提出了一种基于灵敏度分析和不同数据融合的有限元模型识别法，对结构的局部损伤进行识别。在正问题研究中，将结构的局部损伤模拟为结构单元杨氏模量的减少。在反问题中，通过建立实测数据与计算数据的残差为目标方程，引入灵敏度分析与正则化技术，将非线性方程转化为线性方程，进而通过迭代法进行求解。在实际工程中，往往会获得许多不同类型的数据，如模态、频响函数、静力位移数据，不同的数据其相应的灵敏度分析是不同的。假如只单独采用某一种数据，数据量过少且受到结构模型误差的影响会较大，本文通过数据的加权和融合使得目标方程含有尽可能多的实测信息。最后,通过框架和板两个数值算例表明，该方法能有效识别结构的局部损伤，且具有识别精度高，对模拟的测量噪声不大敏感的优点。
Abstract
A finite element model damage identification method based on the sensitivity analysis and hybrid data was proposed.The local damage was considered as a reduction of elemental Young’s modulus of the structure.For its damage identification, the residuals between the measured data and analysis data were taken as the target equation.By introducing the sensitivity analysis and regularization technology, nonlinear equations were transformed into linear equations.Then the iteration method was used to solve the problem.The sensitivity analysis procedure is different corresponding to different types of data, such as the modal, frequency domain, and static displacement data obtained in practical engineering.If only one type of data is used, the amount of data is too small and the influence of the structural model error will be great.So, the object equation was made to contain as much measured information as possible through the fusion and weighting of the data.The numerical examples of frame and plate show that the proposed method is effective to identify local damages,good identified results can be obtained with hybrid data, and it is insensitive to the simulated measurement noise.
关键词
灵敏度分析 /
损伤识别 /
模型修正
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Key words
sensitivity analysis /
damage identification /
model update
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参考文献
[1]. Friswell M, Mottershead J E. Finite Element Model Updating in Structural Dynamics[M]. Kluwer Academic Publishers, 1995.
[2]. Lu Z, Wang L. An enhanced response sensitivity approach for structural damage identification: convergence and performance[J]. International Journal for Numerical Methods in Engineering, 2017, 111(13):1231-1251.
[3]. Farhat C, Hemez F M. Updating finite element dynamic models using an element-by-element sensitivity methodology[J]. AIAA Journal, 1993, 31(9):1702-1711.
[4]. Chen H P, Maung T S. Regularised finite element model updating using measured incomplete modal data[J]. Journal of Sound & Vibration, 2014, 333(21):5566-5582.
[5]. 童宗鹏, 章艺, 沈荣瀛,等. 基于频响函数灵敏度分析的舰艇模型修正[J]. 上海交通大学学报, 2005, 39(11):1847-1850.
DONG Zong-peng, ZHANG Yi, SHEN Rong-ying, et al. Submarine Finite Element Model Updating Method Based on Frequency Response Functions of Vibration[J]. Journal of Shanghai Jiaotong University, 2005, 39(11):1847-1850.
[6]. 杨辰, 王晓军, 邱志平. 基于动静测试的融合灵敏度结构损伤识别方法[J]. 应用力学学报, 2013, 30(5):669-673.
YANG Chen, WANG Xiao-jun, QIU Zhi-ping. Structure damage identification method based on fusion sensitivity with dynamic and static test.[J]. Chinese Journal of Applied Mechanics, 2013, 30(5):669-673.
[7]. Tihonov A N. On the solution of ill-posed problems and the method of regularization[C]// Dokl. Akad. Nauk SSSR. 1963:501-504.
[8]. Hansen P C. Analysis of Discrete Ill-Posed Problems by Means of the L-Curve[J]. Siam Review, 1992, 34(4):561-580.
[9]. U. Prells. A regularization method for the linear error localization of models of elastomechanical systems[J]. Inverse Problems in Science & Engineering, 1996, 3(4):197-217.
[10]. Weber B, Paultre P, Proulx J. Consistent regularization of nonlinear model updating for damage identification[J]. Mechanical Systems & Signal Processing, 2009, 23(6):1965-1985.
[11]. Link M. Updating of Analytical Models — Basic Procedures and Extensions[M]. Kluwer Academic Publishers, 1999.
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