The GCO Method for Time-Dependent Structural Reliability Assessment
Publication: Journal of Engineering Mechanics
Volume 149, Issue 1
Abstract
By taking the advantage of Poisson events, the outcrossing method has been widely applied for time-dependent reliability analysis considering continuous processes. Generally, the outcrossing method can only obtain an upper bound of failure probability, which will overestimate the risk and result in unnecessary maintenance costs. In this study, a general conditional outcrossing (GCO) method for time-dependent reliability analysis was proposed, which can obtain a more accurate probability of failure. The conditional outcrossing rate was defined as the outcrossing rate conditioned on fixing the values of time-invariant random variables, which was introduced to satisfy the assumption of independent outcrossing events. A numerical algorithm for the GCO method was developed with the aid of the Gauss-Legendre quadrature and point estimate method. The application of the GCO method is demonstrated by three examples, including an implicit limit state function with a finite-element model and non-Gaussian nonstationary random processes. The failure probability obtained by the GCO method was found to be in close agreement with that by Monte Carlo simulation, which demonstrates the accuracy of the GCO method.
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Data Availability Statement
All data, models, and code used during the study are available from the corresponding author upon reasonable request.
Acknowledgments
The study is partially supported by the National Natural Science Foundation of China (Grant Nos. 52108104, 51820105014, 51738001, and U19342171) and the 111 Project (Grant No. D21001). The supports are gratefully acknowledged.
References
Abramowitz, M., and I. E. Stegun. 1972. Handbook of mathematical functions. New York: Dover Publications.
Andrieu-Renaud, C., B. Sudret, and M. Lemaire. 2004. “The PHI2 method: A way to compute time-variant reliability.” Reliab. Eng. Syst. Saf. 84 (1): 75–86. https://doi.org/10.1016/j.ress.2003.10.005.
Au, S. K., and Y. Wang. 2014. Engineering risk assessment with subset simulation. Hoboken, NJ: Wiley.
Breitung, K. 1988. “Asymptotic crossing rates for stationary Gaussian vector processes.” Stochastic Processes Appl. 29 (3): 195–207. https://doi.org/10.1016/0304-4149(88)90037-3.
Du, W., Y. X. Luo, and Y. Q. Wang. 2019. “Time-variant reliability analysis using the parallel subset simulation.” Reliab. Eng. Syst. Saf. 182 (Jan): 250–257. https://doi.org/10.1016/j.ress.2018.10.016.
Ellingwood, B. R., and Y. Mori. 1993. “Probabilistic methods for condition assessment and life prediction of concrete structures in nuclear power plants.” Nucl. Eng. Des. 142 (2–3): 155–166. https://doi.org/10.1016/0029-5493(93)90199-J.
Gong, C. Q., and D. M. Frangopol. 2019. “An efficient time-dependent reliability method.” Struct. Saf. 81 (Apr): 101864. https://doi.org/10.1016/j.strusafe.2019.05.001.
Guedes Soares, C. 1992. “Combination of primary load effects in ship structures.” Prob. Eng. Mech. 7 (8): 103–111. https://doi.org/10.1016/0266-8920(92)90013-8.
Hagen, O., and L. Tvedt. 1991. “Vector process outcrossing as parallel system sensitivity measure.” J. Eng. Mech. 117 (10): 2201–2220. https://doi.org/10.100710.1061/(ASCE)0733-9399(1991)117:10(2201.
Hawchar, L., C. P. E. Soueidy, and F. Schoefs. 2017. “Principal component analysis and polynomial chaos expansion for time-dependent reliability problems.” Reliab. Eng. Syst. Saf. 167 (Jun): 406–416. https://doi.org/10.1016/j.ress.2017.06.024.
Hu, Z., and X. Du. 2013. “Time-dependent reliability analysis with joint upcrossing rates.” Struct. Multidiscip. Optim. 48 (Feb): 893–907. https://doi.org/10.1007/s00158-013-0937-2.
Hu, Z., and X. Du. 2015. “First order reliability method for time-variant problems using series expansions.” Struct. Multidiscip. Optim. 51 (Sep): 1–21. https://doi.org/10.1007/s00158-014-1132-9.
Hu, Z., and S. Mahadevan. 2016. “Resilience assessment based on time-dependent system reliability analysis.” J. Mech. Des. 138 (Jan): 111404. https://doi.org/10.1115/1.4034109.
Li, C. Q., A. Firouzi, and W. Yang. 2016. “Closed-form solution to first passage probability for nonstationary lognormal processes.” J. Eng. Mech. 142 (12): 04016103. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001160.
