Role of Cable Forces in the Model Updating of Cable-Stayed Bridges
Publication: Journal of Bridge Engineering
Volume 28, Issue 7
Abstract
This paper presents and discusses the feasibility of complete model updating of cable-stayed bridges using experimental estimates of the cable forces and modal parameters. The procedure is applied to the model updating of a curved cable-stayed bridge in Venice (Italy). Conventional optimization problems of mass and stiffness using ambient vibration data are prone to ill-posedness and ill-conditioning. Generally, the scholar must assume one of the two to achieve a trustworthy optimization. This paper demonstrates that it is possible to assess a large set of parameters affecting the mass and stiffness of a cable-stayed bridge following a step-wise procedure based on ambient vibration tests. Preliminary variance-based sensitivity analysis supports the reduction in the number of parameters to be calibrated. Then, the selected parameters are tuned using a meta-heuristic optimization algorithm. In the considered case study, the sensitivity analyses highlight the significance of the following: the concrete mass, the vertical stiffness of the bearings, and the concrete Young’s modulus of the deck and the tower. However, optimizing all the unknowns using a single objective function does not lead to optima within the search domain. Therefore, the authors show that a three-step optimization is required in the considered case study to achieve convergence within the parameters’ space. As a result, all the twelve modes of the calibrated model perfectly match the experimental ones, with the modal assurance criterion (MAC) higher than 0.9. In addition, the cable forces of the calibrated model present a good match with the experimental ones, with an average percentage error equal to 11%.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like to thank the technical personnel (M. Antico and M. Cucchi) of the VIBLAB Laboratory of Vibrations and Dynamic Monitoring of Structures, Polytechnic of Milan, for their valuable help in conducting the field tests. Moreover, the collaboration of Dr. Fulvio Busatta (University of Cape Town) in implementing the first finite-element model and of Prof. Airong Chen (Tongji University) in performing a risk analysis of the bridge is highly acknowledged. This work was supported by the National Natural Science Foundation of China (Grant No. 51778148). The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51778148).
References
Adeli, H., and J. Zhang. 1995. “Fully nonlinear analysis of composite girder cable-stayed bridges.” Comput. Struct. 54 (2): 267–277. https://doi.org/10.1016/0045-7949(94)00332-W.
Aloisio, A., R. Alaggio, and M. Fragiacomo. 2021. “Bending stiffness identification of simply supported girders using an instrumented vehicle: Full scale tests, sensitivity analysis, and discussion.” J. Bridge Eng. 26 (1): 04020115. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001654.
Aloisio, A., L. Di Battista, R. Alaggio, and M. Fragiacomo. 2020. “Sensitivity analysis of subspace-based damage indicators under changes in ambient excitation covariance, severity and location of damage.” Eng. Struct. 208: 110235. https://doi.org/10.1016/j.engstruct.2020.110235.
Aloisio, A., D. P. Pasca, L. Di Battista, M. M. Rosso, R. Cucuzza, G. C. Marano, and R. Alaggio. 2022a. “Indirect assessment of concrete resistance from fe model updating and Young’s modulus estimation of a multi-span PSC viaduct: Experimental tests and validation.” Structures 37: 686–697. https://doi.org/10.1016/j.istruc.2022.01.045.
Aloisio, A., M. M. Rosso, and R. Alaggio. 2022b. “Experimental and analytical investigation into the effect of ballasted track on the dynamic response of railway bridges under moving loads.” J. Bridge Eng. 27 (10): 04022085. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001934.
Arangio, S., and F. Bontempi. 2015. “Structural health monitoring of a cable-stayed bridge with Bayesian neural networks.” Struct. Infrastruct. Eng. 11 (4): 575–587. https://doi.org/10.1080/15732479.2014.951867.
Asgari, B., S. Osman, and A. Adnan. 2013. “Sensitivity analysis of the influence of structural parameters on dynamic behaviour of highly redundant cable-stayed bridges.” Adv. Civ. Eng. 2013 (1): 426932.
