基于广义岭估计的结构模型修正方法  

Structural Model Updating by a New Generalized Ridge Estimation Method

作　　者：杨秋伟 陈华 李翠红 YANG Qiuwei;CHEN Hua;LI Cuihong(School of Civil Engineering,Shaoxing University,Shaoxing,Zhejiang 312000;School of Civil and Transportation Engineering,Ningbo University of Technology,Ningbo,Zhejiang 315211;Engineering Research Center of Industrial Construction in Civil Engineering of Zhejiang Province,Ningbo University of Technology,Ningbo,Zhejiang 315211)

机构地区：[1]绍兴文理学院土木工程学院,浙江绍兴312000 [2]宁波工程学院建筑与交通工程学院,浙江宁波315211 [3]浙江省土木工程工业化建造工程技术研究中心(宁波工程学院),浙江宁波315211

出　　处：《绍兴文理学院学报》2021年第8期1-7,共7页Journal of Shaoxing University

基　　金：国家自然科学基金资助项目“基于谱分解的柔度扰动新方法及其在结构损伤识别中的应用”(11202138);宁波市“科技创新2025”重大专项科技项目“深水基础建造关键技术与装备”(2019B10076)资助项目.

摘　　要：针对结构模型修正中的病态最小二乘问题,提出一种新的广义岭估计方法,能有效克服数据噪声的不利影响.为了尽量减少广义岭估计中由于引入正则矩阵而带来的额外误差,所提方法充分考虑系数矩阵对角元素之间的差异,提出一个底数可调节的幂函数,用于计算获得广义岭估计中的正则系数对角矩阵,更好地兼顾解的稳定性和准确性.以一个病态方程组和一个桁架结构模型为例验证了所提方法,结果表明,所提方法可以获得比现有方法精度更高的计算结果,具有良好的抗噪声能力,能获得较准确的模型修正结果.A new generalized ridge estimation method is proposed to solve the ill-conditioned least squares problem.The proposed method,applied to the structural finite element model updating,fully considers the differences between the diagonal elements of the coefficient matrix in the linear equation.A formula with an adjustable base number was proposed for calculating the regular coefficients to minimize the extra errors caused by the introduction of the regular matrix in the generalized ridge estimation,with the stability and accuracy of the solution taken into account.Taking an ill-posed system of equations and a truss structure model as examples,the proposed method was verified.The results show that the proposed method which obtains more accurate results than the existing methods can be used to solve the ill-conditioned total least squares problem.

关 键 词：模型修正 测量误差 病态方程组 广义岭估计 正则矩阵 

分 类 号：O32[理学—一般力学与力学基础] TU31[理学—力学]