Novel New Information Non-Equidistant Optimum GM(1,1) and its Application to Line-Drawing Data Processing in Computer Aided Design

Abstract:

Based on grey system, a new kind of new information non-equidistant optimum grey model GM(1,1) to line-drawing data processing in computer aided design was proposed in which the response function is based on new information x(tn) . The objective function is built to make the fitting mean relative error least and the program was compiled with bacterial foraging algorithm (BFA) combined with particle swarm optimization (PSO) algorithm to optimize the background value and modify the initial value x(tn) of response function. The method of precision inspection was introduced. The programming was authorized with MATLAB7.6 language. 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: 349-354
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.439-440.349
• Online since: June 2010
• Authors: You Xin Luo, Bin Zeng
• Keywords: Background Value, Computer Aided Design (CAD), Data Processing, Grey Model, 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] Y.X. LUO L.T. ZHANG, M. LI. Grey system theory and its application to mechanical engineering (in Chinese). ShangSha: National University of Defense technology Press (2001).

[8] S.F. LIU,T.B. GUO,Y.G. DANG, et al. Grey systems and Applications (third edtion)(in Chinese) . Beijing: China Science Press (2004).

[9] Y.X. LUO, M. LI, X.F. LI, et al. . Method and grey GM (1, N) model of line-drawing data processing in computer aided design. Transactions of the Chinese Society for Agricultural machinery, Vol. 34, No. 2(2003), pp.94-96.

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

[11] Dong Hwa Kim, Ajith Abraham, Jae Hoon Cho. A Hybrid Genetic Algorithm and Bacterial Foraging Approach for Global Optimization"(in Chinese), Information Sciences, 177(2007), pp.3918-3937.

DOI: 10.1016/j.ins.2007.04.002

[12] K. Guney, S. Basbug, Interference Suppression of Linear Antenna Arrays by Amplitude-only Control Using a Bacterial Foraging Algorithm, Progress In Electromagnetics Research, 2008. PIER 79, pp.475-497.

DOI: 10.2528/pier07110705

[13] Z.G. CHEN, Y.X. LUO, Y.H. CAOptimization for PID Control Parameters on Hydraulic Servo Control System Based on Bacterial Foraging Oriented by Particle Swarm Optimization. The International Conference on Information Engineering and Computer Science (ICIECS2009), 2009, Wuhan, pp.562-565.

DOI: 10.1109/iciecs.2009.5363433