A minimum zone method for evaluating flatness errors based on PSO algorithm

In this paper, based on the analysis of existent evaluation methods for flatness errors, an intelligent evaluation method is provided. The evolutional optimum model and the calculation process are introduced in detail. According to characteristics of flatness error evaluation, Particle Swarm Optimization (PSO) is proposed to evaluate the minimum zone error. Compared with conventional optimum methods such as simplex search and Powell method, it can find the global optimal solution, and the precision of calculating result is very good. Then, the objective function calculation approaches for using the PSO to evaluate minimum zone error are formulated. Finally, the control experiment results evaluated by different method such as the least square, simplex search, Powell optimum methods and GA, indicate that the proposed method does provide better accuracy on flatness error evaluation, and it has fast convergent speed as well as using computer easily and popularizing application easily.

[1]  Kuang-Chao Fan,et al.  A minimum zone method for evaluating flatness error of gage blocks measured by phase‐shifting interferometry , 1993 .

[2]  S. Hossein Cheraghi,et al.  Circularity error evaluation: Theory and algorithm , 1999 .

[3]  K. Fan,et al.  A new minimum zone method for evaluating straightness errors , 1993 .

[4]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[5]  Xiangyang Zhu,et al.  Flatness tolerance evaluation: an approximate minimum zone solution , 2002, Comput. Aided Des..

[6]  Hirotaka Yoshida,et al.  A PARTICLE SWARM OPTIMIZATION FOR REACTIVE POWER AND VOLTAGE CONTROL CONSIDERING VOLTAGE STABILITY , 2000 .

[7]  S. H. Cheraghi,et al.  Straightness and flatness tolerance evaluation: an optimization approach , 1996 .

[8]  Moon-Kyu Lee,et al.  A new convex-hull based approach to evaluating flatness tolerance , 1997, Comput. Aided Des..

[9]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[10]  Soichiro Suzuki,et al.  Evaluation of minimum zone flatness by means of nonlinear optimization techniques and its verification , 1993 .

[11]  Russell C. Eberhart,et al.  Tracking and optimizing dynamic systems with particle swarms , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[12]  Jyunping Huang,et al.  An efficient approach for solving the straightness and the flatness problems at large number of data points , 2003, Comput. Aided Des..

[13]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[14]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[15]  M. S. Shunmugam,et al.  Evaluation of straightness and flatness error using computational geometric techniques , 1999, Comput. Aided Des..

[16]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[17]  S. Hossein Cheraghi,et al.  Evaluating the geometric characteristics of cylindrical features , 2003 .