改进Tikhonov正则化方法在结构激励识别与响应重构中的应用  

Applying Improved Tikhonov Regularization Method to Excitation Identification and Response Reconstruction of A Structure

作　　者：周雪文 彭珍瑞[1] ZHOU Xuewen;PENG Zhenrui(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《机械科学与技术》2024年第9期1469-1476,共8页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目(62161018);甘肃省自然科学基金项目(20JR10RA234)。

摘　　要：为了改善传递矩阵的病态性,实现利用结构有限测量信息对结构外部激励与未知响应的有效重构,提出了一种用于结构激励识别与响应重构的改进Tikhonov正则化方法。首先,基于状态空间模型构建传递矩阵,并推导结构外部激励识别与响应重构方程。其次,采用改进Tikhonov正则化方法改善传递矩阵的病态性,得到激励方程的正则化解,并结合结构需重构位置对应的传递矩阵重构未知加速度响应。最后,分别对平面二维桁架和简支梁进行数值仿真和试验分析,验证所提方法的可行性。结果表明所提方法能够改善传递矩阵的病态性,提高结构激励识别与响应重构的精度。In order to improve the ill-condition of a transfer matrix and realize the effective reconstruction of the external excitation and unknown response of a structure with its limited measurement information,the improved Tikhonov regularization method for the excitation identification and response reconstruction of the structure is proposed.Firstly,the transfer matrix is constructed based on the state space model,and the external excitation identification and response reconstruction equations are derived.Then,the improved Tikhonov regularization method is used to improve the ill-condition of the transfer matrix.The regularization solution of the excitation equation is obtained.The unknown acceleration response is reconstructed by combining transfer matrixe that correspond to the position of the structure to be reconstructed.Finally,the numerical simulation and experimental analysis of a twodimensional truss and a simply supported beam verify the feasibility of the proposed regularization method.The results show that the proposed method can improve the ill-condition of a transfer matrix and the accuracy of excitation identification and response reconstruction of a structure.

关 键 词：激励识别 响应重构 状态空间 传递矩阵 正则化 

分 类 号：TH113.1[机械工程—机械设计及理论]