A Metamodeling Approach for Uncertainty Analysis of Nondeterministic Systems

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.