1. School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei, Anhui 230009, China;
2. Xi’an Jiaotong University, State Key Laboratory for Manufacturing Systems Engineering, Xi’an, Shannxi 710049, China
Abstract：Three modeling methods are introduced and analyzed, including multiple linear regression model, congruence model which combine multiple linear regression model with AR model of its residual error and autoregressive distributed lag model.Multiple linear regression analysis is a simple and quick modeling method,but thermal error is nonlinear and interactive, and it is difficult to model a precise least squares model of thermal error.The congruence model and autoregressive distributed lag model belong to time series analysis method which has the advanced that the precise mathematical model can be established.The distinctions of the two models are that: the congruence model divided the parameter into two parts to estimate respectively,but autoregressive distributed lag model estimate parameter uniformly,so the accuracy of congruence model is lower than that of the autoregressive distributed lag model,and this conclusion is proved by the actual example that the autoregressive distributed lag model used to calculate the thermal error of precision CNC machine tools is a good way to improve modeling accuracy.
［1］Ramesh R, Mannan M A, Poo A N. Error compensation in machine tools- A review, PartⅡ: Thermal errors［J］.International Journal of Machine Tools and Manufacture,2000, 40（9）: 1257-1284.
［2］Bryan J B. International status of thermal error research［J］.Ann CIRP, 1990, 39（2）:645-656.
［3］Yang J G, Pan Z H. Application of regression orthogonal design in thermal error modeling of machine tools［J］. Aviation Precision Manufacturing Technology, 1999, 35(5): 33-37.
［4］李永祥,童恒超,曹洪涛,等.数控机床热误差的时间序列分析法建模及其应用［J］.四川大学学报（工程科学版）,2006, 38(2): 74-77.
［5］王惠文.偏最小二乘回归方法及其应用［M］.北京:国防工业出版社,1999.
［6］张晓彤.计量经济学基础［M］.天津:南开大学出版社, 2007.
2013, Vol. 34 
