基于一阶应变模态灵敏度的结构损伤定量研究
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摘要
面向基于动态应变监测数据的结构损伤诊断问题,提出了一种仅利用一阶应变模态振型及其灵敏度分析的损伤定量诊断策略。该策略利用事先规定应变测量单元的变形体结构或构件应变响应数据,通过NExT-ERA方法提取进而筛选识别精度较高的某一阶应变模态振型向量,由该阶特征向量求导得到灵敏度矩阵的同时,提出对其进行参考点归一化以避免质量归一化过程,最后通过求解损伤方程组得到单元刚度参量的改变。分别以下承式钢桁梁桥主桁架和装配式T形简支梁桥主梁简化模型为例,验证了该策略的有效性,分析了识别精度、噪声干扰和损伤程度对诊断效果的影响。该研究可为基于实时监测的结构在线诊断提供一定的理论和技术支持。
Aiming at the structural damage detection based on the dynamic strain data,a type of quantitative damage detection diagnosis strategy is proposed by using single-order strain mode shape and its sensitivity analysis.The strategy is implemented as follows.First,the strain data on the pre-defined strain measurement elements of the deformable-body structure or component are utilized to identify one single-order strain mode shape vector based on NExT-ERA method.Then,the sensitivity matrix is derived from the eigenvector derivation and the reference-point normalization is presented for avoiding the mass normalization.On these bases,the changes of the element stiffness parameters can be updated through the damage equations.Two simplified models,including the main truss of a steel truss girder bridge and the main beam of a fabricated T-shaped simple supported girder bridge,have been taken as the illustration to substantiate the proposed strategy.The influences of the identified precision of the strain mode shape,the noises and the extents of damages are investigated,respectively.This study provides a way to a certain extent to help the damage detection based on the structural health monitoring in a real time.
Aiming at the structural damage detection based on the dynamic strain data,a type of quantitative damage detection diagnosis strategy is proposed by using single-order strain mode shape and its sensitivity analysis.The strategy is implemented as follows.First,the strain data on the pre-defined strain measurement elements of the deformable-body structure or component are utilized to identify one single-order strain mode shape vector based on NExT-ERA method.Then,the sensitivity matrix is derived from the eigenvector derivation and the reference-point normalization is presented for avoiding the mass normalization.On these bases,the changes of the element stiffness parameters can be updated through the damage equations.Two simplified models,including the main truss of a steel truss girder bridge and the main beam of a fabricated T-shaped simple supported girder bridge,have been taken as the illustration to substantiate the proposed strategy.The influences of the identified precision of the strain mode shape,the noises and the extents of damages are investigated,respectively.This study provides a way to a certain extent to help the damage detection based on the structural health monitoring in a real time.
引文
[1]李德葆,诸葛鸿程,王波.实验应变模态分析原理和方法[J].清华大学学报(自然科学版),1990,30(2):105—112.Li D B,Zhuge H C,Wang B.On the principle and technique of experimental strain modal snalysis[J].Journal of Tsinghua University:Science and Technology,1990,30(2):105—112.
[2]Yam L H,Leung T P,Li D B,et al.Theoretical and experimental study of modal strain analysis[J].Journal of Sound and Vibration,1996,191(2):251—260.
[3]Adewuyi A P,Wu Z S,Serker K.Strain measurements assessment of vibration-based damage identification methods using displacement and distributed strain measurement[J].Structural Health Monitoring-An International Journal,2009,8(6):443—461.
[4]刘晖,瞿伟廉,李功标,等.光纤光栅传感系统在结构损伤识别中的应用[J].应用基础与工程科学学报,2009,17(3):395—401.Liu H,Qu W L,Li G B,et al.The application of structural damage detection based on Optic Fiber Bragg Grating sensing system[J].Journal of Basic Science and Engineering,2009,17(3):395—401.
[5]吴智深,李素贞,Adewuyi A P.基于应变分布响应的模态分析理论与应用[J].科技导报,2010,28(8):94—103.Wu Z S,Li S Z,Adewuyi A P.Modal analysis based on distributed strain measurements:theory and application[J].Science and Technology Review,2010,28(8):94—103.
[6]徐丽,易伟建,吴高烈.结构局部损伤诊断的应变模态方法-分析与应用[J].自然灾害学报,2006,15(3):157—163.Xu L,Yi W J,Wu G L.Strain mode method for diagnosis of local damage of structure:analysis and application[J].Journal of Natural Disasters,2006,15(3):157—163.
