面向时变模态仅输出辨识的递推动态模式分解方法研究  

Recursive dynamic mode decomposition method for output-only identification of time-varying modal parameters

作　　者：范霆威 马志赛 丁千[1,2] 祁峰 王檑 FAN Tingwei;MA Zhisai;DING Qian;QI Feng;WANG Lei(School of Mechanical Engineering,Tianjin University,Tianjin 300350,China;Tianjin Key Laboratory of Nonlinear Dynamics and Control,Tianjin 300350,China;Beijing Institute of Astronautical System Engineering,Beijing 100076,China)

机构地区：[1]天津大学机械工程学院,天津300350 [2]天津市非线性动力学与控制重点实验室,天津300350 [3]北京宇航系统工程研究所,北京100076

出　　处：《振动工程学报》2025年第4期677-686,共10页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(12272258,11802201);战略火箭创新基金资助项目(ZH2022001);天津市青年人才托举工程(TJSQNTJ-2020-01)。

摘　　要：针对工程结构的激励难以测量、时变模态辨识计算效率低下的问题,提出了一种基于动态模式分解(DMD)的时变模态仅输出递推辨识方法。借鉴投影近似子空间跟踪算法和滑动窗思想对现有DMD方法进行理论拓展,提出DMD方法的递推格式,能够对系统矩阵和本征正交分解基进行递推更新,可用于时变模态的仅输出递推辨识。设计时变质量三自由度结构系统数值算例,搭建变质量充液筒结构系统实验平台,分别对所提递推DMD方法进行数值和实验验证。结果表明,所提递推DMD方法能够仅基于结构系统的振动响应数据准确辨识得到其时变模态,具备良好的仅输出递推辨识能力。Time-varying modal identification is important to obtain the dynamic characteristics of time-varying engineering structures and realize real-time vibration control and online health monitoring of structural systems.Aiming at the problems of measuring the excitation of engineering structures and low efficiency of time-varying modal identification,an output-only recursive identification method based on dynamic mode decomposition(DMD)is proposed in this paper.To extend the theory of the existing DMD method,this paper draws on the projection approximation subspace tracking algorithm and the sliding-window idea,and proposes a recursive format of the DMD method,which can update the system matrix and the proper orthogonal decomposition basis recursively,and can be further used for the output-only recursive modal identification of time-varying systems.A numerical example of a three-degree-of-freedom structural system with time-varying mass and an experimental setup of a liquid-filled cylindrical structural system with variable mass are respectively designed and built to validate the proposed method numerically and experimentally.The results demonstrate that the proposed recursive DMD method is able to accurately identify the modal parameters of the time-varying structures by only using the measured vibration response data,and has good output-only recursive identification capability.

关 键 词：时变系统 模态辨识 动态模式分解 仅输出递推辨识 

分 类 号：O327[理学—一般力学与力学基础]