A statistical learning approach for the design of polycrystalline materials

Important physical properties such as yield strength, elastic modulus, and thermal conductivity depend on the material microstructure. Realization of optimal microstructures is important for hardware components in aerospace applications where there is a need to optimize material properties for improved performance. Microstructures can be tailored through controlled deformation or heat treatment. However, identification of the optimal processing path is a non-trivial (and nonunique) problem. Data-mining techniques are eminently suitable for process design since optimal processing paths can be selected based on available information from a large database-relating processes, properties, and microstructures. In this paper, the problem of designing processing stages that lead to a desired microstructure or material property is addressed by mining over a database of microstructural signatures. A hierarchical X-means classifier is designed to match crystallographic orientation features to a class of microstructural signatures within a database. Instead of the conventional distortion minimization algorithm of k-means, X-means maximizes a Bayesian information measure for calculating cluster centers which allows automatic detection of number of classes. Using the microstructural database, an adaptive data-compression technique based on proper orthogonal decomposition (POD) has been designed to accelerate materials design. In this technique, reduced modes selected adaptively from the database are used to speed up auxiliary microstructure optimization algorithms built over the database.  2009 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 1: 306–321, 2009