基于拉格朗日乘数法的轮对外形轮廓拟合方法  

Fitting Method for Wheel Contour Line Based on Lagrange Multiplier

作　　者：王晓浩[1] 邢宗义[2] 苏钊颐[3] 李兆新[3] 高旭东[1] 

机构地区：[1]南京理工大学机械工程学院,南京硕士研究生210094 [2]南京理工大学自动化学院,南京210094 [3]广州市地下铁道总公司,广州510308

出　　处：《城市轨道交通研究》2015年第7期35-39,152,共6页Urban Mass Transit

基　　金：国家"八六三"高技术研究发展计划(2011AA110506);广州市产学研协同创新重大专项资助项目(201508010010)

摘　　要：为实现轮对外形轮廓线的准确提取,提出了一种基于拉格朗日乘数法的轮对外形轮廓线拟合方法。首先将2D激光位移传感器获得的数据点进行区段划分,然后分别确定每个区段数据点的最小二乘拟合方程,最后根据拟合方程建立最小二乘回归模型,以分段点存在三阶连续导数作为约束条件构建拉格朗日函数,采用拉格朗日乘数法求解获得拟合方程参数。采用现场实测数据进行了轮对外形轮廓线拟合,结果表明拟合的轮廓线在分段点处光滑连续,与实际数据点的最大偏移幅度小于0.1%,满足了外形轮廓线拟合精度要求,可用于轮对磨耗及尺寸参数的精确计算。In order to achieve the accurate extraction of wheel contour line, Lagrange multiplier method is proposed to fit wheel contour line. Firstly, the data points measured by the 2D laser sensor are divided into several sections; then the least-squares fitting equations are established ac- cording to the data points of each section. Finally, a least- squares regression model is built according to the fitting e- quation. By taking the break points of the third-order con- tinuous derivative into account, the Lagrange multiplier method is applied to derive the least-squares solution. The model of actual data is soled and the result shows that the curve is smooth and continuous at the segmented points. The maximum offset amplitude compared with the actual data points is within 0.1%, which could meet the accuracy requirements. So the method proposed in this paper is sig- nificant for improving the detection accuracy of wheel wear and size.

关 键 词：轨道交通车辆 轮对外形轮廓 分段曲线拟合 拉格朗日乘数法 

分 类 号：U270.33[机械工程—车辆工程]