大跨桥结构监测系统的模态识别和误差分析及损伤识别
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摘要
大跨桥梁的结构健康监测用其有限测点上脉动反应的高信噪比数据识别损伤。本文系统地研究了大跨桥结构损伤识别的多个环节,主要创新点有:
(1)用时域NExT-ERA法识别结构模态参数,完善了其理论,并通过a)定义并使用一个新的相关估计的公式,b)利用稳定图中不同系统阶次识别的模态参数的算术平均,提高模态识别精度并形成了改进的NExT-ERA法。推导了从白噪声激励下含测量白噪声的结构反应时程进行模态识别时的有限采样误差。
(2)定义并用等价奇异值和等价向量推导了稀疏模态、小阻尼比时大维数Hankel阵的奇异值和奇异向量与模态参数的对应关系,简化了已有误差公式,推导改进NExT-ERA中模态参数有限采样误差受测量时长、采样频率、信噪比和奇异值等影响的规律。据此提出稳定图法和奇值法选择识别的高精度模态。
(3)提出一个用完备的振型构造的单元模态应变能指标,不但能定位梁式结构的多处损伤,还能指示抗弯刚度分量折减的损伤程度。针对西堠门悬索桥可能发生的损伤,比较了基于完备振型的该指标、坐标模态保证准则和模态柔度差以及基于响应的小波包组分能量变化率识别损伤的能力。
(4)比较了三种模态扩展方法,以将有限测点上的不完备振型扩展到全部自由度,并用扩展振型构造不完备模态应变能指标;直接用不完备振型构造不完备模态柔度差指标,研究了两者的损伤识别能力;然后研究了用改进的遗传算法优化传感器布点,使前述不完备损伤指标对结构可能的损伤最灵敏,又提出使扩展模态误差最小的传感器布点方法,验证了最优布点下不完备损伤指标的识别能力。上述工作是对损伤识别各个环节中方法的系统研究。
(5)对西堠门桥的全桥纯杆单元模型和用正交异性板配合子结构法建立的简化板壳单元表示加劲梁的全桥模型,分别模拟其有限测点上含噪声的脉动反应时程。用上述方法综合研究了两个不完备指标对杆系模型不同位置和程度的刚度分量折减的损伤识别和误差,以及对简化板壳单元模型加劲梁上不同裂缝和锈蚀损伤的识别和误差。同时验证了选择高精度模态方法的有效性和重要性。
For structural health monitoring of long-span bridges, ambient responses with high Signal-Noise Ratio (SNR) measured on limited Degrees-Of-Freedom (DOFs) are used to detect damage. Several aspects of structural damage detection are deeply and systematically studied in this dissertation, and main innovation points are listed as follows:
(1) The Natural Excitation Technique and Eigensystem Realization Algorithm (NExT-ERA) in the time domain are used and improved to identify structural modal parameters. NExT-ERA with two improvements including: a) defining and using a new-developed correlation estimation formula, b) arithmetically averaging modal parameters identified by different system orders related to the stabilization diagram, is proposed to enhance accuracy of modal parameters and named improved NExT-ERA. Finite sampling errors of modal parameters identified from structural ambient responses to Gaussian White Noises (GWN) excitations and contaminated by measuring GWN, are derived.
(2) In improved NExT-ERA, a relationship between singular values and vectors of large-size Hankel matrixes and modal parameters is established by using author-defined equivalent singular values and vectors, on the premise that the modes are sparse and the damping ratios are low. Some existing error formulars are simplified after aplplying this relationship, and then the rules of finite sampling errors influenced by limited measuring time length, sampling rate, SNR, and singular values et al, are derived and analyzed. A stabilization diagram method and an equivalent singular value method are proposed for selecting high accuracy modes from the identified ones.
(3) A new element modal strain energy index is defined basing on the complete modes at all DOFs and used to indicate both locations and extents of multiple damage from reductions in related bending stiffnesses for beam-system structures. For assumed cases of damage in the stiffening girder of the Xihoumen Suspension Bridge, damage detection capacities of this index, the Coordinate Modal Assurance Criterion (COMAC) and modal flexibility change constructed from complete modes, and Sum of Change Ratio (SCR) of wavelet packet component energy of responses, are studied and compared.
(4) Three modal expansion methods are compared and used to expand incomplete modes at limited DOFs to complete DOFs, and then the expanded modes are used to construct‘incomplete’modal strain energy damage indexes. The incomplete modal flexibility change index is directly constructed from incomplete modes. Damage detection with the two incomplete indexes is studied in Xihoumen suspension Bridge. Optimizing Sensor Locations (OSL) based on an improved Genetic Algorithm to make the two incomplete indexes most sensitive to possible damage is discussed, in addition, a Minimum Modal Variance (MMV) method for OSL is proposed. Damage detection based on the two incomplete indexes measured at optimized sensor locations is verified. All the work above is a systematical study of methods in aspects of damage detection.
(5) Noise-contaminated ambient responses at limited DOFs of a beam-system finite element model and a plate-system finite element model with equivalent orthotropic plates and substructure method, are simulated. Capacities and errors of the above methods and the two incomplete indexes for detection of stiffness reductions in beam-system model and simulated cracking and corrosions in plate-system model are studied and discussed, respectively. Methods of selecting high accuracy modes are also verified to be effective and important.
