基于偏最小二乘的数控机床热误差稳健建模算法

Robust modeling method for thermal error of CNC machine tools based on partial least squares algorithm

建立预测模型对热误差进行预测和补偿是解决机床热误差问题的常用方法,该方法中模型的预测精度和稳健性易受环境温度影响而明显下降,对此本文提出了基于偏最小二乘法的热误差稳健建模算法。首先使用相关系数法筛选温度敏感点,并建立热误差偏最小二乘回归预测模型。进而基于全年环境温度下的多批次热误差实验数据,分析最佳的温度敏感点个数。最后建立热误差偏最小二乘回归模型,并与普通多元线性回归模型的预测效果比对分析。结果表明本文所提算法平均预测精度为5.7μm,模型稳健性为0.56μm,相较于普通多元线性回归算法,预测精度和稳健性分别提高13.8%和49.5%。说明本文所提的热误差稳健建模算法能够在环境温度变化较大时保持高预测精度和高稳健性。

Building prediction model to predict and compensate thermal error is a common method to solve the problem of thermal error of machine tools.In this method,the prediction accuracy and robustness of the model are easily affected by the environmental temperature,so a robust thermal error modeling algorithm based on partial least square method is proposed.Firstly,the correlation coefficient method is used to screen the temperature sensitive points,and the partial least squares regression prediction model of thermal error is established.Then,based on the multi batch thermal error experimental data under the annual ambient temperature,the optimal number of temperature sensitive points is analyzed.Finally,the partial least squares regression model of thermal error is established and compared with the ordinary multiple linear regression model.The results show that the average prediction accuracy of the proposed algorithm is 5.7μm,and the robustness of the model is 0.56μm.Compared with the ordinary multiple linear regression algorithm,the prediction accuracy and robustness are improved by 13.8%and 49.5%respectively.It shows that the thermal error robust modeling algorithm proposed in this paper can maintain high prediction accuracy and high robustness when the ambient temperature changes greatly.