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Research Papers

A Metamodeling Approach for Uncertainty Analysis of Nondeterministic Systems

[+] Author and Article Information
Hae-Jin Choi

School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singaporehjchoi@ntu.edu.sg

Janet K. Allen

Systems Realization Laboratory, G.W. Woodruff School of Mechanical Engineering, Georgia Tech, Savannah, GA 31497janet.allen@me.gatech.edu

J. Mech. Des 131(4), 041008 (Mar 24, 2009) (10 pages) doi:10.1115/1.3087565 History: Received September 18, 2007; Revised January 08, 2009; Published March 24, 2009

Modern complex engineering applications are often nondeterministic systems that include sources of uncertainty that cannot be parametrized numerically; this is unparametrizable uncertainty. One example is the uncertainty in the behavior of a mechanical system due to heterogeneous material properties on the microscale (e.g., grain boundary effects on microstructure). Another example is the uncertainty in the performance of a complex topology structure due to random topology imperfections. In this paper, we propose a method for metamodeling these nondeterministic systems for efficient uncertainty analysis in robust design. Generalized linear models for mean responses and heteroscadastic response variances are estimated iteratively in an integrated manner. Estimators that may be used for predicting mean and variance models are introduced. The usefulness of this metamodeling approach is demonstrated with the example of a linear cellular alloy heat exchanger. Applications for these heat exchangers include actively cooled supersonic aircraft skins and engine combustor liners. Linear cellular alloy heat exchangers have unparametrizable uncertainty due to randomly distributed cracks in cell walls, as well as parametrizable uncertainty due to variability in wall thickness and inlet air velocity. Nondeterministic metamodels for estimating total steady state heat transfer rates in linear cellular alloy heat exchangers are developed and the results of using these metamodels are compared with those obtained by the finite element analysis (FEA) models of the linear cellular alloys.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Stochastic simulation and nondeterministic simulation

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Figure 2

Square-cell linear cellular alloy (2)

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Figure 3

Forced convection heat exchanger with graded rectangular LCAs (3)

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Figure 4

An example of the thermal analysis results of the LCA heat exchanger; (a) sectional structure of the LCA and (b) MATLAB output; a temperature profile on inlet section and total steady state heat transfer rate (Q)

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Figure 5

Randomness in temperature profiles and total heat transfer rates by random imperfections in the cell wall

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Figure 6

Heteroscadastic random errors in total heat transfer rates

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Figure 7

Steps for integrated estimation of mean response model and conditional variance function

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Figure 8

Random sampling results in the design space

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Figure 9

The mean function and prediction interval

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Figure 10

Mean and prediction interval estimation of total heat transfer rate

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Figure 11

Sampling process for testing

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Figure 12

Cumulative probability plots of sampling results at (a) μt=1 mm, μv=180 m/s, and (b) μt=1.7 mm, μv=120 m/s

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Figure 13

Histograms and normal probability density plots based on finite element data

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