Astaneh-Asl, A., and R. G. Black. 2001. “Seismic and structural engineering of a curved cable-stayed bridge.” J. Bridge Eng. 6 (6): 439–450. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:6(439).
Babajanian Bisheh, H., G. Ghodrati Amiri, M. Nekooei, and E. Darvishan. 2019. “Damage detection of a cable-stayed bridge using feature extraction and selection methods.” Struct. Infrastruct. Eng. 15 (9): 1165–1177. https://doi.org/10.1080/15732479.2019.1599964.
Bendat, J. S. 1993. “Spectral techniques for nonlinear system analysis and identification.” Shock Vib. 1 (1): 21–31. https://doi.org/10.1155/1993/438416.
Bernal, D. 2004. “Modal scaling from known mass perturbations.” J. Eng. Mech. 130 (9): 1083–1088.
Bernal, D., and B. Gunes. 2002. “Damage localization in output-only systems: A flexibility based approach.” In Proc., of SPIE - The International Society for Optical Engineering. Bellingham, WA: SPIE.
Bonelli, A., O. S. Bursi, R. Ceravolo, S. Santini, N. Tondini, and A. Zasso. 2010. “Dynamic identification and structural health monitoring of a twin deck curved cable-stayed footbridge: The “Ponte Del Mare” of Pescara in Italy.” In Proc., 5th European Workshop on Structural Health Monitoring, 370–375. Lancaster, PA: Destech Publications Inc.
Brandt, A., M. Berardengo, S. Manzoni, M. Vanali, and A. Cigada. 2019. “Global scaling of operational modal analysis modes with the OMAH method.” Mech. Syst. Signal Process. 117: 52–64. https://doi.org/10.1016/j.ymssp.2018.07.017.
Brincker, R., and P. Andersen. 2003. “A way of getting scaled mode shapes in output only modal analysis.” In Proc., 21st Int. Modal Analysis Conf., 141–145. Bristol, UK: IOP Publishing Ltd.
Brincker, R., J. Rodrigues, and P. Andersen. 2004. “Scaling the mode shapes of a building model by mass changes.” In Proc., 22nd Int. Modal Analysis Conf., 119–126. Bethel, CT: Society for Experimental Mechanics (SEM).
Brincker, R., L. Zhang, and P. Andersen. 2000. “Modal identification from ambient responses using frequency domain decomposition.” In Proc., 18th Int. Modal Analysis Conf. 625–630. Bethel, CT: Society for Experimental Mechanics (SEM).
Briseghella, B., G. Fa, A. Aloisio, D. Pasca, L. He, L. Fenu, and C. Gentile. 2021. “Dynamic characteristics of a curved steel–concrete composite cable-stayed bridge and effects of different design choices.” Structures 34: 4669–4681. https://doi.org/10.1016/j.istruc.2021.10.060.
Briseghella, B., E. Siviero, C. Lan, E. Mazzarolo, and T. Zordan. 2010. “Safety monitoring of the cable stayed bridge in the commercial harbor of Venice, Italy.” In Bridge Maintenance, Safety, Management and Life-Cycle Optimization: Proceedings of the 5th International IABMAS Conference, Philadelphia, USA, 11–15 July 2010, edited By D. M. Frangopol, R. Sause and C. Kusko, 379. London: CRC Press.
Brownjohn, J. M., and P.-Q. Xia. 2000. “Dynamic assessment of curved cable-stayed bridge by model updating.” J. Struct. Eng. 126 (2): 252–260. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:2(252).
Bursi, O. S., A. Kumar, G. Abbiati, and R. Ceravolo. 2014. “Identification, model updating, and validation of a steel twin deck curved cable-stayed footbridge.” Comput.-Aided Civ. Infrastruct. Eng. 29 (9): 703–722. https://doi.org/10.1111/mice.2014.29.issue-9.
Caetano, E., S. Silva, and J. Bateira. 2007. “Application of a vision system to the monitoring of cable structures.” In Proc., 7th Int. Symp. on Cable Dynamics, 225–236. Bristol, UK: IOP Publishing Ltd.
