Zhan, Z., Fu, Y., and Yang, R., "On Stochastic Model Interpolation and Extrapolation Methods for Vehicle Design," SAE Int. J. Mater. Manf. 6(3):517-531, 2013, doi:10.4271/2013-01-1386.
Finite Element (FE) models are widely used in automotive for vehicle design. Even with increasing speed of computers, the simulation of high fidelity FE models is still too time-consuming to perform direct design optimization. As a result, response surface models (RSMs) are commonly used as surrogates of the FE models to reduce the turn-around time. However, RSM may introduce additional sources of uncertainty, such as model bias, and so on. The uncertainty and model bias will affect the trustworthiness of design decisions in design processes. This calls for the development of stochastic model interpolation and extrapolation methods that can address the discrepancy between the RSM and the FE results, and provide prediction intervals of model responses under uncertainty. This paper investigates and compares three stochastic methods for model interpolation and extrapolation, and they are: (1) Bayesian inference-based method, (2) Gaussian process modeling-based method, and (3) Copula-based method, and several validation metrics are proposed to evaluate the prediction results. An analytical case study and a vehicle design problem are used to demonstrate the advantages and disadvantages of these methods.