A damage detection method of plate structure using fan-shaped sensor clusters

HAN Yue; MA Chenning; LIU Jinxia; ZHOU Zixian; YAN Shouguo; CUI Zhiwen

doi:10.7498/aps.74.20250382

Abstract

Plate structures are widely used in large-scale engineering fields such as aerospace, hull manufacturing, and construction. However, the plate structure is easily damaged during long-term service or when it is impacted by foreign objects. Such a damage may lead to serious safety accidents.Beamforming and L-shaped sensor cluster (LSSC) localization method can be used to locate the damage on the plate. However, when using beamforming method or LSSC localization method to locate the damages on plate-like structures, there exists blind area.In this paper, by combining the beamforming method and LSSC localization method, a fan-shaped sensor cluster localization method is proposed through arranging five sensors in a fan shape, which can effectively reduce the blind areas. The positions of damages in the plate can be accurately detected by using two groups of fan-shaped sensor clusters and one sensor for transmitting the excitation signal. The feasibility of the fan-shaped sensor cluster localization method is verified through numerical simulations and experiments, and the results are compared with those obtained by using the T-shaped sensor cluster. The results show that the fan-shaped sensor cluster localization method can more accurately identify the damages at different positions. Both simulation and experimental results indicate that the fan-shaped sensor cluster localization method can reduce the blind area and improve the accuracy of damage location.

Keywords:

Authors and contacts

1.
College of Physics, Jilin University, Changchun 130021, China
2.
State Key Laboratory of Acoustics and Marine Information, Chinese Academy of Sciences, Beijing 100190, China
3.
Chongqing Research Institute of Jilin University, Chongqing 401120, China

Corresponding author: LIU Jinxia, jinxia@jlu.edu.cn ; CUI Zhiwen, cuizw@jlu.edu.cn

Funds: Project supported by the Natural Science Foundation of Chongqing, China (Grant No. CSTB2022NSCQ-MSX1109), the State Key Laboratory of Acoustics and Marine Information, Chinese Academy of Sciences (Grant No. SKLA202512), the Research and Innovation Ability Improvement Program for Postgraduate of Education Department of Jilin Province, China (Grant No. JJKH20250050BS), and the Research and Innovation Ability Improvement Program for Postgraduate of Jilin University, China (Grant No. 2024KC040).