Cho, S., J. P. Lynch, J.-J. Lee, and C.-B. Yun. 2010. “Development of an automated wireless tension force estimation system for cable-stayed bridges.” J. Intell. Mater. Syst. Struct. 21 (3): 361–376. https://doi.org/10.1177/1045389X09350719.
Correia, J., F. Ferreira, and C. Maçãs. 2020. “Cable-stayed bridge optimization solution space exploration.” In Proc., 2020 Genetic and Evolutionary Computation Conf. Companion, 261–262. Maharashtra, India: Association for Computing Machinery, Inc.
Daniell, W. E., and J. H. Macdonald. 2007. “Improved finite element modelling of a cable-stayed bridge through systematic manual tuning.” Eng. Struct. 29 (3): 358–371. https://doi.org/10.1016/j.engstruct.2006.05.003.
De Miranda, M., A. De Palma, and A. Zanchettin. 2010. “‘Ponte Del Mare’: Conceptual design and realization of a long span cable-stayed footbridge in Pescara, Italy.” Struct. Eng. Int. 20 (1): 21–25. https://doi.org/10.2749/101686610791555577.
De Miranda, M., and E. Gnecchi-Ruscone. 2010. “Construction of the cable-stayed bridge in the commercial port of Venice, Italy.” Struct. Eng. Int. 20 (1): 13–17. https://doi.org/10.2749/101686610791555630.
Deger, Y., R. Cantieni, and C. de Smet. 1996. “Finite element model optimization of the new rhine bridge based on ambient vibration testing.” In Proc., 3rd European Conf. on Structural Dynamics, 817–822. Rotterdam, Netherlands: A.A Balkema.
Ding, Y., and A. Li. 2008. “Finite element model updating for the runyang cable-stayed bridge tower using ambient vibration test results.” Adv. Struct. Eng. 11 (3): 323–335. https://doi.org/10.1260/136943308785082599.
Fa, G., L. He, L. Fenu, E. Mazzarolo, B. Briseghella, and T. Zordan. 2016. “Comparison of direct and iterative methods for model updating of a curved cable-stayed bridge using experimental modal data.” In Proc., Int. Association for Bridge and Structural Engineering Conf., 538–545. Zürich, Switzerland: International Association for Bridge and Structural Engineering (IABSE).
Fang, S.-E., and R. Perera. 2009. “A response surface methodology based damage identification technique.” Smart Mater. Struct. 18 (6): 065009. https://doi.org/10.1088/0964-1726/18/6/065009.
Fang, S.-E., and R. Perera. 2011. “Damage identification by response surface based model updating using d-optimal design.” Mech. Syst. Signal Process. 25 (2): 717–733. https://doi.org/10.1016/j.ymssp.2010.07.007.
Feng, D., T. Scarangello, M. Q. Feng, and Q. Ye. 2017. “Cable tension force estimate using novel noncontact vision-based sensor.” Measurement 99: 44–52. https://doi.org/10.1016/j.measurement.2016.12.020.
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. L., and L. M. Simoes. 2011. “Optimum design of a controlled cable stayed bridge subject to earthquakes.” Struct. Multidiscip. Optim. 44 (4): 517–528. https://doi.org/10.1007/s00158-011-0628-9.
Friswell, M., and J. E. Mottershead. 1995. Vol. 38 of Finite element model updating in structural dynamics. Berlin, Heidelberg: Springer Science & Business Media.
Gentile, C., and A. Cabboi. 2015. “Vibration-based structural health monitoring of stay cables by microwave remote sensing.” Smart Struct. Syst 16 (2): 263–280. https://doi.org/10.12989/sss.2015.16.2.263.
Gentile, C., and F. Martinez Y Cabrera. 2004. “Dynamic performance of twin curved cable-stayed bridges.” Earthquake Eng. Struct. Dyn. 33 (1): 15–34. https://doi.org/10.1002/(ISSN)1096-9845.
