New Non-Equidistant Optimum GM(1,1) of Line-Drawing Data Processing in Computer Aided Design

Abstract:

Based on the exponential trait of grey model and the definition of integral, the reconstruction method of GM(1,1) model’s background value of non-equal distance sequence was put forward and a kind of non-equidistant optimum grey model GM(1,1) to line-drawing data processing in computer aided design was proposed. The mean relative error is taken as the optimum objective function. The power mutation particle swarm optimization program PMPSO1.0 was compiled with Matlab 7.6 software to make optimization. Two examples were given, their results were compared with the results based other Grey models, respectively. The method can be used for model establishing on equal interval, as well as on non-interval. Moreover, GM(1,1) model’s fitting precision and prediction is advanced and the scope of application is enlarged. The model is simple and practical, and has a generalizing value in the field of CAD.

• Periodical: Key Engineering Materials (Volumes 439-440)
• Pages: 1561-1566
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.439-440.1561
• Online since: June 2010
• Authors: You Xin Luo
• Keywords: Background Value, Computer Aided Design (CAD), Data Processing, Grey Model, Grey System, Non-Equidistant Sequence, Optimizing

References

[1] Y.X. LUO. The gray model and method of test data processing & online monitoring of trial (in Chinese). Journal of Chinese Machine Design, , Vol. 10, No. 6(1993), pp.38-41.

[2] Guan J. H., Li D. H., Shi Y. H., Cai T. Study on the Gray Model for the Measurement in Honing Process of Cylinder Bore of Engine. Advances in Systems Science and Applications, Vol. 3, No. 4(2003), pp.531-536.

[3] Xiong H. J., Chen D. J., Chen M. Y. Study on Gray Method of Data Mining. Advances in Systems Science and Applications, , Vol. 3, No. 2(2003), pp.309-313.

[4] Z.M. HE, Y.X. LUO. Gray model and method of computer aided line-drawing data processing (in Chinese). Transactions of the Chinese Society for Agricultural Machinery, Vol. 33, No. 2 (2002), pp: 94-96.

[5] Y.X. LUO, L.T. ZHANG, A.H. CAI., et al. Grey GM(1, 1) with function-transfer method and application to energy consuming prediction. Kybernets, Vol. 33, No. 2(2004), pp.322-330.

[6] Y. X LUO,D.G. LIAO, Q. X TANG, et al. A Step by Step Optimum Modeling method of GM (1, 1) and Its Application to Fault Diagnosis in NC System of NC Machine Tool. Machine tool & Hydraulics , No. 6(2002), pp.229-231.

[7] Q.Y. WANG). Uncertainty mathematical model of forecast & decision-making (in Chinese). Beijing: Metallurgical industry Press(2001).

[8] Eberhart R C, Shi Y. Comparing inertia weights and constriction factors in particle swarm optimization. Proc. of the 2000 Congress on Evolutionary Computation. Piscataway: IEEE, 2000, pp.84-88.

DOI: 10.1109/cec.2000.870279

[9] X.Y. CHE, Z.M. HE,Y.X. LUO. Complex particle swarm algorithm for the positional forward solution of planar parallel robot. Journal of Machine Design, , Vol. 26, No. 3(2009), pp.46-48.

[10] Z.M. HE, Y.X. LUO, B. ZENG. Power Mutation Particle Swarm Optimization with Hybrid Discrete Variables and its Application to Gear Reducer. Proceedings of the 3rd International Conference on Intelligent Information Technology Application Workshops (IITAW 2009). Nanchang, China, November, (2009).

DOI: 10.1109/iitaw.2009.8

[11] Z. Zhang, Q.C. Meng,R. Xue, et al. A new algorithm for solving nonlinear constrained optimization problems with particle swarm optimizer. Journal of Harbin Institute of Technology, Vol. 38, No. 10(2006), pp.1716-1718.