结构健康监测的传感器优化布置研究进展与展望

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (17) : 82-93.

论文

杨辰

作者信息 +

Advances and prospects for optimal sensor placement of structural health monitoring

YANG Chen

Author information +

文章历史 +

摘要

大尺度、复杂化、长寿命、多功能现代工程结构长期暴露于严苛服役环境，结构功能与状态会偏离初始设计目标，利用结构健康监测技术进行健康诊断和性能评估是保证结构安全、延长使用寿命、降低维修成本的重要手段，而传感器系统作为结构健康监测的首要环节直接决定了结构安全诊断的准确性。随着待监测结构对安全性、功能性需求的日益提高，传感器优化布置越来越复杂，高效、高精度的结构状态变化数据采集系统也对传感器优化布置问题提出了更高的挑战。着重回顾并评述了传感器优化布置方法、评价方法等研究进展，提炼出传感器优化布置中亟待解决的输入参数与性能之间的耦合关系，可靠性分析，大规模传感器布置优化算法的精度、效率与评价等若干关键问题，并对此进行了未来发展展望，包括非完备信息与最优输入参数下传感器优化布置方法，基于信息融合技术的多类型传感器优化布置方法，传感器布置的多目标优化算法综合设计，基于人工智能的传感器优化布置算法策略，低信噪比、多工况下自适应的振动数据采集系统等重点发展方向。

Abstract

Large scale, complex, long life and multi-functional modern engineering structures are exposed to severe service environment for a long time, their structural function and state can deviate from the initial design goal. Using structural health monitoring technology to do health diagnosis and performance evaluation is an important means to ensure structural safety, extend service life and reduce maintenance cost, while sensor system is the primary link of structural health monitoring to directly determine the correctness of structural safety diagnosis. With increasing demands for security and functionality of structures to be monitored, sensor placement is more and more complex, and the high efficiency and high precision data acquisition system of structural state change also poses a higher challenge to the optimization of sensor layout. Here, advances of optimal sensor placement method and evaluation method were reviewed and commented, respectively. Several key problems to be urgently solved including coupling relation between input parameters and performance, reliability analysis, and large scale of sensor placement optimization algorithm’s precision, efficiency and evaluation in optimal sensor placement were extracted. Prospects to be developed in future were described including key development directions of optimal sensor placement method with incomplete information and optimal input parameters, multi-type optimal sensor placement method based on the information fusion technology, integrated design for multi-objective optimization sensor placement algorithm, optimal sensor placement algorithm strategy based on artificial intelligence, and adaptive vibration data sampling system under low signal-to-noise ratio and multiple working conditions.

导出引用

杨辰. 结构健康监测的传感器优化布置研究进展与展望[J]. 振动与冲击, 2020, 39(17): 82-93

YANG Chen. Advances and prospects for optimal sensor placement of structural health monitoring[J]. Journal of Vibration and Shock, 2020, 39(17): 82-93

