基于小波与分形理论的斜拉桥健康监测系统研究
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摘要
大跨度桥梁结构的健康监测是目前桥梁工程界的研究热点之一,是一个涉及到多学科、跨行业的难点课题。由于桥梁结构及其所处环境的复杂性、不确定性,使得国内外的研究都还处于探索和试用阶段。目前,在一些大跨度桥梁上都已安装了健康监测系统,但其主要用于数据采集,而缺乏有效的健康评价支撑。本文在前人研究工作的基础上,根据小波和分形在处理复杂非线性问题时的特点,将其应用于桥梁结构健康监测系统,提出了建立基于小波与分形的斜拉桥健康监测系统的基本框架。为此,本文主要进行了以下几个方面的研究工作。
1.对桥梁进行健康监测的前提,是需要建立一个准确、有效的基准有限元模型。以静测中的位移和动测中的频率作为状态变量,以各项实测值与相应计算值的百分比偏差的平方和作为目标函数,结合ANSYS的优化分析功能,对大型桥梁结构的初始有限元模型的计算参数进行修正。修正过程中引入了约束条件限制各待修正参数和结果数据的变化范围,使得修正后的各参数具有明确的物理意义。修正后的有限元模型为桥梁健康监测计算分析提供了更加切合实际的数学模型,也验证了采用ANSYS进行模型修正的可行性。
2.动力监测是健康监测的重要手段之一,在健康监测系统建立初期对结构的动力性能进行模拟分析是很有必要的。本文综合考虑了车桥耦合振动、路面不平度、风、温度等对结构的影响,为健康监测策略制订提供了切合实际的理论分析数据。
3.在小波分析理论的基础上,深入剖析了Mallat算法中的频率混淆现象以及产生小波包频带错乱现象的原因,并提出了相应的改进算法,有效地消除了频率混淆和小波包频带错乱问题。
4.运用小波分析方法对结构动力系统进行多尺度分析,为小波分析用于结构健康监测提供了坚实的理论基础。将小波分析方法用于结构的模态参数识别、信号滤噪、数据压缩与重构、监测突变信号等方面,均取得了较好的效果。
5.运用小波方法分析了斜拉桥损伤前后的位移、曲率和应变三种模态振型,据此能够较准确地识别结构的损伤位置和损伤程度。
6.运用改进的小波分析算法对健康监测过程中的信号进行了深入分析,发现小波能量分布与结构的自振特性一样能够反映结构的固有特性,并且能够反映结构的局部特性。在小波包分析的基础上,提出了小波能量互熵作为损伤识别的指标。在应用中引入表征各测点局部特性的权重系数,从而较准确有效地识别损伤位置及其程度。
7.针对小波的强局部分析能力和分形的强非线性处理能力,提出了结构损伤诊断的小波细节关联维分析方法。首先对信号进行小波包分解,再计算各小波包的关联维数,并与健康状态下的关联维数比较,通过损伤前后的互熵来识别结构的损伤。实例分析表明,该方法具有较强的损伤诊断能力和抗噪能力。
8.运用广义维数谱对斜拉桥的损伤进行诊断,结果表明损伤程度与敏感维数、互熵之间均呈线性关系,验证了多重分形应用于斜拉桥损伤识别的可行性和有效性。
Currently, the structctural health monitoring (SHM) of long-span bridges is one of the reseach heat points in the field of bridge engineering. Also, SHM is a very difficult task which is related to many subjects and industries. Because of complexity and indetermination in bridge structures and environmental conditions, the research on the SHM is still at the exploring and tryout phase. Nowadays, structural health monitoring systems have been installed on some long-span bridges. However, these systems are mainly used for data acquisition, lacking an effective health assessment support. Based on characteristics in the wavelet and fractal theory for complex nonlinear issues, a basic frame of the bridge health monitoring system is suggested. Following research works have been carried out in this doctoral dissertation.
1. A baseline finite element model that can reflect structural responses comprehensively and correctly is necessary to the health monitoring system. Defining the displacement by static tests and the natural frequency by dynamic tests as state variables (SVs), and taking the objective function as the sum of square of deviation ratios of each test-values and corresponding calculating values, adopting the optimization methods in ANSYS, the initial analysis model of long-span bridge is updated by modifying the calculation parameters in this dissertation. In updating, changing ranges of parameters and results are limited by constraint conditions; therefore, the updated parameters have respective explicit physical meanings. The updated finite element model provides a more practical mathematical model for the bridge health monitoring, and also validates the feasibility of updating model methods by ANSYS optimization design.
