High-Dimensional Reliability Analysis with Error-Guided Active-Learning Probabilistic Support Vector Machine: Application to Wind-Reliability Analysis of Transmission Towers
Publication: Journal of Structural Engineering
Volume 148, Issue 5
Abstract
Adaptive reliability analysis methods based on surrogate models, especially kriging, have been successfully implemented in many problems. However, the application of kriging is limited to low-dimensional problems with noncategorical performance data. Support vector machine (SVM), by contrast, addresses these limitations, but its application in reliability analysis faces several challenges with regard to robustness, accuracy, and efficiency. This study proposed a new adaptive approach based on probabilistic support vector machine for reliability analysis (PSVM-RA). Different from existing methods that only select training points in the margin of the SVM, the proposed method adopts a new learning function that considers the wrong classification probability for each realization and maximizes the potential for new information offered by a candidate sample for the training set. Moreover, the upper bound of the error that is introduced by the SVM in estimating the failure probability is derived based on a Poisson binomial distribution model considering the likelihood of wrong classification for all the points in the margin of the SVM. This upper bound of error was used in the proposed framework as a stopping criterion to guarantee the desired accuracy. Three numerical examples and an engineering application regarding the wind-reliability analysis of transmission towers were investigated to demonstrate the performance of the proposed method. It was demonstrated that PSVM-RA can provide robust estimates of failure probability when other state-of-the-art methods fail. Moreover, it offers a balance between efficiency and accuracy.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author upon reasonable request.
Acknowledgments
This research was partly funded by the US National Science Foundation (NSF) through Grant No. CMMI-2000156; the Lichtenstein endowment at The Ohio State University; and the China Scholarship Council. The opinions and findings presented are those of the authors and do not necessarily reflect the views of the sponsors. In addition, the help from Dr. Yousef M. Darestani, Mr. Ashkan B. Jeddi, and Mr. Chi Zhang on the finite-element models of the transmission tower is greatly appreciated.
References
Aoues, Y., and A. Chateauneuf. 2010. “Benchmark study of numerical methods for reliability-based design optimization.” Struct. Multidiscip. Optim. 41 (2): 277–294. https://doi.org/10.1007/s00158-009-0412-2.
ASCE. 2013. Minimum design loads for buildings and other structures. Reston, VA: ASCE.
Athanasopoulos, A., A. Dimou, V. Mezaris, and I. Kompatsiaris. 2011. “GPU acceleration for support vector machines.” In Proc., 12th Int. Workshop on Image Analysis for Multimedia Interactive Services (WIAMIS 2011). Delft, Netherlands: Delft Univ. of Technology.
Au, S.-K., and J. L. Beck. 2001. “Estimation of small failure probabilities in high dimensions by subset simulation.” Probab. Eng. Mech. 16 (4): 263–277. https://doi.org/10.1016/S0266-8920(01)00019-4.
Bichon, B. J., M. S. Eldred, L. P. Swiler, S. Mahadevan, and J. M. McFarland. 2008. “Efficient global reliability analysis for nonlinear implicit performance functions.” AIAA J. 46 (10): 2459–2468. https://doi.org/10.2514/1.34321.
Bourinet, J.-M., F. Deheeger, and M. Lemaire. 2011. “Assessing small failure probabilities by combined subset simulation and support vector machines.” Struct. Saf. 33 (6): 343–353. https://doi.org/10.1016/j.strusafe.2011.06.001.
Campbell, R. J., and S. Lowry. 2012. Weather-related power outages and electric system resiliency. Washington, DC: Congressional Research Service, Library of Congress.
Chang, C.-C., and C.-J. Lin. 2011. “LIBSVM: A library for support vector machines.” ACM Trans. Intell. Syst. Technol. 2 (3): 1–27. https://doi.org/10.1145/1961189.1961199.
Chen, D.-R., Q. Wu, Y. Ying, and D.-X. Zhou. 2004. “Support vector machine soft margin classifiers: Error analysis.” J. Mach. Learn. Res. 5 (Dec): 1143–1175. https://doi.org/10.5555/1005332.1044698.
Dai, H., H. Zhang, and W. Wang. 2012. “A support vector density-based importance sampling for reliability assessment.” Reliab. Eng. Syst. Saf. 106 (Oct): 86–93. https://doi.org/10.1016/j.ress.2012.04.011.
Darestani, Y. M., A. Shafieezadeh, and K. Cha. 2020. “Effect of modelling complexities on extreme wind hazard performance of steel lattice transmission towers.” Struct. Infrastruct. Eng. 16 (6): 898–915. https://doi.org/10.1080/15732479.2019.1673783.
Djuric, N., L. Lan, S. Vucetic, and Z. Wang. 2013. “BudgetedSVM: A toolbox for scalable SVM approximations.” J. Mach. Learn. Res. 14 (1): 3813–3817.
Echard, B., N. Gayton, and M. Lemaire. 2011. “AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation.” Struct. Saf. 33 (2): 145–154. https://doi.org/10.1016/j.strusafe.2011.01.002.
