Abstract
This paper presents a new method for performing reliability-based design optimization (RBDO) of structures based on sequential optimization and reliability assessment (SORA). SORA is an effective method for solving RBDO that separates uncertainty analysis from optimization loops for reducing computational cost. However, SORA has some limitations, such as an inability to deal with problems involving discrete design variables or discontinuity in a domain, the dependency of solutions on the starting point of numerical solutions, and the lack of guarantee that global optimum solutions will be found. In this paper, a global decoupling method is proposed to tackle these limitations and improve the performance of SORA. This method links SORA enhanced with modified chaos control (ESORA) to an improved differential evolution (IDE) to perform RBDO. To deal with RBDO problems with discrete design variables, a rounding method is integrated into IDE. IDE also utilizes an adaptive selection scheme in a mutation step and an elitist strategy in the selection phase. To improve the efficiency of the method for RBDO problems with highly nonlinear performance functions and nonnormal random variables, a modified chaos control is employed to assess reliability constraints. Five numerical examples are considered to investigate the strength of the proposed method, illustrating its appropriate efficiency and accuracy. The proposed method is also extendable to more complex problems such as system reliability-based structural optimization and RBDO of nonlinear structures.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Ayyub, B. M., U. O. Akpan, T. S. Koko, and T. Dunbar. 2015. “Reliability-based optimal design of steel box structures. I: Theory.” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng. 1 (3): 1–9. https://doi.org/10.1061/AJRUA6.0000829.
Bigham, A., and S. Gholizadeh. 2020. “Topology optimization of nonlinear single-layer domes by an improved electro-search algorithm and its performance analysis using statistical tests.” In Structural and multidisciplinary optimization. New York: Springer.
Chen, Z., H. Qiu, L. Gao, L. Su, and P. Li. 2013. “An adaptive decoupling approach for reliability-based design optimization.” Comput. Struct. 117 (Feb): 58–66. https://doi.org/10.1016/j.compstruc.2012.12.001.
Coello, C. C., M. Rudnick, and A. D. Christiansen. 1994. “Using genetic algorithms for optimal design of trusses.” In Proc., 6th Int. Conf. on Tools with Artificial Intelligence, 88–94. New York: IEEE.
Du, X., and W. Chen. 2004. “Sequential optimization and reliability assessment method for efficient probabilistic design.” ASME J. Mech. Des. 126 (2): 225–233. https://doi.org/10.1115/1.1649968.
Du, X., A. Sudjianto, and W. Chen. 2004. “An integrated framework for optimization under uncertainty using inverse reliability strategy.” ASME J. Mech. Des. 126 (4): 562–570. https://doi.org/10.1115/1.1759358.
Enevoldsen, I., and J. D. Sørensen. 1994. “Reliability-based optimization in structural engineering.” Struct. Saf. 15 (3): 169–196. https://doi.org/10.1016/0167-4730(94)90039-6.
Gholizadeh, S., M. Danesh, and C. Gheyratmand. 2020. “A new Newton metaheuristic algorithm for discrete performance-based design optimization of steel moment frames.” Comput. Struct. 234 (Jul): 106250. https://doi.org/10.1016/j.compstruc.2020.106250.
Gholizadeh, S., and M. Mohammadi. 2017. “Reliability-based seismic optimization of steel frames by metaheuristics and neural networks.” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng. 3 (1): 04016013. https://doi.org/10.1061/AJRUA6.0000892.
Hao, P., R. Ma, Y. Wang, S. Feng, B. Wang, G. Li, H. Xing, and F. Yang. 2019. “An augmented step size adjustment method for the performance measure approach: Toward general structural reliability-based design optimization.” Struct. Saf. 80 (Sep): 32–45. https://doi.org/10.1016/j.strusafe.2019.04.001.
Ho-Huu, V., T. D. Do-Thi, H. Dang-Trung, T. Vo-Duy, and T. Nguyen-Thoi. 2016a. “Optimization of laminated composite plates for maximizing buckling load using improved differential evolution and smoothed finite element method.” Compos. Struct. 146 (Jun): 132–147. https://doi.org/10.1016/j.compstruct.2016.03.016.
