混凝土斜拉桥的模态参数识别与模型修正
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摘要
基于结构动力特性变化的大跨桥梁结构损伤诊断研究越来越受到人们的关注，而大跨混凝土斜拉桥结构的模态参数识别与模型修正，是桥梁健康监测中迫切需要解决但又尚未完全解决的一个极为复杂的问题。本文以惠州合生大桥为原型，面向健康诊断设计制作了1:15的大比例混凝土斜拉桥试验模型，对面向健康诊断的斜拉桥模型设计、斜拉桥模态试验与模态参数识别、斜拉桥有限元建模与模型修正等方面进行了研究。主要内容如下：
(1)对面向健康诊断的混凝土斜拉桥模型设计进行了研究
以广东惠州合生大桥为原型，面向健康诊断设计制作了1:15的大比例混凝土斜拉桥模型，针对模型设计过程中的困难，提出在满足制作条件的前提下，对模型桥主梁和主塔的设计应主要满足抗弯刚度相似的要求，放松对轴向刚度和扭转刚度等参数的相似要求，并给出了模型桥配重和斜拉索简化方法。采用有限元法对模型桥和原型桥的静动力特性及损伤特性进行了分析，分析结果表明模型桥和原型桥的静动力特性及损伤特性具有良好的相似性，可为混凝土斜拉桥的模型设计提供参考。
(2)采用锤击法和环境激励法对模型桥进行了模态试验和模态参数识别研究
采用特征系统实现算法(ERA)对锤击法模态试验数据进行了模态参数识别，得到了模型桥的前21阶模态参数；采用随机减量法结合ERA法对环境激励法模态试验数据进行了模态参数识别，得到了模型桥的前17阶模态参数。分别采用白噪声和实测地脉动非白噪声信号作为激励信号，对梁壳有限元模型进行了时程响应分析，对两种激励下的响应信号进行模态参数识别，将识别结果进行对比可见，非白噪声激励可使模态参数识别定阶过程中产生虚假模态，有限元预分析可为模态参数识别过程中的虚假模态剔除提供一个虚假模态可能出现的范围，另外，非白噪声激励可降低模态频率和模态振型的识别精度。提出了以精细有限元预分析结果为先验知识参考，将稳定图法、实测激励信号及信噪比高的测点信号的频谱分析结果相结合进行定阶和虚假模态剔除的方法，实践表明，该方法能够准确识别模型桥的模态参数并剔除了虚假模态，为环境激励试验模态参数识别中虚假模态的剔除提供一种新思路。
分别从不同参数识别方法和基于MONTE CARLO法的噪声模拟两个方面对锤击法和环境激励法模态参数识别的不确定性进行了分析。结果表明：由不同参数识别方法引起的模态参数的不确定性明显高于由噪声模拟引起的不确定性，因此，不同参数识别方法引起的不确定问题不能忽略；通过基于MONTE CARLO法的噪声模拟给出了锤击法和环境激励法模态参数的统计不确定区间，为模型修正、损伤识别等研究提供基础数据。
(3)锤击法和环境激励法模态频率识别结果差异的对比分析
通过对模型桥张拉预应力前后及张拉预应力后主梁损伤三个工况的锤击法和环境激励法识别的频率差值进行对比，三个工况下锤击法和环境激励法识别的频率差值百分比最大分别为3.64%、1.24%、1.84%，可见，张拉预应力后锤击法和环境激励法识别的模态频率差值比张拉预应力前明显减小，主梁损伤工况锤击法和环境激励法识别的模态频率差值比张拉预应力后增大，由此推测，对于混凝土斜拉桥结构，由于混凝土微裂缝或裂缝的存在，结构的振动幅值大小可能会对主梁和主塔构件的截面刚度产生影响，振动幅值越大结构的刚度越低。
(4)研究了混凝土斜拉桥有限元建模与模型修正
提出了基于参数和目标函数分类的改进的模型修正技术，该模型修正技术通过灵敏度分析对修正参数和目标函数进行优选和分类、排序，逐级进行模型修正。结果表明，改进的模型修正技术有效改善了模型修正的病态问题，能够明显的提高模型修正效率并得到更优的模型修正结果。分别采用单主梁模式、三主梁模式、梁壳模式和实体模式建立了模型斜拉桥的初始有限元模型，采用改进的模型修正技术对各种初始有限元模型进行了模型修正，将修正前后的动力特性计算值与实测数据进行了对比，讨论了不同模式建模方法的计算精度和模型修正效果，以及有限元建模误差来源和模型修正的相关问题。结果表明，初始有限元模型计算误差主要是由建模误差和参数误差引起的；梁单元模型在建模方面有其局限性，单主梁模型无法准确模拟Π形主梁斜拉桥的扭转特性，应根据不同的结构特点和分析目标建立相应的有限元模型；提出模型修正过程中应准确区分建模误差和参数误差，才能得到最符合实际的基准有限元模型。为斜拉桥有限元建模与模型修正提供了参考。
It is more and more attention for the research on vibration based damageidentification of long span bridge recent years. Modal parameter identification andmodel updating of long-span concrete cable-stayed bridge structure is a verycomplicated problem which needs to be solved urgently in bridge health monitoring,and it has not been completely solved yet. Taking the Hesheng bridge as theprototype, a health-diagnosis-oriented concrete cable-stayed model bridge wasdesigned and made with a scale of1:15. A series of works were done in thisdissertation, mainly includes model design of health-diagnosis-oriented concretecable-stayed model, modal testing and modal parameter identification ofcable-stayed bridge, finite element modeling and model updating of cable-stayedbridge. The main investigations are summarized as follows:
(1) Design and fabrication of health-diagnosis-oriented concrete cable-stayedmodel bridge
Taking the Hesheng bridge as the prototype, a health-diagnosis-oriented concretecable-stayed model bridge was designed and made with a scale of1:15.In view of thedifficulties in the process of model design, on the premise of meet the productioncondition, the design of the model bridge girder and tower should meet therequirements that the flexural rigidity is similar, and the axial and torsional stiffnessparameters similar requirements could be relaxed, and the simplified method ofcounterweight and stay-cables was given. The initial finite element models of theprototype and model bridge were established. The static and dynamic characteristicsimilarity of the model and prototype bridge was analyzed at undamaged and damagestates. The results show that after a variety of simplification and treatment the staticand dynamic characteristic and damage characteristic of the model and prototypebridge still have a good similarity. It can provide a reference for the model design ofconcrete cable-stayed bridge.
(2) Modal test and modal parameter identification of the model bridge werecarried out using hammer excitation method and ambient excitation method
