改进蜂群算法在平面度误差评定中的应用

摘要

为了准确快速评定平面度误差,提出将改进人工蜂群( MABC)算法用于平面度误差最小区域的评定.介绍了评定平面度误差的最小包容区域法及判别准则,并给出符合最小区域条件的平面度误差评定数学模型.叙述了MABC算法,该算法在基本人工蜂群算法( ABC)模型的基础上引入两个牵引蜂和禁忌搜索策略.阐述了算法的实现步骤,通过分析选用两个经典测试函数验证了MABC算法的有效性.最后,应用MABC算法对平面度误差进行评定,其计算结果符合最小条件.对一组测量数据的评定显示,MABC算法经过0.436 s可找到最优平面,比ABC算法节省0.411 s,其计算结果比最小二乘法和遗传算法的评定结果分别小18.03μm和6.13 μm.对由三坐标机测得的5组实例同样显示,MABC算法的计算精度比遗传算法和粒子群算法更有优势,最大相差0.9 μm.实验结果表明,MABC算法在优化效率、求解质量和稳定性上优于ABC算法,计算精度优于最小二乘法、遗传算法和粒子群算法,适用于形位误差测量仪器及三坐标测量机.%To realize fast and accurate evaluation for flatness errors, a Modified Artificial Bee Colony (MABC) algorithm was proposed to implement the minimum zone evaluation of flatness errors. The minimum zone method and the criteria for flatness errors were introduced. According to the minimum zone condition, the mathematic model of flatness error evaluation was presented. By introducing two traction bees and a Tabu Strategy(TS), this modified method could enhance the rate of convergence and the quality of optimum solution. The implementation steps of the method were expounded. Then, two test functions were selected in the simulation experiments through analysis, and the results verified the feasibility of MABC algorithm. Finally, proposed approach was used to evaluate flatness errors. The results calculated meet the criterion of minimal condition. On the basis of a group of metrical data, this approach can find the optimal plane by 0. 436 second, which saves 0. 411 second as compared with that of ABC algorithm. In addition, the flatness value from the MABC algorithm is 18. 03 μm lower than that of the Least-Square Method (LSM), and 6. 13 μm than the Genetic Algorithm (GA). According to other five measurement data sets available from the Coordinate Measuring Ma-chines(CMMs), the results obtained by the MABC algorithm are more accurate than those by the GA and Particle Swarm Optimization (PSO), and the maximum gap of flatness values is 0. 9 μm. Experimental results show that the MABC-based approach outperforms ABC-base method in optimization efficiency, solution quality and stability, and its calculating precision is superior to that given by LSM, GA or PSO. It is suited for the evaluation of position measuring instruments and CMMs.