Failure Evaluation of Bridge Deck Based on Parallel Connection Bayesian Network: Analytical Model
Abstract
1. Introduction
2. Development of Bayesian Network for the BD at System Level
2.1. Probabilistic Model of Fatigue Reliability
2.2. Construction of the Bayesian Network for the BD
P(S = 1 | A = 0, B = 1) = 0
P(S = 1 | A = 1, B = 1) = 1
2.3. Computation Algorithm of the Proposed Bayesian Network
3. Numerical Case Study
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
- C is constant for a given material, C = 19,930.2;
- is the stress amplitude (SA);
- N is the total cycle number (CN);
- ni is the CN for the nth cycle;
- f(Se) is the expression of the SA;
- ntot is the total CN.
- t is service life;
- Df follows the lognormal distribution LN (0, 0.294);
- pf is the fatigue failure probability;
- β is fatigue reliability index;
- Dfi is the failure damage of the weld i;
- x is an unknown parameter;
- g(x) is the function of x;
- p(x) is the target function of x;
- E[] is the mathematical expectation.
References
- Gou, H.; Wang, W.; Shi, X.; Pu, Q.; Kang, R. Behavior of steel-concrete composite cable anchorage system. Steel Compos. Struct. 2018, 26, 115–123. [Google Scholar]
- Zhang, Q.; Liu, Y.; Bao, Y.; Jia, D.; Bu, Y.; Li, Q. Fatigue performance of orthotropic steel-concrete composite deck with large-size longitudinal u-shaped ribs. Eng. Struct. 2017, 150, 864–874. [Google Scholar] [CrossRef]
- Cui, C.; Bu, Y.; Bao, Y.; Zhang, Q.; Ye, Z. Strain energy-based fatigue life evaluation of deck-to-rib welded joints in OSD considering combined effects of stochastic traffic load and welded residual stress. J. Bridge Eng. 2018, 23, 04017127. [Google Scholar] [CrossRef]
- Fisher, J.W.; Roy, S. Fatigue of steel bridge infrastructure. Struct. Infrastruct. Eng. 2011, 7, 457–475. [Google Scholar] [CrossRef]
- Fisher, J.W.; Barsom, J.M. Evaluation of cracking in the rib-to-deck welds of the bronx-whitestone bridge. J. Bridge Eng. 2016, 21, 04015065. [Google Scholar] [CrossRef]
- Fu, Z.; Ji, B.; Zhang, C.; Wang, Q. Fatigue performance of roof and u-rib weld of orthotropic steel bridge deck with different penetration rates. J. Bridge Eng. 2017, 22, 04017016. [Google Scholar] [CrossRef]
- Sony, S.; Laventure, S.; Sadhu, A. A literature review of next-generation smart sensing technology in structural health monitoring. Struct. Control Health Monit. 2019, 26, e2321. [Google Scholar] [CrossRef]
- Wang, M.L.; Yim, J. Sensor enriched infrastructure system. Smart Struct. Syst. 2010, 6, 309–333. [Google Scholar] [CrossRef]
- Mufti, A.A. Structural health monitoring of innovative Canadian civil engineering structures. Struct. Health Monit. 2002, 1, 89–103. [Google Scholar] [CrossRef]
- Yun, C.B.; Lee, J.J.; Koo, K.Y. Smart structure technologies from civil infrastructures in Korea: Recent research and applications. Struct. Infrastruct. Eng. 2011, 7, 673–688. [Google Scholar] [CrossRef]
- Pines, D.J.; Aktan, A.E. Status of structural health monitoring of long-span bridges in the United States. Prog. Struct. Eng. Mater. 2002, 4, 372–380. [Google Scholar] [CrossRef]
