Biobjective Optimization of Cable Force for Concrete Cable-Stayed Bridges Considering the Requirements of the Serviceability and Ultimate Limit State
Publication: Journal of Bridge Engineering
Volume 29, Issue 6
Abstract
This study proposes an efficient biobjective cable force optimization strategy for concrete cable-stayed bridges aiming to maximize the safety of the structure under both the serviceability and ultimate limit state required by the design specifications. The multitude of potential load cases within limit states renders cable force optimization approaches challenged to fully satisfy code requirements, leading to encumbered complexity and computational expense. The proposed method utilized a load decoupling approach to separate the effects induced by the cable forces from other load effects to overcome this shortcoming. Furthermore, the relationship between the structural responses and cable forces was established explicitly using the influence matrix method, which aims to eliminate the finite-element method-based structural analysis in the iterations. A practical concrete cable-stayed bridge was utilized to examine the performance of the proposed method. The Pareto optimal fronts yielded by four different multiobjective optimization algorithms show a good agreement with each other, and all the computational time costs by them are less than 50 s for each run. The comparative analysis of different cable stretching plans demonstrates that optimizing the initial stretching cable forces and the final cable forces under the bridge finished state simultaneously can significantly improve the safety of cable-stayed bridges. The results also illustrate that the proposed strategy is a high-efficiency and specification-oriented cable force optimization solution for short-to-medium concrete cable-stayed bridges.
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Data Availability Statement
All data, models, or codes generated or used during the study are available from the corresponding author by request.
Acknowledgments
The authors acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51708436) and the Hubei Provincial Natural Science Foundation of China (2018CFB609).
References
Arellano, H., D. Tolentino, and R. Gómez. 2019. “Optimum criss crossing cables in multi-span cable-stayed bridges using genetic algorithms.” KSCE J. Civ. Eng. 23 (2): 719–728. https://doi.org/10.1007/s12205-018-5736-2.
Atmaca, B. 2021. “Size and post-tensioning cable force optimization of cable-stayed footbridge.” Structures 33: 2036–2049. https://doi.org/10.1016/j.istruc.2021.05.050.
Cao, H., Y. Chen, L. Yang, and L. Feng. 2021. “Hanger pre-tensioning force optimization of steel tied-arch bridges considering operational loads.” Struct. Multidiscip. Optim. 63 (1): 867–880. https://doi.org/10.1007/s00158-020-02717-x.
Cao, H., X. Qian, Z. Chen, and H. Zhu. 2017. “Layout and size optimization of suspension bridges based on coupled modelling approach and enhanced particle swarm optimization.” Eng. Struct. 146: 170–183. https://doi.org/10.1016/j.engstruct.2017.05.048.
Chen, D. W., F. T. K. Au, L. G. Tham, and P. K. K. Lee. 2000. “Determination of initial cable forces in prestressed concrete cable-stayed bridges for given design deck profiles using the force equilibrium method.” Comput. Struct. 74 (1): 1–9. https://doi.org/10.1016/S0045-7949(98)00315-0.
Cheng, J. 2010. “Optimum design of steel truss arch bridges using a hybrid genetic algorithm.” J. Constr. Steel Res. 66 (8–9): 1011–1017. https://doi.org/10.1016/j.jcsr.2010.03.007.
Cid, C., A. Baldomir, and S. Hernández. 2018. “Optimum crossing cable system in multi-span cable-stayed bridges.” Eng. Struct. 160: 342–355. https://doi.org/10.1016/j.engstruct.2018.01.019.
Deb, K., and H. Jain. 2014. “An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints.” IEEE Trans. Evol. Comput. 18 (4): 577–601. https://doi.org/10.1109/TEVC.2013.2281535.
Deb, K., A. Pratap, S. Agarwal, and T. Meyarivan. 2002. “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Trans. Evol. Comput. 6 (2): 182–197. https://doi.org/10.1109/4235.996017.
Fan, Z., W. Li, X. Cai, H. Li, C. Wei, Q. Zhang, K. Deb, and E. Goodman. 2019. “Push and pull search for solving constrained multi-objective optimization problems.” Swarm Evol. Comput. 44: 665–679. https://doi.org/10.1016/j.swevo.2018.08.017.
Feng, Y., C. Lan, B. Briseghella, L. Fenu, and T. Zordan. 2022. “Cable optimization of a cable-stayed bridge based on genetic algorithms and the influence matrix method.” Eng. Optim. 54 (1): 20–39. https://doi.org/10.1080/0305215X.2020.1850709.
Ferreira, F., and L. Simões. 2020. “Synthesis of three dimensional controlled cable-stayed bridges subject to seismic loading.” Comput. Struct. 226: 106137. https://doi.org/10.1016/j.compstruc.2019.106137.
Gao, Q., M.-G. Yang, and J.-D. Qiao. 2017. “A multi-parameter optimization technique for prestressed concrete cable-stayed bridges considering prestress in girder.” Struct. Eng. Mech. 64 (5): 567–577.
