基于应变模态的模态应变能损伤识别方法
|
摘要
传统模态应变能计算需要完备模态振型信息,而模态振型信息中存在转角自由度难以准确获取的问题,为解决该问题,开展基于应变模态的模态应变能损伤识别研究,实现了结构损伤的定量识别。首先,通过基于应变与位移之间的联系,推导出应变模态与位移模态之间的转换矩阵;其次,利用应变模态代替位移模态计算单元模态应变能,建立基于灵敏度分析的损伤识别方程组;最后,根据奇异值截断法求解该方程组识别结构损伤。以一两端固支梁结构为对象,开展数值仿真和实验研究。结果表明,该方法可以有效识别出结构的损伤位置和损伤程度,相对于基于振型扩充的模态应变能损伤识别方法,具有更好精度和抗噪性能。
The traditional modal strain energy calculation needs complete modal shape information.However,it is difficult to accurately obtain the freedom of rotation from the mode shape information.In order to solve the problem,modal strain energy damage identification based on strain mode is studied,and the quantitative identification of structural damage is presented.Based on the relationship between strain and displacement,the transformation matrix between displacement mode and strain mode is obtained;the damage identification equations are derived based on the sensitivity analysis,through the substitution of the displacement modes with strain modes.The structural damage is finally identified via solving the equations using a singular value truncation method.Taking a beam structure with two fixed end as an object,the numerical simulation and experimental investigation are conducted.The results show that both the damage location and severity can be effectively identified from the new proposed method in this paper.Compared with the damage identification method based on modal strain energy and modal expansion,this proposed method has better accuracy and performance under noisy data.The research achievement has a potential value on the structural damage identification of engineering structures.
The traditional modal strain energy calculation needs complete modal shape information.However,it is difficult to accurately obtain the freedom of rotation from the mode shape information.In order to solve the problem,modal strain energy damage identification based on strain mode is studied,and the quantitative identification of structural damage is presented.Based on the relationship between strain and displacement,the transformation matrix between displacement mode and strain mode is obtained;the damage identification equations are derived based on the sensitivity analysis,through the substitution of the displacement modes with strain modes.The structural damage is finally identified via solving the equations using a singular value truncation method.Taking a beam structure with two fixed end as an object,the numerical simulation and experimental investigation are conducted.The results show that both the damage location and severity can be effectively identified from the new proposed method in this paper.Compared with the damage identification method based on modal strain energy and modal expansion,this proposed method has better accuracy and performance under noisy data.The research achievement has a potential value on the structural damage identification of engineering structures.
引文
[1]朱劲松,孙雅丹.基于小波包能量的桥梁损伤识别指标[J].振动、测试与诊断,2015,35(4):715-721.Zhu Jinsong,Sun Yadan.Wavelet packet energy based damage detection index for bridge[J].Journal of Vibration,Measurement&Diagnosis,2015,35(4):715-721.(in Chinese)
[2]Shadan F,Khoshnoudian F,Esfandiari A.A frequency response-based structural damage identification using model updating method[J].Structural Control and Health Monitoring,2016,23(2):286-302.
[3]Liu Fushun,Li Huajun,Li Wei,et al.Experimental study of improved modal strain energy method for damage localisation in jacket-type offshore wind turbines[J].Renewable Energy,2014,72:174-181.
[4]Shi Zhiyu,Law S S,Zhang Lingmi.Structural damage localization from modal strain energy change[J].Journal of Sound and Vibration,1998,218(5):825-844.
[5]Law S S,Shi Zhiyu,Zhang Lingmi.Structural damage detection from incomplete and noisy modal test data[J].Journal of Engineering Mechanics,1998,124(11):1280-1288.
[6]Hu J S L,Wang Shuqing,Li Huajun.Cross-modal strain energy method for estimating damage severity[J].Journal of Engineering Mechanics,2006,132(4):429-437.
[7]Xu Zhaodong,Wu Keyi.Damage detection for space truss structures based on strain mode under ambient excitation[J].Journal of Engineering Mechanics,2012,138(10):1215-1223.