(1)用时域NExT-ERA法识别结构模态参数,完善了其理论,并通过a)定义并使用一个新的相关估计的公式,b)利用稳定图中不同系统阶次识别的模态参数的算术平均,提高模态识别精度并形成了改进的NExT-ERA法。推导了从白噪声激励下含测量白噪声的结构反应时程进行模态识别时的有限采样误差。
(2)定义并用等价奇异值和等价向量推导了稀疏模态、小阻尼比时大维数Hankel阵的奇异值和奇异向量与模态参数的对应关系,简化了已有误差公式,推导改进NExT-ERA中模态参数有限采样误差受测量时长、采样频率、信噪比和奇异值等影响的规律。据此提出稳定图法和奇值法选择识别的高精度模态。
(3)提出一个用完备的振型构造的单元模态应变能指标,不但能定位梁式结构的多处损伤,还能指示抗弯刚度分量折减的损伤程度。针对西堠门悬索桥可能发生的损伤,比较了基于完备振型的该指标、坐标模态保证准则和模态柔度差以及基于响应的小波包组分能量变化率识别损伤的能力。
(4)比较了三种模态扩展方法,以将有限测点上的不完备振型扩展到全部自由度,并用扩展振型构造不完备模态应变能指标;直接用不完备振型构造不完备模态柔度差指标,研究了两者的损伤识别能力;然后研究了用改进的遗传算法优化传感器布点,使前述不完备损伤指标对结构可能的损伤最灵敏,又提出使扩展模态误差最小的传感器布点方法,验证了最优布点下不完备损伤指标的识别能力。上述工作是对损伤识别各个环节中方法的系统研究。
(5)对西堠门桥的全桥纯杆单元模型和用正交异性板配合子结构法建立的简化板壳单元表示加劲梁的全桥模型,分别模拟其有限测点上含噪声的脉动反应时程。用上述方法综合研究了两个不完备指标对杆系模型不同位置和程度的刚度分量折减的损伤识别和误差,以及对简化板壳单元模型加劲梁上不同裂缝和锈蚀损伤的识别和误差。同时验证了选择高精度模态方法的有效性和重要性。
For structural health monitoring of long-span bridges, ambient responses with high Signal-Noise Ratio (SNR) measured on limited Degrees-Of-Freedom (DOFs) are used to detect damage. Several aspects of structural damage detection are deeply and systematically studied in this dissertation, and main innovation points are listed as follows:
(1) The Natural Excitation Technique and Eigensystem Realization Algorithm (NExT-ERA) in the time domain are used and improved to identify structural modal parameters. NExT-ERA with two improvements including: a) defining and using a new-developed correlation estimation formula, b) arithmetically averaging modal parameters identified by different system orders related to the stabilization diagram, is proposed to enhance accuracy of modal parameters and named improved NExT-ERA. Finite sampling errors of modal parameters identified from structural ambient responses to Gaussian White Noises (GWN) excitations and contaminated by measuring GWN, are derived.
(2) In improved NExT-ERA, a relationship between singular values and vectors of large-size Hankel matrixes and modal parameters is established by using author-defined equivalent singular values and vectors, on the premise that the modes are sparse and the damping ratios are low. Some existing error formulars are simplified after aplplying this relationship, and then the rules of finite sampling errors influenced by limited measuring time length, sampling rate, SNR, and singular values et al, are derived and analyzed. A stabilization diagram method and an equivalent singular value method are proposed for selecting high accuracy modes from the identified ones.
(3) A new element modal strain energy index is defined basing on the complete modes at all DOFs and used to indicate both locations and extents of multiple damage from reductions in related bending stiffnesses for beam-system structures. For assumed cases of damage in the stiffening girder of the Xihoumen Suspension Bridge, damage detection capacities of this index, the Coordinate Modal Assurance Criterion (COMAC) and modal flexibility change constructed from complete modes, and Sum of Change Ratio (SCR) of wavelet packet component energy of responses, are studied and compared.
(4) Three modal expansion methods are compared and used to expand incomplete modes at limited DOFs to complete DOFs, and then the expanded modes are used to construct‘incomplete’modal strain energy damage indexes. The incomplete modal flexibility change index is directly constructed from incomplete modes. Damage detection with the two incomplete indexes is studied in Xihoumen suspension Bridge. Optimizing Sensor Locations (OSL) based on an improved Genetic Algorithm to make the two incomplete indexes most sensitive to possible damage is discussed, in addition, a Minimum Modal Variance (MMV) method for OSL is proposed. Damage detection based on the two incomplete indexes measured at optimized sensor locations is verified. All the work above is a systematical study of methods in aspects of damage detection.
(5) Noise-contaminated ambient responses at limited DOFs of a beam-system finite element model and a plate-system finite element model with equivalent orthotropic plates and substructure method, are simulated. Capacities and errors of the above methods and the two incomplete indexes for detection of stiffness reductions in beam-system model and simulated cracking and corrosions in plate-system model are studied and discussed, respectively. Methods of selecting high accuracy modes are also verified to be effective and important.
引文
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