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Sequential optimization and fuzzy reliability analysis for multidisciplinary systems

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Abstract

To meet the rising demand for high reliability in complex multidisciplinary engineering systems, more attention has been paid to reliability-based multidisciplinary design optimization (RBMDO). In this paper, a sequential optimization and fuzzy reliability analysis (SOFRA) method for multidisciplinary systems is developed to decouple the fuzzy reliability analysis from the optimization. In SOFRA, the multidisciplinary design optimization (MDO) and fuzzy reliability analysis are conducted in a sequential manner. Furthermore, a novel adaptive collocation method (ACM) is proposed to conduct the fuzzy reliability analysis for multidisciplinary systems. The ACM arranges points adaptively at the axis of the membership to obtain more accurate results. The shifting distance of the constraint is calculated by the bi-section method. Both numerical and engineering examples are used to demonstrate the validity of the proposed method.

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References

  • Agarwal H, Renaud J (2013) Reliability based design optimization for multidisciplinary systems using response surfaces. Eng Optim 36:291–311

    Article  Google Scholar 

  • Ahn J, Kwon JH (2006) An efficient strategy for reliability-based multidisciplinary design optimization using BLISS. Struct Multidiscip Optim 31:363–372

    Article  Google Scholar 

  • Ben-Haim Y (1994) A non-probabilistic concept of reliability. Struct Saf 14:227–245

    Article  Google Scholar 

  • Ben-Haim Y, Elishakoff I (1995) Discussion on: a non-probabilistic concept of reliability. Struct Saf 17:195–199

    Article  Google Scholar 

  • Cho SG, Jang J, Kim S, Park S, Lee TH, Lee M, Choi JS, Kim HW, Hong S (2016) Nonparametric approach for uncertainty-based multidisciplinary design optimization considering limited data. Struct Multidiscip Optim 54:1671–1688

    Article  Google Scholar 

  • Du X, Guo J, Beeram H (2008) Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidiscip Optim 35:117–130

    Article  MathSciNet  MATH  Google Scholar 

  • Feng K, Lu Z, Pang C, Yun W (2018a) Efficient numerical algorithm of profust reliability analysis: an application to wing box structure. Aerosp Sci Technol 80:203–211

    Article  Google Scholar 

  • Feng K, Lu Z, Pang C (2019) Safety life analysis under required failure credibility constraint for unsteady thermal structure with fuzzy input parameters. Struct Multidiscip Optim. 59:43–59

  • Huang HZ, Yu H, Zhang X, Zeng S, Wang Z (2010) Collaborative optimization with inverse reliability for multidisciplinary systems uncertainty analysis. Eng Optim 42:763–773

    Article  MathSciNet  Google Scholar 

  • Jiang C, Zhang QF, Han X, Qian YH (2014) A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model. Acta Mech 225:383–395

    Article  Google Scholar 

  • Jones AEW, Forbes GW (1995) An adaptive simulated annealing algorithm for global optimization over continuous variables. J Glob Optim 6:1–37

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Lees L (2003) Hypersonic flow. J Spacecr Rocket 40:700–735

    Article  MATH  Google Scholar 

  • Li L, Liu J, Liu S (2014) An efficient strategy for multidisciplinary reliability design and optimization based on CSSO and PMA in SORA framework. Struct Multidiscip Optim 49:239–252

    Article  MathSciNet  Google Scholar 

  • Lin PT, Gea HC (2012) Reliability-based multidisciplinary design optimization using probabilistic gradient-based transformation method. J Mech Des 135:021001

    Article  Google Scholar 

  • Luo Y, Kang Z, Li A (2009) Structural reliability assessment based on probability and convex set mixed model. Comput Struct 87:1408–1415

    Article  Google Scholar 

  • Meng D, Li YF, Huang HZ, Wang Z, Liu Y (2015) Reliability-based multidisciplinary design optimization using subset simulation analysis and its application in the hydraulic transmission mechanism design. J Mech Des 137:051402

    Article  Google Scholar 

  • Mon DL, Cheng CH (1994) Fuzzy system reliability analysis for components with different membership functions. Fuzzy Sets Syst 64:145–157

    Article  MathSciNet  Google Scholar 

  • Oberkampf WL, Helton JC, Joslyn CA, Wojtkiewicz SF, Ferson S (2004) Challenge problems: uncertainty in system response given uncertain parameters. Reliab Eng Syst Saf 85:11–19

    Article  Google Scholar 

  • Pandey D, Tyagi SK (2007) Profust reliability of a gracefully degradable system. Fuzzy Sets Syst 158:794–803

    Article  MathSciNet  MATH  Google Scholar 

  • Qian W, Li M (2018) Convergence analysis of standard particle swarm optimization algorithm and its improvement. Soft Comput 22:4047–4070

    Article  MATH  Google Scholar 

  • Qiu Z, Wang X (2005) Parameter perturbation method for dynamic responses of structures with uncertain-but-bounded parameters based on interval analysis. Int J Solids Struct 42:4958–4970

    Article  MATH  Google Scholar 

  • Qiu Z, Wang X (2009) Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters. Acta Mech Sinica 25:367–379

    Article  MATH  Google Scholar 

  • Sala R, Baldanzini N, Pierini M (2016) Representative surrogate problems as test functions for expensive simulators in multidisciplinary design optimization of vehicle structures. Struct Multidiscip Optim 54:449–468

    Article  MathSciNet  Google Scholar 

  • Sigmund O (2011) On the usefulness of non-gradient approaches in topology optimization. Struct Multidiscip Optim 43:589–596