- Liu, M.; Frangopol, D.M.; Kwon, K. Fatigue reliability assessment of retrofitted steel bridges integrating monitored data. Struct. Saf. 2010, 32, 77–89. [Google Scholar] [CrossRef]
- Kulkarni, S.S.; Achenbach, J.D. Structural health monitoring and damage prognosis in fatigue. Struct. Health Monit. Int. J. 2008, 7, 37–49. [Google Scholar] [CrossRef]
- Deng, Y.; Liu, Y.; Feng, D.; Li, A. Investigation of fatigue performance of welded details in long-span steel bridges using long-term monitoring strain data. Struct. Control Health Monit. 2015, 22, 1343–1358. [Google Scholar] [CrossRef]
- Singh, S.P.; Mohammadi, Y.; Goel, S.; Kaushik, S.K. Prediction of mean and design fatigue lives of steel fibrous concrete beams in flexure. Adv. Struct. Eng. 2007, 10, 25–36. [Google Scholar] [CrossRef]
- Oh, H.B. Fatigue analysis of plain concrete in flexure. J. Struct. Eng. 1986, 112, 273–288. [Google Scholar] [CrossRef]
- Ye, H.; Shuai, C.; Zhang, X.; Xu, X.; Ummenhofer, T. Determination of S-N fatigue curves for damaged steel plates strengthened with prestressed CFRP plates under tension loading. Eng. Struct. 2018, 175, 669–677. [Google Scholar] [CrossRef]
- Cui, C.; Xu, Y.L.; Zhang, Q.H.; Wang, F.Y. Vehicle-induced fatigue damage prognosis of orthotropic steel decks of cable-stayed bridges. Eng. Struct. 2020, 212, 110509. [Google Scholar] [CrossRef]
- Jiang, L.; Liu, Y.; Fam, A.; Wang, K. Fatigue behaviour of non-integral y-joint of concrete-filled rectangular hollow section continuous chord stiffened with perfobond ribs. Eng. Struct. 2019, 191, 611–624. [Google Scholar] [CrossRef]
- Zhu, S.P.; Liu, Q.; Lei, Q.; Wang, Q. Probabilistic fatigue life prediction and reliability assessment of a high pressure turbine disc considering load variations. Int. J. Damage Mech. 2017, 27, 1569–1588. [Google Scholar] [CrossRef]
- Haririardebili, M.A.; Sudret, B. Polynomial chaos expansion for uncertainty quantification of dam engineering problems. Eng. Struct. 2020, 203, 109631. [Google Scholar] [CrossRef]
- Pardo-lgúzquiza, E. Bayesian inference of spatial covariance parameters. Math. Geol. 1999, 31, 47–65. [Google Scholar] [CrossRef]
- Ni, Y.Q.; Wang, Y.W.; Zhang, C. A Bayesian approach for condition assessment and damage alarm of bridge expansion joints using long-term structural health monitoring data. Eng. Struct. 2020, 212, 110520. [Google Scholar] [CrossRef]
- Chiachio, M.; Chiachio, J.; Rus, G.; Beck, J.L. Predicting fatigue damage in composites: A Bayesian framework. Struct. Saf. 2014, 51, 57–68. [Google Scholar] [CrossRef]
- Zhang, R.X.; Mahadevan, S. Model uncertainty and Bayesian updating in reliability-based inspection. Struct. Saf. 2000, 22, 145–160. [Google Scholar] [CrossRef]
- Thanh-Binh, T.; Emilio, B.A.; Younes, A. A dynamic Bayesian Network framework for spatial deterioration modelling and reliability updating of timber structures subjected to decay. Eng. Struct. 2020, 209, 110301. [Google Scholar]
- Gehl, P.; D’Ayala, D. Development of Bayesian Networks for the multi-hazard fragility assessment of bridge systems. Struct. Saf. 2016, 60, 37–46. [Google Scholar] [CrossRef]
