基于随机子空间方法的结构模态分析及损伤识别
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摘要
在结构健康监测中,选取合适的结构模态参数构造损伤指标是损伤识别成功的关键。目前,基于位移模态的损伤识别方法已广泛应用于航空航天、机械及土木工程等领域。而较早以前就有研究者发现,应变模态对结构损伤比位移模态更敏感,更适合用来构造损伤指标。本文采用随机子空间方法进行位移模态和应变模态识别,分别用其构造损伤指标进行损伤识别,并对它们的损伤识别效果进行对比。
首先介绍了峰值法、频域分解法和随机子空间法等模态参数识别方法。通过仿真算例,验证了随机子空间方法不但能准确识别系统的频率,而且能很好地识别系统的模态振型和阻尼。
考察了测量噪音对位移模态参数识别的影响,基于随机子空间识别法的位移模态识别抗噪性较好。由损伤前后位移模态振型变化无法直接识别出结构是否有损伤。采用位移模态构建的模态柔度曲率差(MFC)指标可以识别出损伤部位,但是受噪声干扰严重。
考虑到应变模态比位移模态对损伤更敏感,利用应变信号建立基于应变的随机子空间状态模型进行了应变模态参数识别,并采用应变模态构建的MFC指标进行损伤识别。基于线单元的有限元模型仿真算例结果表明,位移模态与应变模态的固有频率相等;根据应变模态损伤前后振型曲线的突变可以大致定位损伤,而位移模态不行;用应变模态构建的MFC指标抗噪性好,但应变测点位置不位于损伤部位时,就无法识别出损伤位置。位移模态对测点的布置虽然没有像应变模态那样的要求,但抗噪性很差。
作为对比分析,建立了实体有限元模型进行应变模态损伤识别。结果表明,当采用刚度折减来模拟损伤时,只有当应变测点布置在损伤部位时才能识别出损伤;当采用切缝来模拟损伤时,应变测点离损伤部位有一定距离也能识别出损伤,距离越近,识别越准确,抵抗噪声的能力越强;切缝宽度的变化对识别结果基本没有影响;采用切缝模拟构件底部的损伤时,应变测点布置在构件顶部也可以识别损伤,但相对应变测点布置在底部的情况,识别效果受噪声的影响更大。
In structural health monitoring, selecting the appropriate structural modal parameters as damage indexes for damage identification is the key to success. At present, the damage identification method based on the displacement modal has been widely used in aerospace, mechanical, civil engineering and so on. The earlier researchers found that the strain modal is more sensitive than the displacement modal in damage identification, and is more suitable to construct the damage indexes This thesis used stochastic subspace identification method to identify the strain modal and the displacement modal, which were constructed as damage indexes to detect the structural damage, and to compare their results.
Firstly, this thesis introduced pick-peaking method (PP), frequency domain decomposition method (FDD) and stochastic subspace identification method (SSI), such as modal parameter identification method. Through simulation, to verify the SSI method can not only accurately identify the system frequency, but also identify mode shapes and modal damping.
Investigated the impact of measurement noise on the displacement modal parameters identification, which based on the SSI method is better anti-noise. The changes of displacement mode shapes in before and after structural damage can not be directly judged whether there is any damage. Using the modal flexibility curvature (MFC) based on the displacement modal can be located damage position, but seriously affected by noise.
It is considered that the strain modal is more sensitive to structural damage than the displacement modal, this thesis use strain signal to build up stochastic subspace model, to identify the strain modal parameters, and to detect the structural damage by MFC index. Based on linear finite element model, the simulation results show that, the displacement modal frequency is equal to the strain modal. In according to the mutation of the strain mode shapes curve, in before and after injury, can be more or less located the damage position, but not the displacement modal. Using the MFC index of the strain modal is good noise immunity, but can not identify the location of the damage position when the strain measuring points are not at the damage position. The arrangement of displacement measurement points in the displacement modal does not like that kind of request in the strain modal, but very poor noise immunity.
As comparative analysis, this thesis establishes a solid finite element model for damage detection by the strain modal. The results showed that, when using elastic modulus reduction to simulate the structural damage, it can be identified only in the case that the strain measuring points are just in the injury site. When using cut injury to simulate the damage, the structural damage can also be identified when the strain measuring points from the injury site have a certain distance, and the more close distance, the more accurate identification and the stronger noise immunity. The changes of kerf width did not affect the results. When use the kerf to simulate the bottom of the injury, the strain measuring points at the top of beam can be also identifying the damage. But it is, compared with the situation of the strain measuring points at the bottom of beam, greater impact by noise.
