An engineering design methodology with multistage Bayesian surrogates and optimal sampling

This paper, presents an adaptive, surrogate-based, engineering design methodology for the efficient use of numerical simulations of physical models. These surrogates are nonlinear regression models fitted with data obtained from deterministic numerical simulations using optimal sampling. A multistage Bayesian procedure is followed in the formulation of surrogates to support the evolutionary nature of engineering design. Information from computer simulations of different levels of accuracy and detail is integrated, updating surrogates sequentially to improve their accuracy. Data-adaptive optimal sampling is conducted by minimizing the sum of the eigenvalues of the prior covariance matrix. Metrics to quantify prediction errors are proposed and tested to evaluate surrogate accuracy given cost and time constraints. The proposed methodology is tested with a known analytical function to illustrate accuracy and cost tradeoffs. This methodology is then applied to the thermal design of embedded electronic packages with five design parameters. Temperature distributions of embedded electronic chip configurations are calculated using spectral element direct numerical simulations. Surrogates, built from 30 simulations in two stages, are used to predict responses of new design combinations and to minimize the maximum chip temperature.