A local damage identification approach based on improved cross-model cross-mode method
Since the core matrix in the traditional Cross-Model Cross-Mode(CMCM) method is rank-deficient, constraints must be applied artificially for getting a unique solution in a complete model-updating situation. In previous damage identification researches based on the CMCM method, structural masses are often supposed to be unchanged for getting the updated coefficients of stiffness, and the reduction of stiffness is regarded as an indicator of damage. However, element mass changes under operational conditions are obviously a kind of damage. For detecting damage more effectively, we improved the traditional CMCM method, and proposed an improved method as follows. First, evaluate the core matrix from the finite element model under the baseline condition and the measured modal data after damage, take the right singular vector corresponding to the least singular value of the core matrix as a Damage Indication Vector(DIV); secondly, identify the abnormal elements in the DIV by cluster analysis algorithm based on the assumption that damage appears locally, locate damage based on these abnormal elements; finally, derive the extent of damage for each elemental mass and stiffness from the DIV. The advantage of the improved method is its ability to solve the mass and stiffness changes before and after damage for all elements without artificial constraints, thus the error of damage identification caused by imprecise or wrong constraints vanishes. We studied the improved method’s practicability, robustness, and sensitivity to damage by a numerical simulation, and further verified its effectiveness by a 4 degrees of freedom test-bed structure experiment done at the Los Alamos National Laboratory.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian,116024,China
Abstract：Since the core matrix in the traditional Cross-Model Cross-Mode(CMCM) method is rank-deficient, constraints must be applied artificially for getting a unique solution in a complete model-updating situation. In previous damage identification researches based on the CMCM method, structural masses are often supposed to be unchanged for getting the updated coefficients of stiffness, and the reduction of stiffness is regarded as an indicator of damage. However, element mass changes under operational conditions are obviously a kind of damage. For detecting damage more effectively, we improved the traditional CMCM method, and proposed an improved method as follows. First, evaluate the core matrix from the finite element model under the baseline condition and the measured modal data after damage, take the right singular vector corresponding to the least singular value of the core matrix as a Damage Indication Vector(DIV); secondly, identify the abnormal elements in the DIV by cluster analysis algorithm based on the assumption that damage appears locally, locate damage based on these abnormal elements; finally, derive the extent of damage for each elemental mass and stiffness from the DIV. The advantage of the improved method is its ability to solve the mass and stiffness changes before and after damage for all elements without artificial constraints, thus the error of damage identification caused by imprecise or wrong constraints vanishes. We studied the improved method’s practicability, robustness, and sensitivity to damage by a numerical simulation, and further verified its effectiveness by a 4 degrees of freedom test-bed structure experiment done at the Los Alamos National Laboratory.
占超， 李东升， 任亮， 李宏男. 基于改进交叉模型交叉模态法的局部损伤识别方法[J]. 振动与冲击, 2015, 34(7): 127-133.
ZHAN Chao, LI Dong-sheng, REN Liang, LI Hong-nan. A local damage identification approach based on improved cross-model cross-mode method. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(7): 127-133.
[1] 李宏男，李东升. 土木工程结构安全性评估、健康监测及诊断述评 [J]. 地震工程与工程振动，2002，22 (3): 82-90.
LI Hong-nan, LI Dong-sheng. Safety assessment, health monitoring and damage diagnosis for structures in civil engineering[J]. Earthquake Engineering and Engineering Vibration, 2002,22(3):82-90.
[2] 宗周红, 任伟新, 阮毅. 土木工程结构损伤诊断研究进展 [J]. 土木工程学报, 2003, 36(5): 105-10.
ZONG Zhou-hong, REN Wei-xin, RUAN Yi. Recent advances in research on damage diagnosis for civil engineering structures[J]. China Civil Engineering Journal, 2003, 36(5):105-10
[3] Mottershead J E, Friswell M I. Model Updating In Structural Dynamics: A Survey [J]. Journal of Sound and Vibration, 1993, 167 (2): 347-75.
[4] 李辉, 丁桦. 结构动力模型修正方法研究进展 [J]. 力学进展, 2005,35(02): 170-80.
LI Hui, DING Hua. Progress in model updating for structural dynamics[J]. Advances in Mechanics, 2005, 35(2): 170-80.
[5] Friswell Michael, Mottershead John E. Finite element model updating in structural dynamics [M]. Springer, 1995.
[6] Doebling Scott W. Minimum-rank optimal update of elemental stiffness parameters for structural damage identification [J]. AIAA journal, 1996, 34 (12): 2615-21.
[7] Kaouk M, Zimmerman D C, Simmermacher T W. Assessment of Damage Affecting All Structural Properties Using Experimental Modal Parameters [J]. Journal of Vibration and Acoustics, 2000, 122 (4): 456-63.
[8] 侯吉林. 约束子结构模型修正方法 [D]; 哈尔滨工业大学, 2010.
HOU Ji-Lin. Model Updating Based on Substructure Isolation Methods[D], Ph D. Thesis, Harbin Institute of Technology, 2010.
[9] HU S-L J, LI H, WANG S. Cross-model cross-mode method for model updating [J]. Mechanical Systems and Signal Processing, 2007, 21 (4): 1690-703.
[10] 贾辉，李东升. 基于交叉模型交叉模态法的损伤识别研究 [J]. 土木工程与管理学报，2011，28 (3): 133-37.
JIA Hui, LI Dong-sheng. Damage Identification Inversitigation Based on Cross-model Cross-mode Method[J]. Journal of Civil Engineering and Management, 2011, 28(3): 133-37
[11] 王俊荣. 海洋平台结构物损伤检测与模型修正方法研究 [D]; 中国海洋大学, 2009.
WANG Jun-long. Study on damage detection an model updating for offshore platform structure[D], Ph.D. Thesis, Ocean University of China, 2009.
[12] 王俊荣, 张敏, 李华军. 一种基于不完备模态信息的有限元模型修正方法 [J]. 工程力学, 2010, 27 (8): 60-65.
WANG Jun-long, ZHANG Min, LI Hua-jun. A finite element model updating approach based on incomplete modal data[J]. Engineering Mechanics, 2010, 27(8): 60-65
[13] HE Zengyou, XU Xiaofei, DENG Shengchun. Discovering cluster-based local outliers [J]. Pattern Recognition Letters, 2003, 24 (9–10): 1641-50.
[14] Elói Figueiredo, Eric Flynn. Three-story building structure to detect nonlinear effects.
http://institute.lanl.gov/ei/damage_id/data/4DOF_Mat_Format.zip. 2009.
[15] Elói Figueiredo, Gyuhae Park, Joaquim Figueiras, et al. Structural health monitoring algorithm comparisons using standard data sets[R]. LA-14393, Los Alamos, NM (United States): Los Alamos National Laboratory, 2009.
[16] Elói Figueiredo, Todd M.D., Farrar C.R., et al. Autoregressive modeling with state-space embedding vectors for damage detection under operational variability [J]. International Journal of Engineering Science, 2010, 48 (10): 822-34.
[17] Hernandez-Garcia, Miguel R, Masri, et al. An experimental investigation of change detection in uncertain chain-like systems [J]. Journal of Sound and Vibration, 2010, 329 (12): 2395-409.
[18] JUANG J-N. Applied system identification[M]. New Jersey: PTR Prentice Hall Englewood Cliffs Inc, 1994. 175-228.
[19] 沃德•海伦，斯蒂芬•拉门兹，波尔•萨斯. 模态分析理论与实验 [M]. 白化同，郭继忠译. 北京市海淀区：北京理工大学出版社，2001.
