MP DC Materials Process Design & Control Laboratory Statistical learning techniques for exploring process/property/microstructure relationships in polycrystal materials Veera Sundararaghavan & Prof. Nicholas Zabaras July 14, 2005 Statistical learning techniques facilitate data-driven exploration of strategies necessary to design microstructures and affiliated properties. The theme of statistical learning is a structure seeking program that searches and identifies multi-dimensional patterns in microstructure-property databases based on various attributes of the microstructure. These attributes range from simple features such as average grain size and shape to complex multi- dimensional attributes such as orientation distribution function, orientation correlation, and n-point probability functions. These attributes are then affiliated to the processing paths and properties of microstructures. Higher dimensional feature space Microstructural features Feature space Number of clusters identified using Bayesian information criterion Hyper-planes quantify correlation of features with the objective Fig. 1. Statistical learning for microstructures: Single database level using (a) unsupervised X-means algorithm (b) supervised support vector machines. The schematic shows how classes of microstructures are created based on the positions of a discretized statistical feature of microstructures. We are looking at data-driven inverse methods for designing thermo-mechanical processing paths that would tailor polycrystalline microstructures of interest. Due to non-uniqueness in the process path solution and complex nature of the microstructure-property space, this problem cannot be addressed solely using conventional optimization schemes. Through microstructure interrogation schemes based on polycrystal plasticity theory, we create databases that explore significant range of anisotropic properties achievable in polycrystalline microstructures through thermo-mechanical processing. Statistical learning tools based on support vector machines and Bayesian clustering algorithms (Fig. 1) built over such databases unearth a hierarchical structure in the database using extracted microstructural attributes. Applications of such hierarchical databases include the ability to represent and reconstruct microstructures satisfying a given set of features, and the ability to identify a class of processing paths that would result in a given microstructure or a desired property distribution. A typical design methodology involves a combination of classification for providing initial class of solutions and the use of local optimization schemes based on continuum senstitivity analysis and gradient optimization to identify the global solution [2,3]. We have also developed model-reduction techniques based on the method of proper orthogonal decomposition that accelerate such local optimization schemes. A schematic of the design procedure is shown in Fig. 2. We are currently expanding the property design space through development of techniques for tailoring polycrystal stereology apart from texture using databases built through finite element homogenization schemes. In combination with cohesive zone models of intergranular failure, we also plan to develop techniques for achieving optimal fracture resistant properties in polycrystals. Long term goals of such a system would be to exploit additional processing schemes including solidification and change in material chemistry to create databases that can explore a larger range of properties obtainable in such materials. Process sequence-1 Process parameters ODF history Reduced basis Process sequence-2 New process parameters ODF history Reduced basis Classifier Adaptive basis selection Optimization Reduced basis Process Probable Process sequences & Initial parameters Desired texture/property Stage - 1 Stage - 2 New dataset added DATABASE Optimum parameters Fig. 2. Schematic of the database-driven design procedure for microstructures: Using the information in the database, the classification algorithm identifies the processing paths leading to a desired microstructure. This information is given to a local optimization scheme driven by reduced order modes of microstructure that are adaptively selected from the database. References S. Ganapathysubramanian and N. Zabaras, "On the synergy between classification of textures and process sequence selection", in the proceedings of EPD Congress 2004, The Minerals, Metals & Materials Society Annual Meeting & Exhibition, Charlotte, North Carolina, March 14-18, 2004 V. Sundararaghavan and N. Zabaras, "On the synergy between classification of textures and process sequence selection", Acta Materialia, Vol. 53/4, pp. 1015-1027, 2005. V. Sundararaghavan and N. Zabaras, "A data mining approach for the design of polycrystalline materials", in the proceedings of EPD Congress 2005, The Minerals, Metals & Materials Society Annual Meeting & Exhibition, San Francisco, CA, February 13-17,2005. Cornell University College of Engineering Sibley School of Mechanical and Aerospace Engineering