大跨度斜拉桥拉索索力与车辆荷载识别及建模研究
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摘要
随着中国经济的迅猛发展，公路交通运输量不断增加，公路桥梁上的车辆荷载强度和频度均持续上升，这造成了严重的桥梁累积损伤、甚至失效。近十年来因超载而造成的桥梁垮塌事故接连不断，桥梁上实际车辆荷载的识别、实时统计分析、分布规律的研究至关重要。结构健康监测系统的出现和广泛应用，使得实时的识别和监测桥梁上运行的车辆荷载成为可能。目前，关于桥梁荷载的识别研究主要集中在梁桥，对斜拉桥车辆荷载的研究仍十分缺乏，且已有研究方法需要已知车辆荷载位置。此外，斜拉索是斜拉桥上的关键结构构件，其疲劳效应十分突出，目前斜拉索时变索力的监测和识别仍然没有有效的方法。本文研究大跨度斜拉桥斜拉索时变索力识别方法、车辆荷载及其空间分布识别方法、以及车辆荷载建模与极值预测模型。
主要研究内容包括：
首先，提出基于扩展卡尔曼滤波的时变索力识别方法，并进行数值模拟和试验验证。推导考虑支座位移的斜拉索的扩展状态空间运动方程和观测方程，给出基于监测的加速度响应的斜拉索时变索力识别的扩展卡尔曼滤波算法；采用南京长江三桥的斜拉索进行数值计算，验证方法的精度和鲁棒性；进一步通过模型试验，验证方法的识别精度。
其次，提出基于斜拉索振动信息识别桥梁车辆荷载的方法。推导包含车重、车速和上桥时间的扩展状态空间运动方程及斜拉索观测方程，提出基于扩展卡尔曼滤波方法的车重、车速和上桥时间识别算法，采用南京长江三桥进行数值计算，验证本文方法的精度。
再次，提出基于斜拉索索力监测信息的斜拉桥上车辆荷载及其位置识别方法。建立车辆荷载等效力与斜拉索索力之间的关系方程，利用Tikhonov正则化方法降低此病态线性方程求解的不适定性；采用区间理论，研究识别结果的误差上、下界。
提出基于斜拉索索力监测信息的斜拉桥车辆荷载及其空间分布的稀疏优化识别算法。建立车辆荷载与斜拉索索力之间的线性关系方程，采用稀疏优化算法求解上述方程，识别车辆荷载及其空间分布，采用南京长江三桥进行数值计算，验证本文方法的精度及其抗噪性。
最后，在上述车辆荷载识别的基础上，采用南京长江三桥健康监测实测车辆数据，按照密集运行状态和一般运行状态分别统计其到达时间间隔的随机分布；推导适用于任意齐次更新随机过程的极值预测定理；按照密集运行状态和一般运行状态对车重的截口分布分别进行统计建模及极值预测。并进一步统计数据尾部的随机模型，建立具有高精度的尾分布半参数化概率模型，对南京长江三桥车辆荷载的周极值进行预测，并与实测数据进行对比验证。
With rapid development of Chinese economics, traffic volume keeps increasing. The magnitude and frequency of vehicle loads on bridges are rising, which causes serious damages to bridges. There are many collapse accidents of bridges in last decade. It’s urgent to identify vehicle loads and to investigate and update their statistical characteristics. The development and application of structural health monitoring system make it possible to monitoring and identifying vehicle loads on bridge real-time. Meanwhile, up to date and larger amount of data are available from structural health monitoring systems which is a solid foundation of the extreme value research of vehicle loads. The previous researches of moving loads identification paid much attention to the problem on beam bridges and slab bridges. However, there was lack of information on the problem of moving force identification on cable-stayed bridges, and the vehicle loads position must be determined in advance to carry out identification. The existing cable force identification methods were limited to determine the mean value of cable tension during a certain period. To solve these problems, this dissertation is devoted to a relatively systematic study on vehicle loads, with emphasis on, identification of time-varying cable force caused by traffic loads, identification of moving forces and their locations, and vehicle loads modeling and extreme value prediction on the cable-stayed bridge.
