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, features 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 designs 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.; In design optimization applications the classification tree would be used to generate high-performing design alternatives. These can be used as a set of candidate designs or be used in a multi-start search algorithm to further improve the designs. The algorithm is powerful in that the information obtained after solving one system design can be reused to guide the design process of other related systems. This is possible because the Bayesian classification tree can effectively encapsulate the knowledge implicit in each system design optimization, and can work in a feature space that would have the same feature coordinates for systems that may have different sizes (and hence difference design parameter dimensions).; In applications involving spatially random properties, the classification tree would provide pattern-based features that can be used to identify regions of a system with desirable or undesirable local properties. It is shown how this approach can be used to predict the location of damage initiation in composites with randomly located inclusions. In this example, stress analysis is used only in the training set; the predictive tool works rapidly in relatively large samples without further stress analysis. It is shown that the most important pattern-based features can be interpreted using Eshelby's theorem.