小波分析在桥梁预警系统中的应用

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3.0 陈辉 2024-11-19 4 4 5.93MB 104 页 15积分

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摘要

随着我国经济的快速发展，大跨桥梁建设事业也飞速发展，新颖结构、新型

材料和新工艺等不断涌现，桥梁结构的形式和功能也更加复杂，在服役过程中，

桥梁可能会受到各种各样因素的影响而发生损伤，作为生命线工程，大跨度桥梁

的健康和寿命越来越引起有关部门的重视。桥梁的健康监测、检测是提供桥梁安

全养护、正常使用的保证。针对大跨度桥梁安全的预警系统迎时而生，并已成为

国内外学术界和工程界研究的热点。

损伤识别方法是桥梁预警系统的关键内容，现有的损伤识别方法存在着一些

问题：首先，现有指标的损伤识别效果往往停留在数值仿真层面上，在工程实践

中很难应用，损伤识别效果的验证缺乏说服性；其次，现有指标受到结构本身及

环境影响很大，仅适用于一种结构或者某些结构；再次，现有的指标大多是经过

模态分析得到的，模态分析需要结合有限元或者经验判断，其中的误差很大。最

后，现有方法很少是通过对信号直接分析得到的，而且未考虑激励和环境的影响，

所以很难实现桥梁预警的实时性。

针对现有指标存在的问题，分析了桥梁预警系统的特点和对损伤识别方法的

要求，在现有损伤识别方法的基础上，提出了具有实时性和实用性的损伤识别指

标，并通过动力试验证明了其在实际工程中应用的可行性。本文主要工作如下：

一、对桥梁预警系统的重要性进行了介绍，然后再对现有的损伤识别方法进

行了综述，叙述了现有损伤识别方法的优缺点以及适用性。

二、简要介绍了小波分析的来源，以及应用的领域，通过仿真对预警信号小

波降噪技术进行了一定程度的研究。

三、将小波分析和曲率模态相结合，提出了曲率模态小波系数差的损伤识别

方法，通过对简支梁和连续梁进行仿真，得到了很好的识别效果，又对两跨连续

梁模型进行了锤击实验，也可以得到较好的损伤识别，证明了所提指标的优越性。

四、为了能够实现实时在线对桥梁进行监测，提出了针对信号进行分析的损

伤识别方法,将单传感器采集的信号进行小波包能量谱分析，通过欧氏距离模式识

别方法对小波包能量分布向量进行匹配，根据距离大小判断损伤程度的大小。

五、由于小波包能量谱受外界环境激励的影响很大，仅靠小波包能量谱的变

化无法判断桥梁的损伤，提出了虚拟激励响应函数和小波包相结合的损伤识别方

法，通过对梁的数值模拟，得到所提能量累积变异指标不但受外界激励的影响小，

而且也能够实现损伤识别和损伤定位，损伤指标随着损伤程度的增大逐渐增大。

六、设计了斜拉桥模型试验，通过切割主梁模拟斜拉桥的损伤状况，分别在

环境和锤击激励下进行损伤识别试验，针对实验过程中产生的误差，将随机—模

糊均值理论引入，对完好状态结构的虚拟激励响应函数进行随机—模糊均值处理，

实验得到了较好的识别效果，为在实际大跨桥梁预警系统中应用奠定了基础。

关键词：小波分析桥梁预警损伤识别曲率模态小波系数差小波包

虚拟激励响应函数

ABSTRACT

With the development of China, bridge constructions are also developing, new

structures、new materials and new methods are emerged. Bridges’ styles and functions

are more and more complex, varieties of damages may occur during service, As the

lifeline structure, great span bridges’ health and life expectancy have got attention,

Thus the damage identification of bridge structures and online monitoring has become

guarantee of the normal safety running. Bridge alarming systems appear and have

become one research focus of academic community and engineers.

Damage identification method is key part of bridge alarming system. There are

some problems in normal methods. Firstly, damage detection effect of normal methods

are mostly numerical simulated, It is difficult to apply in real bridge. Verification of

damage identification effect is lack persuasive. Secondly, normal method is affected by

structure style and environment, which can only be used in one or some structure.

Thirdly, most normal index is calculated by modal analysis, modal analysis need to be

combined with finite element or experience judge, which contains a lot of errors.

Lastly, normal method rarely analyzed by signals directly, so it is difficult to achieve

online alarming.

In view of normal index of damage identification, analyze characteristic of bridge

alarming system and require of damage identification method, a new method which

contains online and effectiveness is presented, experiment confirms that the method is

feasible for applying in real bridge. What I have done in this paper are:

1. Make introduction of bridge alarming system, then review the existing damage

identification methods, describes the advantages and disadvantages of the existing

damage detection methods and applicability.

2. Wavelet analysis and application field are introduced briefly, according

simulation we can see that wavelet de-noise technology is feasible in bridge alarming

system.

3. Wavelet analysis and curvature mode were combined for damage identification,

wavelet curvature and difference of mode coefficients method is presented, according

simulation for simple beam and continuous beam, damage can be identified effectively,

and experiment is carried out for two-span continuous beam model, the effect of

damage identification which from experiment is confirmed superiority for damage

identification of bridge.

4. For online monitoring of bridge anytime, a new damage identification method

based on signals is proposed, signals from one sensor are analyzed by wavelet packet

energy. According Euclidean distance of wavelet packet energy distribution vector

matching, extent of damage can be got from distance.

