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摘 要
颤振导数的识别是大跨桥梁颤振研究的基础与热点问题,本文回顾了桥梁颤振理
论及颤振导数的发展历程,对桥梁断面颤振导数的识别方法进行了归纳总结。基于节
段模型二维弯扭耦合自由振动风洞试验,本文从模态参数识别方法、试验数据预处理、
试验数据截取等几个方面进行了研究与讨论,给出了一套高效准确的颤振导数识别方
法,并编制了配套的
MATLAB
计算程序。本文的主要研究内容如下:
(
1
)在建立颤振导数与自由振动模态参数之间关系的基础上,介绍了
ITD
法、
本文优化后的
MITD
法及
LSCE
法三种模态参数的识别方法,并通过单自由度仿真试
验实际分析比较了几种方法的特点及将其直接应用于桥梁断面颤振导数识别的不适之
处。
(
2
)在 回顾现有颤振导数识别的最小二乘迭代法
ULS
法和
MLS
法的基础上,通
过引入符合试验数据特性的加权矩阵,推导出加权最小二乘迭代(
WLS
)法。并进行
了二自由度节段模型仿真试验,通过抗噪性试验和初值敏感性试验验证了
WLS
法更
好的抗噪性及计算效率。
(
3
)给出了为最小二乘迭代法提供初值的时程曲线包络线法,并针对试验中实采
数据与有效数据的差异性问题,提出了基于时程曲线包络线法和随机抽样一致性算法
(
RANSAC
)的实验有效数据截取实用方法,并进行了实例验证。
(
4
)针对高风速下通过初始激励获得的自由响应数据信号弱、噪声大、衰减快的
特点,以风荷载作为环境激励,通过随机减量技术从风洞试验中模型在高风速下的随
机振动信号中提取了振动系统的自由衰减信号。
(
5
)基于
MATLAB
语言,编制了前文提出的几种方法所对应的计算模块,开发
出一套完整的可视化颤振导数识别程序,并将该程序应用于节段模型风洞试验之中,
提高了颤振导数的识别精度及效率。
关键词:颤振导数,最小二乘法,随机抽样一致性算法,随机减量法,
MATLAB
风洞试验
ii
Abstract
The identification of flutter derivatives is the foundation and hot issues of flutter
research of long span bridges, this paper reviewed the development course of theory of
bridge flutter and flutter derivatives, methods for identification of flutter derivatives of
bridge decks were summarized. Based on the section model of two-dimensional
bending-torsional coupling free vibration of wind tunnel test, the modal parameter
identification method, data pre-processing, data interception, and several other aspects were
studied and discussed in this paper. A set of efficient and accurate method for identification
of flutter derivatives and the matching MATLAB calculation program were given. The main
research contents of this paper are as follows:
(1) On the establishment of relationship between flutter derivatives and the free
vibration modal parameters, three kinds of modal parameter identification method (the ITD
method, the MITD method optimized by this paper and the LSCE method) were introduced.
And a single degree of freedom simulation test were curried out to practically analysis and
compare the characteristics of these methods and their inapplicability of directly applied to
the identification of flutter derivatives.
(2) Based on the review of existing least square iterative method (ULS method and
MLS method), the method of weighted least squares iterative (WLS method) is derived by
introducing a weighted matrix which is consistent with the characteristic of the test data.
The simulation experiment of the two degree of freedom model is carried out, and the WLS
method is proved to have better anti-noise ability and computational efficiency by immunity
testing and initial value sensitivity testing.
(3) Time-history curve envelope method was given to provide the initial values for
least square iterative method. In order to solve the problem that the difference between the
actual collected data in experiment and the effective data, a practical method based on
random sample consensus algorithm (RANSAC) was proposed and verified through an
example.
(4) For the weak signal, large noise, decaying fast characteristic of free response data
iii
that obtained through the initial incentive in high wind speeds, using wind load as ambient
excitation, the random decrement technique was applied in wind tunnel test of section
model, and the free attenuation signal of system was obtained successfully.
(5) Based on MATLAB language, the calculation modules corresponding to several
previously proposed methods were compiled and a complete set of visual program for
identification of flutter derivatives was developed. And this program was used in section
model wind tunnel test to improve the accuracy and efficiency of the identification of flutter
derivatives.
Key words: Flutter derivatives, Least square method, Random sample consensus,
Random decrement technique, MATLAB, Wind tunnel test
iv
目 录
第一章 绪论 .................................................................................................................... 1
1.1 研究背景及意义 ................................................................................................. 1
1.2 桥梁颤振研究概况 ............................................................................................. 1
1.2.1 古典耦合颤振理论 .................................................................................. 2
1.2.2 分离流颤振理论 ...................................................................................... 2
1.3 颤振导数及其识别方法 ..................................................................................... 3
1.3.1 颤振导数的发展 ...................................................................................... 3
1.3.2 颤振导数的识别方法 .............................................................................. 6
1.4 本文的主要研究内容 ....................................................................................... 10
第二章 基于节段模型风洞试验的颤振导数识别 ........................................................ 12
2.1 二维节段模型风洞试验 ................................................................................... 12
2.2 颤振导数与系统模态参数关系的建立 ........................................................... 13
2.3 几种系统模态参数识别方法及比较 ............................................................... 16
2.3.1 最小二乘法 ............................................................................................ 17
2.3.2 Ibrahim 时域(ITD)法 ........................................................................ 18
2.3.3 改进的 ITD(MITD)法 ...................................................................... 19
2.3.4 最小二乘复指数(LSCE)法 .............................................................. 21
2.3.5 单自由度仿真试验 ................................................................................ 23
2.4 基于最小二乘迭代法的颤振导数识别 ........................................................... 25
2.4.1 总体最小二乘迭代(ULS)法 ............................................................ 25
2.4.2 修正最小二乘迭代(MLS)法 ........................................................... 26
2.4.3 加权最小二乘迭代(WLS)法 ........................................................... 27
2.5 颤振导数识别的数值仿真试验 ....................................................................... 33
2.5.1 抗噪性能试验 ........................................................................................ 35
2.5.2 初始值敏感性试验 ................................................................................ 39
2.6 本章小结 ........................................................................................................... 41
第三章 参数初值的确定与试验数据的截取 ................................................................ 42
v
3.1 概述 ................................................................................................................... 42
3.2 非线性模态参数初值的确定 ........................................................................... 42
3.3 试验有效数据的截取 ....................................................................................... 44
3.3.1 有效数据截取原则 ................................................................................ 44
3.3.2 随机抽样一致性(RANSAC)算法 .................................................... 45
3.3.3 有效数据截取的实现方法 .................................................................... 47
3.3.4 实例验证 ................................................................................................ 49
3.4 高风速区间试验数据获取的随机减量(RDT)法 ....................................... 50
3.5 本章小结 ........................................................................................................... 53
第四章 颤振导数识别方法的 MATLAB 实现及应用 .................................................. 54
4.1 MATLAB 开发环境简介 ................................................................................... 54
4.2 MATLAB 程序的编制 ....................................................................................... 56
4.2.1 核心模块的编制 .................................................................................... 56
4.2.2 GUI 界面开发 ......................................................................................... 57
4.3 实例应用 ........................................................................................................... 59
4.3.1 试验概况 ................................................................................................ 60
4.3.2 试验结果 ................................................................................................ 61
4.4 本章小结 ........................................................................................................... 63
结论与展望 ...................................................................................................................... 64
结论 .......................................................................................................................... 64
展望 .......................................................................................................................... 64
参考文献 .......................................................................................................................... 66
致谢 .................................................................................................................................. 70
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