Mixture product design using latent variable methods

This thesis investigates the use of latent variable methods for the analysis, design and optimization of mixture processes. These strategies simultaneously take into account the selection of raw materials, the selection of the ratios in which to blend them and the selection of process conditions used to manufacture them.;The thesis consists of five main chapters: (i) mixture-property PLS modeling that takes into account the raw material properties, (ii) product development (optimization) based on the mixture-property PLS models, (iii) design of experiments based on the mixture-property PLS models, (iv) multi-block mixture-property PLS modeling and (v) estimation of missing data with auxiliary information.;The mixture-property PLS models presented represent the relationships between the final product properties and the raw material properties, their blend ratios and the process conditions. This contrasts with traditional mixture models that represent only the relationship between raw material ratios and final blend product properties. These mixture-property models provide increased interpretability and improved prediction, and allow for development of new products. Two industrial polymer blending data sets are used to illustrate these models.;An optimization strategy is presented that provides the solutions to the replacement of raw materials while keeping the same product properties, or the design of new products with specified new properties, while at the same time minimizing total raw material cost and minimizing the total number of raw materials used in the formulation. The methodology is illustrated with three blending examples.;New mixture-property design of experiment (DOE) approaches that can be used to efficiently build these models are presented. One mixture-property DOE provides efficient blending experiments to capture stable latent variable models for designing various products over a wide range of mixture and material conditions. A sequential mixture-property DOE allows one to select new material combinations and ratios in a sequential manner with the more limited objective of achieving a set of specified final product properties. The design methodologies are illustrated through two industrial polymer blending problems.;An alternative approach to the mixture-property PLS modeling is presented that does not require the assumption of mixing rules. This multi-block PLS modeling approach directly relates all the data blocks. The method is extended to allow for various types of nonlinearities among the data blocks. The approach is illustrated using data from an industrial coke making operation.;Finally, latent variable approaches for estimating missing data in the matrix of raw material properties are presented. These approaches exploit auxiliary data matrices, as well as the raw material property data matrix itself. Two approaches to incorporating the auxiliary information are presented: a multi-block approach and a novel two stage projection approach. The methodologies are illustrated using two industrial polymer blending problems.