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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (6): 1086-1094    DOI: 10.3785/j.issn.1008-973X.2020.06.005
Civil Engineering     
Fast measurement of static displacement field in cable-strut tensile structure
Xiao-shun WU1(),Chen-hui HUANG1,Xin-tao WANG2,Hua DENG2,*()
1. School of Architectural and Surveying & Mapping Engineering (Nanchang), Jiangxi University of Science and Technology, Nanchang 330013, China
2. Space Structures Research Center, Zhejiang University, Hangzhou 310058, China
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Abstract  

A new expansion method was developed to quickly measure the static displacement field of cable-strut tensile structure. Under a specific load case, the static displacements of a random real structure could be approximated as linear combination of a few contribution modes. Thus, an iterative strategy was suggested to find optimal test locations; unbiased estimation for the combinatorial coefficients of contribution modes were taken to quickly acquire the full static displacements. Regarding the problem that structural modes are not fully orthogonal but used as basis vectors, the principle component analysis method was employed to validate the effectiveness of using structural modes as the replacement of orthogonal basis vectors in the degree-of-freedom space. An annular tensile canopy structure with a span of 200 meters was numerically investigated. Results show that the proposed method can provide high expansion accuracy. For the load case that has many loading locations but only a few contribution modes, the number of test locations can be effectively reduced so that the structural testing efficiency can be greatly improved. Furthermore, it is verified that structural modes contain complete information of orthogonal basis vectors in the degree-of-freedom space, indicating the effectiveness of expressing static displacements based on the linear combination of structural modes.

Key words： space structure      static testing      damage identification      mode shape expansion      structural health monitoring     
Received: 21 May 2019      Published: 06 July 2020
CLC:  TU 311  
  O 327  
  O 329  
Corresponding Authors: Hua DENG     E-mail: wuxiaoshun1981@163.com;denghua@zju.edu.cn
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Xiao-shun WU
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Cite this article:

Xiao-shun WU,Chen-hui HUANG,Xin-tao WANG,Hua DENG. Fast measurement of static displacement field in cable-strut tensile structure. Journal of ZheJiang University (Engineering Science), 2020, 54(6): 1086-1094.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.06.005     OR     http://www.zjujournals.com/eng/Y2020/V54/I6/1086


索杆张力结构静力位移场快速测量

提出一种新的静力位移扩展方法来快速测量索杆张力结构的静力位移场. 在特定荷载作用下，实际结构的静力位移可以近似表示为少数贡献模态的线性组合. 在此基础上，提出一种迭代策略来优选测点位置，以无偏估计贡献模态的组合系数，从而快速获得完整的静力位移. 针对结构模态不完全正交却被用作基向量的问题，引入主成分分析法来论证用结构模态代替自由度空间基向量的有效性. 以某200 m跨环形张力罩棚结构为例进行数值分析. 结果表明，所提方法具有较高的扩展精度，在加载点很多但贡献模态较少的荷载工况下能有效减少测点数量，从而大幅提高静力测试效率. 主成分分析结果表明，结构模态包含自由度空间完整的正交基信息，说明利用结构模态的线性组合来表示静力位移是有效的.