Ho-Huu, V., T. Vo-Duy, T. Luu-Van, L. Le-Anh, and T. Nguyen-Thoi. 2016b. “Optimal design of truss structures with frequency constraints using improved differential evolution algorithm based on an adaptive mutation scheme.” Autom. Constr. 68 (Aug): 81–94. https://doi.org/10.1016/j.autcon.2016.05.004.
Ilonen, J., J. K. Kamarainen, and J. Lampinen. 2003. “Differential evolution training algorithm for feed-forward neural networks.” Neural Process. Lett. 17 (1): 93–105. https://doi.org/10.1023/A:1022995128597.
Jena, P. K., D. N. Thatoi, and D. R. Parhi. 2013. “Differential evolution: An inverse approach for crack detection.” Adv. Acoust. Vibr. 2013: 1–10. https://doi.org/10.1155/2013/321931.
Jiang, C., H. Qiu, L. Gao, X. Cai, and P. Li. 2017. “An adaptive hybrid single-loop method for reliability-based design optimization using iterative control strategy.” Struct. Multidiscip. Optim. 56 (6): 1271–1286. https://doi.org/10.1007/s00158-017-1719-z.
Keshtegar, B., and S. Chakraborty. 2018. “Dynamical accelerated performance measure approach for efficient reliability-based design optimization with highly nonlinear probabilistic constraints.” Reliab. Eng. Syst. Saf. 178 (Oct): 69–83. https://doi.org/10.1016/j.ress.2018.05.015.
Keshtegar, B., P. Hao, and Z. Meng. 2017. “A self-adaptive modified chaos control method for reliability-based design optimization.” Struct. Multidiscip. Optim. 55 (1): 63–75. https://doi.org/10.1007/s00158-016-1471-9.
Le-Anh, L., T. Nguyen-Thoi, V. Ho-Huu, H. Dang-Trung, and T. Bui-Xuan. 2015. “Static and frequency optimization of folded laminated composite plates using an adjusted differential evolution algorithm and a smoothed triangular plate element.” Compos. Struct. 127 (Sep): 382–394. https://doi.org/10.1016/j.compstruct.2015.02.069.
Lee, J. J., and B. C. Lee. 2005. “Efficient evaluation of probabilistic constraints using an envelope function.” Eng. Optim. 37 (2): 185–200. https://doi.org/10.1080/03052150512331315505.
Li, G., Z. Meng, and H. Hu. 2015. “An adaptive hybrid approach for reliability-based design optimization.” Struct. Multidiscip. Optim. 51 (5): 1051–1065. https://doi.org/10.1007/s00158-014-1195-7.
Liang, J., Z. P. Mourelatos, and E. Nikolaidis. 2007. “A single-loop approach for system reliability-based design optimization.” ASME J. Mech. Des. 129 (12): 1215–1224. https://doi.org/10.1115/1.2779884.
Lim, J., and B. Lee. 2016. “A semi-single-loop method using approximation of most probable point for reliability-based design optimization.” Struct. Multidiscip. Optim. 53 (4): 745–757. https://doi.org/10.1007/s00158-015-1351-8.
Melchers, R. E., and A. T. Beck. 2018. Structural reliability analysis and prediction. New York: Wiley.
Meng, Z., G. Li, B. P. Wang, and P. Hao. 2015. “A hybrid chaos control approach of the performance measure functions for reliability-based design optimization.” Comput. Struct. 146 (Jan): 32–43. https://doi.org/10.1016/j.compstruc.2014.08.011.
Meng, Z., D. Yang, H. Zhou, and B. P. Wang. 2018. “Convergence control of single loop approach for reliability-based design optimization.” Struct. Multidiscip. Optim. 57 (3): 1079–1091. https://doi.org/10.1007/s00158-017-1796-z.
Meng, Z., H. Zhou, G. Li, and D. Yang. 2016. “A decoupled approach for non-probabilistic reliability-based design optimization.” Comput. Struct. 175 (Oct): 65–73. https://doi.org/10.1016/j.compstruc.2016.06.008.