The main research works are outlined as following:
First, the identification method of time-varying cable force using extended Kalman filter is proposed, and it is verified through numerical simulation and model experiment in laboratory. Taking the support displacement into consideration, the equation of motion in augmented state space and measurement equation is derived. Based on that, cable time-varying tension identification algorithm is developed based on measured acceleration of the stay cable using extended Kalman filter. The precision and robustness of proposed method is investigated by numerical simulation based on one cable on Nanjing Yangtze River No.3Bridge. Furthermore, a model experiment is conducted to verify the accuracy of proposed method.
Second, an identification approach of vehicle loads on cable-stayed bridge is developed based on monitored vibration of one stay cable. The process equation and measurement equation of the augmented state variable including vehicle weight speed and arrival time is derived, based on which, the identification method of vehicle weight, speed and arrival time is presented. In order to demonstrate the accuracy of proposed method, the numerical simulation is conducted based on Nanjing Yangtze River No.3Bridge.
Third, an identification approach of moving forces and their locations on the cable-stayed bridge is established based on the monitored cable forces. The relationship equation between vehicle loads and cable forces of stay cables is established first, and then the Tikhonov regularization is adopted to overcome the ill-poseness of the equation. Furthermore, the error bound of the identification result is investigated using interval analysis theory.
An identification approach of moving forces and their spatial distributions on cable-stayed bridges is derived from sparse signal reconstruction theory based on monitored cable tension. The vehicle loads and cable tension of stay cables is connected by a linear equation, and then the sparse signal reconstruction theory is introduced to solve this seriously underdetermined equation, from which the vehicle loads and their spatial distributions can be identified. The numerical simulation based on Nanjing Yangtze River No.3Bridge is conducted to verify the accuracy and robustness of the proposed method.
Finally, based on the above research on vehicle loads identification, using the field data from structural health monitoring system on Nanjing Yangtze River No.3Bridge, the probability distribution of the inter-arrival-time in normal status and in dense status are statistically analyzed separately. And the extreme value distribution theorem for any homogeneous renewal process is derived. The probability distributions of vehicle weights in normal status and dense status are investigated separately. And based on the formula derived above, the extreme value distributions of vehicle loads in normal status and dense status are predicted. The stochastic model of the tail part of vehicle loads is investigated, and one semi-parametric probability model with high accuracy is established. Using this tail model, the weekly extreme value distribution is predicted, and then it is compared with in-field data to verify the accuracy of the proposed model and method.
主要研究内容包括：
首先，提出基于扩展卡尔曼滤波的时变索力识别方法，并进行数值模拟和试验验证。推导考虑支座位移的斜拉索的扩展状态空间运动方程和观测方程，给出基于监测的加速度响应的斜拉索时变索力识别的扩展卡尔曼滤波算法；采用南京长江三桥的斜拉索进行数值计算，验证方法的精度和鲁棒性；进一步通过模型试验，验证方法的识别精度。
其次，提出基于斜拉索振动信息识别桥梁车辆荷载的方法。推导包含车重、车速和上桥时间的扩展状态空间运动方程及斜拉索观测方程，提出基于扩展卡尔曼滤波方法的车重、车速和上桥时间识别算法，采用南京长江三桥进行数值计算，验证本文方法的精度。
再次，提出基于斜拉索索力监测信息的斜拉桥上车辆荷载及其位置识别方法。建立车辆荷载等效力与斜拉索索力之间的关系方程，利用Tikhonov正则化方法降低此病态线性方程求解的不适定性；采用区间理论，研究识别结果的误差上、下界。
提出基于斜拉索索力监测信息的斜拉桥车辆荷载及其空间分布的稀疏优化识别算法。建立车辆荷载与斜拉索索力之间的线性关系方程，采用稀疏优化算法求解上述方程，识别车辆荷载及其空间分布，采用南京长江三桥进行数值计算，验证本文方法的精度及其抗噪性。
最后，在上述车辆荷载识别的基础上，采用南京长江三桥健康监测实测车辆数据，按照密集运行状态和一般运行状态分别统计其到达时间间隔的随机分布；推导适用于任意齐次更新随机过程的极值预测定理；按照密集运行状态和一般运行状态对车重的截口分布分别进行统计建模及极值预测。并进一步统计数据尾部的随机模型，建立具有高精度的尾分布半参数化概率模型，对南京长江三桥车辆荷载的周极值进行预测，并与实测数据进行对比验证。