Elawady, A., H. Aboshosha, A. El Damatty, G. Bitsuamlak, H. Hangan, and A. Elatar. 2017. “Aero-elastic testing of multi-spanned transmission line subjected to downbursts.” J. Wind Eng. Ind. Aerodyn. 169 (Oct): 194–216. https://doi.org/10.1016/j.jweia.2017.07.010.
Elawady, A., and A. El Damatty. 2016. “Longitudinal force on transmission towers due to non-symmetric downburst conductor loads.” Eng. Struct. 127 (Nov): 206–226. https://doi.org/10.1016/j.engstruct.2016.08.030.
Ghosh, S., A. Roy, and S. Chakraborty. 2021. “Kriging metamodeling-based Monte Carlo simulation for improved seismic fragility analysis of structures.” J. Earthquake Eng. 25 (7): 1316–1336. https://doi.org/10.1080/13632469.2019.1570395.
Horn, D., A. Demircioğlu, B. Bischl, T. Glasmachers, and C. Weihs. 2018. “A comparative study on large scale kernelized support vector machines.” Adv. Data Anal. Classification 12 (4): 867–883. https://doi.org/10.1007/s11634-016-0265-7.
Huang, X., J. Chen, and H. Zhu. 2016. “Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and subset simulation.” Struct. Saf. 59 (Mar): 86–95. https://doi.org/10.1016/j.strusafe.2015.12.003.
Hurtado, J. E., and D. A. Alvarez. 2003. “Classification approach for reliability analysis with stochastic finite-element modeling.” J. Struct. Eng. 129 (8): 1141–1149. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:8(1141).
Jia, G., and A. A. Taflanidis. 2013. “Kriging metamodeling for approximation of high-dimensional wave and surge responses in real-time storm/hurricane risk assessment.” Comput. Methods Appl. Mech. Eng. 261–262 (Jul): 24–38. https://doi.org/10.1016/j.cma.2013.03.012.
Kiureghian, A. D., and M. D. Stefano. 1991. “Efficient algorithm for second-order reliability analysis.” J. Eng. Mech. 117 (12): 2904–2923. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:12(2904).
Kroetz, H., M. Moustapha, A. T. Beck, and B. Sudret. 2020. “A two-level Kriging-based approach with active learning for solving time-variant risk optimization problems.” Reliab. Eng. Syst. Saf. 203 (Nov): 107033. https://doi.org/10.1016/j.ress.2020.107033.
Li, X., X. Li, and Y. Su. 2016. “A hybrid approach combining uniform design and support vector machine to probabilistic tunnel stability assessment.” Struct. Saf. 61 (Jul): 22–42. https://doi.org/10.1016/j.strusafe.2016.03.001.
Liu, X.-X., and I. Elishakoff. 2020. “A combined Importance Sampling and active learning Kriging reliability method for small failure probability with random and correlated interval variables.” Struct. Saf. 82 (Jan): 101875. https://doi.org/10.1016/j.strusafe.2019.101875.
Loh, W.-L. 1996. “On Latin hypercube sampling.” Ann. Stat. 24 (5): 2058–2080. https://doi.org/10.1214/aos/1069362310.
Marelli, S., and B. Sudret. 2014. “UQLab: A framework for uncertainty quantification in Matlab.” In Vulnerability, uncertainty, and risk: Quantification, mitigation, and management, 2554–2563. Reston, VA: ASCE. https://doi./org/10.1061/9780784413609.257.
Melchers, R. 1989. “Importance sampling in structural systems.” Struct. Saf. 6 (1): 3–10. https://doi.org/10.1016/0167-4730(89)90003-9.
Monger, S. H., E. R. Morgan, A. R. Dyreson, and T. L. Acker. 2016. “Applying the kriging method to predicting irradiance variability at a potential PV power plant.” Renewable Energy 86 (Feb): 602–610. https://doi.org/10.1016/j.renene.2015.08.058.
Moustapha, M., and B. Sudret. 2019. “Surrogate-assisted reliability-based design optimization: A survey and a unified modular framework.” Struct. Multidiscip. Optim. 60 (5): 2157–2176. https://doi.org/10.1007/s00158-019-02290-y.
Pan, Q., and D. Dias. 2017. “An efficient reliability method combining adaptive support vector machine and Monte Carlo simulation.” Struct. Saf. 67 (Jul): 85–95. https://doi.org/10.1016/j.strusafe.2017.04.006.
Platt, J. C. 1999. “Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods.” In Advances in large-margin classifiers, 61–74. Cambridge, MA: MIT Press.
Qian, P. Z. 2009. “Nested Latin hypercube designs.” Biometrika 96 (4): 957–970. https://doi.org/10.1093/biomet/asp045.
