基于单元模态应变能灵敏度的结构损伤识别研究
发布时间:2018-02-28 23:06
本文关键词: 模态应变能 灵敏度 结构损伤识别 贝叶斯统计 有限元 出处:《重庆大学》2014年硕士论文 论文类型:学位论文
【摘要】:近几十年来,由于结构损伤没有及时被发现及处理而带来人员伤亡、经济损失的事件屡见不鲜。为了确保工程结构和生命的安全,减少经济损失、避免更大的灾难,对现有结构进行损伤检测已经刻不容缓,良好的结构损伤识别方法能够提供有效的结构损伤信息,使人们可以对结构进行及时的修复,以便降低结构损伤积累的程度,保证工程结构的正常运行。因此,基于结构损伤检测的重要性,本文首先对当前结构损伤识别方法的基本现状进行了综述,其中重点阐述了基于单元模态应变能的损伤识别方法及基于贝叶斯统计的概率损伤识别方法的研究发展现状,然后提出了本文研究的主要内容和具体思路。 本文在结构动力分析有限元方法、模态应变能和一阶泰勒展开等理论基础上,假定结构损伤表现为单元刚度的降低,,推导出结构单元模态应变能对单元刚度损伤指标的灵敏度的表达式,再运用结构动力特征方程,提出了基于单元模态应变能灵敏度的结构损伤识别方法,并推导出了结构单元损伤方程组,然后又采用解单元损伤病态方程组的四种不同的解法求解单元损伤方程组,使得该损伤识别方法可以同时对结构的损伤位置与损伤程度进行识别。接着本文考虑模态测量的不确定性,阐述了基于贝叶斯统计的损伤定位原理和损伤定量原理,从概率统计层面上推导出了单元损伤概率表达式,提出两种基于单元模态应变能灵敏度的贝叶斯统计损伤识别方法:基于贝叶斯统计定量原理的同时定位与定量的损伤识别方法及改进后的基于贝叶斯统计的先定位后定量的两阶段损伤识别方法。通过以贝叶斯理论为基础的两种方法不仅可以对结构进行定位与定量的损伤识别,而且能计算有限单元损伤存在的概率,这样便可以达到更确切描述结构损伤的目的。 最后用本文所涉及的理论和方法自主编写了基于单元模态应变能灵敏度损伤识别方法及其贝叶斯统计改进前后的损伤识别法的Matlab程序,并对一个简支梁数值算例和一个连续梁数值算例进行各损伤工况下的损伤识别模拟,探讨了单元损伤程度、测量噪声水平等对以上各种损伤识别方法识别结果的影响。识别结果表明,基于单元模态应变能灵敏度损伤识别方法对单元损伤可以准确定位,也可以得到较精确的损伤定量,且具有一定的抗噪能力;而基于单元模态应变能灵敏度的贝叶斯统计的两种损伤识别方法利用一阶模态信息及较少的模态测量次数均可得出良好的单元刚度损伤指标统计识别结果及单元损伤存在概率。 文章最后针对本文研究内容的不足,提出了有待后人进一步研究的相关问题。
[Abstract]:In recent decades, economic losses are common because structural damage has not been detected and dealt with in time. In order to ensure the safety of engineering structures and lives, to reduce economic losses, and to avoid even greater disasters, It is urgent to detect the damage of existing structures. A good method of structural damage identification can provide effective structural damage information and people can repair the structures in time in order to reduce the degree of structural damage accumulation. Therefore, based on the importance of structural damage detection, this paper first summarizes the current basic status of structural damage identification methods. The research and development of damage identification method based on element modal strain energy and probabilistic damage identification method based on Bayesian statistics are described in detail, and the main contents and specific ideas of this paper are put forward. Based on the theory of finite element method, modal strain energy and first order Taylor expansion, the structural damage is assumed to be the reduction of element stiffness. The expression of the sensitivity of structural element modal strain energy to element stiffness damage index is derived, and the structural damage identification method based on element modal strain energy sensitivity is proposed by using the structural dynamic characteristic equation. The damage equations of structural elements are derived, and the damage equations are solved by four different solutions. The damage identification method can identify the damage location and damage degree simultaneously. Secondly, considering the uncertainty of modal measurement, the damage location principle and damage quantitative principle based on Bayesian statistics are described. From the level of probability and statistics, the probabilistic expression of cell damage is derived. Two methods of Bayesian statistical damage identification based on strain energy sensitivity of element mode are proposed: the damage identification method based on Bayesian statistical quantitative principle and the improved method based on Bayesian statistics. The two methods based on Bayesian theory can not only locate and quantitatively identify the damage of structures. Furthermore, the probability of finite element damage can be calculated, so that the structure damage can be described more accurately. Finally, the Matlab program of damage identification method based on the strain energy sensitivity of element mode and the damage identification method before and after Bayesian statistical improvement is programmed by using the theory and method mentioned in this paper. At the same time, a simple supported beam numerical example and a continuous beam numerical example are simulated under various damage conditions, and the damage degree of the element is discussed. The results show that the damage identification method based on the strain energy sensitivity of element mode can locate the damage accurately and obtain more accurate damage quantification. And has certain anti-noise ability; Two damage identification methods based on Bayesian statistics of element modal strain energy sensitivity can obtain good statistical identification results of element stiffness damage index and damage probability using first-order modal information and less number of modal measurements. Finally, aiming at the deficiency of the research content, the paper puts forward the related problems to be further studied by future generations.
【学位授予单位】:重庆大学
【学位级别】:硕士
【学位授予年份】:2014
【分类号】:TU317
【参考文献】
相关期刊论文 前9条
1 史治宇,吕令毅;由模态应变能法诊断结构破损的实验研究[J];东南大学学报;1999年02期
2 唐天国,刘浩吾,陈春华,刘晓森;梁裂缝损伤检测的模态应变能法及试验研究[J];工程力学;2005年S1期
3 韩大建,王文东;基于振动的结构损伤识别方法的近期研究进展[J];华南理工大学学报(自然科学版);2003年01期
4 廖锦翔,袁明武;结构裂缝群的小波方法识别和数值模拟[J];华南理工大学学报(自然科学版);2005年02期
5 袁明,贺国京;基于模态应变能的结构损伤检测方法研究[J];铁道学报;2002年02期
6 李弋;唐天国;刘浩吾;;基于模态应变能法的钢筋混凝土梁裂缝损伤检测试验[J];应用基础与工程科学学报;2010年01期
7 郭国会,易伟建;基于模态参数进行连续梁损伤诊断的数值研究[J];振动与冲击;2001年01期
8 刘晖,瞿伟廉,袁润章;基于模态应变能耗散率理论的结构损伤识别方法[J];振动与冲击;2004年02期
9 郭健,孙炳楠;基于小波变换的桥梁健康监测多尺度分析[J];浙江大学学报(工学版);2005年01期
本文编号:1549345
本文链接:https://www.wllwen.com/guanlilunwen/chengjian/1549345.html