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基于静力测量数据的梁式结构统计模型修正.doc
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基于静力测量数据的梁式结构统计模型修正.doc
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摘 要
随着工程结构变得更加大型,更加复杂,结构的安全性也受到更加广泛的
关注,因此利用有限元模拟技术对实体结构进行各种分析变得十分普遍。在建
模分析过程中,由于建模误差、施工过程中造成的尺寸误差及实际结构在使用
过程中导致的刚度的改变等因素的影响,有限元模型的理论计算结果与结构实
测结果间总存在偏差。因此在实际应用中,需要对有限元模型进行统计修正,
使得修正后有限元模型的理论计算响应值与结构实测响应值能够一致。到目前
为止,已有很多研究有限元模型修正的方法。本文结合其他研究者的工作,利
用静力位移测量数据,对结构的统计模型修正方法进行了研究,并探讨了测量
噪声对计算结果的影响。研究的主要工作包括以下几个方面:
1、对国内外有限元模型修正的方法进行了简单归纳和综述,评价了各种方
法的利弊,得出在概率的范畴内对有限元模型进行统计修正不可避免。同时应
用静力位移进行模型修正时要考虑不同概率分布的测量误差的影响。
2、应用随机有限元方法及静力凝聚法推导了在不考虑测量噪声影响时,基
于静力挠度测量值的统计模型修正方法。利用该方法可以得到结构各单元的修
正系数。数值算例表明,该方法的模型修正结果良好,且经过修正后的理论计
算模型的竖向位移值与结构的实测位移值相一致。
3、考虑到在静力位移的测量过程中,不可避免地存在测量噪声的影响,且
测量噪声的概率分布类型受到多种因素的影响,很难确定其具体的类型。本文
将测量误差的概率分布分为正态分布和非正态分布两种不同情形分别研究。当
测量误差为贝塔分布时,将修正系数按非正交多项式展开,并将位移的测量误
差考虑为多个因素的影响。在数值算例的模拟中,考虑了变异系数的不同对计
算结果的影响。数值算例表明,本文计算方法的结果与蒙特卡洛方法的结果吻
合,表明本文方法的有效性。
关键词:模型修正;静力位移;静力凝聚;修正系数;测量误差;概率分布
Abstract
As engineering structure becomes more large-scale and complex, the safety of
the structure has also drawn more attention, so it becomes very common to use the
finite element simulation technology to conduct various analysis for the real structure.
In the process of modeling analysis, there is always a deviation between the
theoretical calculation results of the finite element model and the measured results
due to the modeling errors, size errors caused by the construction process and the
change of the stiffness in the practical process of use. So it is necessary to conduct
statistical updating for the finite element model in practical applications, so that the
theoretical calculation results of the finite element model after updating are same as
measured results. So far, there have been many methods about finite element model
updating. Combining with the work of other researchers, using the static displacement
measurement data, this paper studied statistical model updating method, and the
effect of measurement noise on the calculation result is discussed. The main work
studied as follows:
1. Has done some work on the simple review and summary to the finite element
model updating method at home and abroad, evaluated the advantages and
disadvantages of various methods, concluding that it is inevitable to conduct
statistical updating for the finite element model in the category of probability. When
conduct model updating using static displacement, measurement errors should be
considered which obey different probability distribution at the same time.
2. By means of stochastic finite element method and the static condensation
method, statistical model updating method based on the static deflection measurement
data was deduced without considering measurement noise. Get the updating
coefficient of each unit by this method. The numerical examples show that the model
updating result of the method is good, and the vertical displacement value of
theoretical calculation model is consistent with the measurement displacement value.
3. Considering that the static displacement measurement process is affected by
measurement noise inevitably, and the type of probability distribution of the
measurement noise is influenced by many factors, so it is difficult to determine its
specific type. The probability distribution of measurement error will be divided into
two different situations of normal distribution and non-normal distribution
respectively in this paper. When measurement error is a β distribution, expand the
updating coefficient according to the orthogonal polynomial, and consider multiple
factors influencing the measurement error of displacement. In the simulation of a
numerical example, consider the effect that the variation of coefficient has on the
results. The numerical examples show that calculation result of the paper is consistent
with the monte-carlo method and proposed method in the paper is effective.
Key words:Model updating;Static displacement;Static condensation;Updating
coefficient;Measurement error;Probability distribution
目录
第一章 绪 论 ........................................................................................1
1.1 有限元模型修正概念.............................................................................1
1.2 国内外研究背景及现状 .........................................................................2
1.3 有限元模型修正的主要方法 ..................................................................5
1.3.1 矩阵型修正法..................................................................................5
1.3.2 参数型修正法..................................................................................5
1.3.3 基于静力测试的模型修正法 .............................................................7
1.3.4 基于静动力结合的模型修正法..........................................................7
1.3.5 基于响应面法的模型修正 ................................................................8
1.3.6 统计的方法 .....................................................................................9
1.4 本文的主要工作..................................................................................10
第二章 基于静力测量数据的梁式结构统计模型修正 .................................11
2.1 绪言...................................................................................................11
2.2 静力凝聚法原理..................................................................................13
2.3 基于静力测试数据的梁式结构统计模型修正方法..................................14
2.3.1 平衡方程......................................................................................14
2.3.2 结构修正系数及其控制方程 ..........................................................14
2.4 数值算例............................................................................................16
2.5 本章小结............................................................................................20
第三章 考虑正态分布测量误差的梁式结构统计模型修正 ..........................21
3.1 绪言...................................................................................................21
3.1.1 测量误差的概念............................................................................21
3.1.2 测量误差的来源及分类 .................................................................21
3.1.3 测量误差的概率分布.....................................................................24
3.2 考虑正态分布测量误差的梁式结构统计模型修正方法...........................24
3.2.1 平衡方程......................................................................................24
3.2.2 结构修正系数及其控制方程 ..........................................................25
3.3 数值算例............................................................................................27
3.4 本章小结............................................................................................32
第四章 考虑非正态分布测量误差的梁式结构统计模型修正 .......................33
4.1 绪言...................................................................................................33
4.2 考虑非正态分布测量误差的梁式结构统计模型修正方法 .......................35
4.2.1 平衡方程......................................................................................35
4.2.2 结构修正系数及其控制方程 ..........................................................36
4.3 数值算例............................................................................................41
4.4 本章小结............................................................................................48
第五章 结论与展望..................................................................................49
5.1 本文研究的主要结论...........................................................................49
5.2 展望...................................................................................................50
参考文献 ....................................................................................................51
攻读硕士学位期间参与研究的课题...............................................................54
致 谢 ......................................................................................................55
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