Quantification of Fatigue Damage for Structural Details in Slender Coastal Bridges Using Machine Learning-Based Methods
Publication: Journal of Bridge Engineering
Volume 25, Issue 7
Abstract
Exposed to the challenging coastal environment, slender bridges could experience significant dynamic responses and complex stress states resulting from the coupled dynamic impacts of wind, wave, and vehicle loads. Cracks could gradually initiate and propagate at structural details that might trigger failures of the structural members or the entire structural system. To predict the remaining fatigue life of slender coastal bridges, stochastic fatigue damage for structural details is quantified using machine learning (ML)-based methods, such as support vector machines (SVM), Gaussian process (GP), neural network (NN), and random forest (RF). Parametric probabilistic models for vehicles, defined based on long-term field measurements, and stochastic loadings from wind and waves, parameterized for various loading scenarios, serve as the input parameters. As for the output of ML models, equivalent fatigue damage accumulation is obtained based on the coupled vehicle-bridge-wind-wave (VBWW) system and stress analysis for complex structural details using multiscale finite-element analysis (FEA). With different training strategies, fatigue life for critical local details is obtained considering the ever-changing coastal environmental conditions. Training and testing results show that the GP algorithm outperforms other algorithms even though all algorithms exhibit the reasonable capability of predicting the fatigue damage accumulation.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The data used to train the machine learning models is available from the corresponding author by request.
Acknowledgments
This material was based upon the work supported by the National Science Foundation under Grant No. CMMI-1537121. The support was greatly appreciated. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsors.
References
Amari, S., and S. Wu. 1999. “Improving support vector machine classifiers by modifying kernel functions.” Neural Networks 12 (6): 783–789. https://doi.org/10.1016/S0893-6080(99)00032-5.
Andrew, A. M. 2001. “An introduction to support vector machines and other kernel-based learning methods.” Kybernetes 30 (1): 103–115.
Aydin, I., M. Karakose, and E. Akin. 2011. “A multi-objective artificial immune algorithm for parameter optimization in support vector machine.” Appl. Soft Comput. 11 (1): 120–129. https://doi.org/10.1016/j.asoc.2009.11.003.
Bernard, S., L. Heutte, and S. Adam. 2009. “On the selection of decision trees in random forests.” In Proc., Int. Joint Conf. on Neural Networks, 302–307. Piscataway, NJ: IEEE.
Bishop, C. M. 2006. Pattern recognition and machine learning. New York: Springer.
Breiman, L. 1996. “Bagging predictors.” Mach. Learn. 24 (2): 123–140.
Breiman, L. 2001. “Random forests.” Mach. Learn. 45 (1): 5–32. https://doi.org/10.1023/A:1010933404324.
Cao, Y., H. Xiang, and Y. Zhou. 2000. “Simulation of stochastic wind velocity field on long-span bridges.” J. Eng. Mech. 126 (1): 1–6. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(1).
Cheng, X., J. Dong, X. Han, and Q. Fei. 2016. “Structural health monitoring-oriented finite-element model for a large transmission tower.” Int. J. Civ. Eng. 16: 79–92.
Cortes, C., and V. Vapnik. 1995. “Support-vector networks.” Mach. Learn. 20: 273–297.
Deodatis, G. 1996. “Simulation of ergodic multivariate stochastic processes.” J. Eng. Mech. 122 (8): 778–787. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:8(778).
Fang, K.-T., and D. K. J. Lin. 2003. “Uniform experimental design and their applications in industry,” in Vol. 22 of Handbook of Statistics, edited by R. Khattree and C. R. Rao, 131–170. Amsterdam, Netherlands: Elsevier.
Foody, G. M., and M. K. Arora. 1997. “An evaluation of some factors affecting the accuracy of classification by an artificial neural network.” Int. J. Remote Sens. 18 (4): 799–810. https://doi.org/10.1080/014311697218764.
Ghahramani, Z. 2013. “Bayesian non-parametrics and the probabilistic approach to modelling.” Philos. Trans. R Soc., Ser. A 371 (1984): 20110553. https://doi.org/10.1098/rsta.2011.0553.
Gordini, M., M. R. Habibi, M. H. Tavana, M. TahamouliRoudsari, and M. Amiri. 2018. “Reliability analysis of space structures using Monte-Carlo simulation method.” Structures 14: 209–219. https://doi.org/10.1016/j.istruc.2018.03.011.
Hagan, M., H. Demuth, M. Beale, and O. De Jesús. 1996. Neural network design. Boston: PWS.
