Structural Reliability Assessment Based on Enhanced Conjugate Unscented Transformation and Improved Maximum Entropy Method
Publication: Journal of Structural Engineering
Volume 147, Issue 12
Abstract
Estimation of statistical moments remains one of the main topics of stochastic analysis whose accuracy greatly affects reliability analysis results. In this work, conjugate unscented transformation (CUT) methods, which can balance accuracy and efficiency, are introduced for the statistical moment estimation of responses. Because of the drawbacks of existing CUT methods, a family of enhanced conjugate unscented transformation (ECUT) methods, including ECUT-4, ECUT-6, and ECUT-8 methods, is proposed for statistical moment estimation by combining the original CUT, variable transformation, and exact dimension reduction method. Then the probability density function of a performance function is reconstructed by the improved maximum entropy method (IMEM) with the available statistical moments as constraints. To demonstrate the accuracy and effectiveness of the proposed methods, five numerical examples, including linear and nonlinear, low-dimensional and high-dimensional, and explicit and implicit performance functions, are investigated, in which the results obtained from the proposed methods are compared with other existing moment methods and a Monte Carlo simulation (MCS) method. The results of the examples show that the proposed ECUT-6 and ECUT-8 methods have fairly high accuracy and efficiency for structural reliability analysis.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors would like to acknowledge the support of the National Key R&D Program of China (Grant No. 2019YFD1101003), the National Natural Science Foundation of China (Grant Nos. 51678092 and 51478064), and NSFC-JSPS China-Japan Scientific Cooperation Project (NSFC Grant No. 51611140123). In addition, the authors would also like to express gratitude to the associate editor and the two anonymous reviewers for their vital and insightful suggestions and comments.
References
Adurthi, N., and P. Singla, and T. Singh. 2012. “The Conjugate Unscented Transform—An approach to evaluate multi-dimensional expectation integrals.” In Proc., American Control Conf. New York: IEEE.
Adurthi, N., and P. Singla, and T. Singh. 2013. “Optimal information collection for nonlinear systems- An application to multiple target tracking and localization.” In Proc., American Control Conf. New York: IEEE.
Ang, A. H.-S., and D. D. Leon. 2005. “Modeling and analysis of uncertainties for risk-informed decisions in infrastructures engineering.” Struct. Infrastruct. 1 (1): 19–31. https://doi.org/10.1080/15732470412331289350.
Ang, A. H.-S., D. D. Leon, and W. Fan. 2019. “Optimal reliability-based aseismic design of high-rise buildings.” Struct. Infrastruct. 16 (4): 520–530. https://doi.org/10.1080/15732479.2019.1653327.
Ang, A. H.-S., and W. H. Tang. 2007. Probability concepts in engineering. 2nd ed. New York: Wiley.
Blatman, G., and B. Sudret. 2011. “Adaptive sparse polynomial chaos expansion based on least angle regression.” J. Comput. Phys. 230 (6): 2345–2367. https://doi.org/10.1016/j.jcp.2010.12.021.
Bucher, C. G., and U. A. 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.
Chen, J. B., and J. Li. 2007. “The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters.” Struct. Saf. 29 (2): 77–93. https://doi.org/10.1016/j.strusafe.2006.02.002.
Der Kiureghian, A. 1987. “Second order reliability approximations.” J. Eng. Mech. 113 (8): 1208–1225. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:8(1208).
Der Kiureghian, A., and T. Dakessian. 1998. “Multiple design points in first and second-order reliability.” Struct. Saf. 20 (1): 37–49. https://doi.org/10.1016/S0167-4730(97)00026-X.
Ditlevsen, O., and H. O. Madsen. 2006. Structural reliability methods. New York: Wiley.
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.
Ellingwood, B. R., and D. M. Frangopol. 2016. “Introduction to the state of the art collection: Risk-based lifecycle performance of structural systems.” J. Struct. Eng. 142 (9): F2016001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001522.
Fan, W., J. Wei, A. H.-S. Ang, and Z. Li. 2016. “Adaptive estimation of statistical moments of the responses of random systems.” Probab. Eng. Mech. 43 (Jan): 50–67. https://doi.org/10.1016/j.probengmech.2015.10.005.
Ghanem, R. G., and P. D. Spanos. 2002. Stochastic finite elements: A spectral approach. 2nd ed. New York: Springer.
He, J., S. Gao, and J. Gong. 2014. “A sparse grid stochastic collocation method for structural reliability analysis.” Struct. Saf. 51 (Nov): 29–34. https://doi.org/10.1016/j.strusafe.2014.06.003.
Heiss, F., and V. Winschel. 2008. “Likelihood approximation by numerical integration on sparse grids.” J. Econom. 144 (1): 62–80. https://doi.org/10.1016/j.jeconom.2007.12.004.
Huang, X., and Y. Zhang. 2013. “Reliability–sensitivity analysis using dimension reduction methods and saddlepoint approximations.” Int. J. Numer. Methods Eng. 93 (8): 857–886. https://doi.org/10.1002/nme.4412.
Li, G., and K. Zhang. 2011. “A combined reliability analysis approach with dimension reduction method and maximum entropy method.” Struct. Multidiscip. Optim. 43 (1): 121–134. https://doi.org/10.1007/s00158-010-0546-2.
Li, J., J. B. Chen, and W. L. Fan. 2007. “The equivalent extreme-value event and evaluation of the structural system reliability.” Struct. Saf. 29 (2): 112–131. https://doi.org/10.1016/j.strusafe.2006.03.002.