2. Dynamic monitoring is an important way for the health monitoring system, analyzing the structural dynamic characters is necessary at the beginning of building up the health monitoring system. In this dissertation, the effects by coupling vibration of vehicle-bridge system, road surface roughness, wind and temperature are synthetically considered, and practicable datas for establishing the health monitoring strategy are offered.
3. Based on the wavelet theory, the reasons of the frequency aliasing in the Mallat algorithm and frequency sub bands disordering of the wavelet package are analyzed profoundly. And an improved algorithm to avoid frequency aliasing and frequency sub bands disordering is presented.
4. Applying wavelet transform, differential equation of multi-scale structural dynamic is obtained, which provides a solid theoretical foundation to structural health monitoring system. With application examples, it is shown that the wavelet analysis is very effective to solve structural modal parameters, denoise signal, compress and reconstruct datas, and detect signal singularity in bridge health monitoring system.
5. Applying wavelet transform to the displacement mode shape, curvature mode shape and stress mode shape of cable-stayed bridge, the results show that this method can be used well for diagnosing the position and degree of sturcutral damages.
6. The improved wavelet algorithm is applied to the signals of health monitoring. The result shows that the wavelet energy, like structural natural frequency, can be used to reflect the structural inherent characteristic and local characteristic as well. Based on the analysis of wavelet package, the concept of wavelet energy cross entropy is proposed to serve as an index for damage diagnosis. By adopting weighted value which represents the local characteristic of structure, the index can diagnoses the location and the degree of damage effectively.
7. Based on powerful ability of the wavelet in signal local analyzing and the fratal in nonlinear processing, a structural damage monitoring method using correlation dimension of wavelet details is proposed. Firstly, the vibration detection signal is decomposed into varying scales of temporal resolution, then the correlation dimension of wavelet details of key frequency bands is calculated. thirdly, cross entropy of the correlation between undamaged and damaged stucture is carried out, which is a diagnosed index. This proposed approach is fully tested with examples, and the results show it possesses sensityivity to damage and strong immunity to noise.
8. Applying the general fractal dimension to diagnose the damage of cable-stayed bridge, it is shown that the sensitive dimension varies directly as degree of damage, and the cross entropy between undamaged and damaged structure as well.
9. A basic frame of health monitoring system for cable-stayed bridge is built up, which integrates with the wavelet and fractal theory.
1.对桥梁进行健康监测的前提,是需要建立一个准确、有效的基准有限元模型。以静测中的位移和动测中的频率作为状态变量,以各项实测值与相应计算值的百分比偏差的平方和作为目标函数,结合ANSYS的优化分析功能,对大型桥梁结构的初始有限元模型的计算参数进行修正。修正过程中引入了约束条件限制各待修正参数和结果数据的变化范围,使得修正后的各参数具有明确的物理意义。修正后的有限元模型为桥梁健康监测计算分析提供了更加切合实际的数学模型,也验证了采用ANSYS进行模型修正的可行性。
2.动力监测是健康监测的重要手段之一,在健康监测系统建立初期对结构的动力性能进行模拟分析是很有必要的。本文综合考虑了车桥耦合振动、路面不平度、风、温度等对结构的影响,为健康监测策略制订提供了切合实际的理论分析数据。
3.在小波分析理论的基础上,深入剖析了Mallat算法中的频率混淆现象以及产生小波包频带错乱现象的原因,并提出了相应的改进算法,有效地消除了频率混淆和小波包频带错乱问题。
4.运用小波分析方法对结构动力系统进行多尺度分析,为小波分析用于结构健康监测提供了坚实的理论基础。将小波分析方法用于结构的模态参数识别、信号滤噪、数据压缩与重构、监测突变信号等方面,均取得了较好的效果。
5.运用小波方法分析了斜拉桥损伤前后的位移、曲率和应变三种模态振型,据此能够较准确地识别结构的损伤位置和损伤程度。
6.运用改进的小波分析算法对健康监测过程中的信号进行了深入分析,发现小波能量分布与结构的自振特性一样能够反映结构的固有特性,并且能够反映结构的局部特性。在小波包分析的基础上,提出了小波能量互熵作为损伤识别的指标。在应用中引入表征各测点局部特性的权重系数,从而较准确有效地识别损伤位置及其程度。
7.针对小波的强局部分析能力和分形的强非线性处理能力,提出了结构损伤诊断的小波细节关联维分析方法。首先对信号进行小波包分解,再计算各小波包的关联维数,并与健康状态下的关联维数比较,通过损伤前后的互熵来识别结构的损伤。实例分析表明,该方法具有较强的损伤诊断能力和抗噪能力。
8.运用广义维数谱对斜拉桥的损伤进行诊断,结果表明损伤程度与敏感维数、互熵之间均呈线性关系,验证了多重分形应用于斜拉桥损伤识别的可行性和有效性。
Currently, the structctural health monitoring (SHM) of long-span bridges is one of the reseach heat points in the field of bridge engineering. Also, SHM is a very difficult task which is related to many subjects and industries. Because of complexity and indetermination in bridge structures and environmental conditions, the research on the SHM is still at the exploring and tryout phase. Nowadays, structural health monitoring systems have been installed on some long-span bridges. However, these systems are mainly used for data acquisition, lacking an effective health assessment support. Based on characteristics in the wavelet and fractal theory for complex nonlinear issues, a basic frame of the bridge health monitoring system is suggested. Following research works have been carried out in this doctoral dissertation.
