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
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Figure 1

Representative response surface

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Figure 2

Schematic of thermal protection of an object

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Figure 3

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

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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

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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

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Figure 6

Sensitivities of regression time based on Eqs. 7,2

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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)

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Figure 8

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




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