Model Verification and Validation of a Cable-Stayed Bridge: Interval-Based Uncertainty Quantification of the Model Parameters
Publication: Journal of Bridge Engineering
Volume 27, Issue 8
Abstract
In simulating engineering structures, the uncertainty quantification and propagation (UQ&P) of model parameters is of paramount importance for model verification and validation (V&V), the fidelity of which has been proven to have a prominent effect on structural safety assessment and decision making. In this study, the parametric uncertainties due to environmental periodicity were inversely quantified in form of intervals through a V&V framework based on the conjunction of interval response surface method (IRSM) and probability box (P-Box), which is adaptable and efficient for real bridge structures. The uncertainties of temperature were first quantified with P-Box, based on a year’s worth of data obtained from the structural health monitoring (SHM) system of a cable-stayed bridge. Following that, the uncertainties of structural frequencies were quantified through a correlation analysis between temperature and frequencies which were filtered by different techniques. The expressions of IRSM were constructed and verified, with frequencies calculated from them agreeing well with those calculated from the finite-element (FE) model simulation. Thereafter, the interval boundary values of the observed frequencies were obtained by searching the tails of the P-Box bounds, thus providing the target intervals for model validation. The parametric intervals were validated efficiently through a two-step calibration procedure based on monotonic analysis. The result shows that the validated model has a good predictive capacity and could serve as a high-fidelity model for further application, with the parametric uncertainties appropriately considered in the form of intervals.
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Data Availability Statement
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request, including the monitored data of temperature and frequencies.
Acknowledgments
This research was supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX18_0162), and by the National Natural Science Foundation of China (Grant No. 52178462). The financial support are gratefully acknowledged.
References
Alam, J., L. A. C. Neves, H. Zhang, and D. Dias-da-Costa. 2022. “Assessment of remaining service life of deteriorated concrete bridges under imprecise probabilistic information.” Mech. Syst. Sig. Process. 167: 108565. https://doi.org/10.1016/j.ymssp.2021.108565.
Asfaram, A., M. Ghaedi, S. Agarwal, I. Tyagi, and V. Kumar Gupta. 2015. “Removal of basic dye Auramine-O by ZnS:Cu nanoparticles loaded on activated carbon: Optimization of parameters using response surface methodology with central composite design.” RSC Adv. 5 (24): 18438–18450. https://doi.org/10.1039/C4RA15637D.
ASME. 2006. Guide for verification and validation in computational solid mechanics. New York: ASME.
Bayane, I., S. G. S. Pai, I. F. C. Smith, and E. Brühwiler. 2021. “Model-based interpretation of measurements for fatigue evaluation of existing reinforced concrete bridges.” J. Bridge Eng. 26 (8): 04021054. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001742.
Beer, M., S. Ferson, and V. Kreinovich. 2013. “Imprecise probabilities in engineering analyses.” Mech. Syst. Sig. Process. 37 (1–2): 4–29. https://doi.org/10.1016/j.ymssp.2013.01.024.
Box, G. E. P., and K. B. Wilson. 1951. “On the experimental attainment of optimum conditions.” J. R. Stat. Soc. Ser. B 13 (1): 1–45.
Bucher, C. G., and U. Bourgund. 1990. “A fast and efficient response surface approach for structural reliability problems.” Struct. Saf. 7 (1): 57–66. https://doi.org/10.1016/0167-4730(90)90012-E.
Byers, W. G. 2004. “Use of stochastic subspace identification methods for post-disaster condition assessment of highway bridges.” In Proc., 13th World Conf. on Earthquake Engineering. Vancouver: Canadian Association for Earthquake Engineering, International Association for Earthquake Engineering.
Chen, X., Z. Shen, and X. Liu. 2019. “Structural dynamics model updating with interval uncertainty based on response surface model and sensitivity analysis.” Inverse Prob. Sci. Eng. 27 (10): 1425–1441. https://doi.org/10.1080/17415977.2018.1554656.
Coskun, A. K., T. S. Rosing, and K. C. Gross. 2008. “Proactive temperature balancing for low cost thermal management in MPSoCs.” In Proc., IEEE/ACM Int. Conf. on Computer-Aided Design, 250–257. San Jose, CA: The ACM Special Interest Group on Design Automation, IEEE Council on Electronic Design Automation.
De-León-Escobedo, D., D.-J. Delgado-Hernández, L.-H. Martinez-Martinez, J.-G. Rangel-Ramírez, and J.-C. Arteaga-Arcos. 2014. “Corrosion initiation time updating by epistemic uncertainty as an alternative to schedule the first inspection time of pre-stressed concrete vehicular bridge beams.” Struct. Infrastruct. Eng. 10 (8): 998–1010. https://doi.org/10.1080/15732479.2013.780084.