1. A baseline finite element model that can reflect structural responses comprehensively and correctly is necessary to the health monitoring system. Defining the displacement by static tests and the natural frequency by dynamic tests as state variables (SVs), and taking the objective function as the sum of square of deviation ratios of each test-values and corresponding calculating values, adopting the optimization methods in ANSYS, the initial analysis model of long-span bridge is updated by modifying the calculation parameters in this dissertation. In updating, changing ranges of parameters and results are limited by constraint conditions; therefore, the updated parameters have respective explicit physical meanings. The updated finite element model provides a more practical mathematical model for the bridge health monitoring, and also validates the feasibility of updating model methods by ANSYS optimization design.
2. Dynamic monitoring is an important way for the health monitoring system, analyzing the structural dynamic characters is necessary at the beginning of building up the health monitoring system. In this dissertation, the effects by coupling vibration of vehicle-bridge system, road surface roughness, wind and temperature are synthetically considered, and practicable datas for establishing the health monitoring strategy are offered.
3. Based on the wavelet theory, the reasons of the frequency aliasing in the Mallat algorithm and frequency sub bands disordering of the wavelet package are analyzed profoundly. And an improved algorithm to avoid frequency aliasing and frequency sub bands disordering is presented.
4. Applying wavelet transform, differential equation of multi-scale structural dynamic is obtained, which provides a solid theoretical foundation to structural health monitoring system. With application examples, it is shown that the wavelet analysis is very effective to solve structural modal parameters, denoise signal, compress and reconstruct datas, and detect signal singularity in bridge health monitoring system.
5. Applying wavelet transform to the displacement mode shape, curvature mode shape and stress mode shape of cable-stayed bridge, the results show that this method can be used well for diagnosing the position and degree of sturcutral damages.
6. The improved wavelet algorithm is applied to the signals of health monitoring. The result shows that the wavelet energy, like structural natural frequency, can be used to reflect the structural inherent characteristic and local characteristic as well. Based on the analysis of wavelet package, the concept of wavelet energy cross entropy is proposed to serve as an index for damage diagnosis. By adopting weighted value which represents the local characteristic of structure, the index can diagnoses the location and the degree of damage effectively.
7. Based on powerful ability of the wavelet in signal local analyzing and the fratal in nonlinear processing, a structural damage monitoring method using correlation dimension of wavelet details is proposed. Firstly, the vibration detection signal is decomposed into varying scales of temporal resolution, then the correlation dimension of wavelet details of key frequency bands is calculated. thirdly, cross entropy of the correlation between undamaged and damaged stucture is carried out, which is a diagnosed index. This proposed approach is fully tested with examples, and the results show it possesses sensityivity to damage and strong immunity to noise.
8. Applying the general fractal dimension to diagnose the damage of cable-stayed bridge, it is shown that the sensitive dimension varies directly as degree of damage, and the cross entropy between undamaged and damaged structure as well.
9. A basic frame of health monitoring system for cable-stayed bridge is built up, which integrates with the wavelet and fractal theory.
引文
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