基于EMD和VARMA模型的结构损伤识别
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摘要
提出了基于EMD和VARMA模型的结构损伤识别方法。该方法首先将结构反应信号用EMD方法分解成一系列固有模态函数,然后将固有模态函数表示为时变VARMA模型并用Kalman滤波方法估计时变VARMA参数,最后根据时变VARMA参数定义一个新的损伤指标用于结构损伤识别。为检验该指标的实际性能,算例中选用ImperialCounty Services Building和Van Nuys Hotel作为基准结构。通过其实测地震反应记录的分析表明:该指标在实际的量测环境和噪声条件下具有较好的敏感性和抗噪能力,可有效地识别结构多处损伤的发生过程和严重程度;由于该指标定义在反应信号特征提取的基础上,无需其他额外的信息,它可同时用于结构整体和局部两个层次损伤的识别;同时,该指标还适于实时(在线)的结构损伤识别或健康监测,因其直接由时变VARMA参数推导得出。最后,对后续研究工作进行了展望。
Based on EMD and vector autoregressive moving average(VARMA) models,a method for structural damage detection was proposed.By using the time varying VARMA model to represent the intrinsic mode functions(IMFs) obtained from the EMD of structural response signal,the Kalman filter was taken to estimate the VARMA coefficients.Then,a novel damage index derived from the VARMA coefficients was presented to detect structural damages.To investigate the real performance of the damage index,the Imperial County Services Building and Van Nuys Hotel were adopted as the benchmark structures in the examples given.The analysis of the actual response records during earthquake shows that the anti-noise ability and sensitivity of damage index are satisfactory in real environments with the presence of actual noise and it can indicate the occurrence and relative severity of structural damages at multiple locations in an efficient manner.Since the damage index is defined based on the feature extraction of a signal with no additional information required,it can be used to detect both global and local structural damages.Also,the damage index can be potentially used in real time(online) damage detection or structural health monitoring,for it is directly derived from time varying VARMA coefficients.Some recommendations for future research were provided.
Based on EMD and vector autoregressive moving average(VARMA) models,a method for structural damage detection was proposed.By using the time varying VARMA model to represent the intrinsic mode functions(IMFs) obtained from the EMD of structural response signal,the Kalman filter was taken to estimate the VARMA coefficients.Then,a novel damage index derived from the VARMA coefficients was presented to detect structural damages.To investigate the real performance of the damage index,the Imperial County Services Building and Van Nuys Hotel were adopted as the benchmark structures in the examples given.The analysis of the actual response records during earthquake shows that the anti-noise ability and sensitivity of damage index are satisfactory in real environments with the presence of actual noise and it can indicate the occurrence and relative severity of structural damages at multiple locations in an efficient manner.Since the damage index is defined based on the feature extraction of a signal with no additional information required,it can be used to detect both global and local structural damages.Also,the damage index can be potentially used in real time(online) damage detection or structural health monitoring,for it is directly derived from time varying VARMA coefficients.Some recommendations for future research were provided.
引文
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[6]Huynh D,He J,Tran D.Damage location vector:a non-destructive structural damage detection technique[J].Computers&Structures,2005,83(28-30):2353-2367.
[7]Kim J T,Stubbs N.Improved damage identification methodbased on modal information[J].Journal of Sound andVibration,2002,252(2):223-238.
[8]邹万杰,瞿伟廉.基于频响函数和遗传算法的结构损伤识别研究[J].振动与冲击,2008,27(12):28-30.
[9]王振林,聂国华.曲率模态和小波包变换在结构损伤识别中的应用[J].振动与冲击,2008,27(1):124-126.
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[11]陈隽,徐幼麟,李杰.经验模分解及小波分析在结构损伤识别中的应用:试验研究[J].地震工程与工程振动,2007,27(1):110-116.
[12]Ma J,Pines D J.Damage detection in a building structuremodel under seismic excitation using dereverberated wavemechanics[J].Engineering Structures,2003,25(3):385-396.
[13]Hou Z,Noori M,Amand R S.Wavelet-based approach forstructural damage detection[J].Journal of EngineeringMechanics ASCE,2000,126(7):677-683.
[14]Dong Y F,Li Y M.Application of time series analysis onperformance evaluation of seismic structures[C].In:Proceedings of the Ninth International Symposium onStructural Engineering for Young Experts.China:Fuzhou;2006,820-826.
[15]Todorovska MI,Trifunac MD.Earthquake damage detectionin the Imperial County Services Building I:The data and timefrequency analysis[J].Soil Dynamics&EarthquakeEngineering,2007,27(6):564-576.
[16]Todorovska MI,Trifunac MD.Earthquake damage detectionin the Imperial County Services Building II:analysis ofnovelties via wavelets[OL].http://www.usc.edu/dept/civil_eng/Earthquake_eng/Selected_Publ/PDF/ICS_Paper_II.pdf,June 6,2008.
[17]Huang N E,Shen Z,Long S R,et al.The empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysis[J].Proc R Soc LondonSer A,1998,454:903-995.
[18]Huang N E,Bethesda M D.Computing instantaneousfrequency by normalizing Hilbert transform[P].US Patent6901353,2005.
[19]李英民,董银峰,赖明.基于EMD和VARMA模型的信号处理方法[J].振动与冲击,2007,26(12):68-73.
[20]熊飞,程远胜,刘均.基于HHT方法的时变多自由度系统的损伤识别[J].振动、测试与诊断,2008,28(2):122-125.
[21]胡劲松,杨世锡,任达千.一种基于EMD的振动信号时频分析新方法研究[J].振动与冲击,2008,27(8):71-73,154.
