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Qi, Qunfen; Scott, Paul J.; Jiang, Xiangqian; Lu, Wenlong (2016)
Publisher: Elsevier BV
Journal: Procedia CIRP
Languages: English
Types: Article
Subjects: TJ

Classified by OpenAIRE into

arxiv: Mathematics::Category Theory
International standards for tolerancing (ISO GPS) have undergone considerable evolutionary changes to meet the demands of the modern information age. Their expanding quantity and complexity have proposed a great obstacle to their informatisation progress. In this paper, a solution to reduce the complexity is coarse-graining the GPS knowledge into five hierarchy levels. A high-level abstraction mathematical theory - category theory is employed to model the GPS hierarchy, in which structures are modelled by categorical concepts such as categories, morphisms, pullbacks, functors and adjoint functors. As category theory is hierarchically structured itself, it can prove that the multi-level GPS framework is constructed in a rigorous manner and is expected to facilitate the future autonomous integration between design and measurement in the manufacturing system.
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    • [1] Srinivasan, V.. A geometrical product specification language based on a classification of symmetry groups. Computer-Aided Design 1999;31(11):659-668.
    • [2] Dantan, J.Y., Ballu, A., Mathieu, L.. Geometrical product specificationsmodel for product life cycle. Computer-Aided Design 2008;40(4):493- 501.
    • [3] Ballu, A., Mathieu, L., Dantan, J.Y.. Global view of geometrical specifications. In: Geometric Product Specification and Verification: Integration of Functionality. Springer; 2003, p. 13-24.
    • [4] ISO 14638. Geometrical product specification(GPS)- Masterplan. Standard; International Organization for Standardization; Geneva, CH; 1995.
    • [5] RoseĀ“n, B.G., Ohlsson, R., Westberg, J.. Interactive surface modelling, an implementation of an expert system for specification of surface roughness and topography. International Journal of Machine Tools and Manufacture 1995;35(2):317-324.
    • [6] Bui, S.H., Muralikrishnan, B., Raja, J.. A framework for internet-based surface texture analysis and information system. Precision engineering 2005;29(3):298-306.
    • [7] Filippi, S., Cristofolini, I.. The design guidelines (dgls), a knowledgebased system for industrial design developed accordingly to iso-gps (geometrical product specifications) concepts. Research in engineering design 2007;18(1):1-19.
    • [8] Xu, Y., Xu, Z., Jiang, X., Scott, P.. Developing a knowledge-based system for complex geometrical product specification (gps) data manipulation. Knowledge-Based Systems 2011;24(1):10-22.
    • [9] Qi, Q., Jiang, X., Liu, X., Scott, P.J.. An unambiguous expression method of the surface texture. Measurement 2010;43(10):1398-1403.
    • [10] Qi, Q., Jiang, X., Scott, P.J.. Knowledge modeling for specifications and verification in areal surface texture. Precision Engineering 2012;36(2):322-333.
    • [11] Anselmetti, B., Chavanne, R., Yang, J.X., Anwer, N.. Quick gps: A new cat system for single-part tolerancing. Computer-Aided Design 2010;42(9):768-780.
    • [12] Eilenberg, S., MacLane, S.. General theory of natural equivalences. Transactions of the American Mathematical Society 1945;:231-294.
    • [13] Spivak, D.I., Kent, R.E.. Ologs: a categorical framework for knowledge representation. PLoS One 2012;7(1):e24274.
    • [14] Baianu, I., Brown, R., Glazebrook, J.F.. A category theory and higher dimensional algebra approach to complex systems biology, meta-systems and ontological theory of levels: emergence of life, society, human consciousness and artificial intelligence. Acta Univers Apul 2011;(Suppl 1):176-99.
    • [15] Healy, M.J., Caudell, T.P.. Ontologies and worlds in category theory: implications for neural systems. Axiomathes 2006;16(1-2):165-214.
    • [16] Healy, M.J., Olinger, R.D., Young, R.J., Taylor, S.E., Caudell, T., Larson, K.W.. Applying category theory to improve the performance of a neural architecture. Neurocomputing 2009;72(13):3158-3173.
    • [17] Haruna, T.. Theory of interface: Category theory, directed networks and evolution of biological networks. BioSystems 2013;114(2):125-148.
    • [18] Diskin, Z., Maibaum, T., Czarnecki, K.. Towards category theory foundations for model management. Tech. Rep.; Tech. Rep. GSDLab-TR 2014- 03-03, University of Waterloo/McMaster University, http://gsd. uwaterloo. ca/node/566; 2014.
    • [19] Qi, Q., Scott, P.J., Jiang, X., Lu, W.. Design and implementation of an integrated surface texture information system for design, manufacture and measurement. Computer-Aided Design 2014;57:41-53.
    • [20] Spivak, D.I.. Category Theory for the Sciences. 1 edition ed.; Cambridge, Massachusetts: MIT Press; 2014. ISBN 9780262028134.
    • [21] McLarty, C.. Elementary categories, elementary toposes. Oxford University Press; 1992.
    • [22] Pierce, B.C.. Basic category theory for computer scientists. MIT press; 1991.
    • [23] ISO 17450-1:2011. Geometrical product specifications (GPS) General concepts, Part 1: Model for geometrical specification and verification. Standard; International Organization for Standardization; Geneva, CH; 2011.
    • [24] Zhang, X., Jiang, X., Scott, P.J.. A new free-form surface fitting method for precision coordinate metrology. Wear 2009;266(5):543-547.
    • [25] Jiang, X., Scott, P., Whitehouse, D.. Freeform surface characterisation-a fresh strategy. CIRP Annals-Manufacturing Technology 2007;56(1):553- 556.
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