Minimum Rank Correction Damage Identification Based on Modal Reduction

LI Guoqing; LUO Shuai; ZHANG Li

doi:10.21656/1000-0887.410138

Volume 41 Issue 10

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LI Guoqing, LUO Shuai, ZHANG Li. Minimum Rank Correction Damage Identification Based on Modal Reduction[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1103-1109. doi: 10.21656/1000-0887.410138

Citation:

LI Guoqing, LUO Shuai, ZHANG Li. Minimum Rank Correction Damage Identification Based on Modal Reduction[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1103-1109. doi: 10.21656/1000-0887.410138

Citation:

LI Guoqing, LUO Shuai, ZHANG Li. Minimum Rank Correction Damage Identification Based on Modal Reduction[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1103-1109. doi: 10.21656/1000-0887.410138

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Minimum Rank Correction Damage Identification Based on Modal Reduction

doi: 10.21656/1000-0887.410138

¹School of Civil Engineering, Shaoxing University, Shaoxing, Zhejiang 312000, P.R.China;²Department of Civil Engineering, Gongqing College of Nanchang University, Jiujiang, Jiangxi 332020, P.R.China

Received Date: 2020-05-13
Rev Recd Date: 2020-05-31
Publish Date: 2020-10-01

Abstract

Abstract

To solve the problem that the measured modal parameters and the finite element analysis modal parameters do not match in damage identification, the residual force vector formula and the minimum rank update formula based on the modal reduction method were derived. Through the calculation of the residual force vectors of damaged and undamaged structures, the change rate of the residual force vector was obtained, and the absolute values of the residual force change rate vector elements were defined as the improved residual force vector. With the improved residual force vector, the correct number of modes used in the minimum rank update method was determined, and the minimum rank update formula based on modal reduction was used to calculate the damage extent. The results show that, under noise interference, the presented method could well locate the damage with incomplete modal data. The damage extent identification based on the derived minimum rank update formula is reliable. The method is robust and accurate in structural damage identification for measured incompleteDOF structures.
- minimum rank update method,
- modal reduction,
- residual force vector,
- noise immunity,
- damage identification

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References(17)

