Accurate Structural Reliability Analysis Using an Improved Line-Sampling-Method-Based Slime Mold Algorithm
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 2
Abstract
Line sampling (LS) is a robust and powerful simulation technique to reduce the computational burden provided by Monte Carlo simulation (MCS) for the reliability analysis of engineering structures. However, when dealing with highly nonlinear and implicit limit-state functions, LS yields instable results as nonconvergence or divergence. In this study, a novel framework that integrates the LS method with the slime mold algorithm (LS-SMA) is proposed to solve complex structural reliability problems. SMA is a new metaheuristic population-based algorithm inspired by the behavior and morphological changes in slime molds that can well solve multivariable optimization problems. In the proposed method, the determination of the important direction of LS is formulated as an unconstrained optimization problem according to the LS theory. Then SMA is employed to solve this optimization problem to decrease the computational cost. Thus, the LS-SMA is able to overcome the drawbacks of LS such as the local convergence and divergence. Seven numerical problems were utilized to investigate the LS-SMA applicability, where its performance was compared with MCS, subset simulation (SS), importance sampling (IS), LS, first-order reliability method (FORM), and first-order control variate method (FOCM). The results demonstrate that the proposed LS-SMA can be applied with high efficiency for solving the reliability problems that involve highly nonlinear or dimensional and complex implicit limit-state functions.
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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 first author thanks Dr. Mohsen Rashki and Dr. Dequan Zhang for their helpful guidance. The authors are grateful to receive comments from both the editor and reviewers, which highly improved the original manuscript.
References
Abdel-Basset, M., V. Chang, and R. Mohamed. 2020. “HSMA_WOA: A hybrid novel Slime mould algorithm with whale optimization algorithm for tackling the image segmentation problem of chest X-ray images.” Appl. Software Comput. J. 95 (Oct): 106642. https://doi.org/10.1016/j.asoc.2020.106642.
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.
Bagheri, M., S. P. Zhu, M. E. A. Ben Seghier, B. Keshtegar, and N. T. Trung. 2020. “Hybrid intelligent method for fuzzy reliability analysis of corroded X100 steel pipelines.” Eng.Comput. 1–15. https://doi.org/10.1007/s00366-020-00969-1.
Binder, K., D. Heermann, L. Roelofs, A. J. Mallinckrodt, and S. McKay. 1993. “Monte Carlo simulation in statistical physics.” Comput. Phys. 7 (2): 156–157. https://doi.org/10.1063/1.4823159.
Castaldo, P., M. Calvello, and B. Palazzo. 2013. “Probabilistic analysis of excavation-induced damages to existing structures.” Comput. Geotech. 53 (Sep): 17–30. https://doi.org/10.1016/j.compgeo.2013.04.008.
de Angelis, M., E. Patelli, and M. Beer. 2015. “Advanced line sampling for efficient robust reliability analysis.” Struct. Saf. 52 (Part B): 170–182. https://doi.org/10.1016/j.strusafe.2014.10.002.
Depina, I., I. Papaioannou, D. Straub, and G. Eiksund. 2017. “Coupling the cross-entropy with the line sampling method for risk-based design optimization.” Struct. Multidiscip. Optim. 55 (5): 1589–1612. https://doi.org/10.1007/s00158-016-1596-x.
De Santana Gomes, W. J. 2019. “Structural reliability analysis using adaptive artificial neural networks.” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B: Mech. Eng. 5 (4): 041004. https://doi.org/10.1115/1.4044040.
Dubourg, V., and B. Sudret. 2014. “Meta-model-based importance sampling for reliability sensitivity analysis.” Struct. Saf. 49 (Jul): 27–36. https://doi.org/10.1016/j.strusafe.2013.08.010.
El Amine Ben Seghier, M., B. Keshtegar, and B. Elahmoune. 2018. “Reliability analysis of low, mid and high-grade strength corroded pipes based on plastic flow theory using adaptive nonlinear conjugate map.” Eng. Fail. Anal. 90 (Aug): 245–261. https://doi.org/10.1016/j.engfailanal.2018.03.029.
Elegbede, C. 2005. “Structural reliability assessment based on particles swarm optimization.” Struct. Saf. 27 (2): 171–186. https://doi.org/10.1016/j.strusafe.2004.10.003.
Eshghi, A. T., and S. Lee. 2019. “Adaptive improved response surface method for reliability-based design optimization.” Eng. Optim. 51 (12): 2011–2029. https://doi.org/10.1080/0305215X.2018.1561885.
Ghalehnovi, M., M. Rashki, and A. Ameryan. 2020. “First order control variates algorithm for reliability analysis of engineering structures.” Appl. Math. Modell. 77 (Part 1): 829–847. https://doi.org/10.1016/j.apm.2019.07.049.
Gong, J. X., and P. Yi. 2011. “A robust iterative algorithm for structural reliability analysis.” Struct. Multidiscip. Optim. 43 (4): 519–527. https://doi.org/10.1007/s00158-010-0582-y.