参考文献

[1]欧进萍. 重大工程结构的智能检测与健康诊断[J]. 工程力学, 2002, 增刊: 44-53.
Ou Jinping. Accumulative damage and safety assessment of key infrastructures[J], Engineering Mechanics, 2002, supplement: 44-53.
[2]马宏伟, 杨桂通. 结构损伤探测的基本方法和研究进展[J]. 力学进展, 1999, 29(4): 513-527.
Ma Hongwei, Yang Guitong. Methods and advances of structural damage detection[J]. Advances in Mechanics, 1999, 29(4): 513-527.
[3]袁慎芳,邱雷,吴键, 等.大型飞机的发展对结构健康监测的需求与挑战[J].航空制造技术,2009,(22):62-67.
Yuan Shenfang, Qiu Lei, Wu Jian, et al. Challenge in structural health monitoring of large aircraft development[J]. Aeronautical Manufacturing Technology,2009,(22):62-67.
[4]武湛君,渠晓溪,高东岳, 等.航空航天复合材料结构健康监测技术研究进展[J].航空制造技术,2016,(15):92-102,109.
Wu Zhanjun, Qu Xiaoxi, Gao Dongyue, et al. Research Progress on Structural Health Monitoring Technology for Aerospace Composite Structure [J]. Aeronautical Manufacturing Technology,2016,(15):92-102,109.
[5]Ko J M, Ni Y Q. Technology developments in structural health monitoring of large-scale bridges[J]. Engineering structures, 2005, 27(12): 1715-1725.
[6]李惠, 鲍跃全, 李顺龙, 赖马树金. 结构健康监测数据科学与工程[M]. 科学出版社, 2016.
Li Hui, Bao yuequan, Li Shunlong, et al. Data science and engineering for structural health monitoring[M]. Science Press, 2016.
[7]卿新林,王奕首,赵琳.结构健康监测技术及其在航空航天领域中的应用[J].实验力学,2012,27(5):517-526.
Qing Xinlin, Wang Yishou, Zhao Lin. Structural health monitoring technology and its application in aeronautics and astronautics[J]. Journal of Experimental Mechanics, 2012, 27(5):517-52.
[8]吴智深, 张建. 结构健康监测先进技术及理论[M]. 科学出版社, 2015.
Wu Zhishen, Zhang Jian. Advanced technology and theory of structural health monitoring[M]. Science Press, 2015.
[9]姜绍飞, 吴兆旗. 结构健康监测与智能信息处理技术及应用[M]. 中国建筑工业出版社, 2011.
Jiang Shaofei, Wu Zhaoqi. Structural health monitoring and intelligent information processing technology and its application[M]. China Architecture & Building Press, 2011.
[10]伊廷华, 李宏男. 结构健康监测[M]. 中国建筑工业出版社, 2009.
Yi Tinghua, Li Hongnan. Structural health monitoring[M]. China Architecture & Building Press, 2009.
[11]刘伟. 空间网格结构健康监测系统关键技术研究[D]. 哈尔滨工业大学, 2009.
Liu Wei. Study on key technologies of health monitoring system for spatial lattice structures. [PhD Thesis]. Harbin Institute of Technology, 2009.
[12]Li J, Law S S. Substructural Damage Detection with Incomplete Information of the Structure[J]. Journal of Applied Mechanics, 2012, 79(4): 1003.
[13]Lynch J P, Loh K J. A summary review of wireless sensors and sensor networks for structural health monitoring[J]. Shock and Vibration Digest, 2006, 38(2): 91-130.
[14]伊廷华, 王相, 李宏男. 考虑敏感性和鲁棒性相协调的多维传感器优化布置方法[J]. 振动工程学报, 2013, 26(4): 467-476.
Yi Tinghua, Wang Xiang, Li Hongnan. Optimal multi-dimensional sensor placement in consideration of the coordination of sensitivity and robustness [J]. Journal of Vibration Engineering, 2013, 26(4): 467-476.
[15]周翠, 李东升, 李宏男. 结构模态测试传感器位置优选[J]. 振动工程学报, 2014(1): 84-90.
Zhou Cui, Li Dongsheng, Li Hongnan. Optimal multi-dimensional sensor placement in consideration of the coordination of sensitivity and robustness [J]. Journal of Vibration Engineering, 2014(1): 84-90.
[16]李东升, 张莹, 任亮,等. 结构健康监测中的传感器布置方法及评价准则[J]. 力学进展, 2011, 41(1):39-50.
Li Dongsheng, Zhang Ying, Ren Liang, et al. Sensor deployment for structural health monitoring and their evaluation [J]. Advances in Mechanics, 2011, 41(1):39-50.
[17]董晓马. 智能结构的损伤诊断及传感器优化配置研究[D]. 东南大学, 2006.
Dong Xiaoma. Research on damage self-diagnosing and sensor optimal placement of smart srtuctures. [PhD Thesis]. Southeast University, 2006.
[18]孙小猛. 基于模态观测的结构健康监测的传感器优化布置方法研究[D]. 大连理工大学, 2009.
Sun Xiaomeng. Study on optimal sensor placement for structural health monitoring with modal measurments. [PhD Thesis]. Dalian University of Technology, 2009.
[19]徐典. 结构损伤识别方法与传感器优化布置研究[D]. 重庆大学, 2011.
Xu Dian. Studies on structural damage detection and optimal sensor placement. [PhD Thesis]. Chongqing University, 2011.
