混凝土桥梁结构损伤识别试验研究
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摘要
结构损伤识别方法是桥梁结构健康监测系统的重要组成部分，而基于结构动力响应的损伤识别方法更是目前的研究热点，本文在国家自然科学基金(51078134)资助下，对混凝土桥梁结构模型修正和基于随机子空间的结构损伤识别算法进行了研究，主要内容包括：
I、模型斜拉桥模态测试及模型修正
(1)对一座主跨12m的独塔混凝土模型斜拉桥进行了模态测试。通过多次锤击试验，获得了主梁竖向和扭转模态、主梁横桥向模态、桥塔面内和面外模态的测试结果，对实测模态结果进行了汇总，为模型修正提供依据。
(2)对模型斜拉桥进行了静动力状态下的模型修正，并对修正后的模型进行了检验。根据模型桥Π形主梁的特点，采用ANSYS建立了空间梁板有限元模型。基于频率灵敏度分析对结构优化参数进行选择，边界条件通过弹簧单元进行模拟。将振型进行详细的分类，模态匹配只在同类型振型之间进行，实践表明，该方法能够解决复杂结构的模态匹配问题。模型修正时使用的目标函数包括动力参数和静力位移，修正后的模型不仅参与优化计算的静力位移、模态参数与实测值更加吻合，没有参与优化的更高阶频率也与实测结果更接近。最后，使用另一状态下的模态测试结果对修正后的有限元模型进行了检验。
II、基于随机子空间的损伤识别算法
对基于随机子空间的多种损伤指标进行了分析评价，在此基础上，提出了一个新的损伤指标(I A)。仿真分析结果表明：模型残差损伤指标、协方差Hankel矩阵损伤指标、离散状态空间矩阵损伤指标(I A)均能有效对损伤程度进行识别，指标值与损伤程度基本呈线性关系，其中，本文提出的损伤指标I A对损伤最敏感，相同损伤程度下指标值最大。使用模型残差损伤指标时，模型的阶数取值比实际阶数稍大时效果更好，使用协方差Hankel矩阵损伤指标时，模型阶数宜比实际阶数小。
III、混凝土斜拉桥损伤试验研究
(1)测试分析了预应力对混凝土结构频率的影响，桥塔和主梁的频率均随着预应力的增加而提高，张拉完桥塔预应力，塔面外一二阶频率分别提高了1.98%、2.81%。张拉完主梁预应力，主梁前四阶频率最大提高为1.69%，其主要原因可能是预应力筋张拉后，预应力使得混凝土结构的一部分微裂缝闭合，提高了截面的刚度，此外，预应力筋张拉后与混凝土结构形成一个整体，共同工作，增加了结构的刚度。
(2)对主梁四个损伤工况的索力变化进行了测试，各工况下边跨索力均有少量增加；工况一和工况二索力变化较小，变化规律不明显；工况三和工况四损伤区域索力减小较明显，可以对损伤位置进行较好的判断。因而，当主梁损伤程度较大时，可以通过拉索索力的变化对损伤进行定位。
(3)对主梁和下游侧桥塔进行了损伤试验，采用基于随机子空间的损伤指标对各损伤工况进行了识别，结果表明：观测标准型损伤指标不能正确识别损伤；模型残差损伤指标的识别效果较差，对判定有无损伤存在一定难度；协方差Hankel矩阵损伤指标(I U、I UV)和离散状态空间矩阵损伤指标(I A)能够较好的识别有无损伤及损伤程度，I A指标对损伤的敏感性和损伤程度的相关性识别效果略好于I U、I UV指标。
(4)采用模型修正的方法对主梁和桥塔的损伤程度进行了定量分析，通过假定损伤区域单元弹性模量降低来模拟损伤，最大损伤时，主梁和桥塔损伤区域单元弹性模量分别降为未损伤状态的61%、88%。
IV、预应力混凝土箱梁足尺模型试验研究
(1)采用条带法编制了预应力混凝土梁的非线性计算程序，并与试验结果进行了对比，结果表明该程序计算结果准确可靠，可用程序对各损伤状态的静力刚度进行计算。对实测的荷载-位移曲线，采用简化方法计算了其卸载曲线，效果良好。
(2)使用盒计数法对小箱梁和空心板的裂缝分布进行了分析，结果表明：小箱梁和空心板的裂缝分布具有分形特征，随着损伤程度的增加，裂缝分形维数增加。损伤过程中的裂缝分形维数与频率存在明显的两折线关系，转折点即为荷载-位移曲线预应力钢筋屈服的特征点。
(3)对损伤过程中的动静力刚度进行了分析，结果表明：未损伤状态时，静力刚度与动力刚度基本一致，各损伤状态的动力刚度下降幅度明显要小于静力刚度，动力刚度与静力刚度的损伤形式具有一致性，可以用静力刚度的模式来对动力刚度进行识别。
Structural damage identification is the important components of the bridgestructural health monitoring system. The structural damage identification based on thedynamic response is the current research focus. The paper is supported by the nationalnatural science foundation of china (51078134), it studied the model updating ofconcrete bridge structure and structural damage identification based on stochasticsubspace method. The main contents include:
I. Modal test and model updating of cable-stayed bridge
(1) Modal testing was carried out on a single tower concrete cable-stayed modelbridge with a12m main span. A serial of modal tests on the model bridge were doneby hammering test, the test results including the vertical and reverse mode of the mainbeam, the cross-bridge mode of the main beam, the bridge tower in-plane mode andthe tower out-plane mode, the measured modal results were integrated to provide abasis for model updating.
