Rigorous Modelling of Quantities for Model-Based Systems Engineering

Abstract

In a model-based engineering approach, many aspects of the model elements need to be characterized or specified through physical quantities. Traditionally, many modelling languages and frameworks have used simple conventions for naming quantities and associating basic numeric types (e.g., real, float, integer) to represent their values. Often the types are enhanced with some kind of annotation to convey applicable measurement units, and, sometimes, their quantity dimension. This can work reasonably well in smaller, single discipline, single tooling environments. However, multi-disciplinary, highly iterative engineering of larger, complex systems, with interfaces across many engineering organizations, demands a more sophisticated approach. The simple approach supported by manual checks quickly reaches its limits. A rigorous semantic approach with systematic checks by machine is needed to prevent the multitude of serious errors that can – and regularly do – arise from mismatches or misinterpretations of quantities and their values. Models themselves, tools, transformations, execution results, etc. are all prone to such mistakes. I daresay most of us have suffered one time or another from such problems. The keynote will present the formal approach taken to develop an extensible model library for version 2 of the OMG Systems Modeling Language (SysML), and compares it with other formal approaches. The SysML v2 semantic model or ontology elaborates on the earlier informative QUDV (Quantities, Units, Dimensions and Values) package of SysML v1. It goes beyond scalar quantities, measurement units and simple scales, by adding support for tensor and vector quantities, integration with coordinate system definition and transformation, as well as representation of free and bound vector spaces. It allows to perform automated quantity value conversion (for a change of unit or scale) and dimensional analysis of expressions that involve quantities. The SysML v2 concrete textual syntax supports a very natural reading of quantity values, e.g., mass = 24 [kg]. The chosen approach uses the terminology of the International Vocabulary of Metrology (see https://jcgm.bipm.org/vim/en/index.html) as a basis. Apart from the semantic model, the library comprises packages that predefine all quantities and units standardized in the ISO/IEC 80000:2019 series (International System of Quantities and SI) as well as a package that captures the US Customary Units, and their conversion factors to SI, as specified in NIST SP 811. A number of practical SysML v2 examples will be shown.