    Article  MathSciNet  MATH  Google Scholar 

  • Sobieszczanski-Sobieski J, Haftka RT (1997) Multidisciplinary aerospace design optimization: survey of recent developments. Struct Multidiscip Optim 14:1–23

    Article  Google Scholar 

  • Tang Z, Lu Z, Xia Y (2013) Numerical method for fuzzy reliability analysis. J Aircr 50:1710–1715

    Article  Google Scholar 

  • Tang Z, Lu Z, Hu J (2014) An efficient approach for design optimization of structures involving fuzzy variables. Fuzzy Sets Syst 255:52–73

    Article  MathSciNet  Google Scholar 

  • Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121:557–564

    Article  Google Scholar 

  • Wang X, Qiu Z, Elishakoff I (2008) Non-probabilistic set-theoretic model for structural safety measure. Acta Mech 198:51–64

    Article  MATH  Google Scholar 

  • Wang L, Wang X, Su H, Lin G (2017a) Reliability estimation of fatigue crack growth prediction via limited measured data. Int J Mech Sci 121:44–57

    Article  Google Scholar 

  • Wang C, Qiu Z, Xu M, Qiu H (2017b) Novel fuzzy reliability analysis for heat transfer system based on interval ranking method. Int J Therm Sci 116:234–241

    Article  Google Scholar 

  • Wang X, Wang R, Chen X, Wang L, Geng X, Fan W (2017c) Interval prediction of responses for uncertain multidisciplinary system. Struct Multidiscip Optim 55:1945–1964

    Article  Google Scholar 

  • Wang L, Ren Q, Ma Y, Wu D (2018a) Optimal maintenance design-oriented nonprobabilistic reliability methodology for existing structures under static and dynamic mixed uncertainties. IEEE Trans Reliab.. https://doi.org/10.1109/TR.2018.2868773

  • Wang L, Xiong C, Hu J, Wang X, Qiu Z (2018b) Sequential multidisciplinary design optimization and reliability analysis under interval uncertainty. Aerosp Sci Technol 80:508–519

    Article  Google Scholar 

  • Wang L, Xiong C, Yang Y (2018c) A novel methodology of reliability-based multidisciplinary design optimization under hybrid interval and fuzzy uncertainties. Comput Methods Appl Mech Eng 337:439–457

    Article  MathSciNet  Google Scholar 

  • Wang L, Xiong C, Wang X, Xu M, Li Y (2018d) A dimension-wise method and its improvement for multidisciplinary interval uncertainty analysis. Appl Math Model 59:680–695

    Article  MathSciNet  Google Scholar 

  • Wang L, Liang J, Zhang Z, Yang Y (2018e) Nonprobabilistic reliability oriented topological optimization for multi-material heat transfer structures with interval uncertainties. Struct Multidiscip Optim. https://doi.org/10.1007/s00158-018-2146-5

  • Wang X, Wang R, Wang L, Chen X, Geng X (2018f) An efficient single-loop strategy for reliability-based multidisciplinary design optimization under non-probabilistic set theory. Aerosp Sci Technol 73:148–163

    Article  Google Scholar 

  • Yang C (2018) Sensor placement for structural health monitoring using hybrid optimization algorithm based on sensor distribution index and FE grids. Struct Control Health Monit 25:e2160

  • Yang C, Zhang X, Huang X, Cheng Z, Zhang X, Hou X (2017) Optimal sensor placement for deployable antenna module health monitoring in SSPS using genetic algorithm. Acta Astronautica 140:213–224

    Article  Google Scholar 

  • Yao W, Chen X, Luo W, Tooren MV, Guo J (2011) Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles. Prog Aerosp Sci 47:450–479

    Article  Google Scholar 

  • Yao W, Chen X, Ouyang Q, Tooren MV (2013) A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory. Struct Multidiscip Optim 48:339–354

    Article  MathSciNet  Google Scholar 

  • Youn BD, Choi KK, Park YH (2003) Hybrid analysis method for reliability-based design optimization. J Mech Des 125:221–232

    Article  Google Scholar 

  • Yu X, Du X (2006) Reliability-based multidisciplinary optimization for aircraft wing design. Struct Infrastruct Eng 2:277–289

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets, information and control. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zaman K, Mahadevan S (2016) Reliability-based design optimization of multidisciplinary system under aleatory and epistemic uncertainty. Struct Multidiscip Optim 55:681–699

  • Zandavi SM, Pourtakdoust SH (2018) Multidisciplinary design of a guided flying vehicle using simplex nondominated sorting genetic algorithm II. Struct Multidiscip Optim 57:705–720

    Article  MathSciNet  Google Scholar 

  • Zhang X, Huang HZ (2010) Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties. Struct Multidiscip Optim 40:165–175

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Nature Science Foundation of China (No. 11602012, 11432002), the Defense Industrial Technology Development Program (No. JCKY2016204B101), the Pre-research Field Foundation of Equipment Development Department of China (No. 61402100103), the Aeronautical Science Foundation of China (No. 2017ZA51012), and the postgraduate innovation practice fund of Beihang University (YCSJ-01-2018-06).

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Authors and Affiliations

  1. Institute of Solid Mechanics, Beihang University, Beijing, 100191, China

    Lei Wang, Chuang Xiong, Xiaojun Wang, Guanhua Liu & Qinghe Shi

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  1. Lei Wang
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  2. Chuang Xiong
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  3. Xiaojun Wang
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  4. Guanhua Liu
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  5. Qinghe Shi
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Correspondence to Lei Wang.

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Wang, L., Xiong, C., Wang, X. et al. Sequential optimization and fuzzy reliability analysis for multidisciplinary systems. Struct Multidisc Optim 60, 1079–1095 (2019). https://doi.org/10.1007/s00158-019-02258-y

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