[7]彭细荣,路新瀛,陈肇元.结构应变模态识别的随机子空间方法[J].振动与冲击,2008,27(6):4—6.Peng X R.Lu X Y,Chen Z Y.Stochastic subspace method for structural strain model parameter identification[J].Journal of Vibration and Shock,2008,27(6):4—6.
[8]顾培英,邓昌.基于环境激励下的工作应变模态频域识别方法[J].振动与冲击,2008,27(8):68—70.Gu P Y,Deng C.Modal parameters identification of operational strain modes under ambient excitation with frequency domain method[J].Journal of Vibration and Shock,2008,27(8):68—70.
[9]Li S Z,Wu Z S.Modal analysis on macro-strain measurements from distributed long-gage fiber optic sensors[J]Journal of Intelligent Material Systems and Structures,2008,19(8):937—946.
[10]Hillary B,Ewins D J.The use of strain gauges in force determination and frequency response function measurements[C].Proc.of the 2nd IMAC,1984,February,627—634.
[11]伊立言.电阻应变计在试验模态分析中的应用[J].振动、测试与诊断,1985,4:11—19.Yi L Y.Applications of strain gauges in experimental modal analysis[J].Journal of Vibration,Measurement&Diagnosis,1985,4:11—19.
[12]Song T C,Zhang P Q,Feng W Q,et al.The Application of the Time Domain Method in Strain Modal Analysis[C].Proc.of the 4th IMAC.1986.
[13]Pandey A K,Biswas M,Samman M M.Damage detection from changes in curvature mode shapes[J].Journal of Sound and Vibration,1991,145:321—332.
[14]周先雁,沈蒲生.用应变模态对混凝土结构进行损伤识别的研究[J].湖南大学学报,1997,24(5):69—74.Zhou X Y,Shen P S.Study of damage assessment of concrete structures by strain model method[J].Journal of Hunan University,1997,24(5):69—74.
[15]徐丽,易伟建,吴高烈.混凝土框架柱刚度变化识别的应变模态方法研究[J].振动与冲击,2006,25(3):1—5.Xu L,Yi W J,Wu G L.The stiffness change identification of concrete frame column using strain mode method[J].Journal of Vibration and Shock,2006,25(3):1—5.
[16]李功标,瞿伟廉.基于应变模态和贝叶斯方法的杆件损伤识别[J].武汉理工大学学报,2007,29(1):135—138.Li G B,Qu W L.Damage detection of bars based on strain mode and bayesian statistical method[J].Journal of Wuhan University of Technology,2007,29(1):135—138.
[17]任权,李洪升,郭杏林.基于应变模态变化率的压力管道无损检测[J].大连理工大学学报,2001,41(6):648—652.Ren Q,Li H S,Guo X L.Undamaged detection of pipe based on modal varied gradient of strain[J].Journal of Dalian University of Technology,2001,41(6):648—652.
[18]邓焱,严普强.梁及桥梁应变模态与损伤测量的新方法[J].清华大学学报(自然科学版),2000,40(11):123—127.Deng Y,Yan P Q.New approach for strain modal measurement and damage detection of bridges[J].Journal of Tsinghua University:Science and Technology,2000,40(11):123—127.
[19]曾欣,徐赵东.基于分布式应变模态残差统计趋势的大跨斜拉桥损伤识别策略[J].振动与冲击,2013,32(7):78—81.Zeng X,Xu Z D.Damage detection strategy based on strain modal residual trend for a long-span cablestayed Bridge[J].Journal of Vibration and Shock,2013,32(7):78—81.
[20]钱管良,顾松年,姜节胜.在线振动监测与故障诊断的一种新途径[J].固体力学学报,1990,11(3):218—228.Qian G L,Gu S N,Jiang J S.A new approach for vibration monitoring and fault diagnosis[J].Acta Mechanica Solida Sinica,1990,11(3):218—228.
[21]顾培英,陈厚群,李同春,等.基于损伤应变模态的结构损伤识别直接指标法[J].自然科学进展,2007,17(2):240—247.Gu P Y,Chen H Q,Li T C,et al.Direct index method of damage detection based on strain mode shape[J].Review of Natural Science,2007,17(2):240—247.
[22]Li S Z,Wu Z S.A model free method for damage locating and quantifying in a beam like structure based on dynamic distributed strain measurements[J].Computer-Aided Civil and Infrastructure Engineering,2008,23:404—413.
