基于核主成分分析的热误差模型自变量优化

Independence variable optimization of thermal error model based on KPCA

为了改善主成分分析对温度场的非线性数据提取能力不足的问题,提出一种核主成分温测点优化法。引入非线性映射函数,将输入的温度数据向特征空间映射,选择高斯径向基为核函数,将特征空间的内积运算变换为输入空间的核函数运算,求出特征值和核特征向量,建立综合自变量。在一台数控加工中心上进行试验,将提出方法建立的预测模型和主成分分析获得的预测模型进行比较,均方根误差降低约36%,最大残差降低29%,结果表明,采用核主成分法建模,能更好提取温度数据特征,可以使试验机床进给系统的热误差预测能力显著提升。

To address the issue that principle component analysis （PCA） shows a poor ability to acquire the characteristic of nonlinearity data, a kernel principle component analysis （KPCA） temperature point optimization method is proposed. Firstly, nonlinearity mapping function is introduced to map the input temperature data into the characteristic space, and a Gaussian radial basis is selected to be a kernel function. Secondly, inner product operation in characteristic space is transformedinto kernel function operation in input space, eigenvalnes and kernel eigenvectors are found. Finally, a comprehensive independent variable is formed. According to an experiment conducted on a CNC machine center,and comparedwith the PCA model, RMSE and Maximum residual error reduces by 36% and 29% , respectively. KPCA can preferably acquire the characteristic of temperature data, and the prediction ability of KPCA model has an obvious improvement.