基于改进交叉模型交叉模态法的局部损伤识别方法

PDF(1623 KB)

振动与冲击 ›› 2015, Vol. 34 ›› Issue (7) : 127-133.

论文

传统的交叉模型交叉模态（CMCM）法由于其核心矩阵的缺秩使其在全局修正时的解不唯一，为得到唯一解必须人为假定约束。以往利用CMCM法进行损伤识别的研究中，通常将损伤前后质量保持不变作为约束求得各单元刚度的修正量，然后将刚度的下降作为判断损伤的依据。然而，结构在极端运营条件下质量的变化也是损伤的一种。为此，本文对传统的CMCM法进行了改进，提出了以下的改进方法：首先，由基准状态下的有限元模型和损伤后实测的结构低阶模态信息求得核心矩阵，将核心矩阵最小奇异值对应的右奇异向量作为损伤指示向量（DIV）；然后，基于损伤的局部性利用聚类分析算法自动识别DIV中的异常元素，将异常元素作为损伤定位的依据；最后，由DIV估计各单元质量和刚度的损伤程度。改进后方法的优势在于：无需人为主观地添加约束即可一次性求出结构各单元质量和刚度损伤前后的变化，避免了错误或不准确的假设给损伤识别结果带来的误差。通过数值实验对该改进方法的可行性、鲁棒性以及损伤敏感性进行了研究，并通过美国洛斯阿拉莫斯国家实验室（LANL）的一个4自由度板柱结构振动台实验对改进方法的有效性做了进一步的验证。#br# 关键词：损伤识别；全局修正；交叉模型交叉模态法；结构健康监测

作者信息 +

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.

Author information +

文章历史 +

摘要

传统的交叉模型交叉模态（CMCM）法由于其核心矩阵的缺秩使其在全局修正时的解不唯一，为得到唯一解必须人为假定约束。以往利用CMCM法进行损伤识别的研究中，通常将损伤前后质量保持不变作为约束求得各单元刚度的修正量，然后将刚度的下降作为判断损伤的依据。然而，结构在极端运营条件下质量的变化也是损伤的一种。为此，本文对传统的CMCM法进行了改进，提出了以下的改进方法：首先，由基准状态下的有限元模型和损伤后实测的结构低阶模态信息求得核心矩阵，将核心矩阵最小奇异值对应的右奇异向量作为损伤指示向量（DIV）；然后，基于损伤的局部性利用聚类分析算法自动识别DIV中的异常元素，将异常元素作为损伤定位的依据；最后，由DIV估计各单元质量和刚度的损伤程度。改进后方法的优势在于：无需人为主观地添加约束即可一次性求出结构各单元质量和刚度损伤前后的变化，避免了错误或不准确的假设给损伤识别结果带来的误差。通过数值实验对该改进方法的可行性、鲁棒性以及损伤敏感性进行了研究，并通过美国洛斯阿拉莫斯国家实验室（LANL）的一个4自由度板柱结构振动台实验对改进方法的有效性做了进一步的验证。

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.

导出引用

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[J]. Journal of Vibration and Shock, 2015, 34(7): 127-133

参考文献

[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.