Damage localization of space trusses based on indicators expressed by cross-model modal strain energy
Xiao-shun WU1(),Ju-wei XIA2,Yue-fang HU1
1. Nanchang Campus, Jiangxi University of Science and Technology, Nanchang 330013, China 2. Zhejiang Wuzhou Project Management Co. Ltd, Hangzhou 310053, China
A new indicator expressed by modal strain energy was proposed to locate the damages of space trusses with large identification dimensions. The proposed indicator not only modified the expression, but also introduced the concept of cross-model modal strain energy. Different from the traditional modal strain energy which was computed based only on mode shapes of the damaged structure, the cross-model modal strain energy was calculated based on mode shapes of both the intact and the damaged structures. Both the qualitative analysis and the Monte Carlo analysis show that compared with the traditional modal strain energy, the cross-model modal strain energy is less affected by the measurement error. A space truss with 392 members was numerically analyzed. Results illustrate that the improvement of indicator expression contributes the most to the improvement of the noise resistance performance of the proposed indicator, while the introduction of cross-model modal strain energy further enhances its robustness. The proposed indicator is more robust than traditional indicators, and it is more applicable to the damage localization of space trusses with large identification dimensions. Enough modes should be selected to guarantee the noise resistance performance of the proposed indicator.
Xiao-shun WU,Ju-wei XIA,Yue-fang HU. Damage localization of space trusses based on indicators expressed by cross-model modal strain energy. Journal of ZheJiang University (Engineering Science), 2020, 54(2): 248-256.
Fig.1Plan view of a space truss with a size of 18 m × 15 m
损伤工况
损伤构件
损伤程度
对应节点
1
81
0.30
41，43
2
101
0.30
88，103
141
0.40
21，36
3
101
0.30
41，43
141
0.40
21，36
300
0.30
68，82
Tab.1Simulated damage scenarios and corresponding nodes of damaged structure
Fig.2Calculation results of MSECI index in damage scenario 1
Fig.3Calculation results of MSEBI in damage scenario 1
Fig.4Calculation results of MSEMI in damage scenario 1
Fig.5Calculation results of TMSEMI in damage scenario 1
模态i
参数
j=101
j=141
j=300
最大值
最小值
波动幅
最大值
最小值
波动幅
最大值
最小值
波动幅
1
CNij
3.09
?1.55
4.64
5.71
?2.17
7.88
127.70
?2.27
129.98
1
FNij
2.21
?1.69
3.91
3.45
?3.23
6.69
26.08
?3.97
30.05
2
CNij
2.34
?1.56
3.90
1.41
?1.16
2.56
122.15
?1.85
124.00
2
FNij
1.76
?1.71
3.46
1.09
?1.19
2.28
22.34
?3.11
25.45
3
CNij
3.06
?1.79
4.85
16.69
?6.51
23.20
7.13
?2.13
9.26
3
FNij
2.15
?2.10
4.25
11.16
?10.97
22.13
4.06
?3.11
7.17
4
CNij
1.02
?0.79
1.81
1.06
?1.00
2.06
1.35
?0.94
2.29
4
FNij
0.78
?0.76
1.55
0.84
?1.01
1.85
1.01
?0.93
1.94
5
CNij
1.44
?1.25
2.69
0.61
?0.36
0.97
9.16
?4.44
13.60
5
FNij
1.28
?1.27
2.55
0.33
?0.24
0.57
6.50
?6.21
12.71
6
CNij
20.09
?2.84
22.93
10.41
?2.59
13.01
395.86
?1.03
396.88
6
FNij
9.44
?5.12
14.56
5.73
?4.61
10.35
22.14
?1.18
23.32
7
CNij
0.95
?0.64
1.58
2.02
?1.40
3.42
20.00
?1.03
21.03
7
FNij
0.71
?0.59
1.30
1.47
?1.51
2.99
4.29
?1.22
5.51
8
CNij
0.56
?0.51
1.07
2.86
?2.11
4.96
2.11
?1.15
3.27
8
FNij
0.44
?0.47
0.91
2.11
?2.55
4.67
1.49
?1.19
2.68
9
CNij
18.40
?1.19
19.59
9.93
?2.07
12.01
0.79
?0.69
1.48
9
FNij
5.09
?1.67
6.76
5.01
?3.54
8.55
0.62
?0.65
1.28
10
CNij
0.52
?0.42
0.94
0.56
?0.42
0.99
3.63
?1.21
4.84
10
FNij
0.34
?0.33
0.67
0.33
?0.31
0.64
1.72
?1.56
3.29
Tab.2Relative fluctuation amplitude of noise to true increment of two types of modal strain energy
Fig.6Calculation results of MSEMI in damage scenario 2
Fig.7Calculation results of MSEMI in damage scenario 3
[1]
ZHANG Z Y, LUO Y Z Restoring method for missing data of spatial structural stressmonitoring based on correlation[J]. Mechanical Systems and Signal Processing, 2017, 91: 266- 277
doi: 10.1016/j.ymssp.2017.01.018
[2]
董石麟, 苗峰, 陈伟刚, 等 新型六杆四面体柱面网壳的构形、静力和稳定性分析[J]. 浙江大学学报: 工学版, 2018, 51 (3): 508- 513 DONG Shi-lin, MIAO Feng, CHEN Wei-gang, et al Configuration, static and stability analysis on new-type six-bar tetrahedral cylindrical lattice shells[J]. Journal of Zhejiang University: Engineering Science, 2018, 51 (3): 508- 513