Gong, J. X., P. Yi, and N. Zhao. 2014. “Non-gradient–based algorithm for structural reliability analysis.” J. Eng. Mech. 140 (6): 04014029. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000722.
Hu, C., and B. D. Youn. 2011. “Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems.” Struct. Multidiscip. Optim. 43 (3): 419–442. https://doi.org/10.1007/s00158-010-0568-9.
Keshtegar, B., and S. Chakraborty. 2018. “A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis.” Appl. Math. Modell. 53 (Jan): 319–332. https://doi.org/10.1016/j.apm.2017.09.017.
Koutsourelakis, P. S., H. J. Pradlwarter, and G. I. Schuëller. 2004. “Reliability of structures in high dimensions, part I: Algorithms and applications.” Probab. Eng. Mech. 19 (4): 409–417. https://doi.org/10.1016/j.probengmech.2004.05.001.
Kumar, C., T. D. Raj, M. Premkumar, and T. D. Raj. 2020. “A new stochastic slime mould optimization algorithm for the estimation of solar photovoltaic cell parameters.” Optik 223 (Dec): 165277. https://doi.org/10.1016/j.ijleo.2020.165277.
Lan, C. M., H. Li, J. Y. Peng, and D. B. Sun. 2016. “A structural reliability-based sensitivity analysis method using particles swarm optimization: Relative convergence rate.” J. Zhejiang Univ.-Sci. A 17 (12): 961–973. https://doi.org/10.1631/jzus.A1500255.
Li, L., and Z. Lu. 2014. “Interval optimization based line sampling method for fuzzy and random reliability analysis.” Appl. Math. Modell. 38 (13): 3124–3135. https://doi.org/10.1016/j.apm.2013.11.027.
Li, S., H. Chen, M. Wang, A. A. Heidari, and S. Mirjalili. 2020. “Slime mould algorithm: A new method for stochastic optimization.” Future Gener. Comput. Syst. 111 (Oct): 300–323. https://doi.org/10.1016/j.future.2020.03.055.
Lim, J., B. Lee, and I. Lee. 2014. “Second-order reliability method-based inverse reliability analysis using hessian update for accurate and efficient reliability-based design optimization.” Int. J. Numer. Methods Eng. 100 (10): 773–792. https://doi.org/10.1002/nme.4775.
Liu, P. L., and A. Der Kiureghian. 1991. “Optimization algorithms for structural reliability.” Struct. Saf., 9(3): 161–177. https://doi.org/10.1016/0167-4730(91)90041-7.
Low, B. K. 2007. “Reliability analysis of rock slopes involving correlated nonnormals.” Int. J. Rock Mech. Min. Sci. 44 (6): 922–935. https://doi.org/10.1016/j.ijrmms.2007.02.008.
Miarnaeimi, F. 2019. Reliability-based design optimization of hydraulic structures using a new algorithm. [In Persian.] Zahedan, Iran: Univ. of Sistan and Baluchestan.
Mirjalili, S., S. Saremi, S. M. Mirjalili, and L. D. S. Coelho. 2016. “Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization.” Expert Syst. Appl. 47 (Apr): 106–119. https://doi.org/10.1016/j.eswa.2015.10.039.
Naess, A., B. J. Leira, and O. Batsevych. 2009. “System reliability analysis by enhanced Monte Carlo simulation.” Struct. Saf. 31 (5): 349–355. https://doi.org/10.1016/j.strusafe.2009.02.004.
Nie, J., and B. R. Ellingwood. 2004. “A new directional simulation method for system reliability. Part I: Application of deterministic point sets.” Probab. Eng. Mech. 19 (4): 425–436. https://doi.org/10.1016/j.probengmech.2004.03.004.
Ohadi, S., and J. Jafari-Asl. 2020. “Multi-objective reliability-based optimization for design of trapezoidal labyrinth weirs.” Flow Meas. Instrum. 77 (Mar): 101787. https://doi.org/10.1016/j.flowmeasinst.2020.101787.
Rashki, M. 2018. “Hybrid control variates-based simulation method for structural reliability analysis of some problems with low failure probability.” Appl. Math. Modell. 60 (Aug): 220–234. https://doi.org/10.1016/j.apm.2018.03.009.
Rashki, M. 2021. “SESC: A new subset simulation method for rare-events estimation.” Mech. Syst. Sig. Process. 150 (Mar): 107139. https://doi.org/10.1016/j.ymssp.2020.107139.
Rashki, M., H. Azarkish, M. Rostamian, and A. Bahrpeyma. 2019. “Classification correction of polynomial response surface methods for accurate reliability estimation.” Struct. Saf. 81 (Nov): 101869. https://doi.org/10.1016/j.strusafe.2019.101869.
Santosh, T. V., R. K. Saraf, A. K. Ghosh, and H. S. Kushwaha. 2006. “Optimum step length selection rule in modified HL-RF method for structural reliability.” Int. J. Press. Vessels Pip. 83 (10): 742–748. https://doi.org/10.1016/j.ijpvp.2006.07.004.
