Multistage bayesian surrogates and optimal sampling for engineering design and process improvement
Ignacio G. Osio · 1996
This work deals with the development of an adaptive engineering design methodology based on Bayesian surrogates of computer simulations and experiments. These surrogates are nonlinear regression models fitted with data obtained from deterministic numerical models and/or experimental data using optimal sampling. Surrogates can be used for design, optimization, sensitivity and tradeoff studies. The statistical theory of Bayesian inference is used in the formulation of surrogates to support the evolutionary nature of engineering design within a multistage approach. Information from computer simulations of different levels of accuracy and detail is integrated, updating surrogates sequentially to improve their accuracy. Surrogates are updated in sequential stages and used to obtain new experimental design combinations according to the requirements and limitations of each problem. Data-adaptive optimal sampling is conducted by minimizing the sum of the eingenvalues of the prior covariance matrix. Metrics to select different surrogate models and quantify prediction errors are proposed and tested. The proposed methodology is tested with known analytical functions to illustrate accuracy and cost tradeoffs. This methodology is also applied to the thermal design of embedded electronic packages with five control parameters. The temperature distributions of embedded electronic chip configurations are calculated using spectral element direct numerical simulations of the heat transfer process. Finally, we apply the methodology to the quality improvement of multidrop microcasted copper samples. This application demonstrates the capability of the methodology to study and optimize physical processes.