[20]刘福强, 张令弥. 作动器/传感器优化配置的研究进展[J]. 力学进展, 2000, 30(4): 526-516.
Liu Fuqiang, Zhang Lingmi. Advances in optimal placement of actuators and sensors [J]. Advances in Mechanics, 2000, 30(4): 526-516.
[21]费庆国, 李爱群, 缪长青, 等. 基于主列筛选的动态测试传感器配置方法研究[J]. 力学学报, 2008, 40(4): 543-549.
Fei Qingguo, Li Aiqun, Miao Changqing, et al. Vibration sensor placement method based on principal subset selection [J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(4): 543-549.
[22]Li D S, Li H N, Frizen C P. On optimal sensor placement criterion for structural health monitoring with representative least squares method[J]. Key Engineering Materials, 2009, 413-414: 383-391
[23]李东升, 李宏男, 王国新, 等. 传感器布设中有效独立法的简捷快速算法[J]. 防灾减灾工程学报, 2009, 29(1): 103-108.
Li Dongsheng, Li Hongnan, Wang Guoxin, et al. Simple and fast computation algorithm of the effective independence for sensor placement [J]. Journal of Disaster Prevention and Mitigation Engineering, 2009, 29(1): 103-108.
[24]刘伟, 高维成, 李惠, 等. 基于有效独立的改进传感器优化布置方法研究[J]. 振动与冲击, 2013, 32(6): 54-62.
Liu Wei, Gao Weicheng, Li Hui, et al. Improved optimal sensor placement methods based on effective independence [J]. Journal of Vibration and Shock, 2013, 32(6): 54-62.
[25]Hernandez E M. Efficient Sensor Placement for State Estimation in Structural Dynamics[J]. Mechanical Systems & Signal Processing, 2017, 85: 789-800.
[26]Mercer J F, Aglietti G S, Kiley A M. Model Reduction and Sensor Placement Methods for Finite Element Model Correlation[J]. Aiaa Journal, 2016, 54(12): 1-14.
[27]Chen B, Huang Z, Zheng D, et al. A Hybrid Method of Optimal Sensor Placement for Dynamic Response Monitoring of Hydro-structures[J]. International Journal of Distributed Sensor Networks, 2017, 13(5): 155014771770772.
[28]Yang C, Lu Z X, Yang Z Y, Liang K. Parameter identification for structural dynamics based on interval analysis algorithm [J]. Acta Astronautica, 2018, 145: 131-140.
[29]Iliopoulos A, Shirzadeh R, Weijtjens W, et al. A Modal Decomposition and Expansion Approach for Prediction of Dynamic Responses on a Monopile Offshore Wind Turbine Using a Limited Number of Vibration Sensors[J]. Mechanical Systems & Signal Processing, 2016, s 68-69: 84-104.
[30]Ostachowicz W, Soman R, Malinowski P. Optimization of sensor placement for structural health monitoring: a review[J]. Structural Health Monitoring, 2019: 1475921719825601.
[31]刘效尧, 蔡健, 刘晖. 桥梁损伤诊断[M]. 人民交通出版社, 2002.
Liu Xiaoyao, Cai Jian, Liu hui. Bridge damage diagnoses [M]. China Communications Press, 2002.
[32]Feng S, Jia J Q. Acceleration sensor placement technique for vibration test in structural health monitoring using microhabitat frog-leaping algorithm[J]. Structural Health Monitoring, 2017 (1) :147592171668837.
[33]Yi T H, Li H N, Gu M. Optimal sensor placement for structural health monitoring based on multiple optimization strategies[J]. Structural Design of Tall and Special Buildings, 2011, 20(7): 881-900.
[34]Yi T H, Li H N, Zhang X D. A modified monkey algorithm for optimal sensor placement in structural health monitoring[J]. Smart Materials and Structures, 2012, 21(10): 105033.
[35]He C, Xing J C, Li J L, et al. A Combined Optimal Sensor Placement Strategy for the Structural Health Monitoring of Bridge Structures[J]. International Journal of Distributed Sensor Networks,2013,(2013-11-26), 2013, 2013(4):1-9.
[36]Jia J, Feng S, Liu W. A triaxial accelerometer monkey algorithm for optimal sensor placement in structural health monitoring[J]. Measurement Science & Technology, 2015, 26(6).
[37]Kammer D C. Sensor Placement for On-orbit Modal Identification and Correlation of Large Space Structures[J]. Journal of Guidance, Control and Dynamics, 1991, 14: 251-259.
[38]Carne T G, Dohrmann C R. A modal test design strategy for model correlation[C]. In: Proceedings of the 13th International Modal Analysis Conference, Nashcille, TN, USA, 1995.
