基于小波变换的结构模态参数识别
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摘要
及时、准确地识别出结构的模态参数是结构健康监测与损伤识别的重要前提。小波分析是众多识别方法中较优越的一种,因其在时-频两域都具有表征信号局部特征的能力,近年来这一方法在线性及非线性系统的参数识别中开始应用。探讨了基于小波脊(R idge)与小波骨架(Ske leton)的模态参数识别方法,针对小波变换中遇到的边端效应问题,提出了基于自回归滑动平均模型(ARM A)的“预测延拓”方法,并以美国土木工程师学会(A SCE)提供的B enchm ark模型为例进行了数值模拟。结果表明,本文提出的方法可以有效地抑制小波边端效应,通过小波变换可以准确地识别出结构的模态参数。
It's important to identify structural modal parameter in time and accurately for structural health monitoring and damage identification.Wavelet analysis is one of the various kinds of identification methods,which has been used in linear and nonlinear system response data since it can decompose signals simultaneously both in time-domain and frequency-domain with adaptive windows.In this paper,the basic theories of continuous wavelet transform are firstly introduced.And then the structural modal parameter identification method based on ridge and skeleton extraction techniques is discussed,following that a novel signal extension method using auto regressive moving average(ARMA) prediction is presented,Finally a numerical simulation is carried out by use of the Benchmark model which was developed by American Society of Civil Engineers(ASCE).The results show that the method presented here can effectively correct end effects errors,and the wavelet transform can identify structural model parameter accurately.
It's important to identify structural modal parameter in time and accurately for structural health monitoring and damage identification.Wavelet analysis is one of the various kinds of identification methods,which has been used in linear and nonlinear system response data since it can decompose signals simultaneously both in time-domain and frequency-domain with adaptive windows.In this paper,the basic theories of continuous wavelet transform are firstly introduced.And then the structural modal parameter identification method based on ridge and skeleton extraction techniques is discussed,following that a novel signal extension method using auto regressive moving average(ARMA) prediction is presented,Finally a numerical simulation is carried out by use of the Benchmark model which was developed by American Society of Civil Engineers(ASCE).The results show that the method presented here can effectively correct end effects errors,and the wavelet transform can identify structural model parameter accurately.
引文
[1]李宏男,李东升.土木工程结构安全性评估、健康监测及诊断述评[J].地震工程与工程振动,2002,22(3):82—90.
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[7]F e ldm an M,B raun S.Iden tification of non linearsystem param eters v ia the instan taneous frequency:app lication of the H ilbert transform and W inger-V ille techn iques[A].P roceed ings of 13th IM AC[C].N ashv ille T ennessee,1995:637—642.
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[9]T orrence C,Com po G P.A practica l gu ide to w ave letana lys is[R].Bu lletin of the Am erican M eteoro log ica lSoc iety,1998,79(1):61—78.
[10]K ijew sk i T L,K areem A.W ave let transform s forsystem iden tification and assoc iated process ingconcerns[A].15th A SCE Eng ineering M echan icsCon ference[C].Co lum b ia U n iveristy,N ew Y ork,2002.6:1—8.
[11]M iha B,Janko S.Enhancem en ts to the con tinuousw ave let transform for dam p ing iden tifications onshort s igna ls[J].M echan ica l System s and S igna lP rocess ing,2004,(18):1 065—1 076.
[12]M eyers S D,K e lly B G,B rien J J.A n in troduction tow ave let ana lys is in oceanography and m eteoro logy:w ith app lication to the d ispers ion ofY ana iw aves[J].M on th ly W eather R ev iew,1993,121:2 858—2 866.
[13]Johnson E A,L am H F,K atafyg iotis L,et a l.Abenchm ark prob lem for structura l hea lth m on itoringand dam age detection[A].P roceed ings of the 14thA SCE Eng ineering M echan ics Con ference[C].A ustin,T exas,2000.
[2]李宏男,孙鸿敏.小波分析在土木工程中的应用[J].世界地震工程,2003,19(2):16—22.
[3]G urley K,K areem A.A pp lication of w ave lettransform s in earthquake,w ind and ocean eng ineering[J].Eng ineering S tructures,1999,(21):149—167.
[4]G rossm ann A,M orlet J.D ecom pos ition of H ardyfunctions in to square in tegrab le w ave lets of constan tshape[J].Journa l of M athem atica l A na lys is,1984,15(4):723—736.
[5]Chu i C K.W ave let ana lys is and app lications:A nin troduction to w ave let[M].A cadem ic P ress,SanD iego,1992.
[6]S taszew sk iW J.Iden tification of dam p ing in M DOFsystem s us ing tim e-sca le decom pos ition[J].Journa lof Sound and V ibration,1997,203(2):283—305.
[7]F e ldm an M,B raun S.Iden tification of non linearsystem param eters v ia the instan taneous frequency:app lication of the H ilbert transform and W inger-V ille techn iques[A].P roceed ings of 13th IM AC[C].N ashv ille T ennessee,1995:637—642.
[8]S taszew sk iW J.Iden tification of non-linear system sus ing m u lti-sca le ridges and ske letons of the w ave lettransform[J].Journa l of Sound and V ibration,1998,214(4):639—658.
[9]T orrence C,Com po G P.A practica l gu ide to w ave letana lys is[R].Bu lletin of the Am erican M eteoro log ica lSoc iety,1998,79(1):61—78.
[10]K ijew sk i T L,K areem A.W ave let transform s forsystem iden tification and assoc iated process ingconcerns[A].15th A SCE Eng ineering M echan icsCon ference[C].Co lum b ia U n iveristy,N ew Y ork,2002.6:1—8.
[11]M iha B,Janko S.Enhancem en ts to the con tinuousw ave let transform for dam p ing iden tifications onshort s igna ls[J].M echan ica l System s and S igna lP rocess ing,2004,(18):1 065—1 076.
[12]M eyers S D,K e lly B G,B rien J J.A n in troduction tow ave let ana lys is in oceanography and m eteoro logy:w ith app lication to the d ispers ion ofY ana iw aves[J].M on th ly W eather R ev iew,1993,121:2 858—2 866.
[13]Johnson E A,L am H F,K atafyg iotis L,et a l.Abenchm ark prob lem for structura l hea lth m on itoringand dam age detection[A].P roceed ings of the 14thA SCE Eng ineering M echan ics Con ference[C].A ustin,T exas,2000.
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