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http://dx.doi.org/10.12989/sem.2021.79.5.619

Frequency-based tension assessment of an inclined cable with complex boundary conditions using the PSO algorithm  

Zhang, Wen-ming (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
Wang, Zhi-wei (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
Feng, Dan-dian (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
Liu, Zhao (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
Publication Information
Structural Engineering and Mechanics / v.79, no.5, 2021 , pp. 619-639 More about this Journal
Abstract
The frequency-based method is the most commonly used method for measuring cable tension. However, the calculation formulas for the conventional frequency-based method are generally based on the ideally hinged or fixed boundary conditions without a comprehensive consideration of the inclination angle, sag-extensibility, and flexural stiffness of cables, leading to a significant error in cable tension identification. This study aimed to propose a frequency-based method of cable tension identification considering the complex boundary conditions at the two ends of cables using the particle swarm optimization (PSO) algorithm. First, the refined stay cable model was established considering the inclination angle, flexural stiffness, and sag-extensibility, as well as the rotational constraint stiffness and lateral support stiffness for the unknown boundaries of cables. The vibration mode equation of the stay cable model was discretized and solved using the finite difference method. Then, a multiparameter identification method based on the PSO algorithm was proposed. This method was able to identify the tension, flexural stiffness, axial stiffness, boundary rotational constraint stiffness, and boundary lateral support stiffness according to the measured multiorder frequencies in a synchronous manner. The feasibility and accuracy of this method were validated through numerical cases. Finally, the proposed approach was applied to the tension identification of the anchor span strands of a suspension bridge (Jindong Bridge) in China. The results of cable tension identification using the proposed method and the existing methods discussed in previous studies were compared with the on-site pressure ring measurement results. The comparison showed that the proposed approach had a high accuracy in cable tension identification. Moreover, the synchronous identification of the flexural stiffness, axial stiffness, boundary rotational constraint stiffness, and boundary lateral support stiffness was highly beneficial in improving the results of cable tension identification.
Keywords
boundary constraint stiffness; cable tension; finite difference method; frequency-based method; multiparameter identification; particle swarm optimization algorithm;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Dan, D., Chen, Y. and Xu, B. (2015), "A PSO driven intelligent model updating and parameter identification scheme for cable-damper system", Shock Vib., 2015, 423898. https://doi.org/10.1155/2015/423898.   DOI
2 Dan, D., Xu, B., Xia, Y., Yan, X. and Jia, P. (2018b), "Intelligent parameter identification for bridge cables based on characteristic frequency equation of transverse dynamic stiffness", J. Low Freq. Noise Vib. Act. Control, 39(3), 678-689. https://doi.org/10.1177/1461348418814617.   DOI
3 Dan, D.H., Xia, Y., Xu, B., Han, F. and Yan, X.F. (2018a), "Multistep and multiparameter identification method for bridge cable systems", J. Bridge Eng., 23(1), 04017111. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001145.   DOI
4 Kennedy, J. and Eberhart, R. (1995), "Particle swarm optimization", Proceedings of ICNN'95-International Conference on Neural Networks, Perth, Australia, November.
5 Eberhart, R.C. and Shi, Y. (2000), "Comparing inertia weights and constriction factors in particle swarm optimization", Proceedings of the 2000 Congress on Evolutionary Computation (CEC00), La Jolla, USA, July.
6 Fang, Z. and Wang, J.Q. (2012), "Practical formula for cable tension estimation by vibration method", J. Bridge Eng., 17(1), 161-164. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000200.   DOI
7 Irvine, H.M. (1981), Cable Structures, The MIT Press, Cambridge, Mass, USA.
8 Jeong, S., Kim, H., Lee, J. and Sim, S.H. (2020), "Automated wireless monitoring system for cable tension forces using deep learning", Struct. Hlth. Monit., 20(4), 1805-1821. https://doi.org/10.1177/1475921720935837.   DOI
9 Kim, S.W., Cheung, J.H., Park, J.B. and Na, S.O. (2020), "Image-based back analysis for tension estimation of suspension bridge hanger cables", Struct. Control. Hlth. Monit., 27(4), e2508. https://doi.org/10.1002/stc.2508.   DOI
10 Liao, W.Y., Ni, Y.Q. and Zheng, G. (2012), "Tension force and structural parameter identification of bridge cables", Adv. Struct. Eng., 15(6), 983-995. https://doi.org/10.1260/1369-4332.15.6.983.   DOI
11 Ma, L. (2017), "A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions", J. Sound Vib., 409, 65-80. https://doi.org/10.1016/j.jsv.2017.07.043.   DOI
12 Ma, L., Xu, H., Munkhbaatar, T. and Li, S.F. (2021), "An accurate frequency-based method for identifying cable tension while considering environmental temperature variation", J. Sound Vib., 490, 115693. https://doi.org/10.1016/j.jsv.2020.115693.   DOI
13 Mebrabi, A.B. and Tabatabai, H. (1998), "Unified finite difference formulation for free vibration of cables", J. Struct. Eng., 124(11), 1313-1322. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:11(1313).   DOI
14 Clerc, M. and Kennedy, J. (2002), "The particle swarm-explosion, stability, and convergence in a multidimensional complex space", IEEE Tran. Evol. Comput., 6(1), 58-73. https://doi.org/10.1109/4235.985692.   DOI
15 Rango, B.J., Serralunga, F.J., Piovan, M.T., Ballaben, J.S. and Rosales, M.B. (2019), "Identification of the tension force in cables with insulators", Meccanica, 54(1-2), 33-46. https://doi.org/10.1007/s11012-018-00941-w.   DOI
16 Ren, W.X., Chen, G. and Hu, W.H. (2005), "Empirical formulas to estimate cable tension by cable fundamental frequency", Struct. Eng. Mech., 20(3), 363-380. https://doi.org/10.12989/sem.2005.20.3.363.   DOI
17 Ni, Y.Q., Ko, J.M. and Zheng, G. (2002), "Dynamic analysis of large-diameter sagged cables taking into account flexural rigidity", J. Sound. Vib., 257(2), 301-319. https://doi.org/10.1006/jsvi.2002.5060.   DOI
18 Kim, B.H. and Park, T. (2007), "Estimation of cable tension force using the frequency-based system identification method", J. Sound Vib., 304(3-5), 660-676. https://doi.org/10.1016/j.jsv.2007.03.012.   DOI
19 Ricciardi, G. and Saitta, F. (2008), "A continuous vibration analysis model for cables with sag and bending stiffness", Eng. Struct., 30(5), 1459-1472. https://doi.org/10.1016/j.engstruct.2007.08.008.   DOI
20 Robinson, J. and Rahmat-Samii,Y. (2004), "Particle swarm optimization in electromagnetics", IEEE Tran. Antennas Propag., 52(2), 397-407. https://doi.org/10.1109/TAP.2004.823969.   DOI
21 Russell, J.C. and Lardner, T.J. (1998), "Experimental determination of frequencies and tension for elastic cables", J. Eng. Mech., 124(10), 1067-1072. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:10(1067).   DOI
22 Shi, Y. and Eberhart, R. (1998), "A modified particle swarm optimizer", 1998 IEEE International Conference on Evolutionary Computation Proceedings, Anchorage, USA, May.