(2) Model updating of the cable-stayed bridge was done based on dynamic testand static test results, the updated model was verified too. According to thecharacteristics of Π section beam, a beam plate model was built by ANSYS software.Optimized parameters were chosen through frequency sensitivity analysis, andboundary conditions were simulated by spring elements. Mode shape was classifiedand modal matching between the same type of mode shape, practice shows that themethod can solve the modal matching problem of complex structure. The objectivefunction of model updating was constructed by dynamic parameters and staticdisplacement. After the model updating, not only the static displacement and modalresults which involved in optimization are more consistent with the measured values,but also the high level frequencies which not involved in optimization are closer tothe measured values. Finally, the updated model was verified by the modal test resultof another state.
II. Damage identification method based on stochastic subspace
Stochastic subspace-based damage indicators were analyzed and evaluated, anew damage indicator (I A) is proposed. The results of simulation show that the modelresidual damage indicator, the covariance of Hankel matrix damage indicator and thediscrete state space matrix damage indicator can identify the damage degree effectively; indicator value versus damage degree is almost linear. The proposeddamage indicatorI Ais the most sensitive to damage, with the same damage degree thevalue of it is the maximum. When use the model residual damage indicator, the effectis better when the order is slightly larger than the actual order. When use thecovariance of Hankel matrix damage index, the effect is better when the order issmaller than the actual order.
III. Damage experimental study on concrete cable-stayed bridge
(1) The impact of prestress to frequency of model bridge was tested. Tower andbeam frequency increased with the increase of prestressing. After the tower tensionedprestress, the first and the second out plane frequencies were increased1.98%and2.81%respectively. After the beam tensioned prestress, the maximum of the first fourfrequencies was increased1.69%. The reason may be parts of the concrete micro-cracks are closed after tensioning, which improved cross-section stiffness. In addition,after tensioning the tendons and the concrete structure become an entity, the two partswork together, so the stiffness of the structure increased.
(2) The cable force change of four beam damage cases were tested, cable force ofthe side span all has a small increase under each case. The cable force change of case1and2is small and the variation rule is not obvious. The cable force decreasesobviously in damage region of case3and4, which can be able to judge the location ofdamage, when the beam is serious damaged, the damage location can be find by thechange of cable force.
(3) The damage tests were carried out on beam and downstream side tower. Ineach damage case, the stochastic subspace-based damage indictors were used toidentify the damage. The results show that: the observation standard damage indicatorcan not identify the damage correctly; the model residual damage indicator isdifficulty to identify the damage; the covariance of Hankel matrix damage indicator(I U、I UV) and the discrete state space matrix damage indicator (I A) can effectivelyidentify whether the structure damaged or not and the damage degree,I Aindicator isslightly better thanI U(orI UV) indicator on the sensitivity and correlation of damagedegree.
(4) The damage degrees of tower and beam were analyzed by model updatingmethod quantitatively. By assuming the elastic modulus decreases in damage regionelement to simulate the damage. In the maximum damage degree, elastic modulus indamage region element of tower and beam were reduced to61%and88%of theundamaged state.
IV. Full scale model test of prestressed concrete box girder
(1) A nonlinear analysis program of prestressed concrete beam was compiledused the finite strip method, and compared the analytical results with the experimentresults, it can be seen that the program is accurate and reliable. The static stiffness ofeach damage state can be calculated by the program. The unloading curve wascalculated by a simplified method which corresponds well to the measured curve.
(2) The crack distribution of box girder and hollow slab was analyzed using boxcounting method. The results show that: the surface crack distributions of the boxgirder and hollow slab possess definite fractal character. With the gradual increase inthe damage severity the box-counting dimension increases gradually. Approximately abilinear relationship exist between the fractal quantities derived from the surfacecrack distributions and the natural frequency, the turning point is the same as thefeature point at which the prestressed reinforcement yields of load deflection curve.