The first21modal parameters of the model bridge were obtained usingEigen-system Realization Algorithm(ERA) from hammer excitation modal test data,and the first17modal parameters of the model bridge were obtained using ERA combined with Random Decrement Technique(RDT) from ambient excitation modaltest data; Using white noise and the measured non-white noise signal as excitationinput, finite element time history response analysis was carried out, and modalparameter identification from simulated response data show that the measurednon-white noise excitation can bring spurious modes, in addition, the non-whitenoise excitation can reduce the identification accuracy of modal frequency and mode.With the finite element analysis results as prior knowledge, combined with thestability diagram method, the spectral characteristics of excitation signal and highsignal to noise ratio measurement point signal, it can give the order and eliminatespurious modes. Practice shows that the method can accurately identify the modalparameters of the model bridge and eliminate false modals effectively. It provides anew way to eliminate the false modals in modal parameter identification of ambientexcitation modal test.
From different parameter identification method and noise simulation based onstatistical Monte Carlo analysis, uncertainty analysis of the parameters identifiedfrom data that obtained from hammer excitation modal test and ambient excitationmodal test was done. The results show that the uncertainty of modal parameterscaused by different identification methods was obviously higher than that caused bynoise simulation, therefore, uncertainty of modal parameters caused by the differentidentification methods can't be ignored; Uncertainty analysis of noise simulationbased on Monte Carlo method gives statistical uncertainty intervals of parametersidentified from data that obtained from hammer excitation modal test and ambientexcitation modal test. It provides useful information for the research of modelupdating and damage identification.
(3) Reason analysis of the difference of modal frequencies identified from datathat obtained from hammer excitation and ambient excitation modal test
Modal test and modal parameter identification of the model bridge was carriedout using hammer excitation method and ambient excitation method at three caseswhich were before and after the prestress reinforcement tensioned and the girderdamage status, the maximum difference of modal frequencies identified from datathat obtained from hammer excitation and ambient excitation modal test at the threecases were3.64%,1.24%,1.84%respectively, it can be seen that the differencereduces after the prestress reinforcement tensioned, and the difference rises at thegirder damage status. It is speculated that for the reason of concrete micro crack orcracks existence, structural vibration amplitude may impact the stiffness of the concrete girder and tower, and the higher vibration amplitude the lower structurestiffness.
(4) Finite element modeling and model updating of concrete cable-stayed bridge
A modified model updating technique based on parameters and objectivefunction classification was present, the modified model updating technique caneffectively improve the ill-condition problems, improve the efficiency of modelupdating and get better results. The initial dynamic finite element models of modelbridge were built by single beam pattern, triple-girder pattern, beam-shell patternand solid pattern respectively, and then the initial finite element models wereupdated by the modified model updating technology. Compared the calculateddynamic characteristics before and after model updating with measured data, thecalculation accuracy and the model updating effect of different finite element modelswere discussed, the error sources of finite element modeling and relevant issues ofmodel updating were analyzed. The results show that the calculation errors of initialfinite element models were mainly caused by modeling errors and parameter errors.Beam element models had limitations in modeling. Model updating shoulddistinguish the modeling errors and parameter errors accurately, then the realisticbaseline finite element model can be acquired. It can provide a reference for thefinite element modeling and model updating of concrete cable-stayed bridge.