Der Kiureghian, A., and O. Ditlevsen. 2009. “Aleatory or epistemic? Does it matter?” Struct. Saf. 31 (2): 105–112. https://doi.org/10.1016/j.strusafe.2008.06.020.
Faes, M. G. R., M. Daub, S. Marelli, E. Patelli, and M. Beer. 2021. “Engineering analysis with probability boxes: A review on computational methods.” Struct. Saf. 93: 102092. https://doi.org/10.1016/j.strusafe.2021.102092.
Fang, G., J. Cao, Y. Yang, L. Zhao, S. Cao, and Y. Ge. 2020. “Experimental uncertainty quantification of flutter derivatives for a PK section girder and its application on probabilistic flutter analysis.” J. Bridge Eng. 25 (7): 04020034. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001567.
Fang, S.-E., Q.-H. Zhang, and W.-X. Ren. 2015. “An interval model updating strategy using interval response surface models.” Mech. Syst. Sig. Process. 60–61: 909–927. https://doi.org/10.1016/j.ymssp.2015.01.016.
Gembicki, F., and Y. Haimes. 1975. “Approach to performance and sensitivity multiobjective optimization: The goal attainment method.” IEEE Trans. Autom. Control 20 (6): 769–771. https://doi.org/10.1109/TAC.1975.1101105.
Han, X., C. Jiang, L. X. Liu, J. Liu, and X. Y. Long. 2014. “Response-surface-based structural reliability analysis with random and interval mixed uncertainties.” Sci. China Technol. Sci. 57 (7): 1322–1334. https://doi.org/10.1007/s11431-014-5581-6.
Heylen, W., S. Lammens, and P. Sas. 1997. Modal analysis theory and testing. Leuven, Belgium: Katholieke Universiteit Leuven.
Hippert, H. S., C. E. Pedreira, and R. C. Souza. 2000. “Combining neural networks and ARIMA models for hourly temperature forecast.” In Proc., Int. Joint Conf. on Neural Networks, 414–419. Como: IEEE Computer Society.
Ji, X., G. Huang, and Y.-G. Zhao. 2020. “Probabilistic flutter analysis of bridge considering aerodynamic and structural parameter uncertainties.” J. Wind Eng. Ind. Aerodyn. 201: 104168. https://doi.org/10.1016/j.jweia.2020.104168.
Jiang, F., Y. Ding, Y. Song, F. Geng, and Z. Wang. 2021. “Digital Twin-driven framework for fatigue life prediction of steel bridges using a probabilistic multiscale model: Application to segmental orthotropic steel deck specimen.” Eng. Struct. 241: 112461. https://doi.org/10.1016/j.engstruct.2021.112461.
Li, H., L. Li, G. Zhou, and L. Xu. 2020. “Effects of various modeling uncertainty parameters on the seismic response and seismic fragility estimates of the aging highway bridges.” Bull. Earthquake Eng. 18 (14): 6337–6373. https://doi.org/10.1007/s10518-020-00934-9.
Liu, N., W. Gao, C. Song, N. Zhang, and Y.-L. Pi. 2013. “Interval dynamic response analysis of vehicle-bridge interaction system with uncertainty.” J. Sound Vib. 332 (13): 3218–3231. https://doi.org/10.1016/j.jsv.2013.01.025.
Liu, Y., and Z. D. Duan. 2012. “Fuzzy finite element model updating of bridges by considering the uncertainty of the measured modal parameters.” Sci. China Technol. Sci. 55 (11): 3109–3117. https://doi.org/10.1007/s11431-012-5009-0.
Mao, J., Z. Yu, and L. Jiang. 2019. “Stochastic analysis of vehicle-bridge coupled interaction and uncertainty bounds of random responses in heavy Haul railways.” Int. J. Struct. Stab. Dyn. 19 (12): 1950144. https://doi.org/10.1142/S021945541950144X.
Medina-Cetina, Z., N. Yousefpour, and J.-L. Briaud. 2020. “Probabilistic evaluation of unknown foundations for Scour susceptible bridges.” J. Bridge Eng. 25 (10): 04020074. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001569.
Moore, R. E., R. B. Kearfott, and M. J. Cloud. 2009. Introduction to interval analysis. Philadelphia: Society for Industrial and Applied Mathematics.
Moufti, S., T. Zayed, and S. Abu Dabous. 2014. “Defect-based condition assessment of concrete bridges: Fuzzy hierarchical evidential reasoning approach.” Transp. Res. Record. 2431 (1): 88–96. https://doi.org/10.3141/2431-12
Oberkampf, W. L., and T. G. Trucano. 2008. “Verification and validation benchmarks.” Nucl. Eng. Des. 238 (3): 716–743. https://doi.org/10.1016/j.nucengdes.2007.02.032.