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References

[1]	胡海峰 2011 博士学位论文 (长沙: 国防科学技术大学) Hu H F 2011 Ph. D. Dissertation (Changsha: National University of Defense Technology
[2]	冉启芳 1999 无损检测 21 75 Ran Q F 1999 Nondestr. Test 21 75
[3]	邬冠华, 熊鸿建 2016 仪器仪表学报 37 1683 Google Scholar Wu G H, Xiong H J 2016 Chin. J. Sci. Instrum. 37 1683 Google Scholar
[4]	马国, 贾华东, 卢长煜, 陈理想, 张贵芝, 张立平, 杨超 2019 无损检测 41 62 Google Scholar Ma G, Jia H D, Lu C Y, Chen L X, Zhang G Z, Zhang L P, Yang C 2019 Nondestr. Test 41 62 Google Scholar
[5]	赵金玲 2017 博士学位论文 (南京: 南京航空航天大学) Zhao J L 2017 Ph. D. Dissertation (Nanjing: Nanjing University of Aeronautics and Astronautics
[6]	孙明健, 刘婷, 程星振, 陈德应, 闫锋刚, 冯乃章 2016 物理学报 65 167802 Google Scholar Sun M J, Liu T, Cheng X Z, Chen D Y, Yan F G, Feng N Z 2016 Acta Phys. Sin. 65 167802 Google Scholar
[7]	Humeida Y, Wilcox P D, Todd M D 2014 NDT E Int. 68 43 Google Scholar
[8]	Luo K, Liu Y J, Liang W 2024 NDT & E Int. 143 103047 Google Scholar
[9]	Chen S J, Zhou S P, Li Y, Xiang Y X, Qi M X 2017 Chin. Phys. Lett. 34 044301 Google Scholar
[10]	王强, 袁慎芳 2008 航空学报 29 1061 Google Scholar Wang Q, Yuan S F 2008 Acta Aeronaut. Astronaut. Sin. 29 1061 Google Scholar
[11]	刘增华, 徐营赞, 何存富, 吴斌 2014 工程力学 31 232 Google Scholar Liu Z H, Xu Y Z, He C F, Wu B 2014 Eng. Mech. 31 232 Google Scholar
[12]	张海燕, 孙修立, 曹亚萍, 陈先华, 于建波 2010 物理学报 59 7111 Google Scholar Zhang H Y, Sun X L, Cao Y P, Chen X H, Yu J B 2010 Acta Phys. Sin. 59 7111 Google Scholar
[13]	Zhang G D, Kundu T, Deymier P A, Runge K 2025 Ultrasonics 145 107492 Google Scholar
[14]	Xu C B, Wang Q, Gao Q J, Deng M X 2025 Mech. Syst. Signal Proc. 223 11926 Google Scholar
[15]	张海燕, 杨杰, 范国鹏, 朱文发, 柴晓冬 2017 物理学报 66 214301 Google Scholar Zhang H Y, Yang J, Fan G P, Zhu W F, Chai X D 2017 Acta Phys. Sin. 66 214301 Google Scholar
[16]	Ambrozinski L, Stepinski T, Uhl T, Ochonski J, Klepka A 2012 Key Eng. Mater. 518 87 Google Scholar
[17]	杨益新, 孙超, 鄢社锋, 马远良, 肖国有 2003 声学学报 28 504 Google Scholar Yang Y X, Sun C, Yan S F, Ma Y L, Xiao G Y 2003 Acta Acust. 28 504 Google Scholar
[18]	McLaskey G C, Glaser S D, Grosse C U 2010 J. Sound Vib. 329 2384 Google Scholar
[19]	Wang W Q, Shao H Z 2014 IEEE J. Sel. Top. Signal Process. 8 106 Google Scholar
[20]	Cantero C S, Aranguren G, Malik M K, Etxaniz J, Martín de la Escalera F 2020 Sensors 20 1445 Google Scholar
[21]	He T, Pan Q, Liu Y G, Liu X D, Hu D Y 2012 Ultrasonics 52 587 Google Scholar
[22]	Li L, Yang K, Bian X Y, Liu Q H, Yang Y Z, Ma F Y 2019 Sensors 19 3152 Google Scholar
[23]	Zhang Z H, Zhong Y T, Xiang J W, Jiang Y Y, Wang Z L 2020 IEEE Sens J. 20 14932 Google Scholar
[24]	Jung H K, Zhou S J, Park G 2019 J. Intell. Mater. Syst. Struct. 30 351 Google Scholar
[25]	Wang Z L, Yuan S F, Qiu L, Liu B 2015 J. Vibroeng. 17 2338
[26]	Zhong Y T, Xiang J W 2019 Smart. Struct. Syst. 24 173 Google Scholar
[27]	Yu L, Giurgiutiu V 2008 Ultrasonics 48 117 Google Scholar
[28]	Kundu T 2012 European Workshop on Structural Health Monitoring Dresden, Germany, July 3–6, 2012 p2
[29]	Kundu T, Nakatani H, Takeda N 2012 Ultrasonics 52 740 Google Scholar
[30]	Ma C N, Zhou Z X, Liu J X, Cui Z W, Kundu T 2023 Ultrasonics 132 107020 Google Scholar
[31]	Yin S X, Cui Z W, Kundu T 2018 Ultrasonics 84 34 Google Scholar
[32]	Yin S X, Xiao H P, Xu C B, Wang J S, Deng M X, Kundu T 2022 Ultrasonics 124 106770 Google Scholar
[33]	Sen N, Gawroński M, Packo P, Uhl T, Kundu T 2021 Mech. Syst. Signal Proc. 153 107489 Google Scholar
[34]	Zhou Z X, Cui Z W, Liu J X, Kundu T 2023 Eng. Fract. Mech. 277 108995 Google Scholar
[35]	Gao Q, Jeon J Y, Park G, Kong Y, Shen Y D, Xiang J W 2021 J. Intell. Mater. Syst. Struct. 33 1028 Google Scholar
[36]	Gao Q, Jeon J Y, Park G, Shen Y D, Xiang J W 2021 Struct. Health. Monit. 21 451 Google Scholar
[37]	Gao Q, Jeon J Y, Xiang J W, Park G 2023 IEEE Sens. J. 23 2970 Google Scholar
[38]	Xue C R, Xu G, Wang X K, Gao J C, Gao D J 2021 Ultrasonics 115 106438 Google Scholar

Cited By

图 1 扇形传感器簇示意图

Figure 1. Schematic diagram of a fan-shaped sensor cluster.

