A methodology for surrogate model building in the engineering design process

This thesis proposes a methodology for building surrogate models in the engineering design process. These surrogate models are substitutes for the true responses, and are also known as metamodels, since they are models of a model. In situations when the cost of data gathering from numerical simulations and experiments is restrictive or when there are no governing equations for the response, these models are beneficial. Metamodels can be used for design, trade off, optimization and robustness studies. The mathematical framework in Bayesian surrogate models employs spatial interpolators (Kriging), in which the assumption of an underlying stochastic process with a multivariate Gaussian distribution is made.; This methodology enables designers to develop models for discrete and continuous parameters, in which constraints can be imposed on the response or the parameters. In these models, the parameters' range can change from stage to stage and parameters can be added and suppressed as the models are built. In the presence of replications for the experiments, the statistical information from replications is integrated into the models to obtain uncertainty measurements. The surrogate models can combine data gathered through numerical simulations and physical experiments. For creating accurate models a framework is developed to use the covariance-based structure when no a priori information is available. These models will allow the designers to create flexible and accurate models that can evolve throughout the design process.; The proposed methodology is examined with test cases using analytical functions. This analysis demonstrates: theoretical implications of the framework, flexibility of the surrogates, advantages in integration of data, and accuracy of the models. In this thesis, Bayesian surrogates are applied to two physical problems, heat removal in electronic cooling and regeneration of bone tissue. For the heat removal problem, the objective is to maximize the heat transfer from a pipe containing a dielectric fluid that passes through a plastic support structure. For the bone regeneration problem, the objective is to study two treatments for alveolar bone augmentation and periodontal regeneration. These applications show the capability of Bayesian surrogate models for product and process development.