23 Triantafyllou, M.S. (1984), "The dynamics of taut inclined cables", Q. J. Mech. Appl. Math., 37(3), 421-440. https://doi.org/10.1093/qjmam/37.3.421.   DOI
24 Casas, J.R. (1994), "A combined method for measuring cable forces: The cable-stayed Alamillo Bridge, Spain", Struct. Eng. Int., 4(4), 235-240. https://doi.org/10.2749/101686694780601700.   DOI
25 Chen, C.C., Wu, W.H., Chen, S.Y. and Lai, G. (2018), "A novel tension estimation approach for elastic cables by elimination of complex boundary condition effects employing mode shape functions", Eng. Struct., 166, 152-166. https://doi.org/10.1016/j.engstruct.2018.03.070.   DOI
26 Chen, C.C., Wu, W.H., Huang, C.H. and Lai, G. (2013), "Determination of stay cable force based on effective vibration length accurately estimated from multiple measurements", Smart. Struct. Syst., 11(4), 411-433. https://doi.org/10.12989/sss.2013.11.4.411.   DOI
27 Chen, C.C., Wu, W.H., Leu, M.R. and Lai, G. (2016), "Tension determination of stay cable or external tendon with complicated constraints using multiple vibration measurements", Measure., 86, 182-195. https://doi.org/10.1016/j.measurement.2016.02.053.   DOI
28 Clerc, M. (1999), "The swarm and the queen: towards a deterministic and adaptive particle swarm optimization", Proceedings of the 1999 Congress on Evolutionary Computation (CEC99), Washington, USA, July.
29 Xu, B., Dan, D. and Zou, Y. (2019), "Accurate identification method and practical formula of suspender tension based on tri-segment suspender dynamic model", Eng. Struct., 200, 109710. https://doi.org/10.1016/j.engstruct.2019.109710.   DOI
30 Triantafyllou, M.S. and Grinfogel, L. (1986), "Natural frequencies and modes of inclined cables", J. Struct. Eng., 112(1), 139-148. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:1(139).   DOI
31 Van den Bergh, F. and Engelbrecht, A.P. (2006), "A study of particle swarm optimization particle trajectories", Inf. Sci., 176(8), 937-971. https://doi.org/10.1016/j.ins.2005.02.003.   DOI
32 Yan, B., Chen, W., Yu, J. and Jiang, X. (2019), "Mode shape-aided tension force estimation of cable with arbitrary boundary conditions", J. Sound Vib., 440, 315-331. https://doi.org/10.1016/j.jsv.2018.10.018.   DOI
33 Zarbaf, S.E.H.A.M., Norouzi, M., Allemang, R., Hunt, V., Helmicki, A. and Venkatesh, C. (2018), "Vibration-based cable condition assessment: A novel application of neural networks", Eng. Struct., 177, 291-305. https://doi.org/10.1016/j.engstruct.2018.09.060.   DOI
34 Zarbaf, S.E.H.A.M., Norouzi, M., Allemang, R.J., Hunt, V.J. and Helmicki, A. (2017), "Stay cable tension estimation of cable-stayed bridges using genetic algorithm and particle swarm optimization", J. Bridge Eng., 22(10), 05017008. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001130.   DOI
35 Zui, H., Shinke, T. and Namita, Y. (1996), "Practical formulas for estimation of cable tension by vibration method", J. Struct. Eng., 122(6), 651-656. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:6(651).   DOI
36 Li, H., Zhang, F. and Jin, Y. (2014), "Real-time identification of time-varying tension in stay cables by monitoring cable transversal acceleration", Struct. Control. Hlth. Monit., 21(7), 1100-1117. https://doi.org/10.1002/stc.1634.   DOI
37 Xie, X. and Li, X. (2014), "Genetic algorithm-based tension identification of hanger by solving inverse eigenvalue problem", Inverse Prob. Sci. Eng., 22(6), 966-987. https://doi.org/10.1080/17415977.2013.848432.   DOI