Omrani, R., B. Mobasher, S. Sheikhakbari, F. Zareian, and E. Taciroglu. 2017. “Variability in the predicted seismic performance of a typical seat-type California bridge due to epistemic uncertainties in its abutment backfill and shear-key models.” Eng. Struct. 148: 718–738. https://doi.org/10.1016/j.engstruct.2017.07.018.
Oura, M., R. Ohba, A. Robins, and S. Kato. 2018. “Validation study for an atmospheric dispersion model, using effective source heights determined from wind tunnel experiments in nuclear safety analysis.” Atmosphere 9 (3): 111. https://doi.org/10.3390/atmos9030111.
Pan, Q., K. Grimmelsman, F. Moon, and E. Aktan. 2011. “Mitigating epistemic uncertainty in structural identification: Case study for a long-span steel arch bridge.” J. Struct. Eng. 137 (1): 1–13. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000248.
SAND (Sandia National Laboratories). 2003. Constructing probability boxes and Dempster–Shafer structures. Albuquerque, NM: SAND.
Shan, D., Q. Li, I. Khan, and X. Zhou. 2015. “A novel finite element model updating method based on substructure and response surface model.” Eng. Struct. 103: 147–156. https://doi.org/10.1016/j.engstruct.2015.09.006.
Sofi, A., and E. Romeo. 2018. “A unified response surface framework for the interval and stochastic finite element analysis of structures with uncertain parameters.” Probab. Eng. Mech. 54: 25–36. https://doi.org/10.1016/j.probengmech.2017.06.004.
Song, Y., J. Mi, Y. Cheng, L. Bai, and K. Chen. 2021. “Reliability assessment for failure-dependent and uncertain systems: A Bayesian network based on copula method and probability-box.” Qual. Reliab. Eng. Int. 37 (5): 1894–1921. https://doi.org/10.1002/qre.2835.
Thangjitham, S., and R. A. Heller. 1986. “Stress response of rocket motors to environmental thermal loads.” J. Spacecr. Rock. 23 (5): 519–526. https://doi.org/10.2514/3.25839.
Welch, P. 1967. “The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms.” IEEE Trans. Audio Electroacoust. 15 (2): 70–73. https://doi.org/10.1109/TAU.1967.1161901.
Williamson, R. C., and T. Downs. 1990. “Probabilistic arithmetic. I. Numerical methods for calculating convolutions and dependency bounds.” Int. J. Approximate Reasoning 4 (2): 89–158. https://doi.org/10.1016/0888-613X(90)90022-T.
Yang, Y., J. Peng, X. Liu, S. C. S. Cai, and J. Zhang. 2021. “Probability analysis of web cracking of corroded prestressed concrete box-girder bridges considering aleatory and epistemic uncertainties.” Eng. Struct. 228: 111486. https://doi.org/10.1016/j.engstruct.2020.111486.
Zhang, Z., and Z. Qiu. 2021. “Fatigue reliability analysis for structures with hybrid uncertainties combining quadratic response surface and polynomial chaos expansion.” Int. J. Fatigue 144: 106071. https://doi.org/10.1016/j.ijfatigue.2020.106071.
Zhong, R., Z. Zong, Q. Liu, and H. Zhou. 2015. “A multiscale finite element model validation method of composite cable-stayed bridge based on structural health monitoring system.” Shock Vib. 2015: 817281.
Zhong, R., Z. Zong, J. Niu, Q. Liu, and P. Zheng. 2016. “A multiscale finite element model validation method of composite cable-stayed bridge based on Probability Box theory.” J. Sound Vib. 370: 111–131. https://doi.org/10.1016/j.jsv.2016.01.055.
Zhu, S., Y. Li, K. Togbenou, and T. Xiang. 2019. “An advanced algorithm to study the effect of uncertainties on the stochastic performance of high-pier bridge under earthquake.” Soil Dyn. Earthquake Eng. 126: 105805. https://doi.org/10.1016/j.soildyn.2019.105805.
Zhu, S.-P., H.-Z. Huang, W. Peng, H.-K. Wang, and S. Mahadevan. 2016. “Probabilistic Physics of failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty.” Reliab. Eng. Syst. Saf. 146: 1–12. https://doi.org/10.1016/j.ress.2015.10.002.
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Published In
Journal of Bridge Engineering
Volume 27 • Issue 8 • August 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Nov 20, 2021
Accepted: Apr 18, 2022
Published online: Jun 10, 2022
Published in print: Aug 1, 2022
Discussion open until: Nov 10, 2022
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