[22]韩海明,沈涛虹,宋汉文.工况模态分析的EMD方法[J].振动与冲击,2002,21(4):69-71.
[23]许福友,陈艾荣,刘剑锋,等.基于EMD处理信号的桥梁颤振导数识别[J].振动与冲击,2008,27(5):144-147,156.
[24]韩建刚,任伟新,孙增寿.结构损伤识别的小波包分析试验研究[J].振动与冲击,2006,25(1):47-50.
[25]Trifunac M D,Ivanovic S S,Todorovska M I.Instrumented7-storey reinforced concrete building in Van Nuys,California:description of damage from the 1994 Northridgeearthquake and strong motion data[R].USC Report CE99-02;1999.
[26]Andersen P.Identification of civil engineering structuresusing ARMA models[D].Aalborg:AalborgUniversity,1997.
[27]Ljung L.System identification:theory for the user[M].2nded.New York:Prentice-Hall,1999.
[28]Flandrin P,Rilling G,Goncalves P.Empirical modedecomposition as a filter bank[J].IEEE Signal Proc.Let.,2004,11(2):112-114.
[2]Carden E P,Fanning P.Vibration based conditionmonitoring:a review[J].Structural Health Monitoring,2004,3(4):355-377.
[3]Fritzen C P,Jennewein D,Kiefer T.Damage detection basedon model updating methods[J].Mechanical Systems andSignal Processing,1998,12(1):163-186.
[4]Teughels A,Maeck J,Roeck G D.Damage assessment byFE model updating using damage functions[J].Computers&Structures,2002,80(25):1869-1879.
[5]Li H J,Yang H Z,Hu S L J.Modal strain energydecomposition method for damage localization in 3d framestructures[J].Journal of Engineering Mechanics ASCE,2006,132(9):941-951.
[6]Huynh D,He J,Tran D.Damage location vector:a non-destructive structural damage detection technique[J].Computers&Structures,2005,83(28-30):2353-2367.
[7]Kim J T,Stubbs N.Improved damage identification methodbased on modal information[J].Journal of Sound andVibration,2002,252(2):223-238.
[8]邹万杰,瞿伟廉.基于频响函数和遗传算法的结构损伤识别研究[J].振动与冲击,2008,27(12):28-30.
[9]王振林,聂国华.曲率模态和小波包变换在结构损伤识别中的应用[J].振动与冲击,2008,27(1):124-126.
[10]陈换过,闫云聚,姜节胜,等.HHT在复合材料机翼盒段结构小损伤检测中的应用[J].振动与冲击,2006,25(3):81-84,98.
[11]陈隽,徐幼麟,李杰.经验模分解及小波分析在结构损伤识别中的应用:试验研究[J].地震工程与工程振动,2007,27(1):110-116.
[12]Ma J,Pines D J.Damage detection in a building structuremodel under seismic excitation using dereverberated wavemechanics[J].Engineering Structures,2003,25(3):385-396.
[13]Hou Z,Noori M,Amand R S.Wavelet-based approach forstructural damage detection[J].Journal of EngineeringMechanics ASCE,2000,126(7):677-683.
[14]Dong Y F,Li Y M.Application of time series analysis onperformance evaluation of seismic structures[C].In:Proceedings of the Ninth International Symposium onStructural Engineering for Young Experts.China:Fuzhou;2006,820-826.
[15]Todorovska MI,Trifunac MD.Earthquake damage detectionin the Imperial County Services Building I:The data and timefrequency analysis[J].Soil Dynamics&EarthquakeEngineering,2007,27(6):564-576.
[16]Todorovska MI,Trifunac MD.Earthquake damage detectionin the Imperial County Services Building II:analysis ofnovelties via wavelets[OL].http://www.usc.edu/dept/civil_eng/Earthquake_eng/Selected_Publ/PDF/ICS_Paper_II.pdf,June 6,2008.
[17]Huang N E,Shen Z,Long S R,et al.The empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysis[J].Proc R Soc LondonSer A,1998,454:903-995.
[18]Huang N E,Bethesda M D.Computing instantaneousfrequency by normalizing Hilbert transform[P].US Patent6901353,2005.
[19]李英民,董银峰,赖明.基于EMD和VARMA模型的信号处理方法[J].振动与冲击,2007,26(12):68-73.
[20]熊飞,程远胜,刘均.基于HHT方法的时变多自由度系统的损伤识别[J].振动、测试与诊断,2008,28(2):122-125.
[21]胡劲松,杨世锡,任达千.一种基于EMD的振动信号时频分析新方法研究[J].振动与冲击,2008,27(8):71-73,154.
[22]韩海明,沈涛虹,宋汉文.工况模态分析的EMD方法[J].振动与冲击,2002,21(4):69-71.
[23]许福友,陈艾荣,刘剑锋,等.基于EMD处理信号的桥梁颤振导数识别[J].振动与冲击,2008,27(5):144-147,156.
[24]韩建刚,任伟新,孙增寿.结构损伤识别的小波包分析试验研究[J].振动与冲击,2006,25(1):47-50.
[25]Trifunac M D,Ivanovic S S,Todorovska M I.Instrumented7-storey reinforced concrete building in Van Nuys,California:description of damage from the 1994 Northridgeearthquake and strong motion data[R].USC Report CE99-02;1999.
[26]Andersen P.Identification of civil engineering structuresusing ARMA models[D].Aalborg:AalborgUniversity,1997.
[27]Ljung L.System identification:theory for the user[M].2nded.New York:Prentice-Hall,1999.
[28]Flandrin P,Rilling G,Goncalves P.Empirical modedecomposition as a filter bank[J].IEEE Signal Proc.Let.,2004,11(2):112-114.
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