With rapid development of Chinese economics, traffic volume keeps increasing. The magnitude and frequency of vehicle loads on bridges are rising, which causes serious damages to bridges. There are many collapse accidents of bridges in last decade. It’s urgent to identify vehicle loads and to investigate and update their statistical characteristics. The development and application of structural health monitoring system make it possible to monitoring and identifying vehicle loads on bridge real-time. Meanwhile, up to date and larger amount of data are available from structural health monitoring systems which is a solid foundation of the extreme value research of vehicle loads. The previous researches of moving loads identification paid much attention to the problem on beam bridges and slab bridges. However, there was lack of information on the problem of moving force identification on cable-stayed bridges, and the vehicle loads position must be determined in advance to carry out identification. The existing cable force identification methods were limited to determine the mean value of cable tension during a certain period. To solve these problems, this dissertation is devoted to a relatively systematic study on vehicle loads, with emphasis on, identification of time-varying cable force caused by traffic loads, identification of moving forces and their locations, and vehicle loads modeling and extreme value prediction on the cable-stayed bridge.
The main research works are outlined as following:
First, the identification method of time-varying cable force using extended Kalman filter is proposed, and it is verified through numerical simulation and model experiment in laboratory. Taking the support displacement into consideration, the equation of motion in augmented state space and measurement equation is derived. Based on that, cable time-varying tension identification algorithm is developed based on measured acceleration of the stay cable using extended Kalman filter. The precision and robustness of proposed method is investigated by numerical simulation based on one cable on Nanjing Yangtze River No.3Bridge. Furthermore, a model experiment is conducted to verify the accuracy of proposed method.
Second, an identification approach of vehicle loads on cable-stayed bridge is developed based on monitored vibration of one stay cable. The process equation and measurement equation of the augmented state variable including vehicle weight speed and arrival time is derived, based on which, the identification method of vehicle weight, speed and arrival time is presented. In order to demonstrate the accuracy of proposed method, the numerical simulation is conducted based on Nanjing Yangtze River No.3Bridge.
Third, an identification approach of moving forces and their locations on the cable-stayed bridge is established based on the monitored cable forces. The relationship equation between vehicle loads and cable forces of stay cables is established first, and then the Tikhonov regularization is adopted to overcome the ill-poseness of the equation. Furthermore, the error bound of the identification result is investigated using interval analysis theory.
An identification approach of moving forces and their spatial distributions on cable-stayed bridges is derived from sparse signal reconstruction theory based on monitored cable tension. The vehicle loads and cable tension of stay cables is connected by a linear equation, and then the sparse signal reconstruction theory is introduced to solve this seriously underdetermined equation, from which the vehicle loads and their spatial distributions can be identified. The numerical simulation based on Nanjing Yangtze River No.3Bridge is conducted to verify the accuracy and robustness of the proposed method.
Finally, based on the above research on vehicle loads identification, using the field data from structural health monitoring system on Nanjing Yangtze River No.3Bridge, the probability distribution of the inter-arrival-time in normal status and in dense status are statistically analyzed separately. And the extreme value distribution theorem for any homogeneous renewal process is derived. The probability distributions of vehicle weights in normal status and dense status are investigated separately. And based on the formula derived above, the extreme value distributions of vehicle loads in normal status and dense status are predicted. The stochastic model of the tail part of vehicle loads is investigated, and one semi-parametric probability model with high accuracy is established. Using this tail model, the weekly extreme value distribution is predicted, and then it is compared with in-field data to verify the accuracy of the proposed model and method.
引文
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