改进混沌粒子群优化的灰色系统模型在机床热误差建模中的应用

Application of improved chaotic particle swarm optimization grey system model to thermal error modeling of machine tools

为减少热误差对数控机床加工精度的影响,提高灰色系统模型(Grey system Model,GM)的预测精度,尝试将改进混沌粒子群优化(Improvemen Chaotic Particle Swarm Optimization,ICPSO)算法引入到灰色系统模型中,提出一种基于改进混沌粒子群优化算法的灰色系统模型数控机床热误差建模方法。首先,建立粒子群优化(Particle Swarm Optimization,PSO)粒子与GM(1,N)系数的映射关系;其次,ICPSO中混沌理论的Logistic映射对粒子群的位置和速度进行初始化,通过优化搜索得到最优GM(1,N)系数和输入子集;最后,建立改进混沌粒子群优化的灰色系统模型(ICPSO-GM),对数控机床热误差进行预测。仿真实验表明,ICPSO-GM预测精度高于GM和人工神经网络(ANN)模型,证明了ICPSO-GM能有效地解决数控机床热误差预测问题。

In order to decrease the influence of thermal errors on machining precision of machine tools and to improve the predic- tion accuracy of Grey system Model（GM）, the Improved Chaotic Particle Swarm Optimization （ICPSO） is introduced into the grey system model. One improved chaotic particle swarm optimization based grey system model is proposed to model the thermal errors of the machine tools. Firstly,the mapping of between particles of PSO and the parameters of grey system model is devel- oped. Next, the Logistic map of chaotic theory of ICPSO initializes the location and velocity of particles. The optimal parameters and input set are obtained by optimizing search with ICPSO. Then, the model based on ICPSO-GM is established to predict the thermal errors of machine tools. The simulation shows that the thermal model of ICPSO-GM has the higher prediction precision than GM and Artificial Neural Network（ANN）. The results indicate that the proposed ICPSO-GM can effectively realize the pre- diction of thermal errors of machine tools.