基于变形场测量数据主元压缩的模型参量反求方法  

Inverse method of model parameters based on deformation measurement data using principal component compression

作　　者：李建宇 任朝 张丽丽 魏凯杰 LI Jian-yu;REN Zhao;ZHANG Li-li;WEI Kai-jie(Tianjin Key Laboratory of Integrated Design and On-Line Monitoring for Light Industry & Food Machinery and Equipment,School of Mechanical Engineering,Tianjin University of Science & Technology,Tianjin 300222,China;School of Science,Tianjin University of Technology and Education,Tianjin 300222,China)

机构地区：[1]天津科技大学机械工程学院,天津市轻工与食品工程机械装备集成设计与在线监控重点实验室,天津300222 [2]天津职业技术师范大学理学院,天津300222

出　　处：《计算力学学报》2020年第2期226-232,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10902077,11772228)资助项目。

摘　　要：利用主元分析法对数字图像相关技术所测结构变形信息进行数据压缩,并进一步用于力学模型未知参量的反求计算。首先,为降低数字图像相关技术所测庞大数据的应用成本,提出利用主元分析法对结构表面变形场数据进行压缩,实现在保留结构表面变形信息主要特征的前提下显著降低数据量的目的;其次,针对压缩后的数据建立了基于最小二乘法的力学模型参量反求模型,并利用高斯牛顿法进行求解;最后,以具体算例从计算精度、收敛速度和抗噪性等方面验证了数据压缩对模型参量反求的效果。研究结果表明,所提方法在显著降低使用数据量的前提下,能够有效提高力学模型参量反求计算的收敛速度,特别是对于包含多个模型参数的反求问题,具有较高的精度和较好的稳定性。The principal component analysis method is used to compress the deformation information of the structure measured by the digital image correlation technology,and further to calculate the unknown parameters of the mechanical model.Firstly,in order to reduce the application cost of the huge data measured by digital image correlation technology,the principal component analysis method is applied to compress the surface deformation data of the structure,so as to reduce the amount of data significantly under the premise of retaining the main features of the surface deformation information.Secondly,the inverse model of mechanical model parameters based on the least-square method is established for the compressed data,and solved by Gauss-Newton method.Finally,numerical examples are given to demonstrate the effect of data compression on the inverse calculation of model parameters.The results show that the proposed method significantly reduces the amount of data,and can effectively improve the convergence speed of the inverse calculation for mechanical model parameters with higher accuracy and better stability,especially for the inverse calculation of multiple model parameters.

关 键 词：数字图像相关 数据压缩 模型参量反求 最小二乘法 高斯牛顿法 

分 类 号：O34[理学—固体力学]