Guo, J., W. Yuan, X. Dang, and M. S. Alam. 2019. “Cable force optimization of a curved cable-stayed bridge with combined simulated annealing method and cubic B-spline interpolation curves.” Eng. Struct. 201: 109813. https://doi.org/10.1016/j.engstruct.2019.109813.
Ha, M.-H., Q.-A. Vu, and V.-H. Truong. 2018. “Optimum design of stay cables of steel cable-stayed bridges using nonlinear inelastic analysis and genetic algorithm.” Structures 16: 288–302. https://doi.org/10.1016/j.istruc.2018.10.007.
Haber, R. B., and J. F. Abel. 1982. “Initial equilibrium solution methods for cable reinforced membranes part I—Formulations.” Comput. Methods Appl. Mech. Eng. 30 (3): 263–284. https://doi.org/10.1016/0045-7825(82)90080-9.
Haifan, X., and F. Lichu. 2001. Advanced theory of bridge structure. Beijing: China Communications Press.
Haji Agha Mohammad Zarbaf, S. E., M. Norouzi, R. J. Allemang, V. J. Hunt, and A. Helmicki. 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.
Hassan, M. M., A. O. Nassef, and A. A. El Damatty. 2012. “Determination of optimum post-tensioning cable forces of cable-stayed bridges.” Eng. Struct. 44: 248–259. https://doi.org/10.1016/j.engstruct.2012.06.009.
Hassan, M. M., A. O. Nassef, and A. A. El Damatty. 2013. “Surrogate function of post-tensioning cable forces for cable-stayed bridges.” Adv. Struct. Eng. 16 (3): 559–578. https://doi.org/10.1260/1369-4332.16.3.559.
Ho, V. L., S. Khatir, G. D. Roeck, T. Bui-Tien, and M. Abdel Wahab. 2020. “Finite element model updating of a cable-stayed bridge using metaheuristic algorithms combined with Morris method for sensitivity analysis.” Smart Struct. Syst. 26 (4): 451–468.
Janjic, D., M. Pircher, and H. Pircher. 2003. “Optimization of cable tensioning in cable-stayed bridges.” J. Bridge Eng. 8 (3): 131–137. https://doi.org/10.1061/(ASCE)1084-0702(2003)8:3(131).
Jie, D., Q. Feng-jiang, D. Jin, and C. Yong-rui. 2019. “Review on cable force optimization method for cable-stayed bridge in completed bridge state.” China J. Highway Transp. 32 (5): 17.
JTG-3362. 2018. Specifications for design of highway reinforced concrete and prestressed concrete bridges and culverts. Beijing: China Communications Press.
JTG-D60. 2015. General specifications for design of highway bridges and culverts. Beijing: China Communications Press.
JTG/T-3365-01. 2020. Specifications for design of highway cable-stayed bridge. Beijing: China Communications Press.
Kasuga, A., H. Arai, J. E. Breen, and K. Furukawa. 1995. “Optimum cable-force adjustments in concrete cable-stayed bridges.” J. Struct. Eng. 121 (4): 685–694. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:4(685).
Latif, M. A., and M. P. Saka. 2019. “Optimum design of tied-arch bridges under code requirements using enhanced artificial bee colony algorithm.” Adv. Eng. Softw. 135: 102685. https://doi.org/10.1016/j.advengsoft.2019.102685.
Lee, T.-Y., Y.-H. Kim, and S.-W. Kang. 2008. “Optimization of tensioning strategy for asymmetric cable-stayed bridge and its effect on construction process.” Struct. Multidiscip. Optim. 35 (6): 623–629. https://doi.org/10.1007/s00158-007-0172-9.
Li, Y., J.-L. Wang, and S.-S. Ge. 2017. “Optimum calculation method for cable force of concrete-filled steel tube arch bridge in inclined cable-stayed construction.” J. Highway Transp. Res. Dev 11 (1): 42–48.
Lute, V., A. Upadhyay, and K. K. Singh. 2009. “Computationally efficient analysis of cable-stayed bridge for GA-based optimization.” Eng. Appl. Artif. Intell. 22 (4–5): 750–758. https://doi.org/10.1016/j.engappai.2009.04.001.
Martins, A. M. B., L. M. C. Simões, and J. H. J. O. Negrão. 2015. “Cable stretching force optimization of concrete cable-stayed bridges including construction stages and time-dependent effects.” Struct. Multidiscip. Optim. 51 (3): 757–772. https://doi.org/10.1007/s00158-014-1153-4.
Martins, A. M. B., L. M. C. Simões, and J. H. J. O. Negrão. 2016. “Optimum design of concrete cable-stayed bridges.” Eng. Optim. 48 (5): 772–791. https://doi.org/10.1080/0305215X.2015.1057057.
