(176e) Data-Driven Optimization of Product Blends Using Multivariate Property Clustering Techniques

Mixture processes play an important role in today’s manufacturing of value-added chemical products such as commodity chemicals, food, cosmetics, oil and pharmaceuticals. In classical non-mixture designs such as factorial and response surface designs, all the factors are orthogonal or independent. This means that it is possible to freely choose the level of a factor regardless of the other factors’ levels. However, this freedom does not exist for mixture designs, because each component in a mixture is dependent upon the settings of the other component settings. In mixture design, the factors are interdependent and the effects of the factors on the responses are not separable. In addition, traditional mixture models are usually employed to investigate the relationships between the blend ratio matrix (R) and the final blend product property matrix (Y) only, given that the properties of the pure raw materials (X) and the process conditions used to manufacture them (Z) are already chosen. However, in the development of formulated products that meet target properties with minimum experiments and minimum total material cost, it is important to simultaneously account for all three degrees of freedom (X, R, and Z) available in the blending operations.

In this paper, projection methods like PCA and PLS are employed to extract and utilize the necessary information from all three degrees of freedom that are available to control the properties of any product manufactured in blending operation. This information is used to build models to simultaneously explore variations in the raw material properties data (X), their blend ratios (R), and process conditions (Z) and the resulting effect on the product quality (Y). These methods capture information about the variance and correlation structure within predictor and quality variables that were present during the production of previous product grades and that are important for consistency of the desired process conditions with past operating procedures. An integrated solution approach is employed that formulates two reverse problems, one for determination of design targets and another for matching of the design targets. The empirical models are used in a reverse problem formulation to ensure that a complete set of candidate materials and their mixtures are found which match the design target subject to the predictive power of the model. Mapping the design problem onto the lower dimensional cluster space utilizing property clustering algorithm facilitates visualization and simultaneous solution of the problem and also avoids combinatorial explosion when dealing with multi-component mixtures.

The method and concepts will be illustrated using a case study describing the design of polymer blending problems in a latent variable space.