Gentile, C., and E. Siviero. 2007. “Dynamic characteristics of the new curved cable-stayed bridge in Porto Marghera (Venice, Italy) from ambient vibration measurements.” In Proc., IMAC-XXV. Bethel, CT: Society for Experimental Mechanics (SEM).
Graff, K. F. 2012. Wave motion in elastic solids. Chelmsford, MA: Courier Corporation.
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.
Halpern, A. B., and D. P. Billington. 2013. “Eminent structural engineer: Michel virlogeux–structural artist of modern French bridges.” Struct. Eng. Int. 23 (3): 350–353. https://doi.org/10.2749/101686613X13627347099836.
He, L., C. Castoro, A. Aloisio, Z. Zhang, G. C. Marano, A. Gregori, C. Deng, and B. Briseghella. 2022. “Dynamic assessment, fe modelling and parametric updating of a butterfly-arch stress-ribbon pedestrian bridge.” Struct. Infrastruct. Eng. 18 (7): 1064–1075. https://doi.org/10.1080/15732479.2021.1995444.
Hofmeister, B., M. Bruns, and R. Rolfes. 2019. “Finite element model updating using deterministic optimisation: A global pattern search approach.” Eng. Struct. 195: 373–381. https://doi.org/10.1016/j.engstruct.2019.05.047.
Horta, L. G., M. C. Reaves, R. D. Buehrle, J. D. Templeton, D. R. Lazor, J. L. Gaspar, R. A. Parks, and P. A. Bartolotta. 2011. “Finite element model calibration approach for ares IX.” In Vol. 3 of Structural dynamics, 1037–1054. Berlin, Heidelberg: Springer.
Hua, X., Y. Ni, Z. Chen, and J. Ko. 2009. “Structural damage detection of cable-stayed bridges using changes in cable forces and model updating.” J. Struct. Eng. 135 (9): 1093–1106. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:9(1093).
Irvine, H. 1981. Cable structures. Cambridge, MA: MIT Press, 15–24.
Jaishi, B., and W.-X. Ren. 2005. “Structural finite element model updating using ambient vibration test results.” J. Struct. Eng. 131 (4): 617–628. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:4(617).
Jones, D. F., S. K. Mirrazavi, and M. Tamiz. 2002. “Multi-objective meta-heuristics: An overview of the current state-of-the-art.” Eur. J. Oper. Res. 137 (1): 1–9. https://doi.org/10.1016/S0377-2217(01)00123-0.
Kaczinski, M. 2016. Steel bridge design handbook: Bearing design. Rep. No. United States. Federal Highway Administration. Office of Bridges and Structures.
Kennedy, J., and R. Eberhart. 1995. “Particle swarm optimization.” In Vol. 4 of Proc., Int. Conf. on Neural Networks, 1942–1948. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE).
Kim, H., and H. Adeli. 2005. “Wavelet-hybrid feedback linear mean squared algorithm for robust control of cable-stayed bridges.” J. Bridge Eng. 10 (2): 116–123. https://doi.org/10.1061/(ASCE)1084-0702(2005)10:2(116).
Kim, K.-S., and B.-I. Lee. 2012. “Current trends in concrete cable stayed bridge.” Mag. Korea Concr. Inst. 24 (2): 10–15.
Li, H., and J. Ou. 2016. “The state of the art in structural health monitoring of cable-stayed bridges.” J. Civ. Struct. Health Monit. 6 (1): 43–67. https://doi.org/10.1007/s13349-015-0115-x.
Lin, K., Y.-L. Xu, X. Lu, Z. Guan, and J. Li. 2020a. “Cluster computing-aided model updating for a high-fidelity finite element model of a long-span cable-stayed bridge.” Earthquake Eng. Struct. Dyn. 49 (9): 904–923. https://doi.org/10.1002/eqe.v49.9.
Lin, K., Y.-L. Xu, X. Lu, Z. Guan, and J. Li. 2020b. “Time history analysis-based nonlinear finite element model updating for a long-span cable-stayed bridge.” Struct. Health Monit. 20 (5): 2566–2584. https://doi.org/10.1177/1475921720963868.
