Abstract
The problem which is actually being addressed in this study includes two parts: One is on establishing time-dependent reliability-based design optimization (tRBDO) formulation under fuzzy and interval uncertainties to obtain the optimal design parameter solution for the time-dependent structure. The other is on presenting a serial single-loop optimization (SSLO) strategy to estimate the optimal design parameter. For addressing the optimal design parameter of the time-dependent structure involving fuzzy and interval uncertainties, a novel tRBDO model with the constraint of time-dependent failure possibility (TDFP) based on the possibility theory of the safety measure is proposed. For evaluating the optimal design parameter, the established SSLO method converts the original triple-loop optimization which is TDFP-index-based approach into a sequence of deterministic optimization, interval value corresponding to the worst case scenario, the estimation of time instant, and the minimum most probable point. Iterative searching step is not needed to find the minimum most probable point at each iteration step in the proposed SSLO strategy; therefore, the computational time is extremely reduced. Several examples are given to demonstrate the efficiency of the proposed approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belegundu AD, Arora JS (1984) A recursive quadratic programming method with active set strategy for optimal design. Int J Numer Methods Eng 20:803–816. https://doi.org/10.1002/nme.1620200503
Cremona C, Gao Y (1997) The possibilistic reliability theory: theoretical aspects and applications. Struct Saf 19:173–201
Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des Trans ASME 126:225–233. https://doi.org/10.1115/1.1649968
Du L, Choi KK (2008) An inverse analysis method for design optimization with both statistical and fuzzy uncertainties, Struct Multidisc Optim 37(2):107–119. https://doi.org/10.1007/s00158-007-0225-0.
Du L, Choi KK, Youn BD (2006) Inverse possibility analysis method for possibility-based design optimization. AIAA J 44:2682–2690. https://doi.org/10.2514/1.16546
Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets Syst 24:279–300. https://doi.org/10.1016/0165-0114(87)90028-5
Elishakoff I, Ferracuti B (2006) Fuzzy sets based interpretation of the safety factor. Fuzzy Sets Syst 157:2495–2512
Fan C, Lu Z, Shi Y (2018) Safety life analysis under the required failure possibility constraint for structure involving fuzzy uncertainty. Struct Multidisc Optim 58:287–303. https://doi.org/10.1007/s00158-017-1896-9
Fan C, Lu Z, Shi Y (2019) Time-dependent failure possibility analysis under consideration of fuzzy uncertainty. Fuzzy Sets Syst 367:19–35. https://doi.org/10.1016/j.fss.2018.06.016
Graf W, Beer M, Mo B (2000) Fuzzy structural analysis using a -level optimization, Comput Mech 26(6):547–565
Hao P, Wang Y, Liu C, Wang B, Wu H (2017) A novel non-probabilistic reliability-based design optimization algorithm using enhanced chaos control method. Comput Methods Appl Mech Eng 318:572–593. https://doi.org/10.1016/j.cma.2017.01.037
Hu Z, Du X (2016) Reliability-based design optimization under stationary stochastic process loads. Eng Optim 48:1296–1312. https://doi.org/10.1080/0305215X.2015.1100956
Hu Y, Lu Z, Wei N, Zhou C (2020) A single-loop Kriging surrogate model method by considering the first failure instant for time-dependent reliability analysis and safety lifetime analysis. Mech Syst Signal Process 145:106963. https://doi.org/10.1016/j.ymssp.2020.106963
Huang ZL, Jiang C, Zhou YS, Luo Z, Zhang Z (2016) An incremental shifting vector approach for reliability-based design optimization. Struct Multidisc Optim 53:523–543. https://doi.org/10.1007/s00158-015-1352-7
Jia B, Lu Z, Wang L (2020) A decoupled credibility-based design optimization method for fuzzy design variables by failure credibility surrogate modeling. Struct Multidisc Optim 62:285–297. https://doi.org/10.1007/s00158-020-02487-6
Jiang C, Fang T, Wang ZX, Wei XP, Huang ZL (2017) A general solution framework for time-variant reliability based design optimization. Comput Methods Appl Mech Eng 323:330–352. https://doi.org/10.1016/j.cma.2017.04.029
Jiang C, Han X, Liu GR (2007) Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Comput Methods Appl Mech Eng 196:4791–4800. https://doi.org/10.1016/j.cma.2007.03.024
Kang Z, Luo Y, Li A (2011) On non-probabilistic reliability-based design optimization of structures with uncertain-but-bounded parameters. Struct Saf 33:196–205. https://doi.org/10.1016/j.strusafe.2011.03.002
