A mathematical foundation to support bidirectional mappings between digital models: an application of multi-scale modelling in manufacturing

With manufacturing going through the Industry 4.0 revolution, a vast amount of data and information exchange leads to an increase in complexity of digitized manufacturing systems. To tackle such complexity, one solution is to design and operate a digital twin model under different levels of abstraction, with different levels of detail, according to the available information and scope of the model. To support efficient, coherent and stable information flows between models with different levels of detail, a mathematical structure, called a delta lens, has been explored and developed to support rigorous bidirectional transitions between the models. To support different types of abstractions in manufacturing, a hybrid delta lens has been proposed and its formal representation is developed to support the generalization of its structure and properties. Benefits of the proposed hybrid delta lenses are demonstrated through an application to an industrial case to support the modelling of an automatic, high-throughput assembly line.