基于最小二乘支持向量机的数控机床热误差建模的研究
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摘要
本文以实现建立支持向量机数控机床热误差模型为主要内容。在分析当前国内外机床热误差补偿建模现状的基础上，提出了用最小二乘支持向量机进行热误差建模的方法。
全文围绕用最小二乘支持向量机进行数控机床热误差建模展开论述。首先论述了统计学习理论和支持向量机的一般理论知识，在把支持向量机引进回归估计领域的基础上，进一步提出了标准支持向量机的改进思路；然后详细论述了最小二乘支持向量机的理论内容，针对最小二乘支持向量机自身的不足之处，介绍了具有稀疏性和鲁棒性的最小二乘支持向量机，并提出了用网格法进行模型参数的选择；接下来介绍了针对CK6140CG数控机床的热误差综合实验，对实验数据进行了简要分析：最后，在Matlab平台上实现了最小二乘支持向量机热误差建模的全过程，并通过对建模数据的残差分析和最小二乘支持向量机模型与最小二乘法模型的对比，验证了最小二乘支持向量机进行热误差建模的优越性。本文的主要内容如下：
第一章，阐述了论文研究背景和意义。在介绍国内外数控机床误差补偿建模研究现状的基础上，分析了当前热误差模型的主要类型和待解决的问题，提出了用支持向量机进行热误差建模的思路；最后概述了课题的来源和主要研究内容。
第二章，主要介绍了统计学习理论和支持向量机。首先介绍了机器学习的基础知识；然后详细阐述了统计学习理论的基本理论，包括VC维理论、推广性的界和结构风险最小化；接下来介绍了最优超平面及其构造；然后论述了支持向量回归机以及核函数的相关知识；最后提出了标准支持向量机的改进思路。
第三章，论述了标准支持向量机的重要变种——最小二乘支持向量机。首先给出了最小二乘支持向量机理论，分析了其特性；然后深入论述了具有稀疏性和鲁棒性的最小二乘支持向量机；最后给出了最小二乘支持向量机参数选择的方法，并提出了用网格法进行参数自动寻优。
第四章，主要论述了数控机床热误差实验。首先介绍了实验设备，包括数控机床、温度采集系统和微位移传感器；然后论述了实验方案，并给出了实验数据。
第五章，本章主要是在Matlab平台上，用程序实现了数控机床热误差建模的全过程。首先采用网格法解决了参数选择问题；然后实现了最小二乘支持向量机的热误差模型，包括初始模型、鲁棒性模型、稀疏性模型和最终模型；接下来进行了模型的数据分析，并通过与最小二乘法模型的对比，验证了最小二乘支持向量机热误差模型的优越性。
第六章，对本文的研究工作和研究成果进行了总结，并对将来的研究工作做出了一定的展望。
The main content of this dissertation is the model of thermal errors for CNC machine tools via support vector machine (SVM). Based on fully understanding and deeply analyzing the current status of the research and application of the thermal error modeling and compensation technique for CNC machine tools, least square support vector machine (LS-SVM) modeling is proposed. Firstly, the principle of statistical learning theory (SLT) and support vector machine (SVM) are introduced. Secondly, the theory of LS-SVM is presented in detail. Lastly, describing the thermal error experiment of machine tools, the LS-SVM modeling is validated in Matlab.
In chapter 1, the background and the significance of the research are stated. The research history and current situation of the thermal error modeling are also provided. After the description of the shortcoming of current thermal error modeling, the SVM modeling is advised and the main content of the dissertation is presented.
In chapter 2, the principle of SLT and SVM is introduced. At first, basic theory of SLT including the VC dimension, the bound of extending and the principle of structural risk minimization (SRM) are presented. Then, the characteristic of support vector machine regression (SVR) and kernel are dissertated. In the end, the improving technique of SVM is discussed.
In chapter 3, the theory of LS-SVM is introduced. The special property of LS-SVM is described firstly. The sparse LS-SVM and the robust LS-SVM are deeply analyzed. At last, the choice about parameter of LS-SVM modeling is discussed, and a new method of parameter choice based on grid search is proposed.
In chapter 4, the experiment of temperature-thermal Errors of CNC machine tools is introduced. The experiment equipments include CNC lathe, the temperature measure system, and the laser CCD displacement sensors. The scheme and the data of this experiment are discussed in detail.
In chapter 5, the whole process of LS-SVM thermal error modeling is described. Firstly, the optimization parameter of this modeling is selected by grid search technique. Secondly, LS-SVM thermal error modeling included initialized modeling, robust modeling and sparse modeling is established. Finally, the superiority of LS-SVM modeling is validated by the data analysis and the contrast of least square modeling.
