Conceptual modelling: Towards detecting modelling errors in engineering applications. (9th December 2019)

• Record Type: Journal Article
• Authors: Gürlebeck, Klaus; Legatiuk, Dmitrii; Nilsson, Henrik; Smarsly, Kay
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 3(2020)
• Page Start: 1243
• Page End: 1252
• Publication Date: 2019-12-09
• Subjects: abstraction -- engineering -- formal approaches -- modelling -- type theory; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5934
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer "simple" objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems.