基于动力测试的桥梁结构损伤识别及性能评定理论与应用研究
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摘要
数量巨大的既有桥梁不同程度地存在损伤与病害，且日益严重，为保证此类桥梁的安全运营并降低总体养护维修费用，如何及时有效地进行损伤识别与评定已成为桥梁工程领域面临的重要课题。基于动力测试的桥梁结构损伤识别与评定因其方便、快捷、可实时等优点而受到广泛关注。本文结合桥梁结构的工程特性，针对动力法损伤识别与评定进行了以下几个方面的研究工作：
1、分析总结各类桥梁结构的常见损伤，讨论损伤单元参数化的方法及其影响，并选取弹性模量退降因子作为待识别的损伤参数。采用矩阵摄动理论分析桥梁结构损伤对桥跨结构固有振动特性的影响，推导固有频率、振型向量对结构损伤参数的一阶、二阶摄动解析公式。并对典型的简支梁、连续梁、拱结构采用数值分析的方法分析典型损伤对桥跨结构固有振动特性的影响。同时介绍了桥梁结构的动力测试理论与方法，为桥梁结构的动力法损伤识别与评定提供了有效的先验知识。
2、分析实际桥梁的边界支承状况，并通过解析分析以及实桥测试、计算分析表明，相对于结构构件轻微损伤对固有振动特性的影响，桥梁结构边界条件变异的影响更为显著。因而提出既有桥梁的动力法损伤识别必须考虑边界条件变异的影响。针对边界条件变异的影响，提出基于固有频率、振型向量摄动分析与最小二乘优化算法相结合的边界条件变异反演理论方法。在边界条件变异反演理论方法的基础上，针对拱桥竖直吊杆的病害问题提出基于边界条件反演的吊杆损伤识别理论方法。并分别用数值算例验证了反演方法识别精度高，且计算量较小。
3、针对通常的桥梁结构损伤，在考虑边界条件变异的预识别之后，分别采用先损伤定位后优化反演分步损伤识别法及损伤参数分组优化反演识别法来实现桥跨结构损伤参数以及边界条件变异参数的反演。前者采用单元模态应变能变化率(MSECR)进行损伤预定位以降低待识别损伤参数数目，后者以参数分组来降低待识别参数，并用参数细分的方法来细化识别损伤参数。两者均采用Marquardt形式下的非线性最小二乘法或改进的Powell法进行优化反演。针对所提出的考虑边界条件变异的结构损伤识别理论方法，提出相应的测点优化布置方法，基于Matlab平台编制相应的损伤识别程序，并以一连续梁结构的损伤数值模拟分析验证了识别方法具有良好的识别精度。
4、对于桥梁结构的实际动力测试中的测试误差问题，分别以解析法和数值模拟法来分析确定性动力测试误差对损伤识别方法的影响状况。结果表明：测试误差明显降低损伤识别的识别精度，甚至造成误判。进而分析在动力测试设备选择、测试方法及信号处理中降低测试误差的方法。
5、分析桥梁结构性能评定现状，提出基于本文动力法损伤识别结果的桥梁结构安全性、耐久性及适用性的评定方法，并初步探讨了基于实测动力参数的直接评定方法理论。
6、最后以主跨240m的斜拉桥——犍为岷江大桥为工程实例，以其换索工程后及换索前的动力测试结果作为损伤前后动力实测参数进行斜拉索的损伤识别，识别与评定结果验证了本文理论方法能够初步应用于工程实践。
There are a great number of existing bridges with different degree of damages and defects which are becoming more and more serious. In order to ensure the safety of the bridges in service and decrease the total fee of maintenance and repair, detecting these bridge damages and assessing them in time becomes an important issue in bridge engineering field. Because of the convenience, fastness and being able to detect on line real time, bridge damage detection and assessment based on dynamic testing attracts much more attention. Based on the feature of bridge structures, some research work on dynamic damage detection and assessment has been done in the following:
1. All kinds of damages of bridge structures are analyzed. The element damage parameterizing methods are discussed and the element modulus decreasing factor is selected as damage detection parameter in this thesis. The effects on natural vibration of bridge structure damage are analyzed by matrix perturbation theory. The first and second order perturbation formula of eigenvalue and eigenvector due to structure damage are directed. The changes of eigenvalue and eigenvector of typical structure as simply-supported beam, continuous beam and arch from typical damages are analyzed by numerical method. And the dynamic testing theory and methods commonly used in actural bridge testing is introduced. These analyses and introductions provide the experiential knowledge to dynamic damage detection and assessment.
2. The boundary conditions of actural bridges are analyzed. The analytical formula and examples of actural bridge testing and calculation show that the change of boundary conditions has much more notable effects on natural vibration results than light structure damages. So that the change of boundary condition must be taken into account in dynamic bridge damage detection is put forward in this thesis. And the boundary condition parameters discernment method is established based on eigenvalue and eigenvector perturbation and least-square optimization theory. Then according to the damages of hanger in arch bridge, the hanger damage discernment method is put forward based on the boundary condition parameters discernment method. The discernment methods are both verified to be of well precision and less calculation effort through numerical examples.
3. According to the common bridge structure damages, after the beforehand detection of boundary condition parameters, the methods of firstly finding damage position then detecting damage degree and damage detection using parameters grouping are respectively set up. The former method adopts modal strain energy change ratio (MSECR) to detect the damage position to decrease the number of damage parameters, and the later decreases the number of damage parameters by parameter grouping and divides the parameter group into new small groups to realize the final damage detection. In both detection methods Marquardt form nonlinear least-square optimization algorithm or modified Powell direct optimization algorithm is used. According to the damage detection methods, the optimization arrangement of dynamic testing points is brought up. The program of the damage detection methods is developed based on Matlab program language, then author verifies that the methods are of fairly well precision with a continuous beam finite element modeling.
4. As to the dynamic testing error of real bridge, the analytical method and the numerical calculation are respectively used to analyze the effects on damage detection results of dynamic testing error. The results show that the existing testing error decreases the damage detection precision, even causes wrong damage detection. So how to decrease the testing error in selecting dynamic testing facilities, testing methods and signal processing is introduced.
5. The art of the state of bridge behavior assessment is introduced, and then the behavior assessment including safety, durability and practicality based on the damage detection methods are erected. And the direct performance assessment based on dynamic parameters is also tentatively discussed.
6. At last, taking the 240m-span cable stayed bridge- Qianwei Minjiang Bridge as example, the dynamic testing results before and after the cable exchange engineering are used as damaged and undamaged dynamic parameters to detect and assess the cable damage. And the detection and assessment results of cable damage verify that the method can be initially applied to engineering practice.
1、分析总结各类桥梁结构的常见损伤，讨论损伤单元参数化的方法及其影响，并选取弹性模量退降因子作为待识别的损伤参数。采用矩阵摄动理论分析桥梁结构损伤对桥跨结构固有振动特性的影响，推导固有频率、振型向量对结构损伤参数的一阶、二阶摄动解析公式。并对典型的简支梁、连续梁、拱结构采用数值分析的方法分析典型损伤对桥跨结构固有振动特性的影响。同时介绍了桥梁结构的动力测试理论与方法，为桥梁结构的动力法损伤识别与评定提供了有效的先验知识。
2、分析实际桥梁的边界支承状况，并通过解析分析以及实桥测试、计算分析表明，相对于结构构件轻微损伤对固有振动特性的影响，桥梁结构边界条件变异的影响更为显著。因而提出既有桥梁的动力法损伤识别必须考虑边界条件变异的影响。针对边界条件变异的影响，提出基于固有频率、振型向量摄动分析与最小二乘优化算法相结合的边界条件变异反演理论方法。在边界条件变异反演理论方法的基础上，针对拱桥竖直吊杆的病害问题提出基于边界条件反演的吊杆损伤识别理论方法。并分别用数值算例验证了反演方法识别精度高，且计算量较小。
3、针对通常的桥梁结构损伤，在考虑边界条件变异的预识别之后，分别采用先损伤定位后优化反演分步损伤识别法及损伤参数分组优化反演识别法来实现桥跨结构损伤参数以及边界条件变异参数的反演。前者采用单元模态应变能变化率(MSECR)进行损伤预定位以降低待识别损伤参数数目，后者以参数分组来降低待识别参数，并用参数细分的方法来细化识别损伤参数。两者均采用Marquardt形式下的非线性最小二乘法或改进的Powell法进行优化反演。针对所提出的考虑边界条件变异的结构损伤识别理论方法，提出相应的测点优化布置方法，基于Matlab平台编制相应的损伤识别程序，并以一连续梁结构的损伤数值模拟分析验证了识别方法具有良好的识别精度。
4、对于桥梁结构的实际动力测试中的测试误差问题，分别以解析法和数值模拟法来分析确定性动力测试误差对损伤识别方法的影响状况。结果表明：测试误差明显降低损伤识别的识别精度，甚至造成误判。进而分析在动力测试设备选择、测试方法及信号处理中降低测试误差的方法。
5、分析桥梁结构性能评定现状，提出基于本文动力法损伤识别结果的桥梁结构安全性、耐久性及适用性的评定方法，并初步探讨了基于实测动力参数的直接评定方法理论。
6、最后以主跨240m的斜拉桥——犍为岷江大桥为工程实例，以其换索工程后及换索前的动力测试结果作为损伤前后动力实测参数进行斜拉索的损伤识别，识别与评定结果验证了本文理论方法能够初步应用于工程实践。