(3) The dynamic and static stiffness of each damage state was analyzed, theresults show that: at the undamaged state, static stiffness and dynamic stiffnessbasically the same, the decease of dynamic stiffness at each damage state issignificantly less than the decrease of static stiffness. The damage form of dynamicstiffness and static stiffness is consistent; it can be use the static stiffness mode toidentify the dynamic stiffness.
I、模型斜拉桥模态测试及模型修正
(1)对一座主跨12m的独塔混凝土模型斜拉桥进行了模态测试。通过多次锤击试验，获得了主梁竖向和扭转模态、主梁横桥向模态、桥塔面内和面外模态的测试结果，对实测模态结果进行了汇总，为模型修正提供依据。
(2)对模型斜拉桥进行了静动力状态下的模型修正，并对修正后的模型进行了检验。根据模型桥Π形主梁的特点，采用ANSYS建立了空间梁板有限元模型。基于频率灵敏度分析对结构优化参数进行选择，边界条件通过弹簧单元进行模拟。将振型进行详细的分类，模态匹配只在同类型振型之间进行，实践表明，该方法能够解决复杂结构的模态匹配问题。模型修正时使用的目标函数包括动力参数和静力位移，修正后的模型不仅参与优化计算的静力位移、模态参数与实测值更加吻合，没有参与优化的更高阶频率也与实测结果更接近。最后，使用另一状态下的模态测试结果对修正后的有限元模型进行了检验。
II、基于随机子空间的损伤识别算法
对基于随机子空间的多种损伤指标进行了分析评价，在此基础上，提出了一个新的损伤指标(I A)。仿真分析结果表明：模型残差损伤指标、协方差Hankel矩阵损伤指标、离散状态空间矩阵损伤指标(I A)均能有效对损伤程度进行识别，指标值与损伤程度基本呈线性关系，其中，本文提出的损伤指标I A对损伤最敏感，相同损伤程度下指标值最大。使用模型残差损伤指标时，模型的阶数取值比实际阶数稍大时效果更好，使用协方差Hankel矩阵损伤指标时，模型阶数宜比实际阶数小。
III、混凝土斜拉桥损伤试验研究
(1)测试分析了预应力对混凝土结构频率的影响，桥塔和主梁的频率均随着预应力的增加而提高，张拉完桥塔预应力，塔面外一二阶频率分别提高了1.98%、2.81%。张拉完主梁预应力，主梁前四阶频率最大提高为1.69%，其主要原因可能是预应力筋张拉后，预应力使得混凝土结构的一部分微裂缝闭合，提高了截面的刚度，此外，预应力筋张拉后与混凝土结构形成一个整体，共同工作，增加了结构的刚度。
(2)对主梁四个损伤工况的索力变化进行了测试，各工况下边跨索力均有少量增加；工况一和工况二索力变化较小，变化规律不明显；工况三和工况四损伤区域索力减小较明显，可以对损伤位置进行较好的判断。因而，当主梁损伤程度较大时，可以通过拉索索力的变化对损伤进行定位。
(3)对主梁和下游侧桥塔进行了损伤试验，采用基于随机子空间的损伤指标对各损伤工况进行了识别，结果表明：观测标准型损伤指标不能正确识别损伤；模型残差损伤指标的识别效果较差，对判定有无损伤存在一定难度；协方差Hankel矩阵损伤指标(I U、I UV)和离散状态空间矩阵损伤指标(I A)能够较好的识别有无损伤及损伤程度，I A指标对损伤的敏感性和损伤程度的相关性识别效果略好于I U、I UV指标。
(4)采用模型修正的方法对主梁和桥塔的损伤程度进行了定量分析，通过假定损伤区域单元弹性模量降低来模拟损伤，最大损伤时，主梁和桥塔损伤区域单元弹性模量分别降为未损伤状态的61%、88%。
IV、预应力混凝土箱梁足尺模型试验研究
(1)采用条带法编制了预应力混凝土梁的非线性计算程序，并与试验结果进行了对比，结果表明该程序计算结果准确可靠，可用程序对各损伤状态的静力刚度进行计算。对实测的荷载-位移曲线，采用简化方法计算了其卸载曲线，效果良好。
(2)使用盒计数法对小箱梁和空心板的裂缝分布进行了分析，结果表明：小箱梁和空心板的裂缝分布具有分形特征，随着损伤程度的增加，裂缝分形维数增加。损伤过程中的裂缝分形维数与频率存在明显的两折线关系，转折点即为荷载-位移曲线预应力钢筋屈服的特征点。
(3)对损伤过程中的动静力刚度进行了分析，结果表明：未损伤状态时，静力刚度与动力刚度基本一致，各损伤状态的动力刚度下降幅度明显要小于静力刚度，动力刚度与静力刚度的损伤形式具有一致性，可以用静力刚度的模式来对动力刚度进行识别。
Structural damage identification is the important components of the bridgestructural health monitoring system. The structural damage identification based on thedynamic response is the current research focus. The paper is supported by the nationalnatural science foundation of china (51078134), it studied the model updating ofconcrete bridge structure and structural damage identification based on stochasticsubspace method. The main contents include:
I. Modal test and model updating of cable-stayed bridge
(1) Modal testing was carried out on a single tower concrete cable-stayed modelbridge with a12m main span. A serial of modal tests on the model bridge were doneby hammering test, the test results including the vertical and reverse mode of the mainbeam, the cross-bridge mode of the main beam, the bridge tower in-plane mode andthe tower out-plane mode, the measured modal results were integrated to provide abasis for model updating.