关键词： 空间结构,  静力测试,  损伤识别,  振型扩展,  结构健康监测 
Fig.1 Diagram of axisymmetric annular tensile canopy structure with span of 200 m
构件组号 构件类型 k Ak / mm2 tk / kN euk / mm
1 上环索 1~24 42 500 20 000 ±15
2 下环索 25~48 42 500 20 000 ±15
3 内侧压杆 49~72 6 225 -1 044.2 ±10
4 上部内侧径向索 73~96 10 525 5 324.5 ±15
5 下部内侧径向索 97~120 10 525 5 324.5 ±15
6 外侧压杆 121~144 7 165 ?1 392.3 ±10
7 上部外侧径向索 145~168 11 625 5 761.5 ±15
8 下部外侧径向索 169~192 11 625 5 761.5 ±15
Tab.1 Member grouping and structural parameters of annular tensile canopy structure
理想结构 实际结构
j |αj| γ j j |αj| γ j
9 2.223 3 1.000 0 9 2.346 4 1.000 0
98 0.862 2 0.387 8 98 0.908 6 0.387 2
148 0.030 6 0.013 8 148 0.032 2 0.013 7
153 0.021 3 0.009 6 153 0.022 5 0.009 6
134 0.009 5 0.004 3 134 0.011 6 0.004 9
Tab.2 First five ideal modes contributing most to express static displacements and combinatorial coefficients (load case 1)
理想结构 实际结构
j |αj| γ j j |αj| γ j
2 9.583 5 1.000 0 2 9.945 1 1.000 0
9 1.111 7 0.116 0 9 1.162 1 0.116 8
3 1.083 3 0.113 0 3 1.122 2 0.112 8
7 0.878 2 0.091 6 7 0.911 9 0.091 7
98 0.431 1 0.045 0 98 0.453 8 0.045 6
42 0.418 3 0.043 6 42 0.432 5 0.043 5
8 0.405 7 0.042 3 8 0.422 1 0.042 4
15 0.334 5 0.034 9 15 0.349 6 0.035 2
13 0.254 8 0.026 6 13 0.262 4 0.026 4
43 0.198 4 0.020 7 43 0.205 6 0.020 7
12 0.195 5 0.020 4 12 0.203 2 0.020 4
49 0.156 7 0.016 3 49 0.162 5 0.016 3
39 0.130 9 0.013 7 39 0.134 9 0.013 6
40 0.124 2 0.013 0 40 0.128 9 0.013 0
50 0.124 0 0.012 9 50 0.128 4 0.012 9
56 0.115 0 0.012 0 56 0.118 7 0.011 9
48 0.096 6 0.010 1 48 0.100 0 0.010 1
102 0.064 9 0.006 8 102 0.066 8 0.006 7
Tab.3 First eighteen ideal modes contributing most to express static displacements and combinatorial coefficients (load case 2)
δu / % 工况1 工况2
Pf1 / % Ps2 / % Pf2 / % Ps2 / %
0 100 0 100 0
10 100 0 100 0
20 91.6 8.4 100 0
30 57.6 42.4 100 0
40 44.4 55.6 100 0
50 39.2 60.8 100 0
Tab.4 Relationships between probability of contribution mode changes and member damage limits
Fig.2 Modal assurance criterion (MAC) values between contribution modes for two different load cases
ε / % 所提方法（4个测点） 所提方法（24个测点） 文献[16]方法（48个测点）
MACmin MVEmax / mm MACmin MVEmax / mm MACmin MVEmax / mm
0 0.999 8 0.001 7 0.999 8 0.001 6 1.000 0 0.000 5
1 0.999 4 0.003 3 0.999 7 0.001 8 0.999 8 0.001 6
2 0.998 4 0.004 8 0.999 4 0.002 6 0.999 2 0.002 9
3 0.996 1 0.007 3 0.999 1 0.003 3 0.998 0 0.004 6
4 0.995 4 0.009 3 0.998 4 0.004 5 0.997 2 0.005 8
5 0.992 8 0.012 7 0.997 8 0.005 5 0.994 2 0.007 8
6 0.991 2 0.014 2 0.994 5 0.006 5 0.992 0 0.008 6
7 0.987 9 0.015 6 0.993 9 0.007 3 0.990 9 0.009 8
8 0.981 7 0.017 3 0.992 8 0.008 7 0.987 4 0.011 2
Tab.5 Displacement expansion Results of real structure （load case 1）
ε / % 所提方法（18个测点） 所提方法（24个测点） 文献[16]方法（24个测点）
MACmin MVEmax / mm MACmin MVEmax / mm MACmin MVEmax / mm
0 0.999 5 0.010 5 0.999 6 0.010 5 1.000 0 0.001 5
1 0.998 9 0.016 9 0.999 4 0.014 3 0.999 9 0.005 6
2 0.997 4 0.024 8 0.998 0 0.018 8 0.999 4 0.011 3
3 0.995 8 0.030 5 0.997 3 0.024 4 0.999 0 0.017 5
4 0.992 4 0.041 8 0.996 1 0.031 6 0.997 9 0.021 5
5 0.990 3 0.044 4 0.995 8 0.034 2 0.997 1 0.025 6
6 0.985 4 0.058 2 0.992 3 0.044 1 0.994 5 0.032 5
7 0.980 3 0.068 3 0.991 2 0.047 6 0.992 6 0.037 8
8 0.977 8 0.072 1 0.986 7 0.053 5 0.990 5 0.042 7
Tab.6 Displacement expansion Results of real structure （load case 2）
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