robust design of experiments. Instead, we consider determining the more easily computed Hessian interaction matrix terms of the variance-contributing noise variables and the variables of any proposed design change. We also relate the Hessian term coefficients to subtractions in Sobol indices and reduction in response variance. Design variable changes that can reduce variability are thereby identified quickly as those with large Hessian terms against noise variables. Furthermore, the Jacobian terms of these design changes can indicate which design variables can shift the mean response, to maintain a desired nominal performance target. Using a combination of easily computed Hessian and Jacobian terms, design changes can be proposed to reduce variability while maintaining a targeted nominal. Lastly, we then recompute the uncertainty and variance decomposition at the more robust design configuration to verify the reduction in variability. This workflow therefore makes use of UQ/SA methods and computes design changes that reduce uncertainty with a minimal 4 runs per design change. An example is shown on a Stirling engine design where the top four variance-contributing tolerances are matched with two design changes identified through Hessian terms, and a new design found with 20% less variance.

Original languageEnglish
Title of host publication47th Design Automation Conference (DAC)
PublisherAmerican Society of Mechanical Engineers
Number of pages10
Volume3B
ISBN (Electronic)978-0-7918-8539-0
DOIs
Publication statusPublished - 2021
MoE publication typeA4 Article in a conference publication
EventASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference - Virtual, Online
Duration: 17 Aug 202119 Aug 2021
Conference number: 18

Conference

ConferenceASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
Abbreviated titleIDETC/CIE
CityVirtual, Online
Period17/08/202119/08/2021

Keywords

  • Robust design
  • Simulation based design
  • Systems engineering
  • Uncertainty analysis
  • Uncertainty modeling

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