Optimum Sensor Placement Method for Cable-Stayed Bridges Based on Damage Identifiability
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摘要: 为使布置在斜拉桥上的传感器识别出的模态参数对结构损伤足够敏感，从传感器优化布置的损伤可识别性要求出发，应用参数试验法和参数相关性理论，提出并得到一种包含所有单元损伤信息的节点自由度损伤信息指标，对该指标排序可获得节点自由度包含损伤信息多少的次序，即每个自由度的损伤敏感性排名，此过程无需优化迭代.在此基础上利用传感器优化布置的第1类方法继续分析，避免了迭代或优化效率低下等缺陷，可得到既满足损伤可识别性，也满足模态可观测性的传感器布置位置.在单塔双索面斜拉桥上，展示了本文方法的实现过程，与EI（effective independence）法相比，损伤信息总量：3阶时高出589；4阶时高出582；5阶时高出591.Abstract: In order to make the modal parameters identified by the sensors on cable-stayed bridges that are sufficiently sensitive to structural damage, a damage information index of the node degree of freedom containing the damage information of all elements was proposed and obtained, considering the damage identifiability requirements for optimum sensor placement, and using the method of parameter study and parameter correlation theory. The damage information regarding the degrees of freedom of the nodes could be ordered by ranking the index, i.e. by ranking the damage sensitivity of each degree of freedom. This process did not require the use of any optimization iterative algorithm. Based on this proposal, the first such method for optimum sensor placement, which can avoid defects such as inefficient iterations and optimization, could be analysed. Finally, the location of the sensor, which could provide satisfactory damage identifiability and modal observability, was obtained. The feasibility of the proposed method was demonstrated using a single-tower double-cable-plane cable-stayed bridge. A comparison of the results with those obtained using the EI method (effective independence method) revealed that the total damage information obtained using the proposed method is greater by factors of 589, 582, and 591 for the 3rd, 4th, and 5th orders, respectively.
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图 2 提取模态数不同时的节点及其损伤信息指标
Figure 2. High damage information index and its nodes with different modal orders
图 4 不同模态阶数时E值(进一步分析后)
Figure 4. E values for different modal order numbers (after further analysis)
图 5 不同模态阶数时MAC值(进一步分析后)
Figure 5. MAC values for different modal order numbers (after further analysis)
表 1 基准有限元模型与实测频率对比
Table 1. Comparison between calculated and measured frequencies
阶数 实测频率/Hz 基准有限元模型频率/Hz 误差/% 1 0.469 951 0.464 782 1.1 2 0.781 907 0.791 290 -1.2 3 0.903 752 0.891 099 1.4 4 1.114 995 1.100 500 1.3 5 1.136 485 1.147 850 -1.0 
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表 2 提取不同模态数时较大的损伤信息指标及对应节点
Table 2. Partial data of the design matrix obtained using the parameter study method
编号 D0_1 D1_1y D1_1z D10_1y D10_1z D11_1y D11_1z D12_1y D12_1z D13_1y 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 4 2 1 1 1 1 1 1 1 1 1 5 1 1 1 0 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 1 7 1 1 1 2 1 1 1 1 1 1 8 1 1 1 1 0 1 1 1 1 1 9 1 1 1 1 1 1 1 1 1 1 10 1 1 1 1 2 1 1 1 1 1 115 1 1 1 1 1 1 1 1 1 1 116 1 1 1 1 1 1 1 1 1 1 117 1 1 1 1 1 1 1 1 1 1 118 1 1 1 1 1 1 1 1 1 1 119 1 1 1 1 1 1 1 1 1 1 120 1 1 1 1 1 1 1 1 1 1 121 1 1 1 1 1 1 1 1 1 1 122 1 1 1 1 1 1 1 1 1 1 123 1 1 1 1 1 1 1 1 1 1 124 1 1 1 1 1 1 1 1 1 1