Lopez Aenlle, M., R. Brincker, and A. Fernandez Canteli. 2005. “Some methods to determine scaled mode shapes in natural input modal analysis.” Proc., Int. Modal Analysis Conf. Bethel, CT: Society for Experimental Mechanics (SEM).
López Aenlle, M., P. Fernández Fernández, R. Brincker, and A. C. Fernández Canteli. 2007. “Scaling factor estimation using an optimized mass change strategy, part 1: Theory.” In Proc., 2nd Int. Operational Modal Analysis Conf. 421–428. Aalborg, Denmark: Aalborg University.
Martí, R., P. M. Pardalos, and M. G. C. Resende. 2018. Handbook of heuristics. 1st ed. Berlin, Heidelberg: Springer.
Martins, A. M., L. M. Simões, and J. H. Negrão. 2020. “Optimization of cable-stayed bridges: A literature survey.” Adv. Eng. Software 149: 102829. https://doi.org/10.1016/j.advengsoft.2020.102829.
Mehrabi, A. B., and H. Tabatabai. 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).
Miranda, L. J. V. 2018. “PySwarms, a research-toolkit for Particle Swarm Optimization in Python.” J. Open Source Software 3 (21): 433. https://doi.org/10.21105/joss.
Nazarian, E., F. Ansari, X. Zhang, and T. Taylor. 2016. “Detection of tension loss in cables of cable-stayed bridges by distributed monitoring of bridge deck strains.” J. Struct. Eng. 142 (6): 04016018. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001463.
Ni, Y., H. Zhou, K. Chan, and J. Ko. 2008. “Modal flexibility analysis of cable-stayed Ting Kau bridge for damage identification.” Comput.-Aided Civ. Infrastruct. Eng. 23 (3): 223–236. https://doi.org/10.1111/mice.2008.23.issue-3.
Ni, Y.-C., Q.-W. Zhang, and J.-F. Liu. 2019. “Dynamic property evaluation of a long-span cable-stayed bridge (Sutong bridge) by a Bayesian method.” Int. J. Struct. Stab. Dyn. 19 (1): 1940010. https://doi.org/10.1142/S0219455419400108.
Park, W., H.-K. Kim, and P. Jongchil. 2012. “Finite element model updating for a cable-stayed bridge using manual tuning and sensitivity-based optimization.” Struct. Eng. Int. 22 (1): 14–19. https://doi.org/10.2749/101686612X13216060212870.
Park, W., J. Park, and H.-K. Kim. 2015. “Candidate model construction of a cable-stayed bridge using parameterised sensitivity-based finite element model updating.” Struct. Infrastruct. Eng. 11 (9): 1163–1177. https://doi.org/10.1080/15732479.2014.938662.
Parloo, E., B. Cauberghe, F. Benedettini, R. Alaggio, and P. Guillaume. 2005. “Sensitivity-based operational mode shape normalisation: Application to a bridge.” Mech. Syst. Signal Process. 19 (1): 43–55. https://doi.org/10.1016/j.ymssp.2004.03.009.
Parloo, E., P. Guillaume, J. Anthonis, W. Heylen, and J. Swevers. 2003. “Modelling of sprayer boom dynamics by means of maximum likelihood identification techniques, part 1: A comparison of input-output and output-only modal testing.” Biosyst. Eng. 85 (2): 163–171. https://doi.org/10.1016/S1537-5110(03)00044-8.
Parloo, E., P. Verboven, P. Cuillame, and M. Overmeire. 2001. “Sensitivity-based mass normalization of mode shape estimates from output-only data.” In Proc., Int. Conf. on Structural System Identification, 627–636. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE).
Parloo, E., P. Verboven, P. Guillaume, and M. Van Overmeire. 2002. “Sensitivity-based operational mode shape normalisation.” Mech. Syst. Signal Process. 16 (5): 757–767. https://doi.org/10.1006/mssp.2002.1498.
