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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (2): 248-256    DOI: 10.3785/j.issn.1008-973X.2020.02.005
土木与交通工程     
基于跨模型模态应变能指标的网架结构损伤定位
伍晓顺1(),夏巨伟2,胡岳芳1
1. 江西理工大学南昌校区，江西 南昌 330013
2. 浙江五洲工程项目管理有限公司，浙江 杭州 310053
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
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摘要：

提出新的模态应变能指标来定位具有较大识别规模的网架结构损伤. 所提指标不仅改进了表达式，还引入了跨模型模态应变能的概念. 与传统模态应变能仅利用损伤结构的模态振型不同，跨模型模态应变能同时利用未损结构和损伤结构的模态振型. 定性分析与蒙特卡洛分析均表明，与传统模态应变能相比，跨模型模态应变能受测量误差的影响较小. 针对某392杆网架结构的数值分析表明，指标表达式的改进对所提指标抗噪性能的提升起主要作用，而跨模型模态应变能的引入有利于进一步改善所提指标的鲁棒性. 所提指标比传统指标具有更强的抗噪能力，更适用于具有较大识别规模的网架结构损伤定位；选取较多的模态参与计算有利于增强所提指标的抗噪能力.
关键词： 空间结构;  损伤识别;  模态应变能;  模态识别;  结构健康监测    
Abstract:

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.
Key words: space structure    damage identification    modal strain energy    modal identification    structural health monitoring
收稿日期: 2018-12-25 出版日期: 2020-03-10
CLC:  TU 311  
基金资助: 国家自然科学基金资助项目（51868026）；江西省教育厅科学技术研究资助项目（GJJ170529）；江西理工大学博士启动资金资助项目
作者简介: 伍晓顺（1981—），男，讲师，博士，从事空间结构研究. orcid.org/0000-0001-8524-7771. E-mail： wuxiaoshun1981@163.com
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引用本文:

伍晓顺,夏巨伟,胡岳芳. 基于跨模型模态应变能指标的网架结构损伤定位[J]. 浙江大学学报(工学版), 2020, 54(2): 248-256.

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.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.02.005    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I2/248

图 1  某18 m× 15 m平板网架示意图
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
表 1  模拟的损伤工况及损伤构件对应节点
图 2  损伤工况1下的MSECI指标计算结果
图 3  损伤工况1下的MSEBI指标计算结果
图 4  损伤工况1下的MSEMI指标计算结果
图 5  损伤工况1下的TMSEMI指标计算结果
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
表 2  2种模态应变能增量所含噪声与真实值的相对波动幅度
图 6  损伤工况2下的MSEMI指标计算结果
图 7  损伤工况3下的MSEMI指标计算结果
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