复杂桥梁结构移动荷载识别的理论与试验研究
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摘要
桥梁受移动车辆荷载的反复作用及超载运输的影响,极易发生疲劳、损伤甚至破坏,严重影响着其正常的使用寿命;桥梁健康监测系统也要求对环境荷载进行实时监测和记录。因此,识别桥梁上移动车辆荷载,对桥梁的健康监测和日常维护以及交通规划等都具有重要的理论意义和工程价值。
本文对多跨连续梁桥、空间梁桥和曲线箱梁桥等复杂桥梁结构上的移动荷载识别理论进行了系统的研究,主要研究工作与创新成果包括以下几个方面:
(1)基于模态叠加法和连续梁固有振动的精确解,建立了移动荷载作用下的等截面连续梁运动方程。利用样条函数逼近法逼近桥梁的动力响应,结合Tikhonov正则化方法和奇异值分解(SVD)得到了荷载识别的正则解。
(2)针对结构形式复杂的桥梁,采用五次Hermitian插值函数作为单元形函数,建立了桥梁结构的有限元模型。在模态空间内,利用Chebyshev正交多项式作为响应和荷载的时间有限元形函数,基于加权残值法,建立了移动荷载识别的时间元模型。并利用截断奇异值分解的正则化方法,得到移动荷载的稳定解。
(3)针对公路与城市立交中普遍采用的空间梁桥结构,建立了桥梁移动荷载识别的空间梁格模型。利用桥梁离散振型,由样条函数逼近法与截断奇异值分解正则化方法得到了移动荷载识别的稳定解,其中采用以模态置信度准则(MAC)矩阵为目标函数的逐步积累法对测点布置进行优化。
(4)针对曲线箱梁桥,基于剪力柔性梁格法建立了曲线箱梁桥的梁格模型,分析了车桥相互作用。采用三角位移函数,基于平衡法,推导了一种考虑剪切变形和转动惯量的新型曲梁单元。根据拉格朗日定理,建立了空间车辆模型,基于逆傅立叶变换法生成了4种等级的桥面不平度。
(5)提出了一种基于BP神经网络的桥梁移动荷载识别方法。采用分阶段识别技术,分步对车辆的位置、车速、车距及荷载进行识别。分别采用正交设计方法、正则化方法和遗传算法对神经网络的样本集设计、训练方法以及初始权值进行了改进和优化。
(6)在试验室内制作了一根2m长的简支钢梁模型和模型小车,考虑了相似条件。对模型梁的弯曲刚度、应变测量和车速进行了标定。试验得到模型梁的前4阶振型和模态参数。通过测得的应变及模态参数,对本文所建立的几种桥梁移动荷载识别方法进行了验证和参数分析。
Fatigue damage and failure may be easily occurred in bridge structures under the repeated action of moving vehicle loads and the effect of traffic overloads, which may influence the normal service life severely. The real-time detection and record on ambient loads environment are also required in the health monitoring system of bridges. Therefore, to identify the moving vehicle loads on bridges has important theoretical significance and engineering value for the health monitoring and daily maintenance of bridges and the traffic planning.
A systematic investigation on identification of moving loads on complex bridges such as multi-span continuous girder, spatial girder and curved box girder is performed in this dissertation. The main researches and innovations are included as follows:
(1) Based on the modal superposition method and the exact solution of natural vibration of a continuous beam, the equations of motion of a uniform continuous girder subjected to a set of moving loads are established. Dynamic responses of the bridge are approached using the spline function approximation method, and the regularized solutions of the moving loads are obtained by combining the Tikhonov regularization with the singular values decomposition (SVD).
(2) Against bridges with complex structural layouts, a finite element model of the bridge structure is established by employing the quintic Hermitian interpolating function as an element shape function. In the modal space, the Chebyshev orthogonal polynomial is taken as the time finite element shape function of responses and forces, and the time finite element model for moving load identification is established based on the weighted-residual method. Then the stable solutions of moving loads are obtained using the regularization method with truncated singular values decomposition.
(3) Against the spatial girder bridges in general use in highway bridges and urban overpasses, a spatial grillage model for moving load identification of bridges is established. By employing the discrete vibration modes of the bridge, the stable solutions for moving load identification is obtained by means of the spline function approximation method and the truncated singular value decomposition regularization method, in which the measuring point placements are optimized using the successive accumulation method in which the modal assurance criterion (MAC) matrix is taken as a target function.
(4) Against curved box girder bridges, a grillage model of the curved box girder is built based on the shear-flexible grillage method, and the vehicle-bridge interaction is investigated. A novel curved beam element considering shearing deformation and rotational inertia is derived using the trigonometric function and based on the equilibrium equation. A spatial vehicle model is established according to the Lagrange principle, and four grades of road irregularity are generated based on the inverse Fourier transforming technique.
(5) A novel BP neural network-based identification method for moving loads of bridges is proposed. Using the stage identification technique, the positions, velocities, distances and loads of vehicles is identified step by step. The design of samples set, training algorithm, and the initial values of weights of the neural network are improved and optimized by using the orthogonal design method, the regularization method and the genetic algorithm respectively.