DownLoad: Full-Size Img PowerPoint

图 2 初步预测结果图　(a)实际角度为80°的预测结果; (b)实际角度为5°时的预测结果

Figure 2. Schematic diagram of initial forecast results: (a) Prediction of an actual DOA of 80°; (b) the prediction of an actual DOA of 5°.

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图 3 2 mm厚铝板相速度频散曲线

Figure 3. Phase velocity dispersion curves of an aluminum plate with a thickness of 2 mm.

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图 4 2 mm厚铝板的群速度频散曲线

Figure 4. Group velocity dispersion curves of an aluminum plate with a thickness of 2 mm.

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图 5 仿真中传感器布局示意图

Figure 5. Schematic diagram of sensors layout in the simulation.

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图 6 t = 70 μs的波场快照(损伤位于(100, –45))

Figure 6. Wavefield snapshot at t = 70 μs (the damage is located at (100, –45)).

DownLoad: Full-Size Img PowerPoint

图 7 (a)损伤位于(100, –45)时, 传感器S₁接收到的损伤信号与无损时的基线信号对比; (b)利用传感器S₁接收到的有损信号减去基线信号得到的差值信号

Figure 7. (a) Damaged signal and the healthy signal received by the S₁ when the damage is located at (100, –45); (b) the differential signal obtained by subtracting the healthy signal from the damaged signal received by the sensor S₁.

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图 8 仿真定位结果示意图　(a) T形传感器簇定位结果; (b)扇形传感器簇定位结果

Figure 8. Schematic diagram of simulation localization results: (a) Localization results of T-shaped sensor cluster; (b) localization results of fan-shaped sensor cluster.

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图 9 (a)实验装置示意图; (b) OLYMPUS 5800脉冲信号发射器; (c)实验中使用示波器接收到的信号; (d) AE144S传感器

Figure 9. (a) Photo of the experimental setup; (b) OLYMPUS 5800 pulse signal transmitter; (c) the signal received by the oscilloscope in the experiment; (d) AE144S sensor.

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图 10 (a)损伤位于(105, –10)时, 下方扇形传感器簇中的S₃接收到的损伤信号与无损时的基线信号对比; (b)经过滤波后, 利用传感器S₃接收到的有损信号减去基线信号得到的差值信号

Figure 10. (a) Damaged aluminum signal and the healthy aluminum signal received by the S₃ of the fan-shaped sensor cluster on the lower side when the damage is located at (105, –10); (b) the differential signal obtained by subtracting the healthy signal from the damaged signal received by the sensor S₃ after filtering.

DownLoad: Full-Size Img PowerPoint

图 11 实验定位结果示意图　(a) T形传感器簇定位结果; (b)扇形传感器簇定位结果

Figure 11. Schematic diagram of experimental localization results: (a) Localization results of T-shaped sensor cluster; (b) localization results of fan-shaped sensor cluster.

DownLoad: Full-Size Img PowerPoint

表 1 铝板材料属性

Table 1. Material parameters of aluminum plate.

材料属性	数值
密度$\rho $/(kg·m^–3)	2700
泊松比$\sigma $	0.33
杨氏模量 E/GPa	70

DownLoad: CSV

表 2 传感器的位置坐标

Table 2. Coordinates of sensors.

传感器标记	坐标/mm	传感器标记	坐标/mm
S₁	(–10.00, –50.00)	S₆	(–10.00, 50.00)
S₂	(0.00, –50.00)	S₇	(0.00, 50.00)
S₃	(10.00, –50.00)	S₈	(10.00, 50.00)
S₄	(7.07, –42.93)	S₉	(–7.07, 57.07)
S₅	(7.07, –57.07)	S₁₀	(–7.07, 42.93)

DownLoad: CSV

表 3 仿真定位结果与误差

Table 3. Simulation localization results and errors.