Martins, A. M. B., L. M. C. Simões, and J. H. J. O. Negrão. 2019. “Optimization of concrete cable-stayed bridges under seismic action.” Comput. Struct. 222: 36–47. https://doi.org/10.1016/j.compstruc.2019.06.008.
Martins, A. M. B., L. M. C. Simões, and J. H. J. O. Negrão. 2020. “Optimization of cable-stayed bridges: A literature survey.” Adv. Eng. Softw. 149: 102829. https://doi.org/10.1016/j.advengsoft.2020.102829.
MIDAS. 2020. MIDAS/CIVIL computer program. Tokyo: MIDAS IT.
Naderian, H., M. M. S. Cheung, Z. Shen, and E. Dragomirescu. 2015. “Integrated finite strip analysis for long-span cable-stayed bridges.” Comput. Struct. 158: 82–97. https://doi.org/10.1016/j.compstruc.2015.05.031.
Ru-cheng, X., J. Li-jun, S. Xin, and X. Hai-Fan. 2001. “Influence matrix method of cable tension optimization for long-span cable-stayed bridges.” In Proc., IABSE Symp. report, Int. Association for Bridge and Structural Engineering, 1–5. Zurich, Switzerland: International Association for Bridge and Structural Engineering (IABSE).
Song, C., R. Xiao, B. Sun, Z. Wang, and C. Zhang. 2023. “Cable force optimization of cable-stayed bridges: A surrogate model-assisted differential evolution method combined with B-spline interpolation curves.” Eng. Struct. 283: 115856. https://doi.org/10.1016/j.engstruct.2023.115856.
Tian, Y., R. Cheng, X. Zhang, F. Cheng, and Y. Jin. 2017a. “An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility.” IEEE Trans. Evol. Comput. 22 (4): 609–622. https://doi.org/10.1109/TEVC.2017.2749619.
Tian, Y., R. Cheng, X. Zhang, and Y. Jin. 2017b. “PlatEMO: A MATLAB platform for evolutionary multi-objective optimization [educational forum].” IEEE Comput. Intell. Mag. 12 (4): 73–87. https://doi.org/10.1109/MCI.2017.2742868.
Tran, N. H., S. Khatir, G. De Roeck, L. Nguyen, T. T. Bui, and M. Abdel Wahab. 2020. “An efficient approach for model updating of a large-scale cable-stayed bridge using ambient vibration measurements combined with a hybrid metaheuristic search algorithm.” Smart Struct. Syst. 25 (4): 487–499.
Wang, L., Z. Xiao, M. Li, and N. Fu. 2023a. “Cable force optimization of cable-stayed bridge based on multiobjective particle swarm optimization algorithm with mutation operation and the influence matrix.” Appl. Sci. 13 (4): 2611. https://doi.org/10.3390/app13042611.
Wang, Y. C., A. S. Vlahinos, and H. Shu. 1997. “Optimization of cable preloading on cable-stayed bridges.” In Proc., Smart Structures and Materials 1997: Smart Systems for Bridges, Structures, and Highways, SPIE, 248–259. Bellingham, WA: SPIE.
Wang, Z., N. Zhang, and Q. Cheng. 2023b. “Multi-objective optimization-based reasonable finished state in long-span cable-stayed bridge considering counterweights.” Structures 40: 1497–1506. https://doi.org/10.1016/j.istruc.2023.03.061.
Wu, X., and B. L. Li. 2015. “Estimation and optimization of cable force in completion state of cable-stayed bridge.” Appl. Mech. Mater. 744–746: 763–766. https://doi.org/10.4028/www.scientific.net/AMM.744-746.763.
Yang, J. 2010. “Determining the rational completion cable forces based on influence matrix method united minimum bending energy method.” Traffic Transp. Stud. 2010: 1417–1424. https://doi.org/10.1061/41123(383)136.
Zhang, J., and F. T. K. Au. 2014. “Calibration of initial cable forces in cable-stayed bridge based on Kriging approach.” Finite Elem. Anal. Des. 92: 80–92. https://doi.org/10.1016/j.finel.2014.08.007.
Zhang, T., and H. F. Bai. 2011. “Analysis of cable-stayed bridge for APDL-based optimization.” Adv. Mater. Res. 243–249: 1567–1572.
Zhang, W.-M., Z.-H. Zhang, G.-M. Tian, and J.-Q. Chang. 2023. “Determining the reasonable completed bridge state of a self-anchored suspension bridge with a spatial cable system based on minimum bending strain energy: An analytical algorithm.” J. Bridge Eng. 28 (5): 04023018. https://doi.org/10.1061/JBENF2.BEENG-5857.
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Published In
Journal of Bridge Engineering
Volume 29 • Issue 6 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jul 13, 2023
Accepted: Jan 2, 2024
Published online: Mar 19, 2024
Published in print: Jun 1, 2024
Discussion open until: Aug 19, 2024
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