基于加权支持向量机的凸轮升程误差拟合方法

J4 ›› 2016, Vol. 38 ›› Issue (05): 1057-1065.

基于加权支持向量机的凸轮升程误差拟合方法

王洪1,2,戴瑜兴1,3,谭彦杰2,李丹4

(1.湖南大学电气与信息工程学院,湖南长沙 410082;2.湖南师范大学工程与设计学院,湖南长沙 410081;
3.温州大学物理与电子信息学院,浙江温州 325035;4.湖南科技职业学院,湖南长沙 410004)

收稿日期:2015-08-26 修回日期:2015-10-27 出版日期:2016-05-25 发布日期:2016-05-25
基金资助:
湖南省自然科学基金（13JJ3056）

A cam lift error fitting method based
on weighted support vector machine

WANG Hong1,2,DAI Yuxing1,3,TAN Yanjie2,LI Dan4

(1.College of Electrical and Information Engineering,Hunan University,Changsha 410082;
2.College of Engineering and Design,Hunan Normal University,Changsha 410081;
3.College of Physics and Electronic Information Engineering,Wenzhou University,Wenzhou 325035;
4.Hunan Vocational College of Science ＆ Technology,Changsha 410004,China)

Received:2015-08-26 Revised:2015-10-27 Online:2016-05-25 Published:2016-05-25

摘要/Abstract

摘要：

针对凸轮磨削加工过程中存在局部升程误差严重超差的问题，提出了加权支持向量机的凸轮升程误差补偿方法。首先根据圆率的符号判断凸轮升程误差值是否连续，然后建立了不连续点与相邻点之间夹角与加权值的关系。通过加权支持向量机对凸轮升程误差值进行拟合。然后将原始凸轮升程值减去经拟合后的凸轮升程误差值，获得新的凸轮升程值。再根据圆率自动调整加权值的系数，使凸轮升程值光滑点数最大，即获得最优的凸轮升程值。对上述算法进行仿真和编程，经YTM833616数控凸轮轴磨床进行磨削验证。实验表明，凸轮升程误差由原来的±0.059 mm降至±0.011 mm，表面粗糙度由Ra032 μm降至Ra025 μm，获得良好的效果。

关键词: 凸轮非圆磨削；凸轮升程误差；加权支持向量机；曲线拟合；鲁棒估计

Abstract:

Aiming at the issue of serious local lift errors in the cam grinding process, we present a cam lift error compensation method based on the weighted support vector machine (WSVM). The circle rate of symbols is used to judge whether the cam lift error values are continuous, and then the relationship of angle and weighted value between discrete points and adjacent points is established. The values of cam lift error are fitted by the WSVM. The new cam lift values are obtained by subtracting the fitted cam lift values from the original cam lift values. Then, the number of smooth points of the cam lift values can be maximized by automatically adjusting the weight coefficients according to the circle rate, therefore, the optimal cam lift values can be obtained. The algorithm is simulated and carried on the CNC camshaft grinder YTM833616. The results show that the cam lift error is reduced from 0.059mm to 0.011 mm, and the surface roughness is decreased from 0.32 μm to 0.25 μm, which demonstrates the good effect of the proposed method.

Key words: cam grinding;cam lift error;weighted support vector;machine curve fitting;robustness estimate

王洪1,2,戴瑜兴1,3,谭彦杰2,李丹4 . 基于加权支持向量机的凸轮升程误差拟合方法[J]. J4, 2016, 38(05): 1057-1065.

WANG Hong1,2,DAI Yuxing1,3,TAN Yanjie2,LI Dan4. A cam lift error fitting method based
on weighted support vector machine [J]. J4, 2016, 38(05): 1057-1065.