[39]Heylen W, Lammens S. Modal analysis theory and testing[M]. Katholieke Unversiteit Leuven, 1998.
[40]DeClerck J P, Avitable P. Development of several new tools for pre-test evaluation[C]. In: Proceedings of the 16th International Modal Analysis Conference, Orlando, Fl, USA, 1998.
[41]Udwadia F E. Methodology for optimum sensor locations for parameter identification in dynamic systems[J]. Journal of Engineering Mechanics-ASCE, 1994, 120: 36-39.
[42]Papadopoulos M, Garicia E. Sensor placement methodologies for dynamic testing[J]. AIAA Journal, 1998, 36:256-263.
[43]Glassburn R S. Evaluation of sensor placement algorithms for on-orbit identification of space platforms[D]. Kentucky: Lexington, 1994.
[44]Chung Y T, Moore D. Selection of measurement locations for experimental modal analysis[C]. In: Proceedings of the 11th International Modal Analysis Conference, Orlando, Fl, USA, 1993.
[45]Pickrel C R. A practical approach to modal pretest design[J]. Mechanical System and Singnal Processing, 1999, 13: 271-295.
[46]Schedlinski C, Link M. An approach to optimal pick-up and exciter placement[C]. In: Proceedings of the 14th International Modal Analysis Conference, Orlando, Fl, USA, 1996.
[47]Park Y S, Kim H B. Sensor placement guide for model comparison and improvement[C]. In: Proceedings of the 14th international Modal Analysis Conference, Orlando, Fl, SA, 1996.
[48]Reynier M, Abou-Kandil H. Sensor location for updating problems[J]. Mechanical System and Singal Processing, 1999, 13(2): 297-314.
[49]Cherng A P. Optimal sensor placement for modal parameter identification using signal subspace correlation techniques[J]. Mechanical Systems and Signal Processing, 1999, 17(2): 361-378.
[50]Penny J, Friswell M I, Garvey S D. Automatic choice of measurement locations for modal survey test[J]. AIAA Journal, 1994, 32: 407-414.
[51]Ewins D J. Modal testing: theory, practice and application[M]. Research Studies Press, 2000.
[52]Friswell M I, Mottershead J E. Finite element model updating in structural dynamics[M]. Kluwer Academic Publisher, 1995.
[53]Flanigan C C, Botos C D. Automated selection of accelerometer locations for modal survey test. In: Proceedings of the 10th International Modal Analysis Conference, Orlando, Fl, USA, 1992
[54]Mercer J F, Aglietti G S, Kiley A M. Model reduction and sensor placement methods for finite element model correlation[J]. AIAA Journal, 2016, 54(12): 1-14.
[55]Meo M, Zumpano G. On the optimal sensor placement techniques for a bridge structure[J]. Engineering Structures, 2005, 27(10):1488-1497.
[56]Li D S, Li H N, Frizen C P. The connection between effective independence and modal kinetic energy methods for sensor placement. Journal of Sound and Vibration, 2007, 305: 945-955
[57]杨雅勋, 郝宪武, 孙磊. 基于能量系数-有效独立法的桥梁结构传感器优化布置[J]. 振动与冲击, 2010, 29(11): 119-123.
Yang Yaxun, Hao Xianwu, Sun Lei. Optimal placement of sensors for a bridge structure based on energy coefficient-effective independence method [J]. Journal of Vibration and Shock, 2010, 29(11): 119-123.
[58]詹杰子, 余岭. 传感器优化布置的有效独立-改进模态应变能方法[J]. 振动与冲击, 2017, 36(1): 82-87.
ZHAN Jie-zi，YU Ling. An effective independenceimproved modal strain energy method for optimal sensor placement. Journal of Vibration and Shock, 2017, 36(1): 82-87.
[59]吴子燕, 代凤娟, 宋静,等. 损伤检测中的传感器优化布置方法研究[J]. 西北工业大学学报, 2007, 25(4): 503-507.
Wu Ziyan, Dai Fengjuan, Song Jing, et al. A more efficient optimal sensor placement method for structure damage detection [J]. Journal of Northwestern Polytechnical University, 2007, 25(4): 503-507.
[60]Chen B, Huang Z, Zheng D, et al. A hybrid method of optimal sensor placement for dynamic response monitoring of hydro-structures[J]. International Journal of Distributed Sensor Networks, 2017, 13(5): 155014771770772.
[61]孙红春, 胥勇. 砂轮划片机模态测试中的传感器测点优化研究[J]. 振动与冲击, 2017, 36(5): 187-191.