[8]Wu Shaoqing,Zhou Jixiang,Rui Shen,et al.Reformulation of elemental modal strain energy method based on strain modes for structural damage detection[J].Advances in Structural Engineering,2016,1:10.
[9]Yan Wangji,Huang Tianli,Ren Weixin.Damage detection method based on element modal strain energy sensitivity[J].Advances in Structural Engineering,2010,13(6):1075-1088.
[10]Yam L Y,Leung T P,Li D B,et al.Theoretical and experimental study of modal strain analysis[J].Journal of Sound and Vibration,1996,191(2):251-260.
[11]Ren Weixin.A singular value decomposition based truncation algorithm in solving the structural damage equations[J].Acta Mechanica Solida Sinica,2005,18(2):181-188.
[12]Guo Yanlin,Kareem A.System identification through non stationary response:wavelet and transformed singular value decomposition-based approach[J].Journal of Engineering Mechanics,2015,141(7):04015013.
[13]Kim D,Sra S,Dhillon I S.A non-monotonic method for large-scale non-negative least squares[J].Optimization Methods and Software,2013,28(5):1012-1039.
[14]Tondreau G,Deraemaeker A.Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method[J].Journal of Sound and Vibration,2014,333(18):4376-4401.
[15]Reynders E,Maes K,Lombaert G,et al.Uncertainty quantification in operational modal analysis with stochastic subspace identification:validation and applications[J].Mechanical Systems and Signal Processing,2016,66:13-30.
[2]Shadan F,Khoshnoudian F,Esfandiari A.A frequency response-based structural damage identification using model updating method[J].Structural Control and Health Monitoring,2016,23(2):286-302.
[3]Liu Fushun,Li Huajun,Li Wei,et al.Experimental study of improved modal strain energy method for damage localisation in jacket-type offshore wind turbines[J].Renewable Energy,2014,72:174-181.
[4]Shi Zhiyu,Law S S,Zhang Lingmi.Structural damage localization from modal strain energy change[J].Journal of Sound and Vibration,1998,218(5):825-844.
[5]Law S S,Shi Zhiyu,Zhang Lingmi.Structural damage detection from incomplete and noisy modal test data[J].Journal of Engineering Mechanics,1998,124(11):1280-1288.
[6]Hu J S L,Wang Shuqing,Li Huajun.Cross-modal strain energy method for estimating damage severity[J].Journal of Engineering Mechanics,2006,132(4):429-437.
[7]Xu Zhaodong,Wu Keyi.Damage detection for space truss structures based on strain mode under ambient excitation[J].Journal of Engineering Mechanics,2012,138(10):1215-1223.
[8]Wu Shaoqing,Zhou Jixiang,Rui Shen,et al.Reformulation of elemental modal strain energy method based on strain modes for structural damage detection[J].Advances in Structural Engineering,2016,1:10.
[9]Yan Wangji,Huang Tianli,Ren Weixin.Damage detection method based on element modal strain energy sensitivity[J].Advances in Structural Engineering,2010,13(6):1075-1088.
[10]Yam L Y,Leung T P,Li D B,et al.Theoretical and experimental study of modal strain analysis[J].Journal of Sound and Vibration,1996,191(2):251-260.
[11]Ren Weixin.A singular value decomposition based truncation algorithm in solving the structural damage equations[J].Acta Mechanica Solida Sinica,2005,18(2):181-188.
[12]Guo Yanlin,Kareem A.System identification through non stationary response:wavelet and transformed singular value decomposition-based approach[J].Journal of Engineering Mechanics,2015,141(7):04015013.
[13]Kim D,Sra S,Dhillon I S.A non-monotonic method for large-scale non-negative least squares[J].Optimization Methods and Software,2013,28(5):1012-1039.
[14]Tondreau G,Deraemaeker A.Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method[J].Journal of Sound and Vibration,2014,333(18):4376-4401.
[15]Reynders E,Maes K,Lombaert G,et al.Uncertainty quantification in operational modal analysis with stochastic subspace identification:validation and applications[J].Mechanical Systems and Signal Processing,2016,66:13-30.