Rahimi, M., A. Shafieezadeh, D. Wood, and E. Kubatko. 2020. “A physics-based approach for predicting time-dependent progression length of backward erosion piping.” Can. Geotech. J. 58 (7): 995–1004. https://doi.org/10.1139/cgj-2019-0854.
Rahimi, M., Z. Wang, A. Shafieezadeh, D. Wood, and E. J. Kubatko. 2019. “An adaptive kriging-based approach with weakly stationary random fields for soil slope reliability analysis.” In Proc., Geo-Congress 2019: Soil Erosion, Underground Engineering, and Risk Assessment, 148–157. Reston, VA: ASCE.
Rocco, C. M., and J. A. Moreno. 2002. “Fast Monte Carlo reliability evaluation using support vector machine.” Reliab. Eng. Syst. Saf. 76 (3): 237–243. https://doi.org/10.1016/S0951-8320(02)00015-7.
Song, C., R. Xiao, and B. Sun. 2018. “Optimization of cable pre-tension forces in long-span cable-stayed bridges considering the counterweight.” Eng. Struct. 172 (Oct): 919–928. https://doi.org/10.1016/j.engstruct.2018.06.061.
Song, C., C. Zhang, A. Shafieezadeh, and R. Xiao. 2022. “Value of information analysis in non-stationary stochastic decision environments: A reliability-assisted POMDP approach.” Reliab. Eng. Syst. Saf. 217 (Jan): 108034. https://doi.org/10.1016/j.ress.2021.108034.
Song, H., K. K. Choi, I. Lee, L. Zhao, and D. Lamb. 2013. “Adaptive virtual support vector machine for reliability analysis of high-dimensional problems.” Struct. Multidiscip. Optim. 47 (4): 479–491. https://doi.org/10.1007/s00158-012-0857-6.
Ungkurapinan, N. 2000. “A study of joint slip in galvanized bolted angle connections.” Master’s thesis, Dept. of Civil and Geological Engineering, Univ. of Manitoba.
Uriz, P., F. C. Filippou, and S. A. Mahin. 2008. “Model for cyclic inelastic buckling of steel braces.” J. Struct. Eng. 134 (4): 619–628. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:4(619).
Vapnik, V. 2013. The nature of statistical learning theory. New York: Springer.
Vapnik, V. N. 1999. “An overview of statistical learning theory.” IEEE Trans. Neural Netw. 10 (5): 988–999. https://doi.org/10.1109/72.788640.
Wang, Y., K. Duan, L. Liu, and H. Guo. 2020. “Reliability analysis of large span cable-stayed bridges based on support vector machine.” In Proc., IOP Conf. Series: Earth and Environmental Science, 052103. Bristol, UK: IOP Publishing.
Wang, Z., and A. Shafieezadeh. 2019a. “ESC: An efficient error-based stopping criterion for kriging-based reliability analysis methods.” Struct. Multidiscip. Optim. 59 (5): 1621–1637. https://doi.org/10.1007/s00158-018-2150-9.
Wang, Z., and A. Shafieezadeh. 2019b. “REAK: Reliability analysis through Error rate-based Adaptive Kriging.” Reliab. Eng. Syst. Saf. 182 (Feb): 33–45. https://doi.org/10.1016/j.ress.2018.10.004.
Wong, C. J., and M. D. Miller. 2009. Guidelines for electrical transmission line structural loading. Reston, VA: ASCE.
Wu, J. 2010. “A fast dual method for HIK SVM learning.” In Proc., European Conf. on Computer Vision, 552–565. Springer.
Wu, Q., and D.-X. Zhou. 2005. “SVM soft margin classifiers: Linear programming versus quadratic programming.” Neural Comput. 17 (5): 1160–1187. https://doi.org/10.1162/0899766053491896.
Zhang, C., and A. Shafieezadeh. 2021. “A quantile-based sequential approach to reliability-based design optimization via error-controlled adaptive Kriging with independent constraint boundary sampling.” Struct. Multidiscip. Optim. 63 (5): 2231–2252. https://doi.org/10.1007/s00158-020-02798-8.
Zhang, C., C. Song, and A. Shafieezadeh. 2022. “Adaptive reliability analysis for multi-fidelity models using a collective learning strategy.” Struct. Saf. 94 (Jan): 102141. https://doi.org/10.1016/j.strusafe.2021.102141.
Zhao, H.-B. 2008. “Slope reliability analysis using a support vector machine.” Comput. Geotech. 35 (3): 459–467. https://doi.org/10.1016/j.compgeo.2007.08.002.
Zhao, Y.-G., and T. Ono. 2001. “Moment methods for structural reliability.” Struct. Saf. 23 (1): 47–75. https://doi.org/10.1016/S0167-4730(00)00027-8.
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Journal of Structural Engineering
Volume 148 • Issue 5 • May 2022
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© 2022 American Society of Civil Engineers.
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Received: Oct 4, 2021
Accepted: Jan 6, 2022
Published online: Feb 28, 2022
Published in print: May 1, 2022
Discussion open until: Jul 28, 2022
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