References

[1]	何绪飞, 艾剑良, 宋智桃. 多元数据融合在无人机结构健康监测中的应用[J]. 应用数学和力学, 2018,39(4): 395-402.(HE Xufei, AI Jianliang, SONG Zhitao. Multi-source data fusion for health monitoring of unmanned aerial vehicle structures[J]. Applied Mathematics and Mechanics,2018,39(4): 395-402.(in Chinese))
[2]	CUI H Y, DU H Y, ZHAO F Y, et al. Damage identification in a plate structure based on a cross-direction strain measurement method[J].Measurement,2020,158: 107714. DOI: 10.1016/j.measurement.2020.107714.
[3]	HUANG X Y, LIU Z L, ZHANG X Y, et al. Surface damage detection for steel wire ropes using deep learning and computer vision techniques[J]. Measurement,2020,〖STHZ〗 161: 107843. DOI: 10.1016/j.measurement.2020.107843.
[4]	KANKANAMGE Y, HU Y F, SHAO X Y. Application of wavelet transform in structural health monitoring[J]. Earthquake Engineering and Engineering Vibration,2020,19(3): 515-532.
[5]	YU L, CHENG L, YAM L H, et al. Application of eigenvalue perturbation theory for detecting small structural damage using dynamic responses[J]. Composite Structures,2007,78: 402-409.
[6]	YANG Q W. A new damage identification method based on structural flexibility disassembly[J]. Journal of Vibration and Control,2011,17(7): 1000-1008.
[7]	杨秋伟, 刘济科. 基于最小秩修正的结构损伤识别方法[J]. 机械强度, 2007,29(6): 891-893.(YANG Qiuwei, LIU Jike. Structural damage identification based on the minimum rank update method[J]. Journal of Mechanical Strength,2007,29(6): 891-893.(in Chinese))
[8]	蒋舸, 冯晓东. 空间桁架结构残余力最小秩修正法损伤识别[J]. 机械强度, 2019,41(6): 1480-1485.(JIANG Ge, FENG Xiaodong. Residual force minimum rank update method for damage identification of space truss structures[J]. Journal of Mechanical Strength,2019,41(6): 1480-1485.(in Chinese))
[9]	杨秋伟, 刘济科. 结构损伤检测的最小秩修正方法[J]. 振动与冲击, 2008,27(4): 7-9.(YANG Qiuwei, LIU Jike. Structural damage detection with minimum-rank update method[J]. Journal of Vibration and Shock,2008,27(4): 7-9.(in Chinese))
[10]	罗虹, 李军, 曹友强, 等. 有限元模型动力缩聚中主副自由度选取方法[J]. 机械设计, 2010,27(12): 11-14.(LUO Hong, LI Jun, CAO Youqiang, et al. Methods for selecting the master and slave degrees of freedom in dynamic condensation technique of finite element models[J]. Journal of Machine Design,2010,27(12): 11-14.(in Chinese))
[11]	刘伟, 高维成, 孙毅. 自由度匹配技术在网壳结构损伤识别应用中的比较研究[J]. 振动与冲击, 2007,26(2): 107-111, 179-180.(LIU Wei, GAO Weicheng, SUN Yi. Comparative study of model match techniques used in damage detection on reticulated shell[J]. Journal of Vibration and Shock,2007,26(2): 107-111, 179-180.(in Chinese))
[12]	伊廷华, 李宏男, 顾明. 基于模型缩聚的广州新电视塔传感器优化布置研究[J]. 工程力学, 2012,29(3): 55-61.(YI Tinghua, LI Hongnan, GU Ming. Reserach on optimal sensor placement of Guangzhou new TV tower based on model reduction[J]. Engineering Mechanics,2012,29(3): 55-61.(in Chinese))
[13]	杨秋伟, 刘济科. 一种改进的模型缩聚方法[J]. 力学与实践, 2006,28(2): 70-72.(YANG Qiuwei, LIU Jike. An improved method for structural finite element modal reduction[J]. Mechanics and Engineering,2006,28(2): 70-72.(in Chinese))
[14]	孙增寿, 王冉. 基于残余力向量的桁架梁损伤识别研究[J]. 力学与实践, 2016,38(5): 526-530.(SUN Zengshou, WANG Ran. Damage recognition of truss structure based on residual force vector[J]. Mechanics and Engineering,2016,38(5): 526-530.(in Chinese))
[15]	孟凡豪, 于靖军, 马文硕. 基于动态测量柔度矩阵的弦索桥吊索损伤检测[J]. 振动与冲击, 2019,38(14): 267-275.(MENG Fanhao, YU Jingjun, MA Wenshuo. Damage detection of suspension bridge sling based on dynamic measurement flexibility matrix[J]. Journal of Vibration and Shock,2019,38(14): 267-275.(in Chinese))
[16]	刘春城, 侯尚雨, 侯立群. 基于多尺度模型的输电塔裂纹损伤识别及抗噪性能分析[J]. 水电能源科学, 2016,34(2): 177-181, 216.(LIU Chuncheng, HOU Shangyu, HOU Liqun. Transmission tower crack damage identification and analysis of anti-noise performance based on multi-scale model[J]. International Journal Hydroelectric Energy,2016,34(2): 177-181, 216.(in Chinese))
[17]	黄立新, 岳世燕, 胡中明, 等. 功能梯度经典梁损伤识别模态应变能变化率法的抗噪音性能研究[J]. 玻璃钢/复合材料, 2016(2): 35-39.(HUANG Lixin, YUE Shiyan, HU Zhongming, et al. A study of anti-noise properties of modal strain energy change ratio method for the damage identification of functionally graded classical beam[J]. Fiber Reinforced Plastics/Composites,2016(2): 35-39.(in Chinese))