基于Levenberg-Marquardt算法的线性热变形补偿系数矩阵优化  

Optimization of linear thermal deformation compensation coefficient matrix based on Levenberg-Marquardt algorithm

作　　者：俞慈君[1] 宋凯[1] 李江雄[1] 金涨军[1] 樊新田[2] 章明[1] 

机构地区：[1]浙江大学机械工程学院浙江省先进制造技术重点研究实验室,浙江杭州310027 [2]中航工业西安飞机工业(集团)有限责任公司,陕西西安710089

出　　处：《浙江大学学报（工学版）》2016年第6期1056-1064,共9页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(51505422);国家自然科学基金创新研究群体科学基金项目(51521064);中央高校基本科研业务费专项资金资助项目(2015FZA4002)

摘　　要：根据增强参考系统点(ERS点)热变形的线性特点,建立ERS点线性热变形模型,利用线性热变形补偿系数矩阵对ERS点热变形进行补偿.提出一种基于Levenberg-Marquardt(LM)算法的线性热变形补偿系数矩阵优化方法,构建多组补偿后的ERS理论值与测量值之间最小加权距离误差函数的优化模型,采用LM算法求解.以壁板工装为例,通过仿真计算得出在多优化参数、多数据量情况下,优化时间在可以接受的工程应用范围内.通过实验验证了该方法有效地减小了转站误差,修正转站参数,得到的单位温度下的热变形系数矩阵稳定可靠.According to the linear feature of enhanced reference system（ERS）point thermal deformation the linear thermal deformation model of ERS points was established,and the thermal deformation of ERS points was compensated by linear thermal deformation compensation coefficient matrix.A linear thermal deformation compensation coefficient matrix optimization method based on Levenberg-Marquardt（LM）algorithm was presented.An optimization model of the minimum weighted distance error function between the ERS theoretical value compensated and the actual measurement value was constructed.A panel fixture was studied as an example and the simulation showed that the optimization time is within the acceptable engineering application in the case of multi parameters and data.Finally,the experimental results verify that the proposed method can effectively reduce the registration error and correct the registration parameters,and the thermal deformation coefficient matrix is stable and reliable.

关 键 词：大尺寸测量 转站误差 激光跟踪仪 LEVENBERG-MARQUARDT算法 线性热变形 

分 类 号：V262.4[航空宇航科学与技术—航空宇航制造工程]