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表 3 仿真试验部分节点的前5阶归一化振型值
Table 3. Normalized mode shape values of the first five orders of the partial nodes obtained via simulation
m 编号 n1_10 n1_11 n1_12 n1_13 n1_14 n1_15 1 -0.378 680 36 -0.325 459 43 0.381 806 59 0.327 921 69 -0.483 310 82 -0.431 545 09 2 -0.378 650 13 -0.325 432 84 0.381 763 70 0.327 884 42 -0.483 275 11 -0.431 511 80 3 -0.378 680 36 -0.325 459 43 0.381 806 59 0.327 921 69 -0.483 310 82 -0.431 545 09 4 -0.378 711 20 -0.325 486 55 0.381 850 31 0.327 959 68 -0.483 347 22 -0.431 579 04 5 -0.378 649 96 -0.325 436 72 0.381 794 24 0.327 910 07 -0.483 258 80 -0.431 504 99 6 -0.378 680 36 -0.325 459 43 0.381 806 59 0.327 921 69 -0.483 310 82 -0.431 545 09 7 -0.378 711 35 -0.325 482 57 0.381 819 17 0.327 933 54 -0.483 363 83 -0.431 585 96 8 -0.378 659 60 -0.325 440 35 0.381 756 87 0.327 883 06 -0.483 287 81 -0.431 523 01 9 -0.378 680 36 -0.325 459 43 0.381 806 59 0.327 921 69 -0.483 310 82 -0.431 545 09 10 -0.378 701 53 -0.325 478 88 0.381 857 27 0.327 961 07 -0.483 334 27 -0.431 567 60 115 -0.378 757 57 -0.325 521 09 0.381 843 80 0.327 955 16 -0.483 426 98 -0.431 640 48 116 -0.378 638 92 -0.325 422 16 0.381 717 47 0.327 850 20 -0.483 262 92 -0.431 500 08 117 -0.378 680 36 -0.325 459 43 0.381 806 59 0.327 921 69 -0.483 310 82 -0.431 545 09 118 -0.378 722 62 -0.325 497 43 0.381 897 46 0.327 994 58 -0.483 359 65 -0.431 590 98 119 -0.378 625 12 -0.325 416 08 0.381 781 03 0.327 898 45 -0.483 224 64 -0.431 475 60 120 -0.378 680 36 -0.325 459 43 0.381 806 59 0.327 921 69 -0.483 310 82 -0.431 545 09 121 -0.378 736 68 -0.325 503 63 0.381 832 65 0.327 945 38 -0.483 398 66 -0.431 615 93 122 -0.378 647 64 -0.325 429 82 0.381 733 81 0.327 863 89 -0.483 273 47 -0.431 509 78 123 -0.378 680 36 -0.325 459 43 0.381 806 59 0.327 921 69 -0.483 310 82 -0.431 545 09 124 -0.378 713 72 -0.325 489 62 0.381 880 80 0.327 980 62 -0.483 348 89 -0.431 581 09
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表 4 不同模态阶数时传感器布点位置
Table 4. Sensor locations for different mode shape orders
提取模态数/个 传感器布点位置 3 2 3 4 5 6 7 8 9 10 11 43 76 77 78 79 80 81 82 83 84 4 43 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 5 3 4 5 6 43 68 69 71 72 74 75 76 77 78 79 80 81 82 83 84
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表 5 最终的传感器布点位置
Table 5. Final sensor locations
提取模态数/个 传感器布点位置 3 2 4 6 8 10 43 77 79 81 84 4 43 66 68 70 72 74 76 78 80 84 5 3 5 43 68 71 75 77 80 82 84
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表 6 EI法的传感器布点位置
Table 6. Sensor locations using the EI method
提取模态数/个 传感器布点位置 3 4 8 20 22 42 43 64 66 78 82 4 6 18 20 22 42 43 64 66 68 80 5 5 15 18 20 22 64 66 68 71 81
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