Pasca, D. P., A. Aloisio, M. Fragiacomo, and R. Tomasi. 2021. “Dynamic characterization of timber floor subassemblies: Sensitivity analysis and modeling issues.” J. Struct. Eng. 147 (12): 05021008. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003179.
Petersen, Ø. W., and O. Øiseth. 2017. “Sensitivity-based finite element model updating of a pontoon bridge.” Eng. Struct. 150: 573–584. https:// doi.org/10.1016/j.engstruct.2017.07.025.
Petersen, Ø. W., O. Øiseth, T. S. Nord, and E. Lourens. 2018. “Estimation of the full-field dynamic response of a floating bridge using Kalman-type filtering algorithms.” Mech. Syst. Signal Process. 107: 12–28. https://doi.org/10.1016/j.ymssp.2018.01.022.
Pinqi, X., and J. M. Brownjohn. 2003. “Finite element modeling and model updating of a cable-stayed bridge.” J. Vib. Eng. 16 (2): 219–223.
Rainieri, C., and G. Fabbrocino. 2014. Operational modal analysis of civil engineering structures. New York: Springer.
Saisana, M., A. Saltelli, and S. Tarantola. 2005. “Uncertainty and sensitivity analysis techniques as tools for the quality assessment of composite indicators.” J. R. Stat. Soc. A 168 (2): 307–323. https://doi.org/10.1111/j.1467-985X.2005.00350.x.
Saltelli, A., and I. M. Sobol’. 1995. “Sensitivity analysis for nonlinear mathematical models: Numerical experience.” Matematicheskoe Modelirovanie 7 (11): 16–28.
Schlune, H., M. Plos, and K. Gylltoft. 2009. “Improved bridge evaluation through finite element model updating using static and dynamic measurements.” Eng. Struct. 31 (7): 1477–1485. https://doi.org/10.1016/j.engstruct.2009.02.011.
Sehgal, S., and H. Kumar. 2016. “Structural dynamic model updating techniques: A state of the art review.” Arch. Comput. Methods Eng. 23 (3): 515–533. https://doi.org/10.1007/s11831-015-9150-3.
Shahverdi, H., C. Mares, and J. Mottershead. 2005. “Model structure correction and updating of aeroengine casings using fictitious mass modifications.” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 219 (1): 19–30. https://doi.org/10.1243/095440605X8342.
Sheibani, M., and A. Ghorbani-Tanha. 2021. “Obtaining mass normalized mode shapes of motorway bridges based on the effect of traffic movement.” Structures 33: 2253–2263. https://doi.org/10.1016/j.istruc.2021.05.056.
Simoen, E., G. De Roeck, and G. Lombaert. 2015. “Dealing with uncertainty in model updating for damage assessment: A review.” Mech. Syst. Signal Process. 56: 123–149. https://doi.org/10.1016/j.ymssp.2014.11.001.
Siringoringo, D. M., and Y. Fujino. 2007. “Dynamic characteristics of a curved cable-stayed bridge identified from strong motion records.” Eng. Struct. 29 (8): 2001–2017. https://doi.org/10.1016/j.engstruct.2006.10.009.
Sobol’, I. M. 1990. “On sensitivity estimation for nonlinear mathematical models.” Matematicheskoe Modelirovanie 2 (1): 112–118.
Song, W.-K., S.-E. Kim, and S. S. Ma. 2007. “Nonlinear analysis of steel cable-stayed bridges.” Comput.-Aided Civ. Infrastruct. Eng. 22 (5): 358–366. https://doi.org/10.1111/mice.2007.22.issue-5.
Storn, R., and K. Price. 1997. “Differential evolution–A simple and efficient heuristic for global optimization over continuous spaces.” J. Global Optim. 11 (4): 341–359. https://doi.org/10.1023/A:1008202821328.
Talebinejad, I., C. Fischer, and F. Ansari. 2011. “Numerical evaluation of vibration-based methods for damage assessment of cable-stayed bridges.” Comput.-Aided Civ. Infrastruct. Eng. 26 (3): 239–251. https://doi.org/10.1111/mice.2011.26.issue-3.
