基于天牛须改进粒子群算法的平面度误差评定研究

A Particle Swarm O ptim ization Algorithm Based on Beetle Antennae Search for Flatness Error Evaluation

基于天牛须改进粒子群算法(BAS-PSO)对平面度误差进行了评定研究。首先,建立基于最小区域的平面度误差评定的数学模型,并将目标函数转化为非线性最优化问题;接着,在粒子群算法(PSO)的基础上,引入局部搜索能力较强的天牛须算法(BAS),加速全局搜索和局部搜索的并行计算,避免算法早熟收敛并陷入局部最优,提高平面度误差评定的精度和效率;最后,通过Rosenbrock和Schaffer测试函数,验证BAS-PSO的有效性,采用BASPSO对目标函数进行求解。实验结果表明该算法相对于BAS和PSO均取得较好的寻优效果。将该算法应用到平面度误差实例测量中,得出平面度公差值为0.006 15 mm;相比最小二乘法(LSM)、遗传算法(GA)、BAS和PSO算法,公差值分别减少了0.002 3 mm,0.001 27 mm,0.000 58 mm,0.000 37 mm;验证了该算法的可行性及优越性。

A particle swarm optimization algorithm based on the beetle antennae search algorithm( BAS-PSO) is proposed to evaluate flatness errors. Firstly,a mathematical model for evaluating the flatness error based on the minimum region is established and the objective function is transformed into a nonlinear optimization problem. Secondly,on the basic of particle swarm optimization algorithm( PSO),the beetle antennae search algorithm( BAS) with strong global search ability is introduced. As a result,the parallel computation of global search and local search is sped up to avoid premature convergence and falling into local optimization,and the accuracy and efficiency of flatness error evaluation is improved.Finally,the effectiveness of BAS-PSO is experimented by Rosenbrock and Schaffer test functions,BAS-PSO is used to solve the objective function based on the evaluation mathematical model of flatness error of the minimum region,the experimental results show that the algorithm is better than BAS and PSO. The algorithm was applied to the sample measurement of flatness error,the tolerance value of flatness is 0. 006 15 mm,the average tolerances of BAS-PSO are reduced 0. 002 3 mm,0. 001 27 mm,0. 000 58 mm,and 0. 003 7 mm compering with the least square method( LSM),genetic algorithm( GA),BAS,and PSO,which verified the feasibility and superiority of the algorithm.