Keshtegar B, Hao P (2018) A hybrid descent mean value for accurate and efficient performance measure approach of reliability-based design optimization. Comput Methods Appl Mech Eng 336:237–259. https://doi.org/10.1016/j.cma.2018.03.006
Ling C, Lu Z, Sun B, Wang M (2019) An efficient method combining active learning Kriging and Monte Carlo simulation for profust failure probability. Fuzzy Sets Syst 1:1–19. https://doi.org/10.1016/j.fss.2019.02.003
Meng Z, Keshtegar B (2019) Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization. Comput Methods Appl Mech Eng 344:95–119. https://doi.org/10.1016/j.cma.2018.10.009
Mourelatos ZP, Zhou J (2005) Reliability estimation and design with insufficient data based on possibility theory. AIAA J 43:1696–1705. https://doi.org/10.2514/1.12044
Royset JO, Der Kiureghian A, Polak E (2001) Reliability-based optimal structural design by the decoupling approach. Reliab Eng Syst Saf 73:213–221. https://doi.org/10.1016/S0951-8320(01)00048-5
Schuëller GI, Jensen HA (2008) Computational methods in optimization considering uncertainties: an overview. Comput Methods Appl Mech Eng 198:2–13. https://doi.org/10.1016/j.cma.2008.05.004
Shi Y, Lu Z, Huang Z, Xu L, He R (2020a) Advanced solution strategies for time-dependent reliability based design optimization. Comput Methods Appl Mech Eng 364:112916. https://doi.org/10.1016/j.cma.2020.112916
Shi Y, Lu Z, Xu L, Zhou Y (2020b) Novel decoupling method for time-dependent reliability-based design optimization. Struct Multidisc Optim 61:507–524. https://doi.org/10.1007/s00158-019-02371-y
Tang ZC, Lu ZZ, Hu JX (2014) An efficient approach for design optimization of structures involving fuzzy variables. Fuzzy Sets Syst 255:52–73. https://doi.org/10.1016/j.fss.2014.05.017
Tu J, Choi KK, Park YH (1999) A new study on reliability- based design optimization. J Mech Des Trans ASME 121:557–564. https://doi.org/10.1115/1.2829499
Wang L, Lu Z, Jia B (2020) A decoupled method for credibility-based design optimization with fuzzy variables. Int J Fuzzy Syst 22:844–858. https://doi.org/10.1007/s40815-020-00813-0
Wang C, Qiu Z, Xu M, Li Y (2017) Novel reliability-based optimization method for thermal structure with hybrid random, interval and fuzzy parameters. Appl Math Model 47:573–586. https://doi.org/10.1016/j.apm.2017.03.053
Wang L, Ren Q, Ma Y, Wu D (2019b) Optimal maintenance design-oriented nonprobabilistic reliability methodology for existing structures under static and dynamic mixed uncertainties. IEEE Trans Reliab 68:496–513. https://doi.org/10.1109/TR.2018.2868773
Wang L, Xiong C (2019) A novel methodology of sequential optimization and non-probabilistic time-dependent reliability analysis for multidisciplinary systems. Aerosp Sci Technol 94:105389. https://doi.org/10.1016/j.ast.2019.105389
Wang L, Xiong C, Wang X, Liu G, Shi Q (2019a) Sequential optimization and fuzzy reliability analysis for multidisciplinary systems. Struct Multidisc Optim 60:1079–1095. https://doi.org/10.1007/s00158-019-02258-y
Xiong C, Wang L, Liu G, Shi Q (2019) An iterative dimension-by-dimension method for structural interval response prediction with multidimensional uncertain variables. Aerosp Sci Technol 86:572–581. https://doi.org/10.1016/j.ast.2019.01.032
Yao W, Chen X, Luo W, Van Tooren M, Guo J (2011) Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles. Prog Aerosp Sci 47:450–479. https://doi.org/10.1016/j.paerosci.2011.05.001
Zadeh LA (1965) Fuzzy Sets. Inf Control 8:338–353
Zhang J, Taflanidis AA, Medina JC (2017) Sequential approximate optimization for design under uncertainty problems utilizing Kriging metamodeling in augmented input space. Comput Methods Appl Mech Eng 315:369–395. https://doi.org/10.1016/j.cma.2016.10.042
Acknowledgements
This work was supported by the Special Scientific Research Project of Education Department of Shaanxi Province (No. 20JK0731), the China Scholarship Council (No. 202108610168), and Shaanxi Natural Science Foundation General Program (No. 2020JM-481).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares to have no conflict of interest.
Replication of results
For replication of the results of all test examples, the main MATLAB codes have been uploaded as the supplementary material. The reader can change the response function and the input variables in the corresponding source codes to reproduce the results of all cases shown in the manuscript.
Additional information
Responsible Editor: Yoojeong Noh
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Fan, C., Shi, Y., Li, L. et al. Advanced solution framework for time-dependent reliability-based design optimization under fuzzy and interval uncertainties. Struct Multidisc Optim 65, 25 (2022). https://doi.org/10.1007/s00158-021-03142-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00158-021-03142-4