[23]管德清,黄燕.基于应变模态小波变换的框架结构损伤识别研究[J].计算力学学报,2010,27(2):325—329.Guan D Q,Huang Y.Damage identification of frame structure by means of wavelet analysis of strain mode[J].Chinese Journal of Computation Mechanics,2010,27(2):325—329.
[24]侯立群,赵雪峰,欧进萍,等.结构损伤诊断不确定性方法研究进展[J].振动与冲击,2014,33(18):50—58.Hou L Q,Zhao X F,Ou J P,et al.A review of nondeterministic methods for structural damage diagnosis[J].Journal of Vibration and Shock,2014,33(18):50—58.
[25]苏娟,陆秋海,管迪华.神经网络法在定量损伤识别研究中的应用[J].清华大学学报(自然科学版),1999,39(4):68—70.Su J,Lu Q H,Guna D H.Applications of neural networks in quantitative analysis of damage detection[J].Journal of Tsinghua University:Science and Technology,1999,39(4):68—70.
[26]黄东梅,瞿伟廉.高耸塔架结构节点损伤的指标分析与反分析两步诊断法[J].华中科技大学学报,2003,20(2):61—64.Huang D M,Qu W L.Two-step detection approach to joint damage in high-rise tower structures by index analysis and reverse analysis[J].Journal of Huazhong University of Science and Technology,2003,20(2):61—64.
[27]彭细荣,路新流,隋允康,等.基于应变模态及结构优化技术的结构损伤程度识别方法[J].北京工业大学学报,2009,35(2):145—151.Peng X R.Lu X L,Sui R K,et al.Damage degree identification method based on strain mode and structural optimization[J].Journal of Beijing University of Technology,2009,35(2):145—151.
[28]Wu Z S,Li S Z.Two-level damage detection strategy based on modal parameters from distributed dynamic macro-strain measurements[J].Journal of Intelligent Material Systems and Structures,2007,18(7):667—676.
[29]Fox R L,Kapoor M P.Rates of change of Eigen value and Eigenvectors[J].AIAA Journal,1968,12:2426—2429.
[30]Nelson R B.Simplified calculation of Eigenvector derivatives[J].AIAA Journal,1976,4:1201—1205.
[31]陈集丰.特征向量导数的简便计算法[J].航空学报,1988,9(1):97—102.Chen J F.A simplified method for calculating Eigenvectors[J].Chinese Journal of Aeronautics,1988,9(1):97—102.
[32]Sanayei M,Saletnik M J G.Parameter estimation of structures from static strain measurements,I:formulation[J].Journal of Structural Engineering,1996,122(5):555—562.
[33]李德葆.实验应变/应力模态分析若干问题的进展评述[J].振动与冲击,1996,15(1):13—17.Li D B.A general review on several fundamental points of experimental strain/stress modal analysis[J].Journal of Vibration and Shock,1996,15(1):13—17.
[34]James G H,Carne T G,Lauffer J P.The natural excitation technique(NExT)for modal parameter extraction from operating structures[J].Journal of Analytical and Experimental Modal Analysis,1995,10(4):260—277.
[35]Juang J N,Pappa R S.An eigensystem realization algorithm for modal parameter identification and model reduction[J].Journal of Guidance,Contorl,and Dynamics,1985,8(5):620—627.
[36]刘福强,张令弥.一种改进的特征系统实现算法及其在智能结构中的应用[J].振动工程学报,1999,12(3):316—322.Liu F Q,Zhang L M.An improved eigensystem realization algorithm and its application to modal parameter identification of intelligent space trusses[J].Journal of Vibration Engineering,1999,12(3):316—322.
[37]李惠彬.大型工程结构模态参数识别技术[M].北京:北京理工大学出版社,1997.Li H B.Modal Identification Technology for Large Structure[M].Beijing:Beijing Insitute of Technology Press,1997.
[2]Yam L H,Leung T P,Li D B,et al.Theoretical and experimental study of modal strain analysis[J].Journal of Sound and Vibration,1996,191(2):251—260.
[3]Adewuyi A P,Wu Z S,Serker K.Strain measurements assessment of vibration-based damage identification methods using displacement and distributed strain measurement[J].Structural Health Monitoring-An International Journal,2009,8(6):443—461.
[4]刘晖,瞿伟廉,李功标,等.光纤光栅传感系统在结构损伤识别中的应用[J].应用基础与工程科学学报,2009,17(3):395—401.Liu H,Qu W L,Li G B,et al.The application of structural damage detection based on Optic Fiber Bragg Grating sensing system[J].Journal of Basic Science and Engineering,2009,17(3):395—401.
