Bayesian Classifiers for Uncertainty Modeling with Applications to Global Optimization and Solid Mechanics Problems

In this dissertation, it is shown how pattern recognition approaches developed in computer science can be seamlessly combined with statistical techniques to produce a knowledge-driven search algorithm. Two different classes of applications are used to demonstrate the wide applicability of the algorithm. The first class of applications is in global design optimization. The second is in the structural mechanics of systems with spatially random properties. Two functional mappings are used. The first is from a high-dimensional work space, defining the raw parameters of a problem, to a low-dimensional feature space. Here, fea-tures are knowledge-laden coordinates that are defined with the help of a domain expert. It is noted that the expert need not know which region of feature space may contain de-signs of systems with desirable behavior- the expert need only provide features that may be relevant to system performance. A Bayesian classification tree is then used to reduce the dimension of the feature space and identify regions of feature space that may contain system designs with desirable behavior