基于离散小波变换的时变结构物理参数识别
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摘要
利用离散小波变换将时变结构的时变参数在多尺度上展开为概貌信号和细节信号,忽略高频细节信号,仅由低频概貌信号估计时变参数,将时变结构识别问题转化为时不变结构识别问题。基于时变结构的输入和输出信号用最小二乘法识别低频尺度展开系数,从而重构得到原始时变参数。对于噪音引起的方程不适定性问题,采用Tikhonov正则化方法减小其影响。通过1个具有时变刚度和阻尼的2层框架结构的数值模拟验证该方法的有效性。识别结果表明:该方法可以有效识别结构时变刚度,时变阻尼识别结果对噪音较敏感。
A method of identifying physical parameter of time-varying structure based on discrete wavelet transform was presented.A time-varying parameter was expended on multi-scale as approximate and detail signal by discrete wavelet basis.By ignoring detail signal,the time-varying parameter was evaluated only using approximate signal,so the identification problem of time-varying was transformed to time-invariant problem.Based on the input and output signal of structure,the scale expand coefficients of low frequency can be identified using least square method,and then the original time-varying parameter can be reconstructed.For the ill-posed problem of identification equation caused by noise,Tikhonov regularization method was used to decrease its influence.The effectiveness and accuracy of the proposed method were validated via a numerical simulation of a two story frame structure with time-varying stiffness and damping.The results show that the presented algorithm can be used to identify the time-varying stiffness,the identified result of time-varying damping is very sensitive to noise.
A method of identifying physical parameter of time-varying structure based on discrete wavelet transform was presented.A time-varying parameter was expended on multi-scale as approximate and detail signal by discrete wavelet basis.By ignoring detail signal,the time-varying parameter was evaluated only using approximate signal,so the identification problem of time-varying was transformed to time-invariant problem.Based on the input and output signal of structure,the scale expand coefficients of low frequency can be identified using least square method,and then the original time-varying parameter can be reconstructed.For the ill-posed problem of identification equation caused by noise,Tikhonov regularization method was used to decrease its influence.The effectiveness and accuracy of the proposed method were validated via a numerical simulation of a two story frame structure with time-varying stiffness and damping.The results show that the presented algorithm can be used to identify the time-varying stiffness,the identified result of time-varying damping is very sensitive to noise.
引文
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[15]任宜春,易伟建,谢献忠.地震作用下结构时变物理参数识别[J].地震工程与工程振动,2007,27(4):98102.REN Yi-chun,YI Wei-jian,XIE Xian-zhong.Identification of time-variant physical parameters of structure under earthquake loading[J].Journal of Earthquake Engineering and Engineering Vibration,2007,27(4):98102.
[16]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,2000.YANG Fu-sheng.Engineering analysis and application[M].Beijing:Science Press,2000.
[2]续秀忠,张志谊,华宏星,等.应用时变参数建模方法辨识时变模态参数[J].航空学报,2003,24(3):230233.XU Xiu-zhong,ZHANG Zhi-yi,HUA Hong-xing,et al.Identification of time-variant modal parameters by a time-varying parametric approach[J].Acta Aeronautica et Astronautica Sinica,2003,24(3):230233.
[3]Liu K.Identification of linear time-varying systems[J].Journal of Sound and Vibration,1997,206(4):487500.
[4]Liu K,Deng L.Experimental verification of an algorithm for identification of linear time-varying systems[J].Journal of Sound and Vibration,2004,279(3):11701180.
[5]庞世伟,于开平,邹经湘.识别时变结构模态参数的改进子空间方法[J].应用力学学报,2005,2(2):184188.PANG Shi-wei,YU Kai-ping,ZOU Jing-xiang.Improved subspace method with application in linear time-varying structural modal parameter identification[J].Chinese Journal of Applied Mechanics,2005,2(2):184188.
[6]吴日强,于开平,邹经湘.改进的子空间方法及其在时变结构参数辨识中的应用[J].工程力学,2002,19(4):6770.WU Ri-qiang,YU Kai-ping,ZOU Jing-xiang.An improved subspace method and its application to parameter identification of time-varying structures[J].Engineering Mechanics,2002,19(4):6770.
[7]Hou Z K,Hera A,Shinde A.Wavelet-based structural health monitoring of earthquake excited structures[J].Computer-Aided Civil and Infrastructure Engineering,2006,21(4):268279.
[8]Hera A,Shinde A,HOU Zhi-kun.Issues in tracking instantaneous modal parameters for structural health monitoring using wavelet approach[C]//Proceedings of the23rd International Modal Analysis Conference(IMAC XXIII).Orlando,2005:338347.
[9]Tsatsanis M K,Giannakis G B.Time-varying system identification and Model Validation using wavelets[J].Transactions on Signal Processing,1993,41(12):35123523.
[10]Shi Z Y,Law S S.Identification of linear time-varying dynamical systems using Hilbert transform and empirical mode decomposition method[J].Journal of Applied Mechanics,2007,74(2):223230.
[11]Ghanem R,Romeo F.A wavelet-based approach for the identification of linear time-varying dynamical systems[J].Journal of Sound and Vibration,2000,234(4):555576.
[12]Cooper J E,Worden K.On-line physical parameter estimation with adaptive forgetting factors[J].Mechanical Systems and Signal Processing,2000,14(5):705730.
[13]Yang J N,LIN Si-lian.On-line identification of non-linear hysteretic structures using an adaptive tracking technique[J].Non-linear Mechanics,2004,39(9):14811491.
[14]李会娜,史治宇.基于自由响应数据的时变系统物理参数识别[J].振动工程学报,2007,20(4):348351.LI Hui-na,SHI Zhi-yu.Physical parameter identification of time-varying system based on free response data[J].Journal of Vibration Engineering,2007,20(4):348351.
[15]任宜春,易伟建,谢献忠.地震作用下结构时变物理参数识别[J].地震工程与工程振动,2007,27(4):98102.REN Yi-chun,YI Wei-jian,XIE Xian-zhong.Identification of time-variant physical parameters of structure under earthquake loading[J].Journal of Earthquake Engineering and Engineering Vibration,2007,27(4):98102.
[16]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,2000.YANG Fu-sheng.Engineering analysis and application[M].Beijing:Science Press,2000.
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