(1)对面向健康诊断的混凝土斜拉桥模型设计进行了研究
以广东惠州合生大桥为原型，面向健康诊断设计制作了1:15的大比例混凝土斜拉桥模型，针对模型设计过程中的困难，提出在满足制作条件的前提下，对模型桥主梁和主塔的设计应主要满足抗弯刚度相似的要求，放松对轴向刚度和扭转刚度等参数的相似要求，并给出了模型桥配重和斜拉索简化方法。采用有限元法对模型桥和原型桥的静动力特性及损伤特性进行了分析，分析结果表明模型桥和原型桥的静动力特性及损伤特性具有良好的相似性，可为混凝土斜拉桥的模型设计提供参考。
(2)采用锤击法和环境激励法对模型桥进行了模态试验和模态参数识别研究
采用特征系统实现算法(ERA)对锤击法模态试验数据进行了模态参数识别，得到了模型桥的前21阶模态参数；采用随机减量法结合ERA法对环境激励法模态试验数据进行了模态参数识别，得到了模型桥的前17阶模态参数。分别采用白噪声和实测地脉动非白噪声信号作为激励信号，对梁壳有限元模型进行了时程响应分析，对两种激励下的响应信号进行模态参数识别，将识别结果进行对比可见，非白噪声激励可使模态参数识别定阶过程中产生虚假模态，有限元预分析可为模态参数识别过程中的虚假模态剔除提供一个虚假模态可能出现的范围，另外，非白噪声激励可降低模态频率和模态振型的识别精度。提出了以精细有限元预分析结果为先验知识参考，将稳定图法、实测激励信号及信噪比高的测点信号的频谱分析结果相结合进行定阶和虚假模态剔除的方法，实践表明，该方法能够准确识别模型桥的模态参数并剔除了虚假模态，为环境激励试验模态参数识别中虚假模态的剔除提供一种新思路。
分别从不同参数识别方法和基于MONTE CARLO法的噪声模拟两个方面对锤击法和环境激励法模态参数识别的不确定性进行了分析。结果表明：由不同参数识别方法引起的模态参数的不确定性明显高于由噪声模拟引起的不确定性，因此，不同参数识别方法引起的不确定问题不能忽略；通过基于MONTE CARLO法的噪声模拟给出了锤击法和环境激励法模态参数的统计不确定区间，为模型修正、损伤识别等研究提供基础数据。
(3)锤击法和环境激励法模态频率识别结果差异的对比分析
通过对模型桥张拉预应力前后及张拉预应力后主梁损伤三个工况的锤击法和环境激励法识别的频率差值进行对比，三个工况下锤击法和环境激励法识别的频率差值百分比最大分别为3.64%、1.24%、1.84%，可见，张拉预应力后锤击法和环境激励法识别的模态频率差值比张拉预应力前明显减小，主梁损伤工况锤击法和环境激励法识别的模态频率差值比张拉预应力后增大，由此推测，对于混凝土斜拉桥结构，由于混凝土微裂缝或裂缝的存在，结构的振动幅值大小可能会对主梁和主塔构件的截面刚度产生影响，振动幅值越大结构的刚度越低。
(4)研究了混凝土斜拉桥有限元建模与模型修正
提出了基于参数和目标函数分类的改进的模型修正技术，该模型修正技术通过灵敏度分析对修正参数和目标函数进行优选和分类、排序，逐级进行模型修正。结果表明，改进的模型修正技术有效改善了模型修正的病态问题，能够明显的提高模型修正效率并得到更优的模型修正结果。分别采用单主梁模式、三主梁模式、梁壳模式和实体模式建立了模型斜拉桥的初始有限元模型，采用改进的模型修正技术对各种初始有限元模型进行了模型修正，将修正前后的动力特性计算值与实测数据进行了对比，讨论了不同模式建模方法的计算精度和模型修正效果，以及有限元建模误差来源和模型修正的相关问题。结果表明，初始有限元模型计算误差主要是由建模误差和参数误差引起的；梁单元模型在建模方面有其局限性，单主梁模型无法准确模拟Π形主梁斜拉桥的扭转特性，应根据不同的结构特点和分析目标建立相应的有限元模型；提出模型修正过程中应准确区分建模误差和参数误差，才能得到最符合实际的基准有限元模型。为斜拉桥有限元建模与模型修正提供了参考。
It is more and more attention for the research on vibration based damageidentification of long span bridge recent years. Modal parameter identification andmodel updating of long-span concrete cable-stayed bridge structure is a verycomplicated problem which needs to be solved urgently in bridge health monitoring,and it has not been completely solved yet. Taking the Hesheng bridge as theprototype, a health-diagnosis-oriented concrete cable-stayed model bridge wasdesigned and made with a scale of1:15. A series of works were done in thisdissertation, mainly includes model design of health-diagnosis-oriented concretecable-stayed model, modal testing and modal parameter identification ofcable-stayed bridge, finite element modeling and model updating of cable-stayedbridge. The main investigations are summarized as follows:
(1) Design and fabrication of health-diagnosis-oriented concrete cable-stayedmodel bridge
Taking the Hesheng bridge as the prototype, a health-diagnosis-oriented concretecable-stayed model bridge was designed and made with a scale of1:15.In view of thedifficulties in the process of model design, on the premise of meet the productioncondition, the design of the model bridge girder and tower should meet therequirements that the flexural rigidity is similar, and the axial and torsional stiffnessparameters similar requirements could be relaxed, and the simplified method ofcounterweight and stay-cables was given. The initial finite element models of theprototype and model bridge were established. The static and dynamic characteristicsimilarity of the model and prototype bridge was analyzed at undamaged and damagestates. The results show that after a variety of simplification and treatment the staticand dynamic characteristic and damage characteristic of the model and prototypebridge still have a good similarity. It can provide a reference for the model design ofconcrete cable-stayed bridge.