SUN Hongchun, XU Yong. Optimal placement of sensors for modal testing of dicing saws. Journal of Vibration and Shock, 2017, 36(5): 187-191.
[62]Cruz A, Vélez W, Thomson P. Optimal sensor placement for modal identification of structures using genetic algorithms-a case study: the olympic stadium in cali, colombia[J]. Annals of Operations Research, 2010, 181(1): 769-781.
[63]Liu W, Gao W C, Sun Y, et al. Optimal sensor placement for spatial lattice structure based on genetic algorithms[J]. Journal of Sound and Vibration, 2008, 317(1-2): 175-189.
[64]Yao L, Sethares W A, Kammer D C. Sensor placement for on-orbit modal identification via a genetic algorithm[J]. AIAA Journal, 2012, 31(10): 1922-1928.
[65]Jung B K, Cho J R, Jeong W B. Sensor placement optimization for structural modal identification of flexible structures using genetic algorithm[J]. Journal of Mechanical Science and Technology, 2015, 29(7): 2775-2783.
[66]Mahdavi S H, Razak H A. Optimal sensor placement for time-domain identification using a wavelet-based genetic algorithm[J]. Smart Materials and Structures, 2016, 25(6): 065006.
[67]Downey A, Hu C, Laflamme S. Optimal sensor placement within a hybrid dense sensor network using an adaptive genetic algorithm with learning gene pool[J]. Structural Health Monitoring, 2017(10): 147592171770253.
[68]Seyedpoor S M. A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization[J]. Advances in Swarm Intelligence, 2012, 47(1):1-8.
[69]赵建华, 张陵, 孙清. 利用粒子群算法的传感器优化布置及结构损伤识别研究[J]. 西安交通大学学报, 2015(1):79-85.
Zhao Jianhua, Zhang Ling, Sun Qing. Optimal placement of sensors for structural damage identification using improved particle swarm optimization [J]. Journal of Xi'an Jiaotong University, 2015(1):79-85.
[70]Yi T H, Li H N, Zhang X D. Health monitoring sensor placement optimization for canton tower using immune monkey algorithm[J]. Structural Control and Health Monitoring, 2015, 22(1): 123-138.
[71]Yi T H, Li H N, Wang C. Multiaxial sensor placement optimization in structural health monitoring using distributed wolf algorithm[J]. Structural Control and Health Monitoring, 2016, 23(4): 719-734.
[72]Li S, Zhang H, Liu S, et al. Optimal sensor placement using FRFs-based clustering method[J]. Journal of Sound and Vibration, 2016, 385: 69-80.
[73]Yoganathan D, Kondepudi S, Kalluri B, et al. Optimal sensor placement strategy for office buildings using clustering algorithms[J]. Energy and Buildings, 2018, 158: 1206-1225.
[74]张恒, 李世其, 刘世平, 等. 一种聚类优化的传感器布置方法研究[J]. 振动与冲击, 2017, 36(14): 61-65.
Zhang Heng Li Shi-qi Liu Shi-ping et, al. An optimal sensor placement by using clustering method. Journal of Vibration and Shock, 2017, 36(14): 61-65.
[75]Sun H, Büyüköztürk O. Optimal sensor placement in structural health monitoring using discrete optimization[J]. Smart Materials and Structures, 2015, 24(12): 125034.
[76]Lu W, Wen R, Teng J, et al. Data correlation analysis for optimal sensor placement using a bond energy algorithm[J]. Measurement, 2016, 91: 509-518.
[77]Lian J J, He L J, Ma B, et al. Optimal sensor placement for large structures using the nearest neighbour index and a hybrid swarm intelligence algorithm[J]. Smart Materials and Structures, 2013, 22(9): 692-700.
[78]Li B, Kiureghian A D. Robust Optimal Sensor Placement for Operational Modal Analysis Based on Maximum Expected Utility[J]. Mechanical Systems & Signal Processing, 2016, 75: 155-175.
[79]Molyboha A, Zabarankin M. Stochastic optimization of sensor placement for diver detection[J]. Operations research, 2012, 60(2): 292-312.
[80]Guratzsch R F, Mahadevan S. Structural health monitoring sensor placement optimization under uncertainty[J]. AIAA journal, 2010, 48(7): 1281-1289.
[81]Castro-Triguero R, Saavedra Flores E I, DiazDelaO F A, et al. Optimal sensor placement in timber structures by means of a multi-scale approach with material uncertainty[J]. Structural Control and Health Monitoring, 2014, 21(12): 1437-1452.