Sawada, K., A. Matsuo, and H. Shimizu. 2011. “Randomized line search techniques in combined GA for discrete sizing optimization of truss structures.” Struct. Multidiscip. Optim. 44 (3): 337–350. https://doi.org/10.1007/s00158-011-0629-8.
Shayanfar, M. A., M. A. Barkhordari, and M. A. Roudak. 2017. “An efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method.” Commun. Nonlinear Sci. Numer. Simul. 47 (Jun): 223–237. https://doi.org/10.1016/j.cnsns.2016.11.021.
Song, K., Y. Zhang, X. Yu, and B. Song. 2019. “A new sequential surrogate method for reliability analysis and its applications in engineering.” IEEE Access 7: 60555–60571. https://doi.org/10.1109/ACCESS.2019.2915350.
Song, K., Y. Zhang, X. Zhuang, X. Yu, and B. Song. 2020. “An adaptive failure boundary approximation method for reliability analysis and its applications.” Eng. Comput. 1–16. https://doi.org/10.1007/s00366-020-01011-0.
Tolson, B. A., H. R. Maier, A. R. Simpson, and B. J. Lence. 2004. “Genetic algorithms for reliability-based optimization of water distribution systems.” J. Water Resour. Plann. Manage. 130 (1): 63–72. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:1(63).
Wei, D., and S. Rahman. 2007. “Structural reliability analysis by univariate decomposition and numerical integration.” Probab. Eng. Mech. 22 (1): 27–38. https://doi.org/10.1016/j.probengmech.2006.05.004.
Xiao, M., J. Zhang, and L. Gao. 2020. “A system active learning Kriging method for system reliability-based design optimization with a multiple response model.” Reliability Eng. Syst. Saf. 199 (Jul): 106935. https://doi.org/10.1016/j.ress.2020.106935.
Xiao, M., J. Zhang, L. Gao, S. Lee, and A. T. Eshghi. 2019. “An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability.” Struct. Multidiscip. Optim. 59 (6): 2077–2092. https://doi.org/10.1007/s00158-018-2176-z.
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.
Xuan, S. N. 2007. “Algorithmes probabilistes appliqués à la durabilité et à la mecanique des ouvrages de gé de génie civil.” [In French.] Doctoral dissertation, Ph. D. thesis, Institute of Applied Sciences Toulouse, Univ. of Toulouse.
Yang, M., D. Zhang, and X. Han. 2020. “New efficient and robust method for structural reliability analysis and its application in reliability-based design optimization.” Comput. Methods Appl. Mech. Eng. 366 (Jul): 113018. https://doi.org/10.1016/j.cma.2020.113018.
Yao, W., G. Tang, N. Wang, and X. Chen. 2019. “An improved reliability analysis approach based on combined FORM and Beta-spherical importance sampling in critical region.” Struct. Multidiscip. Optim. 60 (1): 35–58. https://doi.org/10.1007/s00158-019-02193-y.
Zhang, J., M. Xiao, L. Gao, and J. Fu. 2018. “A novel projection outline based active learning method and its combination with Kriging metamodel for hybrid reliability analysis with random and interval variables.” Comput. Methods Appl. Mech. Eng. 341 (Nov): 32–52. https://doi.org/10.1016/j.cma.2018.06.032.
Zhang, X., Z. Lu, W. Yun, K. Feng, and Y. Wang. 2020. “Line sampling-based local and global reliability sensitivity analysis.” Struct. Multidiscip. Optim. 61 (1): 267–281. https://doi.org/10.1007/s00158-019-02358-9.
Zhao, H., M. Zhao, and C. Zhu. 2016. “Reliability-based optimization of geotechnical engineering using the artificial bee colony algorithm.” KSCE J. Civ. Eng. 20 (5): 1728–1736. https://doi.org/10.1007/s12205-015-0117-6.
Zhong, C., M. Wang, C. Dang, and W. Ke. 2020a. “Structural reliability assessment by salp swarm algorithm–based FORM.” Qual. Reliab. Eng. Int. 36 (4): 1224–1244. https://doi.org/10.1002/qre.2626.
Zhong, C., M. Wang, C. Dang, W. Ke, and S. Guo. 2020b. “First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis.” Struct. Multidiscip. Optim. 62 (4): 1951–1968. https://doi.org/10.1007/s00158-020-02587-3.
Zio, E., and N. Pedroni. 2010. “An optimized Line Sampling method for the estimation of the failure probability of nuclear passive systems.” Reliability Eng. Syst. Saf. 95 (12): 1300–1313. https://doi.org/10.1016/j.ress.2010.06.007.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 2 • June 2021
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© 2021 American Society of Civil Engineers.
History
Received: Sep 23, 2020
Accepted: Dec 14, 2020
Published online: Mar 8, 2021
Published in print: Jun 1, 2021
Discussion open until: Aug 8, 2021
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