Moosavian, N., and B. K. Roodsari. 2014. “Soccer league competition algorithm: A novel meta-heuristic algorithm for optimal design of water distribution networks.” Swarm Evol. Comput. 17 (Aug): 14–24. https://doi.org/10.1016/j.swevo.2014.02.002.
Rosenblatt, M. 1952. “Remarks on a multivariate transformation.” Ann. Math. Stat. 23 (3): 470–472. https://doi.org/10.1214/aoms/1177729394.
Shayanfar, M., R. Abbasnia, and A. Khodam. 2014. “Development of a GA-based method for reliability-based optimization of structures with discrete and continuous design variables using OpenSees and Tcl.” Finite Elem. Anal. Des. 90 (Nov): 61–73. https://doi.org/10.1016/j.finel.2014.06.010.
Storn, R. 1996. “On the usage of differential evolution for function optimization.” In Proc., North American Fuzzy Information Processing, 519–523. New York: IEEE.
Storn, R. 1999. “System design by constraint adaptation and differential evolution.” IEEE Trans. Evol. Comput. 3 (1): 22–34. https://doi.org/10.1109/4235.752918.
Storn, R., and K. Price. 1997. “Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces.” J. Global Optim. 11 (4): 341–359. https://doi.org/10.1023/A:1008202821328.
Tahk, M. J., M. S. Park, H. W. Woo, and H. J. Kim. 2009. “Hessian approximation algorithms for hybrid optimization methods.” Eng. Optim. 41 (7): 609–633. https://doi.org/10.1080/03052150902736879.
Tang, H., S. Xue, and C. Fan. 2008. “Differential evolution strategy for structural system identification.” Comput. Struct. 86 (21–22): 2004–2012. https://doi.org/10.1016/j.compstruc.2008.05.001.
Tu, J., K. K. Choi, and Y. H. Park. 1999. “A new study on reliability-based design optimization.” ASME J. Mech. Des. 121 (4): 557–564. https://doi.org/10.1115/1.2829499.
Wang, Z., H. Tang, and P. Li. 2009. “Optimum design of truss structures based on differential evolution strategy.” In Proc., Int. Conf. on Information Engineering and Computer Science, 1–5. New York: IEEE.
Wu, C. Y., and K. Y. Tseng. 2010. “Truss structure optimization using adaptive multi-population differential evolution.” Struct. Multidiscip. Optim. 42 (4): 575–590. https://doi.org/10.1007/s00158-010-0507-9.
Wu, Y. T., H. R. Millwater, and T. A. Cruse. 1990. “Advanced probabilistic structural analysis method for implicit performance functions.” AIAA J. 28 (9): 1663–1669. https://doi.org/10.2514/3.25266.
Yang, D., and P. Yi. 2009. “Chaos control of performance measure approach for evaluation of probabilistic constraints.” Struct. Multidiscip. Optim. 38 (1): 83–92. https://doi.org/10.1007/s00158-008-0270-3.
Youn, B. D., and K. K. Choi. 2004. “An investigation of nonlinearity of reliability-based design optimization approaches.” ASME J. Mech. Des. 126 (3): 403–411. https://doi.org/10.1115/1.1701880.
Youn, B. D., K. K. Choi, and L. Du. 2005. “Adaptive probability analysis using an enhanced hybrid mean value method.” Struct. Multidiscip. Optim. 29 (2): 134–148. https://doi.org/10.1007/s00158-004-0452-6.
Youn, B. D., K. K. Choi, and Y. H. Park. 2003. “Hybrid analysis method for reliability-based design optimization.” ASME J. Mech. Des. 125 (2): 221–232. https://doi.org/10.1115/1.1561042.
Yu, S., Z. Wang, and Z. Wang. 2019. “Time-dependent reliability-based robust design optimization using evolutionary algorithm.” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B: Mech. Eng. 5 (2): 020911. https://doi.org/10.1115/1.4042921.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 1 • March 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: May 7, 2020
Accepted: Jul 16, 2020
Published online: Nov 23, 2020
Published in print: Mar 1, 2021
Discussion open until: Apr 23, 2021
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.