Modeling the integration between specifications and verification for cylindricity based on category theory

Abstract

Geometrical product specifications (GPS) is a standard system defined by ISO/TC213 which covers the standardization for micro-and macro-geometry specifications to make it suitable for the requirements of modern technologies. In addition, it integrates specifications and verification to make geometrical specifications more unambiguous and unique. Data modeling is a primary task in building an integrated information system for the application of geometrical characteristics consistent with the GPS standard system. It is feasible to extend this data modeling method to the whole GPS information system. This paper presents data modeling for the integration between specifications and verification for cylindricity consistent with GPS based on the category theory. The categorical data modeling method represents and stores all the elements and the relationships between them concerning the specifications and the verification process for cylindricity by categories, objects and morphisms; the established categories can be extended flexibly; the relationships between the objects were refined by pull back structures; and the manipulations of the model, such as query and the closure of query, are realized successfully by functor transforms in category theory.

Towards a tolerance representation model for generating tolerance specification schemes and corresponding tolerance zones

“…The category theory model was firstly presented by Wang et al [36] to characterize the information of profile surface texture. It has later been applied by Lu et al [37] to represent the tolerance information in specification and verification via certain categorical constructors, which include category, object, morphism, pull back, product, functor, and natural transformation. The category theory model can provide an abstract representation of tolerance information.…”

A review of representation models of tolerance information

“…It has later been applied by Lu et al [40] to systematically describe the information of geometrical product specifications (GPS) via certain categorical constructors in category theory, which include category, subcategory, object, morphism, instance, pull back, product, functor, and natural transformation. The model provides an abstract representation of the tolerance specifications described in natural language in technical handbooks and tolerancing standards.…”

“…Currently, the representation model used in industry is the EXPRESS model [29][30][31], while at the same time, other representation models, such as surface graph model [32][33][34], representational primitive model [35,36], technologically and topologically related surface (TTRS) model [37], unified modeling language (UML) model [38], extensive markup language (XML) model [39], category theory model [40][41][42][43], GeoSpelling model [44], relationship model [45,46], and ontology-based model [47][48][49][50], have been presented within the academia. The coexistence of different kinds of representation models triggers a series of questions and discussions within the academia and the industry.…”

Explicitly representing the semantics of composite positional tolerance for patterns of holes

“…& Categorical language model. To solve the ambiguous problem caused by describing GPS specifications in natural language in tolerancing standards and technical handbooks, Lu et al [37] used category language to construct a representation model of the specifications and verification for geometrical tolerances in the framework of the next generation GPS. The representation model was then used by Xu et al [38] and Qi et al [39] to develop a knowledgebased system for the manipulation of complicated GPS information.…”