Li, Q. W., C. Wang, and B. R. Ellingwood. 2015. “Time-dependent reliability of aging structures in the presence of non-stationary loads and degradation.” Struct. Saf. 52 (13): 132–141. https://doi.org/10.1016/j.strusafe.2014.10.003.
Liu, P. L., and A. Der Kiureghian. 1986. “Multivariate distribution models with prescribed marginals and covariances.” Prob. Eng. Mech. 1 (2): 105–112. https://doi.org/10.1016/0266-8920(86)90033-0.
Lu, Z. H., Y. Leng, Y. Dong, C. H. Cai, and Y. G. Zhao. 2019. “Fast integration algorithms for time-dependent structural reliability analysis considering correlated random variables.” Struct. Saf. 78 (12): 23–32. https://doi.org/10.1016/j.strusafe.2018.12.001.
Mori, Y., and B. R. Ellingwood. 1993. “Reliability-based service-life assessment of aging concrete structures.” J. Struct. Eng. 119 (5): 1600–1621. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:5(1600).
Qian, H. M., Y. F. Li, and H. Z. Huang. 2020. “Improved model for computing time-variant reliability based on outcrossing rate.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 6 (4): 04020043. https://doi.org/10.1061/AJRUA6.0001090.
Qian, H. M., Y. F. Li, and H. Z. Huang. 2021. “Time-variant system reliability analysis method for a small failure probability problem.” Reliab. Eng. Syst. Saf. 205 (10): 107261. https://doi.org/10.1016/j.ress.2020.107261.
Rice, S. O. 1944. “Mathematical analysis of random noise.” Bell Syst. Technol. J. 23 (7): 282–332. https://doi.org/10.1002/j.1538-7305.1944.tb00874.x.
Shinozuka, M. 1964. “Probability of failure under random loading.” J. Eng. Mech. Div. 90 (5): 147–170. https://doi.org/10.1061/JMCEA3.0000534.
Sonal, S. D., S. Ammanagi, O. Kanjilal, and C. S. Manohar. 2018. “Experimental estimation of time variant system reliability of vibrating structures based on subset simulation with Markov chain splitting.” Reliab. Eng. Syst. Saf. 178 (5): 55–68. https://doi.org/10.1016/j.ress.2018.05.007.
Sudret, B. 2008. “Analytical derivation of the outcrossing rate in time-variant reliability problems.” Struct. Infrastruct. Eng. 4 (5): 353. https://doi.org/10.1080/15732470701270058.
Wang, C. 2020. “Stochastic process-based structural reliability considering correlation between upcrossings.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 6 (4): 06020002. https://doi.org/10.1061/AJRUA6.0001093.
Wang, C., B. Michael, and A. Bilal. 2021. “Time-dependent reliability of aging structures: Overview of assessment methods.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 7 (4): 03121003. https://doi.org/10.1061/AJRUA6.0001176.
Wang, C., H. Zhang, and M. Beer. 2019. “Structural time-dependent reliability assessment with new power spectral density function.” J. Struct. Eng. 145 (12): 04019163. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002476.
Wang, Z., and W. Chen. 2017. “Confidence-based adaptive extreme response surface for time-dependent reliability analysis under random excitation.” Struct. Saf. 64 (Jun): 76–86. https://doi.org/10.1016/j.strusafe.2016.10.001.
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.
Zhang, X. Y., Z. H. Lu, S. Y. Wu, and Y. G. Zhao. 2021. “An efficient method for time-variant reliability including finite element analysis.” Reliab. Eng. Syst. Saf. 210 (Apr): 107534. https://doi.org/10.1016/j.ress.2021.107534.
Zhang, X. Y., Z. H. Lu, Y. G. Zhao, and C. Q. Li. 2022a. “Conditional time-dependent limit state function model considering damages and its application in reliability evaluation of CRTS II track slab.” Appl. Math. Modell. 101 (55): 654–672. https://doi.org/10.1016/j.apm.2021.09.018.
Zhang, X. Y., Z. H. Lu, Y. G. Zhao, and C. Q. Li. 2022b. “The GLO method: An efficient algorithm for time-dependent reliability analysis based on outcrossing rate.” Struct. Saf. 97 (5): 102204. https://doi.org/10.1016/j.strusafe.2022.102204.
Zhao, Y. G., and Z. H. Lu. 2021. Structural reliability: Approaches from perspectives of statistical moments. Hoboken, NJ: Wiley.
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.
Zhou, W., C. Q. Gong, and H. P. Hong. 2017. “New perspective on application of first-order reliability method for estimating system reliability.” J. Eng. Mech. 143 (9): 101864. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001280.
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Received: Jan 11, 2022
Accepted: Aug 27, 2022
Published online: Nov 2, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 2, 2023
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