(2) Modal test and modal parameter identification of the model bridge werecarried out using hammer excitation method and ambient excitation method
The first21modal parameters of the model bridge were obtained usingEigen-system Realization Algorithm(ERA) from hammer excitation modal test data,and the first17modal parameters of the model bridge were obtained using ERA combined with Random Decrement Technique(RDT) from ambient excitation modaltest data; Using white noise and the measured non-white noise signal as excitationinput, finite element time history response analysis was carried out, and modalparameter identification from simulated response data show that the measurednon-white noise excitation can bring spurious modes, in addition, the non-whitenoise excitation can reduce the identification accuracy of modal frequency and mode.With the finite element analysis results as prior knowledge, combined with thestability diagram method, the spectral characteristics of excitation signal and highsignal to noise ratio measurement point signal, it can give the order and eliminatespurious modes. Practice shows that the method can accurately identify the modalparameters of the model bridge and eliminate false modals effectively. It provides anew way to eliminate the false modals in modal parameter identification of ambientexcitation modal test.
From different parameter identification method and noise simulation based onstatistical Monte Carlo analysis, uncertainty analysis of the parameters identifiedfrom data that obtained from hammer excitation modal test and ambient excitationmodal test was done. The results show that the uncertainty of modal parameterscaused by different identification methods was obviously higher than that caused bynoise simulation, therefore, uncertainty of modal parameters caused by the differentidentification methods can't be ignored; Uncertainty analysis of noise simulationbased on Monte Carlo method gives statistical uncertainty intervals of parametersidentified from data that obtained from hammer excitation modal test and ambientexcitation modal test. It provides useful information for the research of modelupdating and damage identification.
(3) Reason analysis of the difference of modal frequencies identified from datathat obtained from hammer excitation and ambient excitation modal test
Modal test and modal parameter identification of the model bridge was carriedout using hammer excitation method and ambient excitation method at three caseswhich were before and after the prestress reinforcement tensioned and the girderdamage status, the maximum difference of modal frequencies identified from datathat obtained from hammer excitation and ambient excitation modal test at the threecases were3.64%,1.24%,1.84%respectively, it can be seen that the differencereduces after the prestress reinforcement tensioned, and the difference rises at thegirder damage status. It is speculated that for the reason of concrete micro crack orcracks existence, structural vibration amplitude may impact the stiffness of the concrete girder and tower, and the higher vibration amplitude the lower structurestiffness.
(4) Finite element modeling and model updating of concrete cable-stayed bridge
A modified model updating technique based on parameters and objectivefunction classification was present, the modified model updating technique caneffectively improve the ill-condition problems, improve the efficiency of modelupdating and get better results. The initial dynamic finite element models of modelbridge were built by single beam pattern, triple-girder pattern, beam-shell patternand solid pattern respectively, and then the initial finite element models wereupdated by the modified model updating technology. Compared the calculateddynamic characteristics before and after model updating with measured data, thecalculation accuracy and the model updating effect of different finite element modelswere discussed, the error sources of finite element modeling and relevant issues ofmodel updating were analyzed. The results show that the calculation errors of initialfinite element models were mainly caused by modeling errors and parameter errors.Beam element models had limitations in modeling. Model updating shoulddistinguish the modeling errors and parameter errors accurately, then the realisticbaseline finite element model can be acquired. It can provide a reference for thefinite element modeling and model updating of concrete cable-stayed bridge.
引文
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