Determination of the Sensitivity of Heat Transfer Systems Using Global Sensitivity and Gaussian Processes

[+] Author and Article Information
A. F. Emery

Department of Mechanical Engineering,  University of Washington, Seattle, WA 98195-2600emery@u.washington.edu

D. Bardot

Department of Mechanical Engineering,  University of Washington, Seattle, WA 98195-2600

J. Heat Transfer 129(8), 1075-1081 (Sep 26, 2006) (7 pages) doi:10.1115/1.2737478 History: Received March 21, 2006; Revised September 26, 2006

A critical aspect of the design of systems or experiments is a sensitivity analysis to determine the effects of the different variables. This is usually done by representing the response by a Taylor series and evaluating the first-order derivatives at a nominal operating point. When there is uncertainty about the operating point, the common approach is the construction of a response surface and Monte Carlo sampling based on the probability distribution of these uncertain variables. Because of the expense of Monte Carlo sampling, it is important to restrict the analysis to those variables to which the response is most sensitive. Identification of the most sensitive parameters can be conveniently done using Global sensitivity, which both defines the most critical variables and also quantifies the effects of interacting variables. This also can be a computationally expensive process and, for complex models, is generally prohibitively expensive. A solution is the use of Gaussian processes that allows one to create a response surface using easy-to-evaluate functions. This paper describes the use of these ideas for a heat transfer problem.

Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Representative response surface

Grahic Jump Location
Figure 4

(a) Sensitivity to k(Sk*) over the range of k and h0 and (b) sensitivity to h0(sh0*) over the range of k and h0

Grahic Jump Location
Figure 5

Time histories for (a) ∑Si for T(A) and (b) for Si[T(A)] and SiT[T(A)], (c) effect of uncertain parameters on T(A) and (d) standard deviation of T(A) based on Eqs. 7,2

Grahic Jump Location
Figure 6

Sensitivities of regression time based on Eqs. 7,2

Grahic Jump Location
Figure 7

Comparing the contours of the exact temperatures (solid lines) and m(x) from the Gaussian process (dashed lines);  * denotes the design points (for κ=1, Bi0=10, BiL=100)

Grahic Jump Location
Figure 8

Variances computed from (a) the Gaussian process and (b) the exact model (Eq. 12)

Grahic Jump Location
Figure 2

Schematic of thermal protection of an object

Grahic Jump Location
Figure 3

Time histories of sensitivity S* to k and to h0 evaluated at knom and h0nom



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