基于正则化的机床热误差自适应稳健建模算法  

Adaptive robust modeling method for machine tool thermal error based on regularization

作　　者：魏新园 钱牧云 赵洋洋 潘巧生 苗恩铭 Wei Xinyuan;Qian Muyun;Zhao Yangyang;Pan Qiaosheng;Miao Enming(School of Electrical and Information Engineering,Anhui University of Technology,Ma'anshan 243032,China;School of Instrument Science and Opto-electronics Engineering,Hefei University of Technology,Hefei 230009,China;School of Mechanical Engineering,Chongqing University of Technology,Chongqing 400054 China)

机构地区：[1]安徽工业大学电气与信息工程学院,马鞍山243032 [2]合肥工业大学仪器科学与光电工程学院,合肥230009 [3]重庆理工大学机械工程学院,重庆400054

出　　处：《仪器仪表学报》2022年第5期77-85,共9页Chinese Journal of Scientific Instrument

基　　金：国家重点研发计划项目(2020YFB1712900,2020YFB1712904);安徽省重点研究与开发计划项目(2022f04020005)资助。

摘　　要：通过建立预测模型对机床热误差进行补偿,是有效解决热误差造成机床精度下降问题的常用方法。本文提出一种基于正则化的数控机床热误差自适应稳健建模算法,能够在建模过程中自适应选择温度敏感点(TSPs),并具有高预测精度和稳健性。首先基于结构风险最小化原则对热误差建模稳健性机理进行分析,进而利用正则化算法中LASSO解的稀疏性实现自适应TSP选择。然后基于不同实验条件的热误差数据,分析所提建模算法的预测效果,并与常用的多元线性回归、BP神经网络和岭回归算法进行比对分析。结果表明,本文所提建模算法具有最高的预测精度和稳健性,分别为5.22和1.69μm。最后,利用所建立的预测模型进行热误差补偿实验,以验证本文所提建模算法的实际补偿效果。The formulation of the prediction model to compensate for the thermal error of machine tools is a common method to effectively solve the decline of machine tool accuracy caused by thermal error.This article proposes an adaptive robust modeling method for thermal error of computer numerical control machine tools based on regularization,which can adaptively select temperature-sensitive points(TSPs) in the modeling process,and has high prediction accuracy and robustness.Firstly,the robustness mechanism of thermal error modeling is analyzed,which is based on the principle of structural risk minimization.Secondly,the sparsity of the solution of least absolute shrinkage and selection operator(LASSO) in regularization algorithms is used to realize adaptive TSP selection.Then,based on the thermal error data under different experimental conditions,the prediction effect of the proposed modeling method is analyzed and compared with the commonly used multiple linear regression,back propagation(BP) neural network,and ridge regression algorithms.Results show that the proposed modeling method has the highest prediction accuracy and robustness,which are 5.22 and 1.69 μm,respectively.Finally,the thermal error compensation experiment is implemented by using the established prediction model to evaluate the actual compensation effect of the proposed modeling method.

关 键 词：热误差 预测模型 正则化 稳健性 自适应 

分 类 号：TH161[机械工程—机械制造及自动化] TG659[金属学及工艺—金属切削加工及机床]