Parameterization of Large Variability Using the Hyper-Dual Meta-Model

One major problem in the design of aerospace components is the nonlinear changes in the response due to a change in the geometry and material properties. Many of these components have small nominal values and any change can lead to a large variability. In order to characterize this large variability, traditional methods require either many simulation runs or the calculations of many higher-order derivatives. Each of these paths requires a large amount of computational power to evaluate the response curve. In order to perform uncertainty quantification (UQ) analysis, even more simulation runs are required. The hyper-dual meta-model (HDM) is introduced and used to characterize the response curve with the use of basis functions. The information of the response is generated with the utilization of the hyper-dual (HD) step to determine the sensitivities at a few number of simulation runs to greatly enrich the response space. This paper shows the accuracy of this method for two different systems with parameterizations at different stages in the design analysis.