样品台热误差的稳健RBF建模方法
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摘要
为提高中子衍射谱仪在残余应力测量过程中的样品定位精度,考虑样品台热误差对定位精度的影响,提出了样品台热误差的稳健RBF建模方法。首先通过热结构有限元仿真分析了样品台温度场及热变形的特点;然后根据样品台运动位置、测量点位置、测温点温度变化和测量点热变形的有限元仿真数据,建立了未训练的RBF网络模型;针对建模所用温度数据中存在干扰的问题,在网络训练中以稳健损失函数为目标函数,采用梯度下降法调节隐节点的宽度和权值,最终建立了样品台热误差稳健RBF解析预测模型。仿真结果表明,该建模方法可减少训练样本中温度数据受干扰的影响,提高模型的稳健性,能准确地预测样品台热误差,预测精度小于3μm。
In order to improve the accuracy of the sample localization in the residual stress measurement of the neutron diffraction spectrometer,the influence of the sample stage thermal error on the positioning accuracy was considered,and a robust RBF modeling method is proposed. Firstly,the characteristics of the temperature field and thermal deformation were analyzed by finite element simulation. Then,an unsupervised RBF model was established based on the simulation data of the stage movement position,the measurement point position,the temperature change and the measured point thermal deformation. In order to solve the problem of interference in temperature data,the robustness loss function was used as the objective function in the network training,and the width and weight of the hidden nodes were adjusted by the gradient descent method. Finally,the robust RBF thermal error prediction model was established. The simulation results show that the modeling method can reduce the influence of interference and predict the thermal error of the sample stage accurately. The prediction accuracy was less than 3 μm.
In order to improve the accuracy of the sample localization in the residual stress measurement of the neutron diffraction spectrometer,the influence of the sample stage thermal error on the positioning accuracy was considered,and a robust RBF modeling method is proposed. Firstly,the characteristics of the temperature field and thermal deformation were analyzed by finite element simulation. Then,an unsupervised RBF model was established based on the simulation data of the stage movement position,the measurement point position,the temperature change and the measured point thermal deformation. In order to solve the problem of interference in temperature data,the robustness loss function was used as the objective function in the network training,and the width and weight of the hidden nodes were adjusted by the gradient descent method. Finally,the robust RBF thermal error prediction model was established. The simulation results show that the modeling method can reduce the influence of interference and predict the thermal error of the sample stage accurately. The prediction accuracy was less than 3 μm.
引文
[1]中华人民共和国国家质量监督检验检疫总局.无损检测测量残余应力的中子衍射方法:GB/T 26140—2010[S].北京:中国标准出版社,2011.
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[9]张瀛,洪珍玉,江巍.基于RBF网络的中国信贷规模稳健预测[J].系统工程理论与实践,2014(12):3022-3033.
[10]王海娜.线性回归模型的若干稳健估计方法及应用实例[D].济南:山东大学,2013.
[11]吕妍菲.数控机床热特性分析计算及试验研究[D].大连:大连理工大学,2012.
[12]陈艳国.回归预测模型的稳健性分析(异常值处理)[J].工程地质计算机应用,2005(3):22-25.
[13]苏美娟,邓伟. RBF神经网络的一种快速鲁棒学习算法[J].苏州大学学报(工科版),2007(1):17-20.
[14] HARALAMBOS S,ALEX A,GEORGE B. A fast training algorithm for RBF networks based on subtractive clustering[J]. Neurocomputing,2003(51):501-505.
[15] EN-MING M,YA-YUN G,LIAN-CHUN D,et al. Temperature-sensitive point selection of thermal error model of CNC machining center[J]. The International Journal of Advanced Manufacturing Technology,2014,74(5/6/7/8):681-691.
[2] ARONSON B R. War Against Thermal Expansion[J]. Manufacturing Engineering,1996,116(6):45-50.
[3]苗恩铭,龚亚运,徐祗尚,等.数控机床热误差补偿模型稳健性比较分析[J].机械工程学报,2015(7):130-135.
[4]李永祥,童恒超,曹洪涛,等.数控机床热误差的时序分析法建模及其应用[J].四川大学学报(工程科学版),2006(2):74-78.
[5] YANG H,NI J. Dynamic neural network modeling for nonlinear,nonstationary machine tool thermally induced error[J].International Journal of Machine Tools and Manufacture,2005,45(4/5):455-465.
[6]闫嘉钰,杨建国.灰色GM(X,N)模型在数控机床热误差建模中的应用[J].中国机械工程,2009(11):1297-1300.
[7] ZHANG Y,YANG J G,JIANG H. Machine tool thermal error modeling and prediction by grey neural network[J]. The International Journal of Advanced Manufacturing Technology,2011,59(9/10/11/12):1065-1072.
[8]梁旭坤,何志坚.基于模糊RBF神经网络的数控机床热误差建模[J].机械设计与研究,2013,29(5):71-74,80.
[9]张瀛,洪珍玉,江巍.基于RBF网络的中国信贷规模稳健预测[J].系统工程理论与实践,2014(12):3022-3033.
[10]王海娜.线性回归模型的若干稳健估计方法及应用实例[D].济南:山东大学,2013.
[11]吕妍菲.数控机床热特性分析计算及试验研究[D].大连:大连理工大学,2012.
[12]陈艳国.回归预测模型的稳健性分析(异常值处理)[J].工程地质计算机应用,2005(3):22-25.
[13]苏美娟,邓伟. RBF神经网络的一种快速鲁棒学习算法[J].苏州大学学报(工科版),2007(1):17-20.
[14] HARALAMBOS S,ALEX A,GEORGE B. A fast training algorithm for RBF networks based on subtractive clustering[J]. Neurocomputing,2003(51):501-505.
[15] EN-MING M,YA-YUN G,LIAN-CHUN D,et al. Temperature-sensitive point selection of thermal error model of CNC machining center[J]. The International Journal of Advanced Manufacturing Technology,2014,74(5/6/7/8):681-691.