From Model-Driven Architecture and Model-Based Systems Engineering via Formal Concept Analysis to Graph-Based Design Languages and Back: A Scientific Discourse

Most modern digital approaches to engineering are based on models and their model transformations. Most of these model transformations are mathematically speaking non-bijective mappings — so-called projections — where some information of the original model is lost during the mapping. From a theoretical point of view it is therefore of great interest to exactly examine the properties of these model transformations. In this paper at first the characteristics of a model are briefly explained. Then some of the most common model-based engineering approaches are reviewed and compared regarding their models and model transformations. In this examination the missing existence of an inverse transformation (a so-called text-to-model transformation, T2M) of a typical model transformation (a so-called model-to-text transformation, M2T) is identified. That discovery may well hold the key to the realization of a so-called round-trip engineering. The required existence of the inverse transformation to this round-trip engineering is then generically postulated as having the nature of a pattern recognition problem. For illustration purposes and a better understanding of the interpretation of the inverse transformation as a pattern recognition problem, a case study for the reconstruction of an abstract model from the concrete model is given using CAD-Data of a satellite. Since CAD models belong to geometry, dimensionless geometric moment invariants play a key role in the generic solution of the pattern recognition problem contained in this example.