Enabling metrology-oriented specification of geometrical variability: A categorical approach

In this paper a metrology-oriented specification schema is proposed to enrich the specification semantics with sufficient metrological information. It is designed particularly for applications where non-traditional measurement methods are applied; and it can also identify any redundancies, inconsistencies or incompletenesses of a specification. The proposed schema is based on category theoretical semantics which uses category theory as the foundation to model the semantics. A set of verification operations that derived from the measurement process was firstly formalised using the categorical semantics. Then a set of full faithful functors were constructed to map the set of verification operations to a set of specification operations. A set of simplification rules was then developed to deduce all of the necessary specification objects which are independent to each other. Then the residual specification objects provide a compact structure of the specification. Three test cases were conducted to validate the proposed schema. An industrial computed tomography (CT) measurement process for an impeller manufacturing using selective laser sintering (SLS) technique, was modelled and a set of independent specification elements was then deduced. The other two test cases for checking redundancy and incompleteness on general ISO specifications were carried out. The results show that the proposed schema works for proposing semantic enriched specification that are characterised by non-traditional measurement methods and for testing redundancy and incompleteness of specifications based on geometrical product specifications and verification (GPS) standards system.