编号	实际损伤坐标/mm	T形传感器簇		扇形传感器簇
编号	实际损伤坐标/mm	预测损伤坐标/mm	误差/mm	预测损伤坐标/mm	误差/mm
D1	(46.00, 123.00)	(45.93, 125.16)	2.16	(46.29, 125.73)	2.75
D2	(–90.00, 20.00)	(–75.34, 11.45)	16.97	(–94.02, 24.28)	5.87
D3	(130.00, 60.00)	(133.83, 70.07)	10.77	(133.48, 64.39)	5.61
D4	(30.00, –100.00)	(34.30, –107.32)	8.49	(32.96, –105.08)	5.88
D5	(–60.00, –60.00)	(–54.31, –63.35)	9.27	(–54.58, –56.65)	6.37
D6	(105.00, –10.00)	(93.94, –6.28)	11.67	(105.19, –6.87)	3.14
D7	(–35.00, 115.00)	(–35.72, 118.03)	3.11	(–33.22, 113.27)	2.48
D8	(100.00, –45.00)	(84.55, –33.09)	19.51	(97.29, –44.28)	2.80

DownLoad: CSV

表 4 实验定位结果与误差

Table 4. Experimental localization results and errors.

编号	实际损伤坐标/mm	T形传感器簇		扇形传感器簇
编号	实际损伤坐标/mm	预测损伤坐标/mm	误差/mm	预测损伤坐标/mm	误差/mm
D1	(46.00, 123.00)	(42.39, 115.11)	8.68	(43.22, 114.82)	8.64
D2	(–90.00, 20.00)	(–106.88, 22.25)	17.03	(–96.76, 20.04)	6.76
D3	(130.00, 60.00)	(141.36, 66.56)	13.12	(124.69, 56.48)	6.37
D4	(30.00, –100.00)	(29.52, –97.61)	2.44	(31.51, –103.49)	3.80
D5	(–60.00, –60.00)	(–65.45, –60.33)	5.46	(–65.40, –60.12)	5.40
D6	(105.00, –10.00)	(94.63, –12.02)	10.56	(111.13, –14.78)	7.77
D7	(–35.00, 115.00)	(–36.40, 121.49)	6.64	(–40.94, 119.23)	7.29
D8	(100.00, –45.00)	(90.54, –33.69)	14.74	(106.07, –47.88)	6.72