Han, H., and X. Jiang. 2014. “Overcome support vector machine diagnosis overfitting.” Cancer Inf. 13 (Suppl. 1): 145–158. https://doi.org/10.4137/CIN.S13875.
Hertz, J., A. Krogh, and R. Palmer. 1991. Introduction To The theory of neural computation. Boulder, CO: Westview Press.
Ho, T. K. 1993. “Recognition of handwritten digits by combining independent learning vector quantization.” In Proc., 2nd Int. Conf. on Document Analysis and Recognition, 818–821. Piscataway, NJ: IEEE.
Ho, T. K. 1995. “Random decision forests.” In Vol. 1 of Proc., 3rd Int. Conf. on Document Analysis and Recognition, 278–282. Piscataway, NJ: IEEE.
Ho, T. K. 2002. “A data complexity analysis of comparative advantages of decision forest constructors.” Pattern Anal. Appl. 5: 102–112.
Huang, H. H., C. L. Jiang, and P. Qin. 2012. Report on meteorological characteristics at jiangshun bridge. [In Chinese.] Guangdong, China: Guangdong Provincial Meteorological Observatory.
Kendell, A. 1988. An introduction to numerical analysis. 2nd ed. Hoboken, NJ: John Wiley and Sons.
Li, Q., Q. Meng, J. Cai, H. Yoshino, and A. Mochida. 2009. “Predicting hourly cooling load in the building: A comparison of support vector machine and different artificial neural networks.” Energy Convers. Manage. 50 (1): 90–96. https://doi.org/10.1016/j.enconman.2008.08.033.
Li, X., Y. Zhu, and Z. Jin. 2016. “Nonstationary random vibration performance of train-bridge coupling system with vertical track irregularity.” Shock Vib. 2016 (1): 1–19. https://doi.org/10.1155/2016/1450895.
Lu, N., M. Noori, and Y. Liu. 2016. “Fatigue reliability assessment of welded steel bridge decks under stochastic truck loads via machine learning.” J. Bridge Eng. 22 (1): 04016105. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000982.
Marquardt, D. W. 1963. “An algorithm for least-squares estimation of nonlinear parameters.” J. Soc. Ind. Appl. Math. 11 (2): 431–441. https://doi.org/10.1137/0111030.
Ni, Y. Q., X. W. Ye, and J. M. Ko. 2010. “Monitoring-based fatigue reliability assessment of steel bridges: Analytical model and application.” J. Struct. Eng. 136 (12): 1563–1573. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000250.
Ni, Y. Q., X. W. Ye, and J. M. Ko. 2012. “Modeling of stress spectrum using long-term monitoring data and finite mixture distributions.” J. Eng. Mech. 138 (2): 175–183. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000313.
Raghavendra, S., and P. C. Deka. 2014. “Support vector machine applications in the field of hydrology: A review.” Appl. Soft Comput. 19: 372–386. https://doi.org/10.1016/j.asoc.2014.02.002.
Rasmussen, C. E., and C. K. I. Williams 2006. Gaussian processes for machine learning. Cambridge, MA: MIT Press.
Robnik-Sikonja, M. 2004. “Improving random forests.” In Proc., European Conf. on Machine Learning, 359–370. Berlin: Springer.
Scardapane, S., and D. Wang. 2017. “Randomness in neural networks: An overview.” Wiley Interdiscip. Rev.: Data Min. Knowl. Discovery 7 (2): e1200. https://doi.org/10.1002/widm.1200.
Scholkopf, B., and A. J. Smola. 2003. Learning with kernels: Support vector machines, regularization, optimization, and beyond. Cambridge, MA: MIT Press.
Schwieder, M., P. J. Leitão, S. Suess, C. Senf, and P. Hostert. 2014. “Estimating fractional shrub cover using simulated enmap data: A comparison of three machine learning regression techniques.” Remote Sens. 6 (4): 3427–3445. https://doi.org/10.3390/rs6043427.
Segal, M. R. 2004. Machine learning benchmarks and random forest regression. Technical Rep. Center for Bioinformatics and Molecular Biostatistics. San Francisco: Univ. of California.
Snoek, J., H. Larochelle, and R. Adams. 2012. “Practical Bayesian optimization of machine learning algorithms.” In Vol. 4 of Proc., 26th Annual Conf. on Neural Information Processing Systems, 2951–2959. Stateline, Nevada: Harrah's Lake Tahoe.
Statnikov, A., L. Wang, and C. F. Aliferis. 2008. “A comprehensive comparison of random forests and support vector machines for microarray-based cancer classification.” BMC Bioinf. 9: 319–310. https://doi.org/10.1186/1471-2105-9-319.