[82]Castro-Triguero R, Murugan S, Gallego R, et al. Robustness of optimal sensor placement under parametric uncertainty[J]. Mechanical Systems and Signal Processing, 2013, 41(1-2): 268-287.
[83]Vincenzi L, Simonini L. Influence of model errors in optimal sensor placement[J]. Journal of Sound and Vibration, 2017, 389: 119-133.
[84]Kim T, Youn B D, Oh H. Development of a stochastic effective independence (SEfI) method for optimal sensor placement under uncertainty[J]. Mechanical Systems and Signal Processing, 2018, 111: 615-627.
[85]Papadimitriou C, Lombaert G. The effect of prediction error correlation on optimal sensor placement in structural dynamics[J]. Mechanical Systems and Signal Processing, 2012, 28: 105-127.
[86]Qiu Z, Elishakoff I. Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis[J]. Computer methods in applied mechanics and engineering, 1998, 152(3-4): 361-372.
[87]Qiu Z, Wang X. Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach[J]. International Journal of Solids and structures, 2003, 40(20): 5423-5439.
[88]王磊, 王晓军, 邱志平. 不确定性结构分析与优化设计专题• 编者按[J]. 中国科学: 物理学力学天文学, 2018 (1): 2.
Wang Lei, Wang Xiaojun, Qiu Zhiping. Special topic: Uncertainty-based structural analysis and design optimization [J]. SCIENTIA SINICA Physica,Mechanica & Astronomica, 2018 (1): 2.
[89]Yang C, Lu Z X, Yang Z Y. Robust optimal sensor placement for uncertain structures with interval parameters [J]. IEEE Sensors Journal, 2018, 18(5): 2031-2041.
[90]Yang C, Lu Z X. An interval effective independence method for optimal sensor placement based on non-probabilistic approach [J]. SCIENCE CHINA Technological Sciences, 2017, 60(2): 186-198.
[91]Stephan C. Sensor placement for modal identification[J]. Mechanical Systems and Signal Processing, 2012, 27(1):461-470.
[92]Friswell M I, Castrotriguero R. Clustering of sensor locations using the effective independence method[J]. AIAA Journal, 2015, 53(5): 1-3.
[93]Li D S, Li H N, Fritzen C P. Comments on “Clustering of sensor locations using the effective independence method”[J]. AIAA Journal, 2016, 54(6): 1-2.
[94]何龙军, 练继建, 马斌,等. 基于距离系数-有效独立法的大型空间结构传感器优化布置[J]. 振动与冲击, 2013, 32(16): 13-18.
He Longjun, Lian Jijian, Ma Bin, et al. Optimal sensor placement for large space structures based on distance coefficient-effective independence method [J]. Journal of Vibration and Shock, 2013, 32(16): 13-18.
[95]张建伟, 刘轩然, 赵瑜,等. 基于有效独立-总位移法的水工结构振测传感器优化布置[J]. 振动与冲击, 2016, 35(8): 148-153.
Zhang Jianwei, Liu Xuanran, Zhao Yu, et al. Optimal sensor placement for hydraulic structures based on effective independence-total displacement method [J]. Journal of Vibration and Shock, 2016, 35(8): 148-153.
[96]Bonisoli E, Delprete C, Rosso C. Proposal of a modal-geometrical-based master nodes selection criterion in modal analysis[J]. Mechanical Systems and Signal Processing, 2009, 23: 606-620.
[97]Vincenzi L, Simonini L. Influence of model errors in optimal sensor placement[J]. Journal of Sound and Vibration, 2017, 389: 119-133.
[98]蔡智恒，周金柱，唐宝富，等. 面向结构形变重构的应变传感器优化布局[J]. 振动与冲击, 2019, 38(14): 83-88.
CAI Zhiheng，ZHOU Jinzhu，TANG Baofu，et al. Optimal strain sensor placement for structural deformation reconstruction. Journal of Vibration and Shock, 2019, 38(14): 83-88.
[99]Yang C, Zhang X P, Huang X Q, et al. Optimal sensor placement for deployable antenna module health monitoring in ssps using genetic algorithm[J]. Acta Astronautica, 2017, 140: 213-224.
[100]Yang C, Liang K, Zhang X P, Geng X Y. Sensor placement algorithm for structural health monitoring with redundancy elimination model based on sub-clustering strategy [J]. Mechanical Systems and Signal Processing, 2019, 124: 369-387.