5. Because the wavelet packet energy spectrum will be affected by external

environment greatly, so damage identification can not be found only from wavelet

packet energy spectrum, damage identification method based on f virtual excitation

response function and wavelet packet is proposed. Through simulation of simple beam

and continuous beam, we can see that identification index grows with damage extent.

6. Through a cable-stayed bridge modal experiment can see that application of

damage index is effective. According different state and carry on damage detection

respectively. For the error which generated from the process hammering,

random-fuzzy mean theory is introduced, virtual excitation response function from

healthy bridge is carried out random-fuzzy mean, damage can be detected very well.

It is feasible for using in bridge alarming system.

Key Word: wavelet analysis, bridge alarming, damage identification,

wavelet curvature model difference, wavelet packet, virtual excitation

response function

中文摘要

ABSTRACT

第一章绪论........................................................................................................... 1

§1.1 引言.............................................................................................................. 1

§1.2 桥梁健康监测的概况.................................................................................. 4

§1.3 现有桥梁损伤识别方法.............................................................................. 5

§1.3.1 基于固有频率的损伤识别................................................................... 6

§1.3.2 基于振型变化的损伤识别................................................................... 7

§1.3.3 基于柔度矩阵的损伤识别................................................................... 7

§1.3.4 基于频响函数的损伤识别................................................................... 8

§1.3.5 基于神经网络的损伤识别................................................................... 8

§1.3.6 基于 Hilbert-Huang 变换的损伤识别..................................................9

§1.4 小波分析在损伤识别中的应用................................................................ 10

§1.4.1 基于时域响应的分析方法................................................................. 10

§1.4.2 基于空间域响应的分析方法............................................................. 12

§1.4.3 小波损伤识别研究存在的问题......................................................... 12

§1.5 本文课题来源和研究内容........................................................................ 13

第二章小波分析理论........................................................................................... 17

§2.1 傅立叶分析................................................................................................ 17

§2.1.1 傅立叶级数......................................................................................... 18

§2.1.2 傅立叶变换......................................................................................... 18

§2.1.3 短时傅立叶变换................................................................................. 19

§2.2 连续小波变换............................................................................................ 19

§2.3 离散小波变换............................................................................................ 20

§2.4 多分辨率分析............................................................................................ 21

§2.5 小波包分析................................................................................................ 23

§2.5.1 小波包分析思想.................................................................................. 23

§2.5.2 小波包分析的定义与性质.................................................................. 24

§2.6 常用小波基函数介绍................................................................................ 25

§2.6.1 Haar 小波 ............................................................................................ 26

§2.6.2 Meyer 小波..........................................................................................26

§2.6.3 Morlet 小波......................................................................................... 27

§2.6.4 Daubechies 小波................................................................................. 27

§2.6.5 sym N 小波 .......................................................................................... 27

§2.6.6 Bior 小波 ............................................................................................. 28

§2.7 小结............................................................................................................ 28

第三章面向桥梁预警的小波降噪....................................................................... 29

§3.1 小波对信号的多尺度表达........................................................................ 29

§3.2 现有小波降噪方法简介............................................................................ 31

§3.2.1 小波变换模极大值去噪..................................................................... 31

§3.2.2 小波系数相关性去噪......................................................................... 33

§3.2.3 小波阈值去噪..................................................................................... 33

§3.2.4 平移不变法降噪................................................................................. 34

§3.3 小波降噪分析............................................................................................ 35

§3.3.1 噪声特性和降噪步骤......................................................................... 35

§3.3.2 阈值函数和阈值的选择..................................................................... 36

§3.4 小波降噪仿真分析.................................................................................... 38

§3.5 基于小波包的降噪.................................................................................... 43

§3.6 小结............................................................................................................. 44

第四章曲率模态和小波分析的损伤识别研究................................................... 45

§4.1 基于曲率模态的损伤识别方法研究........................................................ 46

§4.1.1 曲率模态基本原理............................................................................. 46

§4.1.2 基于曲率模态的数值模拟................................................................. 47

§4.2 基于曲率模态和小波系数差的损伤识别................................................ 51

§4.2.1 损伤识别步骤..................................................................................... 51

§4.2.2 数值算例............................................................................................. 52

§4.3 模型实验验证............................................................................................ 54

§4.3.1 实验模型............................................................................................. 54

§4.3.2 实验结果............................................................................................. 56

第五章基于小波包能量的损伤识别................................................................... 58

§5.1 基于欧式距离的小波包能量特征向量的损伤识别................................ 60

§5.2 数值模拟分析............................................................................................ 60

§5.3 小波函数的选择........................................................................................ 66

§5.4 小结............................................................................................................ 67

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摘要：

摘要随着我国经济的快速发展，大跨桥梁建设事业也飞速发展，新颖结构、新型材料和新工艺等不断涌现，桥梁结构的形式和功能也更加复杂，在服役过程中，桥梁可能会受到各种各样因素的影响而发生损伤，作为生命线工程，大跨度桥梁的健康和寿命越来越引起有关部门的重视。桥梁的健康监测、检测是提供桥梁安全养护、正常使用的保证。针对大跨度桥梁安全的预警系统迎时而生，并已成为国内外学术界和工程界研究的热点。损伤识别方法是桥梁预警系统的关键内容，现有的损伤识别方法存在着一些问题：首先，现有指标的损伤识别效果往往停留在数值仿真层面上，在工程实践中很难应用，损伤识别效果的验证缺乏说服性；其次，现有指标受到结构本身及环境影响很大...

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