[5]吴智深,李素贞,Adewuyi A P.基于应变分布响应的模态分析理论与应用[J].科技导报,2010,28(8):94—103.Wu Z S,Li S Z,Adewuyi A P.Modal analysis based on distributed strain measurements:theory and application[J].Science and Technology Review,2010,28(8):94—103.
[6]徐丽,易伟建,吴高烈.结构局部损伤诊断的应变模态方法-分析与应用[J].自然灾害学报,2006,15(3):157—163.Xu L,Yi W J,Wu G L.Strain mode method for diagnosis of local damage of structure:analysis and application[J].Journal of Natural Disasters,2006,15(3):157—163.
[7]彭细荣,路新瀛,陈肇元.结构应变模态识别的随机子空间方法[J].振动与冲击,2008,27(6):4—6.Peng X R.Lu X Y,Chen Z Y.Stochastic subspace method for structural strain model parameter identification[J].Journal of Vibration and Shock,2008,27(6):4—6.
[8]顾培英,邓昌.基于环境激励下的工作应变模态频域识别方法[J].振动与冲击,2008,27(8):68—70.Gu P Y,Deng C.Modal parameters identification of operational strain modes under ambient excitation with frequency domain method[J].Journal of Vibration and Shock,2008,27(8):68—70.
[9]Li S Z,Wu Z S.Modal analysis on macro-strain measurements from distributed long-gage fiber optic sensors[J]Journal of Intelligent Material Systems and Structures,2008,19(8):937—946.
[10]Hillary B,Ewins D J.The use of strain gauges in force determination and frequency response function measurements[C].Proc.of the 2nd IMAC,1984,February,627—634.
[11]伊立言.电阻应变计在试验模态分析中的应用[J].振动、测试与诊断,1985,4:11—19.Yi L Y.Applications of strain gauges in experimental modal analysis[J].Journal of Vibration,Measurement&Diagnosis,1985,4:11—19.
[12]Song T C,Zhang P Q,Feng W Q,et al.The Application of the Time Domain Method in Strain Modal Analysis[C].Proc.of the 4th IMAC.1986.
[13]Pandey A K,Biswas M,Samman M M.Damage detection from changes in curvature mode shapes[J].Journal of Sound and Vibration,1991,145:321—332.
[14]周先雁,沈蒲生.用应变模态对混凝土结构进行损伤识别的研究[J].湖南大学学报,1997,24(5):69—74.Zhou X Y,Shen P S.Study of damage assessment of concrete structures by strain model method[J].Journal of Hunan University,1997,24(5):69—74.
[15]徐丽,易伟建,吴高烈.混凝土框架柱刚度变化识别的应变模态方法研究[J].振动与冲击,2006,25(3):1—5.Xu L,Yi W J,Wu G L.The stiffness change identification of concrete frame column using strain mode method[J].Journal of Vibration and Shock,2006,25(3):1—5.
[16]李功标,瞿伟廉.基于应变模态和贝叶斯方法的杆件损伤识别[J].武汉理工大学学报,2007,29(1):135—138.Li G B,Qu W L.Damage detection of bars based on strain mode and bayesian statistical method[J].Journal of Wuhan University of Technology,2007,29(1):135—138.
[17]任权,李洪升,郭杏林.基于应变模态变化率的压力管道无损检测[J].大连理工大学学报,2001,41(6):648—652.Ren Q,Li H S,Guo X L.Undamaged detection of pipe based on modal varied gradient of strain[J].Journal of Dalian University of Technology,2001,41(6):648—652.
[18]邓焱,严普强.梁及桥梁应变模态与损伤测量的新方法[J].清华大学学报(自然科学版),2000,40(11):123—127.Deng Y,Yan P Q.New approach for strain modal measurement and damage detection of bridges[J].Journal of Tsinghua University:Science and Technology,2000,40(11):123—127.
[19]曾欣,徐赵东.基于分布式应变模态残差统计趋势的大跨斜拉桥损伤识别策略[J].振动与冲击,2013,32(7):78—81.Zeng X,Xu Z D.Damage detection strategy based on strain modal residual trend for a long-span cablestayed Bridge[J].Journal of Vibration and Shock,2013,32(7):78—81.
[20]钱管良,顾松年,姜节胜.在线振动监测与故障诊断的一种新途径[J].固体力学学报,1990,11(3):218—228.Qian G L,Gu S N,Jiang J S.A new approach for vibration monitoring and fault diagnosis[J].Acta Mechanica Solida Sinica,1990,11(3):218—228.
