- Volume 3 Issue 4
DOI QR Code
Bayesian estimation of tension in bridge hangers using modal frequency measurements
- Papadimitriou, Costas (University of Thessaly, Department of Mechanical Engineering) ;
- Giakoumi, Konstantina (University of Thessaly, Department of Mechanical Engineering) ;
- Argyris, Costas (University of Thessaly, Department of Mechanical Engineering) ;
- Spyrou, Leonidas A. (Centre for Research and Technology Hellas (CERTH), Institute for Research and Technology) ;
- Panetsos, Panagiotis (Egnatia Odos S.A., Capital Maintenance Department)
- Received : 2016.07.22
- Accepted : 2016.10.10
- Published : 2016.12.25
The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20 compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.
Supported by : European Social Fund (ESF), Greek National Resources
- Angelikopoulos, P., Papadimitriou, C. and Koumoutsakos, P. (2012), "Bayesian uncertainty quantification and propagation in molecular dynamics simulations: A high performance computing framework", J. Chem. Phys., 137(14), 455-461.
- Barcilon, V. (1976), "Inverse problem for a vibrating beam", J. Appl. Math. Phys., 27, 347-358. https://doi.org/10.1007/BF01590507
- Beck, J.L. and Katafygiotis, L.S. (1998), "Updating models and their uncertainties. I: Bayesian statistical framework", J. Eng. Mech. - ASCE, 124(4), 455-461. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(455)
- Beck, J.L. and Yuen, K.V. (2004), "Model selection using response measurements: Bayesian probabilistic approach", J. Eng. Mech. - ASCE, 130(2), 192-203. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:2(192)
- Belleri, A. and Moaveni, B. (2015), "Identification of tensile forces in tie rods with unknown boundary conditions", Proceedings of the 7th International Conference of Inteligent Infrastructure SHMII, July 1-3, 2015, Torino, Italy.
- Bellino, A., Garibaldi, L., Fasana, A. and Marchesiello, S. (2011), "Tension estimation of cables with different boundary conditions by means of the added mass technique", International Conference of Surveilance 6, Oct. 25-26, 2011, University of Technology of Compiegne, France.
- Bellino, A., Marchesiello, S., Fasana, A. and Garibaldi, L. (2010), "Cable tension estimation by means of vibration response and moving mass technique", Mecanique et Industries, 11, 505-512. https://doi.org/10.1051/meca/2010058
- Bokaian, A. (1990), "Natural frequencies of beams under tensile axial loads", J. Sound Vib., 142, 481-498. https://doi.org/10.1016/0022-460X(90)90663-K
- Ceballos, M.A. and Prato, C.A. (2008), "Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests", J. Sound Vib., 317, 127-141. https://doi.org/10.1016/j.jsv.2008.02.048
- Ching, J. and Chen, Y.C. (2007), "Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging", J. Eng. Mech. - ASCE, 133(7), 816-832. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:7(816)
- Ewins, D.J. (2000), Modal Testing: Theory, Practice and Application, Second edition, Research Studies Press Ltd., Baldock, England.
- Fang, Z. and Wang, J.Q. (2012), "Practical formula for cable tension estimation by vibration method", J. Bridge Eng. - ASCE, 17(1), 161-164. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000200
Hadjidoukas, P.E., Angelikopoulos, P., Papadimitriou, C. and Koumoutsakos, P. (2015), "
$\Pi$4U: A high performance computing framework for Bayesian uncertainty quantification of complex models", J. Comput. Phys., 284(1), 1-21. https://doi.org/10.1016/j.jcp.2014.12.006
- Hansen, N., Muller, S.D. and Koumoutsakos, P. (2003), "Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES)", Evolutionary Comput., 11(1), 1-18. https://doi.org/10.1162/106365603321828970
- Heylen, W., Lammens, S. and Sas, P. (1995), Modal Analysis Theory and Testing, Department of Mechanical Engineering, Katholieke Universiteit Leuven, Leuven, Belgium.
- Huang, Y.H., Fu, J.Y., Wang, R.H., Gan, Q. and Liu, A.R. (2015), "Unified practical formulas for vibration-based method of cable tension estimation", Adv. Struct. Eng., 18(3), 405-422. https://doi.org/10.1260/1369-43184.108.40.2065
- Humar, J.L. (2001), Dynamics of Structures, A.A. Balkema.
- Kim, B.H. and Park, T. (2007), "Estimation of cable tension force using the frequency-based system identification method", J. Sound Vib., 304, 660-676. https://doi.org/10.1016/j.jsv.2007.03.012
- Lagomarsino, S. and Calderini, C. (2005), "The dynamical identification of the tensile force in ancient tie-rods", Eng. Struct., 27, 846-856. https://doi.org/10.1016/j.engstruct.2005.01.008
- Nam, H. and Nghia, N.T. (2011), "Estimation of cable tension using measured natural frequencies", Procedia Eng., 14, 1510-1517. https://doi.org/10.1016/j.proeng.2011.07.190
- Ni, Y.Q., Ko, J.M. and Zheng, G. (2010), "Dynamic analysis of large diameter sagged cables taking into account flexural rigidity", J. Sound Vib., 257, 301-319.
- Park, K.S., Seong, T.R. and Noh, M.H. (2015), "Feasibility study on tension estimation technique for hanger cables using the FE model-based system identification method", Hindawi Publishing Corporation, Mathematical Problems in Engineering, Volume 2015, Article ID 512858, 12 pages.
- 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
- Simoen, E., Moaveni, B., Conte, J.L. and Lombaert, G. (2013), "Uncertainty quantification in the assessment of progressive damage in a 7-story full-scale building slice", J. Eng. Mech. - ASCE, 139(12), 1818-1830. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000610
- Vanik, M.W., Beck, J.L. and Au, S.K. (2000), "Bayesian probabilistic approach to structural health monitoring", J. Eng. Mech. - ASCE, 126(7), 738-745. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:7(738)
- William, T.T. (1996), Theory of Vibration With Applications, CRC Press.
- Yuen, K.V. (2010), Bayesian Methods for Structural Dynamics and Civil Engineering, Wiley.
- Yuen, K.V. and Mu, H.Q. (2011), "Peak ground acceleration estimation by linear and nonlinear models with reduced order Monte Carlo simulation", Comput. - Aided Civil Infrastruct. Eng., 26(1), 30-47.
- Yuen, K.V. and Mu, H.Q. (2015), "Real-time system identification: an algorithm for simultaneous model class selection and parametric identification", Comput. - Aided Civil Infrastruct. Eng., 30(10), 785-801. https://doi.org/10.1111/mice.12146
- Zui, H., Shinke, T. and Namyuita, Y. (1996), "Practical formula for estimation of cable tension by vibration method", J. Struct. Eng. - ASCE, 122(6), 651-656. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:6(651)
- Model Order Identification for Cable Force Estimation Using a Markov Chain Monte Carlo-Based Bayesian Approach vol.18, pp.12, 2018, https://doi.org/10.3390/s18124187
- Time-Variant Seismic Performance of Offshore RC Bridge Columns with Uncertainty pp.1793-6764, 2018, https://doi.org/10.1142/S0219455418501493