Multi-layer designs and composite gaussian process models with engineering applications
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This thesis consists of three chapters, covering topics in both the design and modeling aspects of computer experiments as well as their engineering applications. The first chapter systematically develops a new class of space-filling designs for computer experiments by splitting two-level factorial designs into multiple layers. The new design is easy to generate, and our numerical study shows that it can have better space-filling properties than the optimal Latin hypercube design. The second chapter proposes a novel modeling approach for approximating computationally expensive functions that are not second-order stationary. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the second one models local details. The new predictor also incorporates a flexible variance model, which makes it more capable of approximating surfaces with varying volatility. The third chapter is devoted to a two-stage sequential strategy which integrates analytical models with finite element simulations for a micromachining process.