[3]
陈志华, 楼舒阳, 闫翔宇, 等 天津理工大学体育馆新型复合式索穹顶结构风振效应分析[J]. 空间结构, 2017, 23 (3): 21- 29 CHEN Zhi-hua, LOU Shu-yang, YAN Xiang-yu, et al Time-history analysis of wind vibration response for the cable dome of gymnasium at Tianjin University of Technology[J]. Spatial Structures, 2017, 23 (3): 21- 29
姚激, 顾嗣淳 巴黎戴高乐机场候机楼倒塌事故原因初析[J]. 建筑结构, 2006, 36 (1): 96- 97 YAO Ji, GU Si-chun Paris airport terminal collapse: lessons for the future[J]. Building Structure, 2006, 36 (1): 96- 97
[6]
徐菁, 郭稳, 王秀丽, 等 基于AR模型与BP神经网络的网壳结构损伤识别方法研究[J]. 空间结构, 2015, 21 (2): 66- 71 XU Jing, GUO Wen, WANG Xiu-li, et al Study on the damage detection method for latticed shell structures[J]. Spatial Structures, 2015, 21 (2): 66- 71
[7]
DING B D, FENG D S, LV H L, et al Damage detection in grid structures using limited modal test data[J]. Mathematical Problems in Engineering, 2017, 1089645
[8]
侯吉林, 王真真, 欧进萍, 等 基于附加虚拟质量的结构损伤识别方法[J]. 计算力学学报, 2013, 30 (6): 770- 776 HOU Ji-lin, WANG Zhen-zhen, OU Jin-ping, et al Structural damage identification using additional virtual masses[J]. Chinese Journal of Computational Mechanics, 2013, 30 (6): 770- 776
doi: 10.7511/jslx201306004
[9]
KIM N, KIM H, LEE J Damage detection of truss structures using two-stage optimization based on micro genetic algorithm[J]. Journal of Mechanical Science and Technology, 2014, 28 (9): 3687- 3695
doi: 10.1007/s12206-014-0830-y
[10]
高维成, 刘伟, 钱成 基于剩余模态力和模态应变能理论的网架结构损伤识别[J]. 工程力学, 2007, 24 (5): 93- 100 GAO Wei-chen, LIU Wei, QIAN Cheng Damage detection of space truss using residual modal force and modal strain energy[J]. Engineering Mechanics, 2007, 24 (5): 93- 100
doi: 10.3969/j.issn.1000-4750.2007.05.016
[11]
NOBAHARI M, GHASEMI M R, SHABAKHTY N A fast and robust method for damage detection of truss structures[J]. Applied Mathematical Modelling, 2019, 68: 368- 382
doi: 10.1016/j.apm.2018.11.025
[12]
CIAMBELLA J, PAU A, VESTRONI F Modal curvature-based damage localization in weakly damaged continuous beams[J]. Mechanical Systems and Signal Processing, 2019, 121: 171- 182
doi: 10.1016/j.ymssp.2018.11.012
[13]
唐盛华, 周楠, 方志, 等 基于振型加权模态柔度的梁桥损伤识别方法[J]. 地震工程与工程振动, 2017, 37 (6): 98- 106 TANG Sheng-hua, ZHOU Nan, FANG Zhi, et al Damage identification method for beam bridge based on mode shape weighted modal flexibility[J]. Earthquake Engineering and Engineering Dynamics, 2017, 37 (6): 98- 106
[14]
王卓, 闫晓宇, 闫维明 基于振型相关度的网壳结构状态特征向量试验研究[J]. 空间结构, 2015, 21 (1): 14- 18 WANG Zhuo, YAN Xiao-yu, YAN Wei-ming Experimental study on structural condition characteristic vector of latticed domes based on modal correlation[J]. Spatial Structures, 2015, 21 (1): 14- 18
[15]
SHI Z Y, LAW S S, ZHANG L M Structural damage localization from modal strain energy change[J]. Journal of Sound and Vibration, 1998, 218 (5): 825- 844
doi: 10.1006/jsvi.1998.1878
[16]
SEYEDPOOR S M A two stage method for structural damage detection using a modal strain energy based index and particleswarm optimization[J]. International Journal of Non-Linear Mechanics, 2012, 47: 1- 8
[17]
郭惠勇, 李正良 基于应变能等效指标的结构损伤识别技术研究[J]. 固体力学学报, 2013, 34 (3): 286- 291 GUO Hui-yong, LI Zheng-liang Structural damage identification method based on strain energy equivalence parameter[J]. Chinese Journal of Solid Mechanics, 2013, 34 (3): 286- 291
doi: 10.3969/j.issn.0254-7805.2013.03.009
[18]
TAN Z X, THAMBIRATNAM D P, CHAN T H T, et al Detecting damage in steel beams using modal strain energy based damage index and artificial neural network[J]. Engineering Failure Analysis, 2017, 79: 253- 262
doi: 10.1016/j.engfailanal.2017.04.035
[19]
宋玉普, 张亮, 刘志鑫 测量模态不完整情况下空间网架结构的损伤识别[J]. 土木工程学报, 2009, 42 (1): 11- 15 SONG Yu-pu, ZHANG Liang, LIU Zhi-xin Damage identification of space truss with incomplete measured data[J]. China Civil Engineering Journal, 2009, 42 (1): 11- 15
[20]
李永梅, 周冰, 张微敬 基于模态应变能和小波分析方法的网壳结构损伤识别研究[J]. 空间结构, 2012, 18 (4): 24- 29 LI Yong-mei, ZHOU Bing, ZHANG Wei-jing Study on damage location to reticulated shell structures based on wavelet analysis of modal strain energy[J]. Spatial Structures, 2012, 18 (4): 24- 29
