贝叶斯证据框架下的LS-SVM多工况数控机床热误差建模

最小二乘支持向量机(LS-SVM)模型是表征数控机床热误差特性的有效工具，但该模型中的参数设置直接影响建模的精度。传统的基于交叉验证法或网格法的参数获取方法存在计算量大、精度低的缺点，且同一组模型常数往往不能准确表征机床多种工况条件下所产生的热误差。为解决这一问题，提出了一种基于贝叶斯证据框架理论的LS-SVM多工况参数优化方法。通过测量不同工况下数控机床温度值与主轴热变形量，采用贝叶斯证据框架的3个推断对LS-SVM模型进行训练并对参数进行辨识和优化，推导出了不同工况所对应的最优模型和参数。热误差建模实验验证了该参数优化方法的有效性，结果显示，经优化的模型具有泛化能力强、预测精度高、计算速度快的特点，能够较准确地描述多种典型工况条件下的实际热误差特性。

Modeling of CNC Machine Tool Thermal Errors Based on LS-SVM within Bayesian Evidence Framework

LS-SVM is an effective tool for machine error modeling. The traditional methods to set the parameters of LS-SVM which determined the modeling accuracy included ten-fold cross validation and grid method. However, using these methods, parameter calculation was complex and prone to low accuracy. Moreover, the LS-SVM model with only one set of parameters was hard to precisely describe the thermal error behaviors under the different work conditions. In order to solve these problems, based on Bayesian evidence framework a novel method was proposed to identify and optimize LS-SVM parameters under multiple working conditions. Three inferring levels of Bayesian evidence framework were used to derive the optimal model parameters corresponding to the different operating conditions. A series of experiments for thermal error modeling verified the validity of this method. LS-SVM model based on Bayesian evidence framework has good generalization ability, accurate prediction, and rapid calculation speed, so it can describe the actual thermal error characteristics more accurately under multiple work conditions.