[21]顾培英,陈厚群,李同春,等.基于损伤应变模态的结构损伤识别直接指标法[J].自然科学进展,2007,17(2):240—247.Gu P Y,Chen H Q,Li T C,et al.Direct index method of damage detection based on strain mode shape[J].Review of Natural Science,2007,17(2):240—247.
[22]Li S Z,Wu Z S.A model free method for damage locating and quantifying in a beam like structure based on dynamic distributed strain measurements[J].Computer-Aided Civil and Infrastructure Engineering,2008,23:404—413.
[23]管德清,黄燕.基于应变模态小波变换的框架结构损伤识别研究[J].计算力学学报,2010,27(2):325—329.Guan D Q,Huang Y.Damage identification of frame structure by means of wavelet analysis of strain mode[J].Chinese Journal of Computation Mechanics,2010,27(2):325—329.
[24]侯立群,赵雪峰,欧进萍,等.结构损伤诊断不确定性方法研究进展[J].振动与冲击,2014,33(18):50—58.Hou L Q,Zhao X F,Ou J P,et al.A review of nondeterministic methods for structural damage diagnosis[J].Journal of Vibration and Shock,2014,33(18):50—58.
[25]苏娟,陆秋海,管迪华.神经网络法在定量损伤识别研究中的应用[J].清华大学学报(自然科学版),1999,39(4):68—70.Su J,Lu Q H,Guna D H.Applications of neural networks in quantitative analysis of damage detection[J].Journal of Tsinghua University:Science and Technology,1999,39(4):68—70.
[26]黄东梅,瞿伟廉.高耸塔架结构节点损伤的指标分析与反分析两步诊断法[J].华中科技大学学报,2003,20(2):61—64.Huang D M,Qu W L.Two-step detection approach to joint damage in high-rise tower structures by index analysis and reverse analysis[J].Journal of Huazhong University of Science and Technology,2003,20(2):61—64.
[27]彭细荣,路新流,隋允康,等.基于应变模态及结构优化技术的结构损伤程度识别方法[J].北京工业大学学报,2009,35(2):145—151.Peng X R.Lu X L,Sui R K,et al.Damage degree identification method based on strain mode and structural optimization[J].Journal of Beijing University of Technology,2009,35(2):145—151.
[28]Wu Z S,Li S Z.Two-level damage detection strategy based on modal parameters from distributed dynamic macro-strain measurements[J].Journal of Intelligent Material Systems and Structures,2007,18(7):667—676.
[29]Fox R L,Kapoor M P.Rates of change of Eigen value and Eigenvectors[J].AIAA Journal,1968,12:2426—2429.
[30]Nelson R B.Simplified calculation of Eigenvector derivatives[J].AIAA Journal,1976,4:1201—1205.
[31]陈集丰.特征向量导数的简便计算法[J].航空学报,1988,9(1):97—102.Chen J F.A simplified method for calculating Eigenvectors[J].Chinese Journal of Aeronautics,1988,9(1):97—102.
[32]Sanayei M,Saletnik M J G.Parameter estimation of structures from static strain measurements,I:formulation[J].Journal of Structural Engineering,1996,122(5):555—562.
[33]李德葆.实验应变/应力模态分析若干问题的进展评述[J].振动与冲击,1996,15(1):13—17.Li D B.A general review on several fundamental points of experimental strain/stress modal analysis[J].Journal of Vibration and Shock,1996,15(1):13—17.
[34]James G H,Carne T G,Lauffer J P.The natural excitation technique(NExT)for modal parameter extraction from operating structures[J].Journal of Analytical and Experimental Modal Analysis,1995,10(4):260—277.
[35]Juang J N,Pappa R S.An eigensystem realization algorithm for modal parameter identification and model reduction[J].Journal of Guidance,Contorl,and Dynamics,1985,8(5):620—627.
[36]刘福强,张令弥.一种改进的特征系统实现算法及其在智能结构中的应用[J].振动工程学报,1999,12(3):316—322.Liu F Q,Zhang L M.An improved eigensystem realization algorithm and its application to modal parameter identification of intelligent space trusses[J].Journal of Vibration Engineering,1999,12(3):316—322.
[37]李惠彬.大型工程结构模态参数识别技术[M].北京:北京理工大学出版社,1997.Li H B.Modal Identification Technology for Large Structure[M].Beijing:Beijing Insitute of Technology Press,1997.