- Yazdani, A.; Shahidzadeh, M.; Takada, T. Bayesian Networks for disaggregation of structural reliability. Struct. Saf. 2020, 82, 101892. [Google Scholar] [CrossRef]
- Dong, P. A structural stress definition and numerical implementation for fatigue analysis of welded joints. Int. J. Fatigue 2001, 23, 865–876. [Google Scholar] [CrossRef]
- Kyuba, H.; Dong, P. Equilibrium-equivalent structural stress approach to fatigue analysis of a rectangular hollow section joint. Int. J. Fatigue 2005, 27, 85–94. [Google Scholar] [CrossRef]
- Hashin, Z. A reinterpretation of the Palmgren-Miner rule for fatigue life prediction. Int. J. Appl. Mech. 1980, 47, 446–447. [Google Scholar] [CrossRef]
- Wirsching, P.H. Fatigue reliability for offshore structures. J. Struct. Eng. 1984, 110, 2340–2356. [Google Scholar] [CrossRef]
- Bayes, T. An essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond. 1763, 53, 370–418. [Google Scholar] [CrossRef]
- Mahadevan, S.; Zhang, R.; Smith, N. Bayesian networks for system reliability reassessment. Struct. Saf. 2001, 23, 231–251. [Google Scholar] [CrossRef]
- Mirzaei Aliabadi, M.; Aghaei, H.; Kalatpour, O.; Soltanian, A.R.; Nikravesh, A. Analysis of human and organizational factors that influence mining accidents based on Bayesian network. Int. J. Occup. Saf. Ergon. 2020, 26, 670–677. [Google Scholar] [CrossRef]
- Alex, K.; Oswaldo, M.N.; Thomas, Y.; Wim, C.; Johan, M.; Bruno, C. A two-dimension dynamic Bayesian Network for large-scale degradation modeling with an application to a bridges network. Comput. Aided Civ. Infrastruct. Eng. 2017, 32, 641–656. [Google Scholar]
- Geyer, C.J. Practical Markov Chain Monte Carlo. Stat. Sci. 1992, 7, 473–483. [Google Scholar] [CrossRef]
- Andrieu, C.; De Freitas, N.; Doucet, A.; Jordan, M.I. An introduction to MCMC for machine learning. Mach. Learn. 2003, 50, 5–43. [Google Scholar] [CrossRef]
Numerical Case Study | Welds | Sd | nd | ||
---|---|---|---|---|---|
μ | σ | μ | σ | ||
Numerical case study 1 | A | ln (10) | 0.1 | ln (3000) | 0.05 |
B | ln (10) | 0.1 | ln (3000) | 0.05 | |
Numerical case study 2 | A | ln (10) | 0.1 | ln (3000) | 0.05 |
B | ln (5) | 0.1 | ln (2000) | 0.05 | |
Numerical case study 3 | A | ln (10) | 0.1 | ln (1000) | 0.05 |
B | ln (5) | 0.1 | ln (5000) | 0.05 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Ding, Y.; Dong, J.; Yang, T.; Zhou, S.; Wei, Y. Failure Evaluation of Bridge Deck Based on Parallel Connection Bayesian Network: Analytical Model. Materials 2021, 14, 1411. https://doi.org/10.3390/ma14061411
Ding Y, Dong J, Yang T, Zhou S, Wei Y. Failure Evaluation of Bridge Deck Based on Parallel Connection Bayesian Network: Analytical Model. Materials. 2021; 14(6):1411. https://doi.org/10.3390/ma14061411
Chicago/Turabian StyleDing, Yang, Jingliang Dong, Tonglin Yang, Shuangxi Zhou, and Yongqi Wei. 2021. "Failure Evaluation of Bridge Deck Based on Parallel Connection Bayesian Network: Analytical Model" Materials 14, no. 6: 1411. https://doi.org/10.3390/ma14061411
APA StyleDing, Y., Dong, J., Yang, T., Zhou, S., & Wei, Y. (2021). Failure Evaluation of Bridge Deck Based on Parallel Connection Bayesian Network: Analytical Model. Materials, 14(6), 1411. https://doi.org/10.3390/ma14061411