In chapter 6, the study contents and conclusion of the dissertation have been summarized, and the further research works have been forecasted.
全文围绕用最小二乘支持向量机进行数控机床热误差建模展开论述。首先论述了统计学习理论和支持向量机的一般理论知识，在把支持向量机引进回归估计领域的基础上，进一步提出了标准支持向量机的改进思路；然后详细论述了最小二乘支持向量机的理论内容，针对最小二乘支持向量机自身的不足之处，介绍了具有稀疏性和鲁棒性的最小二乘支持向量机，并提出了用网格法进行模型参数的选择；接下来介绍了针对CK6140CG数控机床的热误差综合实验，对实验数据进行了简要分析：最后，在Matlab平台上实现了最小二乘支持向量机热误差建模的全过程，并通过对建模数据的残差分析和最小二乘支持向量机模型与最小二乘法模型的对比，验证了最小二乘支持向量机进行热误差建模的优越性。本文的主要内容如下：
第一章，阐述了论文研究背景和意义。在介绍国内外数控机床误差补偿建模研究现状的基础上，分析了当前热误差模型的主要类型和待解决的问题，提出了用支持向量机进行热误差建模的思路；最后概述了课题的来源和主要研究内容。
第二章，主要介绍了统计学习理论和支持向量机。首先介绍了机器学习的基础知识；然后详细阐述了统计学习理论的基本理论，包括VC维理论、推广性的界和结构风险最小化；接下来介绍了最优超平面及其构造；然后论述了支持向量回归机以及核函数的相关知识；最后提出了标准支持向量机的改进思路。
第三章，论述了标准支持向量机的重要变种——最小二乘支持向量机。首先给出了最小二乘支持向量机理论，分析了其特性；然后深入论述了具有稀疏性和鲁棒性的最小二乘支持向量机；最后给出了最小二乘支持向量机参数选择的方法，并提出了用网格法进行参数自动寻优。
第四章，主要论述了数控机床热误差实验。首先介绍了实验设备，包括数控机床、温度采集系统和微位移传感器；然后论述了实验方案，并给出了实验数据。
第五章，本章主要是在Matlab平台上，用程序实现了数控机床热误差建模的全过程。首先采用网格法解决了参数选择问题；然后实现了最小二乘支持向量机的热误差模型，包括初始模型、鲁棒性模型、稀疏性模型和最终模型；接下来进行了模型的数据分析，并通过与最小二乘法模型的对比，验证了最小二乘支持向量机热误差模型的优越性。
第六章，对本文的研究工作和研究成果进行了总结，并对将来的研究工作做出了一定的展望。
The main content of this dissertation is the model of thermal errors for CNC machine tools via support vector machine (SVM). Based on fully understanding and deeply analyzing the current status of the research and application of the thermal error modeling and compensation technique for CNC machine tools, least square support vector machine (LS-SVM) modeling is proposed. Firstly, the principle of statistical learning theory (SLT) and support vector machine (SVM) are introduced. Secondly, the theory of LS-SVM is presented in detail. Lastly, describing the thermal error experiment of machine tools, the LS-SVM modeling is validated in Matlab.
In chapter 1, the background and the significance of the research are stated. The research history and current situation of the thermal error modeling are also provided. After the description of the shortcoming of current thermal error modeling, the SVM modeling is advised and the main content of the dissertation is presented.
In chapter 2, the principle of SLT and SVM is introduced. At first, basic theory of SLT including the VC dimension, the bound of extending and the principle of structural risk minimization (SRM) are presented. Then, the characteristic of support vector machine regression (SVR) and kernel are dissertated. In the end, the improving technique of SVM is discussed.
In chapter 3, the theory of LS-SVM is introduced. The special property of LS-SVM is described firstly. The sparse LS-SVM and the robust LS-SVM are deeply analyzed. At last, the choice about parameter of LS-SVM modeling is discussed, and a new method of parameter choice based on grid search is proposed.
In chapter 4, the experiment of temperature-thermal Errors of CNC machine tools is introduced. The experiment equipments include CNC lathe, the temperature measure system, and the laser CCD displacement sensors. The scheme and the data of this experiment are discussed in detail.
In chapter 5, the whole process of LS-SVM thermal error modeling is described. Firstly, the optimization parameter of this modeling is selected by grid search technique. Secondly, LS-SVM thermal error modeling included initialized modeling, robust modeling and sparse modeling is established. Finally, the superiority of LS-SVM modeling is validated by the data analysis and the contrast of least square modeling.
In chapter 6, the study contents and conclusion of the dissertation have been summarized, and the further research works have been forecasted.
引文
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