Li, Y., and B. R. Ellingwood. 2006. “Hurricane damage to residential construction in the US: Importance of uncertainty modeling in risk assessment.” Eng. Struct. 28 (7): 1009–1018. https://doi.org/10.1016/j.engstruct.2005.11.005.
Liu, P. L., and A. Der Kiureghian. 1986. “Multivariate distribution models with prescribed marginal and covariances.” Probab. Eng. Mech. 1 (2): 105–112. https://doi.org/10.1016/0266-8920(86)90033-0.
Liu, R., W. Fan, Y. Wang, A. H.-S. Ang, and Z. Li. 2019. “Adaptive estimation for statistical moments of response based on the exact dimension reduction method in terms of vector.” Mech. Syst. Signal Process. 126 (Jul): 609–625. https://doi.org/10.1016/j.ymssp.2019.02.035.
Phoon, K. K., S. P. Huang, and S. T. Quek. 2002. “Simulation of second-order processes using Karhunen-Loeve expansion.” Comput. Struct. 80 (12): 1049–1060. https://doi.org/10.1016/S0045-7949(02)00064-0.
Rackwitz, R. 2001. “Reliability analysis—A review and some perspectives.” Struct. Saf. 23 (4): 365–395. https://doi.org/10.1016/S0167-4730(02)00009-7.
Rahman, S., and H. Xu. 2004. “A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics.” Probab. Eng. Mech. 19 (4): 393–408. https://doi.org/10.1016/j.probengmech.2004.04.003.
Rajan, A., and Y. C. Kuang. 2018. “Moment-constrained maximum entropy method for expanded uncertainty evaluation.” IEEE Access 6 (1): 4072–4082. https://doi.org/10.1109/ACCESS.2017.2787736.
Rosenblatt, M. 1952. “Remarks on a multivariate transformation.” Ann. Math. Stat. 23 (3): 470–472. https://doi.org/10.1214/aoms/1177729394.
Rubinstein, R., and D. Kroese. 2016. Simulation and the Monte Carlo method. In Wiley series in probability and statistics. New York: Wiley.
Xiao, S., and Z. Lu. 2016. “Structural reliability analysis using combined space partition technique and unscented transformation.” J. Struct. Eng. 142 (11): 04016089. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001553.
Xiao, S., and Z. Lu. 2018. “Reliability analysis by combining higher-order unscented transformation and fourth-moment method.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A 4 (1): 04017034. https://doi.org/10.1061/AJRUA6.0000944.
Xu, H., and S. Rahman. 2004. “A generalized dimension-reduction method for multidimensional integration in stochastic mechanics.” Int. J. Numer. Methods Eng. 61 (12): 1992–2019. https://doi.org/10.1002/nme.1135.
Xu, J., and C. Dang. 2018. “A new bivariate dimension reduction method for efficient structural reliability analysis.” Mech. Syst. Signal Process. 115 (Jan): 281–300. https://doi.org/10.1016/j.ymssp.2020.107309.
Youn, D. B., Z. Xi, and P. Wang. 2008. “Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis.” Struct. Multidiscip. Optim. 37 (1): 13–28. https://doi.org/10.1007/s00158-007-0210-7.
Zhang, X., and M. D. Pandey. 2013. “Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method.” Struct. Saf. 43 (Jul): 28–40. https://doi.org/10.1016/j.strusafe.2013.03.001.
Zhao, Y. G., and A. H.-S. Ang. 2003. “System reliability assessment by method of moments.” J. Struct. Eng. 129 (10): 1341–1349. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:10(1341).
Zhao, Y. G., and A. H.-S. Ang. 2012. “On the first-order third-moment reliability method.” Struct. Infrastruct. 8 (5): 517–527. https://doi.org/10.1080/15732479.2010.539072.
Zhao, Y. G., and Z. H. Lu. 2007. “Fourth-moment standardization for structural reliability assessment.” J. Struct. Eng. 133 (7): 916–924. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:7(916).
Zhao, Y. G., and T. Ono. 1999. “A general procedure for first/second-order reliability method (FORM/SORM).” Struct. Saf. 21 (2): 95–112. https://doi.org/10.1016/S0167-4730(99)00008-9.
Zhao, Y. G., and T. Ono. 2000. “New point-estimates for probability moments.” J. Eng. Mech. 126 (4): 433–436. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:4(433).
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.
Zhou, J., and A. S. Nowak. 1988. “Integration formulas to evaluate functions of random variables.” Struct. Saf. 5 (4): 267–284. https://doi.org/10.1016/0167-4730(88)90028-8.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 147 • Issue 12 • December 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Feb 4, 2021
Accepted: Jul 26, 2021
Published online: Sep 28, 2021
Published in print: Dec 1, 2021
Discussion open until: Feb 28, 2022
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.
Cited by
- Cheng Wang, Zhengliang Li, Tao Wang, Bo Yu, Wind Uplift Fragility Assessment Method of 360° Standing Seam Roof System and Its Application in Wind Damage Estimation of UHV Converter Station, Journal of Structural Engineering, 10.1061/JSENDH.STENG-11976, 149, 5, (2023).
- Zhengqi Tang, Zhengliang Li, Tao Wang, Probabilistic bearing capacity assessment for unequal-leg angle cross-bracings in transmission towers, Journal of Constructional Steel Research, 10.1016/j.jcsr.2022.107672, 200, (107672), (2023).
- Zhengqi Tang, Zhengliang Li, Tao Wang, GPR-based prediction and uncertainty quantification for bearing capacity of steel tubular members considering semi-rigid connections in transmission towers, Engineering Failure Analysis, 10.1016/j.engfailanal.2022.106854, 142, (106854), (2022).