数控机床热误差时间序列模型预测稳健性的提升

Improvement of forecasting robustness of time series model for thermal error on CNC machine tool

针对数控机床热误差建模应用的时间序列算法受严重多重共线性的影响存在预测稳健性不足的问题,提出一种提升时间序列预测稳健性的方法。该方法将时间序列算法与能够抑制多重共线性的建模算法相结合,从而既可通过在模型中加入温度滞后值来提供更全面的温度信息,又可对温度滞后值引入的更为严重的多重共线性进行处理。文中以时间序列算法中的分布滞后(DL)算法、共线性抑制算法中的主成分回归(PCR)算法为例,采用主成分分布滞后(PCDL)算法建立了机床热误差补偿模型,并将其与DL算法的预测精度和稳健性进行了比较。结果显示,PCDL算法因为抑制了多重共线性的影响,其模型预测精度和稳健性远优于DL模型,预测精度提升了约9μm。本文所述方法可为时间序列数据建模在不同领域内的应用提供参考。

When the time series algorithm is used to establish a thermal error compensation model for a Computer Numerical Controlled（CNC）Machine,it shows a shortcoming of forecasting robustness caused by the severe multiple collinearity.This paper proposes a method for improving the forecasting robustness of the time series algorithm.This algorithm combines the time series algorithm with the modeling algorithms which are able to suppress multiple collinearity.Thus,it not only provides more comprehensive temperature information by adding the temperature lag values in the thermal error model,but also deals with the severe multiple collinearity brought by the added temperature lag values.The Distribution Lag（DL）algorithm that belongs to time series algorithms and Principal Component Regression（PCR）algorithm that can suppress the multiple collinearity are selected as the examples,and a modeling method for establishing the thermal error compensation model of the machine tool is proposed by the Principal Component Distribution Lag（PCDL）algorithm.The forecasting ac-curacy and robustness of PCDL algorithm are compared with that of DL algorithm.The results show that the PCDL algorithm suppress the impact of multiple collinearity,so,its model′s forecasting accuracy and robustness are far better than that of DL model,and the forecasting accuracy is improved about 9μm.The proposed method provides a good reference for the application of time series data modeling in different fields.