(6) A simply supported steel beam with 2 m length and a model car are fabricated in laboratory, considering the similarity conditions. Bending stiffness of model beam, measurement of strain and speed of car are calibrated. The first four modes and its modal parameters of the model beam are obtained by test. Through the measured strains and modal parameters, the proposed methods for moving load identification of bridges are validated and parameter investigated.
本文对多跨连续梁桥、空间梁桥和曲线箱梁桥等复杂桥梁结构上的移动荷载识别理论进行了系统的研究,主要研究工作与创新成果包括以下几个方面:
(1)基于模态叠加法和连续梁固有振动的精确解,建立了移动荷载作用下的等截面连续梁运动方程。利用样条函数逼近法逼近桥梁的动力响应,结合Tikhonov正则化方法和奇异值分解(SVD)得到了荷载识别的正则解。
(2)针对结构形式复杂的桥梁,采用五次Hermitian插值函数作为单元形函数,建立了桥梁结构的有限元模型。在模态空间内,利用Chebyshev正交多项式作为响应和荷载的时间有限元形函数,基于加权残值法,建立了移动荷载识别的时间元模型。并利用截断奇异值分解的正则化方法,得到移动荷载的稳定解。
(3)针对公路与城市立交中普遍采用的空间梁桥结构,建立了桥梁移动荷载识别的空间梁格模型。利用桥梁离散振型,由样条函数逼近法与截断奇异值分解正则化方法得到了移动荷载识别的稳定解,其中采用以模态置信度准则(MAC)矩阵为目标函数的逐步积累法对测点布置进行优化。
(4)针对曲线箱梁桥,基于剪力柔性梁格法建立了曲线箱梁桥的梁格模型,分析了车桥相互作用。采用三角位移函数,基于平衡法,推导了一种考虑剪切变形和转动惯量的新型曲梁单元。根据拉格朗日定理,建立了空间车辆模型,基于逆傅立叶变换法生成了4种等级的桥面不平度。
(5)提出了一种基于BP神经网络的桥梁移动荷载识别方法。采用分阶段识别技术,分步对车辆的位置、车速、车距及荷载进行识别。分别采用正交设计方法、正则化方法和遗传算法对神经网络的样本集设计、训练方法以及初始权值进行了改进和优化。
(6)在试验室内制作了一根2m长的简支钢梁模型和模型小车,考虑了相似条件。对模型梁的弯曲刚度、应变测量和车速进行了标定。试验得到模型梁的前4阶振型和模态参数。通过测得的应变及模态参数,对本文所建立的几种桥梁移动荷载识别方法进行了验证和参数分析。
Fatigue damage and failure may be easily occurred in bridge structures under the repeated action of moving vehicle loads and the effect of traffic overloads, which may influence the normal service life severely. The real-time detection and record on ambient loads environment are also required in the health monitoring system of bridges. Therefore, to identify the moving vehicle loads on bridges has important theoretical significance and engineering value for the health monitoring and daily maintenance of bridges and the traffic planning.
A systematic investigation on identification of moving loads on complex bridges such as multi-span continuous girder, spatial girder and curved box girder is performed in this dissertation. The main researches and innovations are included as follows:
(1) Based on the modal superposition method and the exact solution of natural vibration of a continuous beam, the equations of motion of a uniform continuous girder subjected to a set of moving loads are established. Dynamic responses of the bridge are approached using the spline function approximation method, and the regularized solutions of the moving loads are obtained by combining the Tikhonov regularization with the singular values decomposition (SVD).
(2) Against bridges with complex structural layouts, a finite element model of the bridge structure is established by employing the quintic Hermitian interpolating function as an element shape function. In the modal space, the Chebyshev orthogonal polynomial is taken as the time finite element shape function of responses and forces, and the time finite element model for moving load identification is established based on the weighted-residual method. Then the stable solutions of moving loads are obtained using the regularization method with truncated singular values decomposition.
(3) Against the spatial girder bridges in general use in highway bridges and urban overpasses, a spatial grillage model for moving load identification of bridges is established. By employing the discrete vibration modes of the bridge, the stable solutions for moving load identification is obtained by means of the spline function approximation method and the truncated singular value decomposition regularization method, in which the measuring point placements are optimized using the successive accumulation method in which the modal assurance criterion (MAC) matrix is taken as a target function.
(4) Against curved box girder bridges, a grillage model of the curved box girder is built based on the shear-flexible grillage method, and the vehicle-bridge interaction is investigated. A novel curved beam element considering shearing deformation and rotational inertia is derived using the trigonometric function and based on the equilibrium equation. A spatial vehicle model is established according to the Lagrange principle, and four grades of road irregularity are generated based on the inverse Fourier transforming technique.
(5) A novel BP neural network-based identification method for moving loads of bridges is proposed. Using the stage identification technique, the positions, velocities, distances and loads of vehicles is identified step by step. The design of samples set, training algorithm, and the initial values of weights of the neural network are improved and optimized by using the orthogonal design method, the regularization method and the genetic algorithm respectively.
(6) A simply supported steel beam with 2 m length and a model car are fabricated in laboratory, considering the similarity conditions. Bending stiffness of model beam, measurement of strain and speed of car are calibrated. The first four modes and its modal parameters of the model beam are obtained by test. Through the measured strains and modal parameters, the proposed methods for moving load identification of bridges are validated and parameter investigated.
引文
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