Tian, Y., L. Wang, and J. Zhang. 2021. “Time-varying frequency-based scaled flexibility identification of a posttensioned concrete bridge through vehicle–bridge interaction analysis.” Struct. Control Health Monit. 28 (1): e2631. https://doi.org/10.1002/stc.v28.1.
Tian, Y., J. Zhang, and Y. Han. 2019. “Structural scaling factor identification from output-only data by a moving mass technique.” Mech. Syst. Signal Process. 115: 45–59. https://doi.org/10.1016/j.ymssp.2018.05.040.
Virlogeux, M. 1999. “Recent evolution of cable-stayed bridges.” Eng. Struct. 21 (8): 737–755. https://doi.org/10.1016/S0141-0296(98)00028-5.
Wen, Q., X. Hua, Z. Chen, Y. Yang, and H. Niu. 2016. “Control of human-induced vibrations of a curved cable-stayed bridge: Design, implementation, and field validation.” J. Bridge Eng. 21 (7): 04016028. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000887.
Wilson, J. C., and T. Liu. 1991. “Ambient vibration measurements on a cable-stayed bridge.” Earthquake Eng. Struct. Dyn. 20 (8): 723–747. https://doi.org/10.1002/(ISSN)1096-9845.
Wolpert, D., and W. Macready. 1997. “No free lunch theorems for optimization.” IEEE Trans. Evol. Comput. 1 (1): 67–82. https://doi.org/10.1109/4235.585893.
Xiao, X., Y. L. Xu, and Q. Zhu. 2015. “Multiscale modeling and model updating of a cable-stayed bridge. II: Model updating using modal frequencies and influence lines.” J. Bridge Eng. 20 (10): 04014113. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000723.
Yang, D.-H., T.-H. Yi, H.-N. Li, and Y.-F. Zhang. 2018. “Monitoring and analysis of thermal effect on tower displacement in cable-stayed bridge.” Measurement 115: 249–257. https://doi.org/10.1016/j.measurement.2017.10.036.
Zárate, B. A., and J. M. Caicedo. 2008. “Finite element model updating: Multiple alternatives.” Eng. Struct. 30 (12): 3724–3730. https://doi.org/10.1016/j.engstruct.2008.06.012.
Zhang, E., D. Shan, S. Guo, J. Ren, and Q. Li. 2017. “Influence of curvature radius on static and dynamic characteristics of curved cable-stayed bridge.” In Proc., IABSE Symposium: Engineering the Future, 793–800. Zürich, Switzerland: International Association for Bridge and Structural Engineering (IABSE).
Zhang, Q., T.-Y. P. Chang, and C. C. Chang. 2001. “Finite-element model updating for the Kap Shui Mun cable-stayed bridge.” J. Bridge Eng. 6 (4): 285–293. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:4(285).
Zhang, Y. N., and J. Xie. 2019. “Compressive behaviour of laminated neoprene bridge bearing pads under thermal aging condition.” Mater. Sci. Forum 972: 118–122. https://doi.org/10.4028/www.scientific.net/MSF.972.
Zhao, W., G. Zhang, and J. Zhang. 2020. “Cable force estimation of a long-span cable-stayed bridge with microwave interferometric radar.” Comput.-Aided Civ. Infrastruct. Eng. 35 (12): 1419–1433. https://doi.org/10.1111/mice.v35.12.
Zhu, Q., Y. L. Xu, and X. Xiao. 2015. “Multiscale modeling and model updating of a cable-stayed bridge. I: Modeling and influence line analysis.” J. Bridge Eng. 20 (10): 04014112. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000722.
Zhu, R., F. Li, D. Zhang, and J. Tao. 2019. “Effect of joint stiffness on deformation of a novel hybrid FRP–aluminum space truss system.” J. Struct. Eng. 145 (11): 04019123. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002426.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 28 • Issue 7 • July 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Nov 11, 2022
Accepted: Mar 12, 2023
Published online: May 3, 2023
Published in print: Jul 1, 2023
Discussion open until: Oct 3, 2023
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.