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中文摘要：
针对多元线性回归无偏估计算法在处理具有多重共线性的机床热误差数据建模中出现的模型参数估计失真问题,提出了一种用于处理共线性数据的无偏估计拆分算法。该算法将建模过程分成多个步骤完成,每步只对一个自变量进行回归,从而达到弱化自变量共线性的目的。以LeaderwayV450型数控加工中心为实验对象,根据在不同季度内测量的多批次空转实验数据,将无偏估计拆分算法与传统多元线性回归的模型精度和稳健性进行了验证。研究结果显示,无偏估计拆分模型的预测精度和稳健性远优于经典多元线性回归模型,尤其对于跨季度数据预测,该算法优势更大。
英文摘要：
Considering the distortion problems of estimated model parameters when dealing with the modeling of multi-collinear thermal error data of CNC machine by the multiple linear regression without offset estimation algorithm,a split unbiased estimation algorithm used for dealing with collinear data was proposed herein.The algorithm divided the modeling process into several steps,and in each step only one independent variable was regressed so as to avoid the collinear problem.In addition,taking Leaderway-V450 machining center as the experimental object,according to batches of idling experimental data which were measured on different seasons,the accuracy and robustness of SUE algorithm were compared with that of MLR algorithm.The results show that,the accuracy and robustness of SUE model is much better than that of MLR model,especially for forecasting these data on different seasons,the advantages of this algorithm is more obvious.
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