This paper develops a two-stage grey-box modeling approach that combines manufacturing knowledge-based (white-box) models with statistical (black-box) metamodels to improve model reusability and predictability. A white-box model can use various types of existing knowledge such as physical theory, high fidelity simulation or empirical data to build the foundation of the general model. The residual between a white-box prediction and empirical data can be represented with a black-box model. The combination of the white-box and black-box models provides the parallel hybrid structure of a grey-box. For any new point prediction, the estimated residual from the black-box is combined with white-box knowledge to produce the final grey-box solution. This approach was developed for use with manufacturing processes, and applied to a powder bed fusion additive manufacturing process. It can be applied in other common modeling scenarios. Two illustrative case studies are brought into the work to test this grey-box modeling approach; first for pure mathematical rigor and second for manufacturing specifically. The results of the case studies suggest that the use of grey-box models can lower predictive errors. Moreover, the resulting black-box model that represents any residual is a usable, accurate metamodel.
Evaluation of Nutrient Management Plans Using an Integrated Modeling Approach
