The effectiveness of using Computer Aided Engineering (CAE) tools to support design decisions is often hindered by the enormous computational demand of complex analysis models, especially when uncertainty is considered. Approximations of analysis models, also known as “metamodels”, are widely used to replace analysis models for optimization under uncertainty. However, due to the inherent nonlinearity in occupant responses during a crash event and relatively large numbers of uncertain variables and responses, naive application of metamodeling techniques can yield misleading results with little or no warning from the algorithms which generate the metamodels. Furthermore, in order to improve the quality of metamodels, a relatively large number of design of experiments (DOE) and comparatively expensive metamodeling techniques, such as Kriging or radial basis function (RBF), are necessary. Thus, sampling-based methods, e.g. Monte Carlo simulations, for obtaining the statistical quantities of system responses during the optimization loop may still be inefficient even for these metamodels. In recent years, analytical uncertainty propagation via metamodels is proposed by Chen et al. 2004, which provides analytical formulation of mean and variance evaluations via a variety of metamodeling techniques to reduce the computational time and improve the convergence behavior of optimization under uncertainty. An occupant restraint system design problem is used as an example to test the applicability of this method.

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