DownLoad: CSV

[1]	胡海峰 2011 博士学位论文 (长沙: 国防科学技术大学) Hu H F 2011 Ph. D. Dissertation (Changsha: National University of Defense Technology
[2]	冉启芳 1999 无损检测 21 75 Ran Q F 1999 Nondestr. Test 21 75
[3]	邬冠华, 熊鸿建 2016 仪器仪表学报 37 1683 Google Scholar Wu G H, Xiong H J 2016 Chin. J. Sci. Instrum. 37 1683 Google Scholar
[4]	马国, 贾华东, 卢长煜, 陈理想, 张贵芝, 张立平, 杨超 2019 无损检测 41 62 Google Scholar Ma G, Jia H D, Lu C Y, Chen L X, Zhang G Z, Zhang L P, Yang C 2019 Nondestr. Test 41 62 Google Scholar
[5]	赵金玲 2017 博士学位论文 (南京: 南京航空航天大学) Zhao J L 2017 Ph. D. Dissertation (Nanjing: Nanjing University of Aeronautics and Astronautics
[6]	孙明健, 刘婷, 程星振, 陈德应, 闫锋刚, 冯乃章 2016 物理学报 65 167802 Google Scholar Sun M J, Liu T, Cheng X Z, Chen D Y, Yan F G, Feng N Z 2016 Acta Phys. Sin. 65 167802 Google Scholar
[7]	Humeida Y, Wilcox P D, Todd M D 2014 NDT E Int. 68 43 Google Scholar
[8]	Luo K, Liu Y J, Liang W 2024 NDT & E Int. 143 103047 Google Scholar
[9]	Chen S J, Zhou S P, Li Y, Xiang Y X, Qi M X 2017 Chin. Phys. Lett. 34 044301 Google Scholar
[10]	王强, 袁慎芳 2008 航空学报 29 1061 Google Scholar Wang Q, Yuan S F 2008 Acta Aeronaut. Astronaut. Sin. 29 1061 Google Scholar
[11]	刘增华, 徐营赞, 何存富, 吴斌 2014 工程力学 31 232 Google Scholar Liu Z H, Xu Y Z, He C F, Wu B 2014 Eng. Mech. 31 232 Google Scholar
[12]	张海燕, 孙修立, 曹亚萍, 陈先华, 于建波 2010 物理学报 59 7111 Google Scholar Zhang H Y, Sun X L, Cao Y P, Chen X H, Yu J B 2010 Acta Phys. Sin. 59 7111 Google Scholar
[13]	Zhang G D, Kundu T, Deymier P A, Runge K 2025 Ultrasonics 145 107492 Google Scholar
[14]	Xu C B, Wang Q, Gao Q J, Deng M X 2025 Mech. Syst. Signal Proc. 223 11926 Google Scholar
[15]	张海燕, 杨杰, 范国鹏, 朱文发, 柴晓冬 2017 物理学报 66 214301 Google Scholar Zhang H Y, Yang J, Fan G P, Zhu W F, Chai X D 2017 Acta Phys. Sin. 66 214301 Google Scholar
[16]	Ambrozinski L, Stepinski T, Uhl T, Ochonski J, Klepka A 2012 Key Eng. Mater. 518 87 Google Scholar
[17]	杨益新, 孙超, 鄢社锋, 马远良, 肖国有 2003 声学学报 28 504 Google Scholar Yang Y X, Sun C, Yan S F, Ma Y L, Xiao G Y 2003 Acta Acust. 28 504 Google Scholar
[18]	McLaskey G C, Glaser S D, Grosse C U 2010 J. Sound Vib. 329 2384 Google Scholar
[19]	Wang W Q, Shao H Z 2014 IEEE J. Sel. Top. Signal Process. 8 106 Google Scholar
[20]	Cantero C S, Aranguren G, Malik M K, Etxaniz J, Martín de la Escalera F 2020 Sensors 20 1445 Google Scholar
[21]	He T, Pan Q, Liu Y G, Liu X D, Hu D Y 2012 Ultrasonics 52 587 Google Scholar
[22]	Li L, Yang K, Bian X Y, Liu Q H, Yang Y Z, Ma F Y 2019 Sensors 19 3152 Google Scholar
[23]	Zhang Z H, Zhong Y T, Xiang J W, Jiang Y Y, Wang Z L 2020 IEEE Sens J. 20 14932 Google Scholar
[24]	Jung H K, Zhou S J, Park G 2019 J. Intell. Mater. Syst. Struct. 30 351 Google Scholar
[25]	Wang Z L, Yuan S F, Qiu L, Liu B 2015 J. Vibroeng. 17 2338
[26]	Zhong Y T, Xiang J W 2019 Smart. Struct. Syst. 24 173 Google Scholar
[27]	Yu L, Giurgiutiu V 2008 Ultrasonics 48 117 Google Scholar
[28]	Kundu T 2012 European Workshop on Structural Health Monitoring Dresden, Germany, July 3–6, 2012 p2
[29]	Kundu T, Nakatani H, Takeda N 2012 Ultrasonics 52 740 Google Scholar
[30]	Ma C N, Zhou Z X, Liu J X, Cui Z W, Kundu T 2023 Ultrasonics 132 107020 Google Scholar
[31]	Yin S X, Cui Z W, Kundu T 2018 Ultrasonics 84 34 Google Scholar
[32]	Yin S X, Xiao H P, Xu C B, Wang J S, Deng M X, Kundu T 2022 Ultrasonics 124 106770 Google Scholar
[33]	Sen N, Gawroński M, Packo P, Uhl T, Kundu T 2021 Mech. Syst. Signal Proc. 153 107489 Google Scholar
[34]	Zhou Z X, Cui Z W, Liu J X, Kundu T 2023 Eng. Fract. Mech. 277 108995 Google Scholar
[35]	Gao Q, Jeon J Y, Park G, Kong Y, Shen Y D, Xiang J W 2021 J. Intell. Mater. Syst. Struct. 33 1028 Google Scholar
[36]	Gao Q, Jeon J Y, Park G, Shen Y D, Xiang J W 2021 Struct. Health. Monit. 21 451 Google Scholar
[37]	Gao Q, Jeon J Y, Xiang J W, Park G 2023 IEEE Sens. J. 23 2970 Google Scholar
[38]	Xue C R, Xu G, Wang X K, Gao J C, Gao D J 2021 Ultrasonics 115 106438 Google Scholar

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