参考文献［17］

［1］	Cripps R J,Hussain M Z,Zhu S.Smooth polynomial approximation of spiral arcs［J］.Journal of Computational and Applied Mathematics,2009,233 (3):22272234.
［2］	Tang Hao,Deng Zhaohui,Wan Linlin,et al.Application of cam lift fitting method based on alternativepoint interpolation in grinding process［J］.Journal of Mechanical Engineering,2012,23(12):191198.(in Chinese)
［3］	Chen Jincheng,Xu Zhiming,Xu Zhengfei,et al.Research on adaptive algorithm for generating smooth motion profile of highspeed machining based on piecewise 3order spline curve［J］.Journal of Mechanical Engineering,2002,38(5):6165.(in Chinese)
［4］	Zhang Jumei,Wang Honglun.Bspline curve fitting based on genetic algorithms and the simulated annealing algorithm ［J ］.Computer Engineering & Science,2011,33(3):191193.(in Chinese)
［5］	Xu Zuan.The mathematical treatment of the measured data of engine CAM lift ［J］.Chinese Internal Combustion Engine Engineering,1984(12):28.(in Chinese)
［6］	Jing Ling, Wang Nong. Support vector machine in curve smoothing reconstruction［J］.Computer Engineering and Applications,2005,41(30):6668.(in Chinese)
［7］	Zhou Yanli, Wang Lie. A support vector machine in curve smoothing and convex reconstruction［J］.Aeronautical Computing Technique,2007,37(7):5052.(in Chinese)
［8］	Wang Hong,Dai Yuxing,Xu Jun,et al.Optimization method of workpiece rotation shaft speed of CNC camshaft grinding machine［J］.Journal of Mechanical Engineering,2014,50 (15):205212.(in Chinese)
［9］	Suykens J A K, De Brabanter J, Lukas L, et al.Weighted least squares support vector machines:Robustness and sparse approximation［J］.Neurocomputing,2002,48(14):85105.
［10］	Gan Xusheng,Zhang Hongcai,Cheng Yongmei,et al.Aerodynamic parameter fitting based on robust least squares support vector machines［J］.Computer Engineering and Applications,2007,43(31):233239.(in Chinese)
［11］	Ouyang Jun,Yan Guirong,Wang Teng.Space truss modeling based on improved weighted least square support vector machines［J］.Journal of Xi’an Jiaotong University,2007,41(1):119121.(in Chinese)
［12］	Xu Da, Wu Xinxing, Hu Junbiao, et al.Implementation of least square support vector machine for prediction［C］∥Proc of the Advanced Manufacturing Technology Top BBS and the 8th Manufacturing Automation and Information Technology Seminar,2009:6568.(in Chinese)
［13］	Lin Shengliang,Liu Zhi.Parameter selection in SVM with RBF kernel function［J］.Journal of Zhejiang University of Technology,2007,35(2):163176.(in Chinese)
［14］	Chapelle O, Vapnik V． Choosing multiple parameters for support vector machines［J］．Machine Learning,2002,46(1):131159.
［15］	Keerthi S S,Lin C J.Asymptotic behaviors of support vector machines with Gaussian kernel［J］.Neural Computation,2003,15(7):16671689.
［16］	A method for selecting parameter of SVM with RBF kernel［EB/OL］.［20110301］.http://wenku.baidu.com/view /c392cbefaeaad1f346933f 47.html.(in Chinese)
［17］	Zhao Dongfu.Interactive fairing processing for spatial discrete points［J］.Journal of Machine Design,2003,20(4):3032.(in Chinese)
	附中文参考文献：
［2］	唐浩,邓朝辉,万林林,等.基于交替隔点插值的凸轮升程拟合方法在磨削加工中的应用［J］.机械工程学报，2012，23(12)：191198.
［3］	陈金成,徐志明,徐正飞,等.基于分段三次样条曲线的高速加工平滑运动轮廓自适应算法研究［J］.机械工程学报,2002，38(5):6165.
［4］	张聚梅,王洪伦.基于遗传算法和模拟退火算法的B样条曲线拟合［J］.计算机工程与科学2011,33(3):191193.
［5］	徐祖安.发动机凸轮升程实测数据的数学处理［J］.内燃机工程,1984(12):28.
［6］	经玲,王弄.支持向量回归模型在曲线光顺拟合中的改进［J］.计算机工程与应用,2005,41(30):6668.
［7］	周彦利,王烈.曲线保凸光顺拟合中的支持向量回归模型［J］.航空计算技术,2007,37(7):5052.
［8］	王洪,戴瑜兴,许君,等.数控凸轮轴磨床工件旋转轴转速优化方法［J］,机械工程学报,2014,50(15):205212.
［10］	甘旭升,张洪才,程咏梅,等.基于鲁棒最小二乘支持向量机的气动参数拟合［J］.计算机工程与应用,2007,43(31):233239.
［11］	欧阳军,闫桂荣，王腾.基于改进的加权最小二乘支持向量机的空间桁架建模［J］. 西安交通大学学报,2007,41(1):119121.
［12］	徐达,武新星，胡俊彪,等.最小二乘支持向量机回归预测模型研究与实现［C］∥全国先进技术高层论坛暨第八届制造业自动化与信息化技术研讨会,2009:6568.
［13］	林升梁,刘志.基于RBF核函数的支持向量机参数选择［J］.浙江工业大学学报,2007,35(2):163176.
［16］	一种RBF核SVM的参数选择方法［EB/OL］.［20110301］.http://wenku.baidu.com/view/c392cbefaeaad1f346933f4 7.html.
［17］	赵东福.空间离散点的交互光顺处理［J］.机械设计,2003,20(4):3032.