Metamodels – simple, data-driven approximations of the input/output relationship of complex models – are widely used to approximate the response of computationally-intensive engineering simulations. They are formulated based on observations (experiments) of the original simulation model. Among the variety of metamodeling techniques, Kriging (i.e., Gaussian process regression) has gained significant popularity, especially for UQ (uncertainty quantification) applications, because of its computational efficiency, flexibility in providing accurate approximations even for complex models and ability to quantify the uncertainty in the associated predictions (i.e., providing a local metamodel prediction error).
This thesis investigates the iterative/adaptive Kriging metamodel development for UQ analysis of engineering applications involving complex numerical models. The iterative development is primarily examined in the context of two different fundamental UQ tasks: (i) stochastic sampling and density approximation, and (ii) design optimization under uncertainty. The foundation of the adaptive approach is the iterative formulation of the metamodel to efficiently accomplish the specific task at hand. Convergence criteria are developed to assess whether the metamodel refinement across subsequent iterations provides different UQ results. If convergence has not been achieved (differences exist), additional experiments are obtained using an adaptive sample-based design of experiments (DoE) that targets for the system input domain of importance with respect to the UQ analysis. Rather that establishing global accuracy, this approach facilitates convergence to accurate solutions leveraging adaptively refined metamodels to facilitate high accuracy predictions only with respect to the UQ task at hand. Different convergence criteria, iterative approaches and DoE strategies are established for each of the aforementioned UQ tasks. For the stochastic sampling and density approximation task, two different implementation settings are examined: rare event simulation and Bayesian posterior sampling. For the design under uncertainty task implementation to both single-objective and multi-objective problems are examined, in all instances adopting metamodel development in the augmented input space, so that uncertainty propagation and design optimization are simultaneously supported.
Beyond these two specialized tasks, the adaptive metamodel development is further examined with respect to two realistic applications: (i) real-time hurricane risk assessment and (ii) hydrodynamic interaction characterization of wave energy converters (WEC). For the first application adaptive implementation is examined with respect to the selection of storms informing the metamodel and with respect to characteristics related to climate change. For the second application focus is on establishing a hierarchical interaction decomposition so that metamodels in lower dimensional input space can be used to provide predictions for large dimensional WEC arrays. Adaptivity is established in this instance with respect to the hierarchical decomposition.