Su, G., L. Peng, and L. Hu. 2017. “A Gaussian process-based dynamic surrogate model for complex engineering structural reliability analysis.” Struct. Saf. 68: 97–109. https://doi.org/10.1016/j.strusafe.2017.06.003.
Su, G., B. Yu, Y. Xiao, and L. Yan. 2014. “Gaussian process machine-learning method for structural reliability analysis.” Adv. Struct. Eng. 17 (9): 1257–1270. https://doi.org/10.1260/1369-4332.17.9.1257.
Svetnik, V., A. Liaw, and C. Tong. 2004. “Variable selection in random forest with application to quantitative structure–activity relationship.” In Proc., 7th Course on Ensemble Methods for Learning Machines, 1–8. Berlin: Springer.
Svetnik, V., Liaw, A., Tong, C., Culberson, J. C., Sheridan, R. P., and Feuston, B. P. 2003. “Random forest: A classification and regression tool for compound classification and QSAR modeling.” J. Chem. Inform. Comput. Sci. 43 (6): 1947–1958. https://doi.org/10.1021/ci034160g.
Tang, Z., C. de Almeida, and P. A. Fishwick. 1991. “Time series forecasting using neural networks vs. Box–Jenkins methodology.” Simulation 57 (5): 303–310. https://doi.org/10.1177/003754979105700508.
Tipping, M. E. 2000. “The relevance vector machine.” In Proc., of the 12th Int. Conf. on Neural Information Processing Systems, 652–658. Cambridge, MA: MIT Press.
Tsymbal, A., M. Pechenizkiy, and P. Cunningham. 2006. “Dynamic integration with random forest.” In Proc., European Conf. on Machine Learning, 801–808. Berlin: Springer.
Vapnik, V. 1995. The nature of statistical learning theory. New York: Springer.
Vapnik, V., S. E. Golowich, and A. Smola. 1997. “Support vector method for function approximation, regression estimation, and signal processing.” In Proc., 9th Int. Conf. on Neural Information Processing Systems, 281–287. Cambridge, MA: MIT Press.
Warren, S. M., and P. Walter. 1943. “A logical calculus of the ideas immanent in nervous activity.” Bull. Math. Biophys. 5 (4): 115–133. https://doi.org/10.1007/BF02478259.
Widrow, B., and M. E. Hoff. 1960. Adaptive switching circuits. 1960 IRE WESCON convention record. New York: IRE.
Yuan, H., W. Zhang, J. Kim, and Y. Liu. 2017. “A nonlinear grain-based fatigue damage model for civil infrastructure under variable amplitude loads.” Int. J. Fatigue 104: 389–396. https://doi.org/10.1016/j.ijfatigue.2017.07.026.
Zhang, W., and C. S. Cai. 2012. “Fatigue reliability assessment for existing bridges considering vehicle speed and road surface conditions.” J. Bridge Eng. 17 (3): 443–453. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000272.
Zhang, W., C. S. Cai, and F. Pan. 2013a. “Finite element modeling of bridges with equivalent orthotropic material method for multi-scale dynamic loads.” Eng. Struct. 54: 82–93. https://doi.org/10.1016/j.engstruct.2013.03.047.
Zhang, W., C. S. Cai, and F. Pan. 2013b. “Fatigue reliability assessment for long-span bridges under combined dynamic loads from winds and vehicles.” J. Bridge Eng. 18 (8): 735–747. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000411.
Zhang, W., and H. Yuan. 2014. “Corrosion fatigue effects on life estimation of deteriorated bridges under vehicle impacts.” Eng. Struct. 71: 128–136. https://doi.org/10.1016/j.engstruct.2014.04.004.
Zhu, J., and W. Zhang. 2018. “Probabilistic fatigue damage assessment of coastal slender bridges under coupled dynamic loads.” Eng. Struct. 166: 274–285. https://doi.org/10.1016/j.engstruct.2018.03.073.
Zhu, J., W. Zhang, and M. Wu. 2018. “Coupled dynamic analysis of vehicle-bridge-wind-wave system.” J. Bridge Eng. 23 (8): 04018054. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001268.
Zien, A., G. Rätsch, S. Mika, B. Schölkopf, T. Lengauer, and K. R. Müller. 2000. “Engineering support vector machine kernels that recognize translation initiation sites.” Bioinformatics 16 (9): 799–807. https://doi.org/10.1093/bioinformatics/16.9.799.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 25 • Issue 7 • July 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Apr 17, 2019
Accepted: Jan 13, 2020
Published online: Apr 20, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 21, 2020
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.