(2) Model updating of the cable-stayed bridge was done based on dynamic testand static test results, the updated model was verified too. According to thecharacteristics of Π section beam, a beam plate model was built by ANSYS software.Optimized parameters were chosen through frequency sensitivity analysis, andboundary conditions were simulated by spring elements. Mode shape was classifiedand modal matching between the same type of mode shape, practice shows that themethod can solve the modal matching problem of complex structure. The objectivefunction of model updating was constructed by dynamic parameters and staticdisplacement. After the model updating, not only the static displacement and modalresults which involved in optimization are more consistent with the measured values,but also the high level frequencies which not involved in optimization are closer tothe measured values. Finally, the updated model was verified by the modal test resultof another state.
II. Damage identification method based on stochastic subspace
Stochastic subspace-based damage indicators were analyzed and evaluated, anew damage indicator (I A) is proposed. The results of simulation show that the modelresidual damage indicator, the covariance of Hankel matrix damage indicator and thediscrete state space matrix damage indicator can identify the damage degree effectively; indicator value versus damage degree is almost linear. The proposeddamage indicatorI Ais the most sensitive to damage, with the same damage degree thevalue of it is the maximum. When use the model residual damage indicator, the effectis better when the order is slightly larger than the actual order. When use thecovariance of Hankel matrix damage index, the effect is better when the order issmaller than the actual order.
III. Damage experimental study on concrete cable-stayed bridge
(1) The impact of prestress to frequency of model bridge was tested. Tower andbeam frequency increased with the increase of prestressing. After the tower tensionedprestress, the first and the second out plane frequencies were increased1.98%and2.81%respectively. After the beam tensioned prestress, the maximum of the first fourfrequencies was increased1.69%. The reason may be parts of the concrete micro-cracks are closed after tensioning, which improved cross-section stiffness. In addition,after tensioning the tendons and the concrete structure become an entity, the two partswork together, so the stiffness of the structure increased.
(2) The cable force change of four beam damage cases were tested, cable force ofthe side span all has a small increase under each case. The cable force change of case1and2is small and the variation rule is not obvious. The cable force decreasesobviously in damage region of case3and4, which can be able to judge the location ofdamage, when the beam is serious damaged, the damage location can be find by thechange of cable force.
(3) The damage tests were carried out on beam and downstream side tower. Ineach damage case, the stochastic subspace-based damage indictors were used toidentify the damage. The results show that: the observation standard damage indicatorcan not identify the damage correctly; the model residual damage indicator isdifficulty to identify the damage; the covariance of Hankel matrix damage indicator(I U、I UV) and the discrete state space matrix damage indicator (I A) can effectivelyidentify whether the structure damaged or not and the damage degree,I Aindicator isslightly better thanI U(orI UV) indicator on the sensitivity and correlation of damagedegree.
(4) The damage degrees of tower and beam were analyzed by model updatingmethod quantitatively. By assuming the elastic modulus decreases in damage regionelement to simulate the damage. In the maximum damage degree, elastic modulus indamage region element of tower and beam were reduced to61%and88%of theundamaged state.
IV. Full scale model test of prestressed concrete box girder
(1) A nonlinear analysis program of prestressed concrete beam was compiledused the finite strip method, and compared the analytical results with the experimentresults, it can be seen that the program is accurate and reliable. The static stiffness ofeach damage state can be calculated by the program. The unloading curve wascalculated by a simplified method which corresponds well to the measured curve.
(2) The crack distribution of box girder and hollow slab was analyzed using boxcounting method. The results show that: the surface crack distributions of the boxgirder and hollow slab possess definite fractal character. With the gradual increase inthe damage severity the box-counting dimension increases gradually. Approximately abilinear relationship exist between the fractal quantities derived from the surfacecrack distributions and the natural frequency, the turning point is the same as thefeature point at which the prestressed reinforcement yields of load deflection curve.
(3) The dynamic and static stiffness of each damage state was analyzed, theresults show that: at the undamaged state, static stiffness and dynamic stiffnessbasically the same, the decease of dynamic stiffness at each damage state issignificantly less than the decrease of static stiffness. The damage form of dynamicstiffness and static stiffness is consistent; it can be use the static stiffness mode toidentify the dynamic stiffness.
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