Bayesian surrogate modeling of deterministic simulation codes for probablistic analysis

A Bayesian Gaussian process modeling framework is presented for uncertainty analysis of systems using existing deterministic black-box simulation codes. It is argued that the Bayesian modeling approach is statistically more meaningful as compared to response surface methods which use least-square regression techniques. Further, the present framework allows for the possibility of computing error estimates of the computed statistics. An adaptive design of experiments strategy is also presented for improving the accuracy of the model. Numerical studies are presented for a structural reliability analysis problem. The results indicate that the Bayesian approach holds promise for significantly reducing the computational cost of simulation based approaches. Further, the error estimates computed using the Bayesian approach are shown to become reasonably tighter with increase in the number of design points.

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