There are a great number of existing bridges with different degree of damages and defects which are becoming more and more serious. In order to ensure the safety of the bridges in service and decrease the total fee of maintenance and repair, detecting these bridge damages and assessing them in time becomes an important issue in bridge engineering field. Because of the convenience, fastness and being able to detect on line real time, bridge damage detection and assessment based on dynamic testing attracts much more attention. Based on the feature of bridge structures, some research work on dynamic damage detection and assessment has been done in the following:
1. All kinds of damages of bridge structures are analyzed. The element damage parameterizing methods are discussed and the element modulus decreasing factor is selected as damage detection parameter in this thesis. The effects on natural vibration of bridge structure damage are analyzed by matrix perturbation theory. The first and second order perturbation formula of eigenvalue and eigenvector due to structure damage are directed. The changes of eigenvalue and eigenvector of typical structure as simply-supported beam, continuous beam and arch from typical damages are analyzed by numerical method. And the dynamic testing theory and methods commonly used in actural bridge testing is introduced. These analyses and introductions provide the experiential knowledge to dynamic damage detection and assessment.
2. The boundary conditions of actural bridges are analyzed. The analytical formula and examples of actural bridge testing and calculation show that the change of boundary conditions has much more notable effects on natural vibration results than light structure damages. So that the change of boundary condition must be taken into account in dynamic bridge damage detection is put forward in this thesis. And the boundary condition parameters discernment method is established based on eigenvalue and eigenvector perturbation and least-square optimization theory. Then according to the damages of hanger in arch bridge, the hanger damage discernment method is put forward based on the boundary condition parameters discernment method. The discernment methods are both verified to be of well precision and less calculation effort through numerical examples.
3. According to the common bridge structure damages, after the beforehand detection of boundary condition parameters, the methods of firstly finding damage position then detecting damage degree and damage detection using parameters grouping are respectively set up. The former method adopts modal strain energy change ratio (MSECR) to detect the damage position to decrease the number of damage parameters, and the later decreases the number of damage parameters by parameter grouping and divides the parameter group into new small groups to realize the final damage detection. In both detection methods Marquardt form nonlinear least-square optimization algorithm or modified Powell direct optimization algorithm is used. According to the damage detection methods, the optimization arrangement of dynamic testing points is brought up. The program of the damage detection methods is developed based on Matlab program language, then author verifies that the methods are of fairly well precision with a continuous beam finite element modeling.
4. As to the dynamic testing error of real bridge, the analytical method and the numerical calculation are respectively used to analyze the effects on damage detection results of dynamic testing error. The results show that the existing testing error decreases the damage detection precision, even causes wrong damage detection. So how to decrease the testing error in selecting dynamic testing facilities, testing methods and signal processing is introduced.
5. The art of the state of bridge behavior assessment is introduced, and then the behavior assessment including safety, durability and practicality based on the damage detection methods are erected. And the direct performance assessment based on dynamic parameters is also tentatively discussed.
6. At last, taking the 240m-span cable stayed bridge- Qianwei Minjiang Bridge as example, the dynamic testing results before and after the cable exchange engineering are used as damaged and undamaged dynamic parameters to detect and assess the cable damage. And the detection and assessment results of cable damage verify that the method can be initially applied to engineering practice.
引文
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