首先介绍了峰值法、频域分解法和随机子空间法等模态参数识别方法。通过仿真算例,验证了随机子空间方法不但能准确识别系统的频率,而且能很好地识别系统的模态振型和阻尼。
考察了测量噪音对位移模态参数识别的影响,基于随机子空间识别法的位移模态识别抗噪性较好。由损伤前后位移模态振型变化无法直接识别出结构是否有损伤。采用位移模态构建的模态柔度曲率差(MFC)指标可以识别出损伤部位,但是受噪声干扰严重。
考虑到应变模态比位移模态对损伤更敏感,利用应变信号建立基于应变的随机子空间状态模型进行了应变模态参数识别,并采用应变模态构建的MFC指标进行损伤识别。基于线单元的有限元模型仿真算例结果表明,位移模态与应变模态的固有频率相等;根据应变模态损伤前后振型曲线的突变可以大致定位损伤,而位移模态不行;用应变模态构建的MFC指标抗噪性好,但应变测点位置不位于损伤部位时,就无法识别出损伤位置。位移模态对测点的布置虽然没有像应变模态那样的要求,但抗噪性很差。
作为对比分析,建立了实体有限元模型进行应变模态损伤识别。结果表明,当采用刚度折减来模拟损伤时,只有当应变测点布置在损伤部位时才能识别出损伤;当采用切缝来模拟损伤时,应变测点离损伤部位有一定距离也能识别出损伤,距离越近,识别越准确,抵抗噪声的能力越强;切缝宽度的变化对识别结果基本没有影响;采用切缝模拟构件底部的损伤时,应变测点布置在构件顶部也可以识别损伤,但相对应变测点布置在底部的情况,识别效果受噪声的影响更大。
In structural health monitoring, selecting the appropriate structural modal parameters as damage indexes for damage identification is the key to success. At present, the damage identification method based on the displacement modal has been widely used in aerospace, mechanical, civil engineering and so on. The earlier researchers found that the strain modal is more sensitive than the displacement modal in damage identification, and is more suitable to construct the damage indexes This thesis used stochastic subspace identification method to identify the strain modal and the displacement modal, which were constructed as damage indexes to detect the structural damage, and to compare their results.
Firstly, this thesis introduced pick-peaking method (PP), frequency domain decomposition method (FDD) and stochastic subspace identification method (SSI), such as modal parameter identification method. Through simulation, to verify the SSI method can not only accurately identify the system frequency, but also identify mode shapes and modal damping.
Investigated the impact of measurement noise on the displacement modal parameters identification, which based on the SSI method is better anti-noise. The changes of displacement mode shapes in before and after structural damage can not be directly judged whether there is any damage. Using the modal flexibility curvature (MFC) based on the displacement modal can be located damage position, but seriously affected by noise.
It is considered that the strain modal is more sensitive to structural damage than the displacement modal, this thesis use strain signal to build up stochastic subspace model, to identify the strain modal parameters, and to detect the structural damage by MFC index. Based on linear finite element model, the simulation results show that, the displacement modal frequency is equal to the strain modal. In according to the mutation of the strain mode shapes curve, in before and after injury, can be more or less located the damage position, but not the displacement modal. Using the MFC index of the strain modal is good noise immunity, but can not identify the location of the damage position when the strain measuring points are not at the damage position. The arrangement of displacement measurement points in the displacement modal does not like that kind of request in the strain modal, but very poor noise immunity.
As comparative analysis, this thesis establishes a solid finite element model for damage detection by the strain modal. The results showed that, when using elastic modulus reduction to simulate the structural damage, it can be identified only in the case that the strain measuring points are just in the injury site. When using cut injury to simulate the damage, the structural damage can also be identified when the strain measuring points from the injury site have a certain distance, and the more close distance, the more accurate identification and the stronger noise immunity. The changes of kerf width did not affect the results. When use the kerf to simulate the bottom of the injury, the strain measuring points at the top of beam can be also identifying the damage. But it is, compared with the situation of the strain measuring points at the bottom of beam, greater impact by noise.
引文
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[2] Wang M. L.and Pran K. L. A systematic Numerical Analysis of the Damage Index MethodUsed for Bridge Diagnostics[J]. Smart Systems for Bridge Structures and Highways, Proceedings of SPIE, Newport Beach, CA, 2000, Vol.3988:154-164.
[3] Pandey A K & Biswas M. Damage Detection in Structures Using Changes in Flexibility[J]. Journal of Sound and Vibration, 1994, 169:3-17.
[4]韩大建,王文东.基于振动的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, vol.31, No.1.
[5]唐小兵.结构损伤识别及数值模拟[D].湖北:武汉理工大学, 2004.
[6]沃德.海伦,斯蒂芬.拉门兹,波尔.萨斯著,白化同,郭继重译,屠良尧校,模态分析理论和试验[M]北京理工大学出版社. 2001.
[7] Ewins D.J. Modal Testing: Theory and Practice[M]. Chichester, England John Wiley&Sons,1984.
[8]曹树谦,张文德,萧龙翔.振动结构模态分析-理论、试验与应用[M].天津:天津大学出版社; 2000.
[9] Heylen W., Lammens S., and Sas P. Modal Analysis Theory and Testing[M]. Prenrice-Ha11, Englewood Cliffs, NJ, 1999.
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