[101]Yang C. Sensor placement for structural health monitoring using hybrid optimization algorithm based on sensor distribution index and FE grids [J]. Structural Control and Health Monitoring, 2018, e2160.
[102]Yang C, Zheng W Z, Zhang X P. Optimal sensor placement for spatial lattice structure based on three-dimensional redundancy elimination model [J]. Applied Mathematical Modelling, 2019, 66: 576-591.
[103]Santi L M, Sowers T S, Aguila R B. Optimal sensor selection for health monitoring systems[C]. NASA/TM-2005-213955, AIAA-2005-4485, 2005.
[104]Yi T H, Li H N. Methodology developments in sensor placement for health monitoring of civil infrastructures[J]. International Journal of Distributed Sensor Networks, 2012: 601-617.
[105]伊廷华, 李宏男, 顾明. 结构健康监测中基于多重优化策略的传感器布置方法[J]. 建筑结构学报, 2011, 32(12): 217-223.
Yi Tinghua, Li Hongnan, Gu Ming. Multiple optimization strategies based sensor placement method for structural health monitoring [J]. Journal of Building Structures, 2011, 32(12): 217-223.
[106]Zhang J, Maes K, Roeck G D, et al. Optimal sensor placement for multi-setup modal analysis of structures[J]. Journal of Sound and Vibration, 2017, 401: 214-232.
[107]Yang W, Sun L, Yu G. Optimal Sensor placement methodology for uncertainty reduction in the assessment of structural condition[J]. Structural Control and Health Monitoring, 2017, 24(6): e1927.
[108]Yuen K, Kuok S. Efficient Bayesian Sensor Placement Algorithm for Structural Identification: A General Approach for Multi-Type Sensory Systems[J]. Earthquake Engineering & Structural Dynamics, 2015, 44(5): 757-774.
[109]Li B B, Li D S, Zhao X F, et al. Optimal sensor placement in health monitoring of suspension bridge[J]. Science China Technological Sciences, 2012, 55(7): 2039-2047.
[110]Liu K, Yan R J, Soares C G. Optimal sensor placement and assessment for modal identification[J]. Ocean Engineering, 2018, 165: 209-220.
[111]王娟. 结构时域辨识方法及传感器优化布置问题研究[D]. 北京交通大学, 2013.
Wang Juan. Studies on structural system identification and optimal sensor placement methods in time domain. [PhD Thesis]. Beijing Jiaotong Technology, 2013.
[112]Salehpour-Oskouei F, Pourgol-Mohammad M. Sensor placement determination in system health monitoring process based on dual information risk and uncertainty criteria[J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2018, 232(1): 65-81.
[113]Zhang C D, Xu Y L. Optimal multi-type sensor placement for response and excitation reconstruction[J]. Journal of Sound and Vibration, 2016, 360: 112-128.
[114]Zhang J, Maes K, De Roeck G, et al. Optimal sensor placement for multi-setup modal analysis of structures[J]. Journal of Sound and Vibration, 2017, 401: 214-232.
[115]Zhang X H, Xu Y L, Zhu S, et al. Dual-type sensor placement for multi-scale response reconstruction[J]. Mechatronics, 2014, 24(4): 376-384.
[116]Lin J F, Xu Y L, Law S S. Structural damage detection-oriented multi-type sensor placement with multi-objective optimization[J]. Journal of Sound and Vibration, 2018, 422: 568-589.
[117]Soman R, Kyriakides M, Onoufriou T, et al. Numerical evaluation of multi-metric data fusion based structural health monitoring of long span bridge structures[J]. Structure and Infrastructure Engineering, 2018, 14(6): 673-684.
[118]Domingo-Perez F, Lazaro-Galilea J L, Wieser A, et al. Sensor placement determination for range-difference positioning using evolutionary multi-objective optimization[J]. Expert Systems with Applications, 2016, 47: 95-105.
[119]Xu Y L, Zhang X H, Zhu S, et al. Multi-type sensor placement and response reconstruction for structural health monitoring of long-span suspension bridges[J]. Science bulletin, 2016, 61(4): 313-329.
[120]曾超, 汤宝平, 肖鑫, 等. 低功耗机械振动无线传感器网络节点结构设计[J]. 振动与冲击, 2017, 36(14): 33-37.
ZENG Chao，TANG Bao-ping，XIAO Xin，et al. Low power architecture design method of mechanical vibration wireless sensor networks node. Journal of Vibration and Shock, 2017, 36(14): 33-37.