自回归分布滞后模型在数控机床热误差建模中的应用

Application of Autoregressive Distributed Lag Model to Thermal Error Compensation of Machine Tools

对多元线性回归模型、回归与残差AR叠合模型和自回归分布滞后模型3种热误差建模方法进行了介绍与比对分析。多元线性回归模型方法简单快捷，但因热误差呈非线性且具有互交作用，较难获得精确热误差数学模型。后两个模型均属时间序列分析方法，其优点是能够比较精确地建立热误差数学模型，两者的区别是叠合模型把参数估计分成两部分，而自回归分布滞后模型是统一估计参数，因此叠合模型的精度要低于自回归分布滞后模型精度，并通过实例验证，自回归分布滞后模型在精密数控机床热误差建模中具有较好的建模精度。

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.