Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A new local update-based method for reliability-based design optimization

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Reliability-based design optimization (RBDO) is often associated with computationally expensive computer simulations in practical engineering applications, in which both objective and constraint functions may be implicit and time-consuming to evaluate. To improve the efficiency of RBDO, metamodels are often employed to substitute the implicit and expensive functions. In this paper, a new local update-based method is proposed for RBDO under the approximation of both objective and constraint functions. In this method, Kriging metamodels are employed to replace both objective and constraint functions, and sequential optimization and reliability assessment (SORA) is adopted to perform RBDO. Meanwhile, a local update method is developed for the approximation of objective and constraint functions, termed as LUOC. In LUOC, two local update strategies are proposed. For the constraint functions, one local update strategy judges the active constraints and then sequentially refines their Kriging metamodels in the local regions around the most probable target points obtained by SORA. For the objective function, the other local update strategy based on expected improvement is developed to refine the Kriging metamodel in the local region around the SORA solution with considering the Kriging prediction variance. Three examples including a battery design application are presented to test the accuracy and efficiency of the proposed method for RBDO.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126:225–233. https://doi.org/10.1115/1.1649968

    Article  Google Scholar 

  2. Lee I, Choi KK, Du L, Gorsich D (2008) Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems. Comput Methods Appl Mech Eng 198:14–27. https://doi.org/10.1016/j.cma.2008.03.004

    Article  MATH  Google Scholar 

  3. Hu Z, Du X (2015) First order reliability method for time-variant problems using series expansions. Struct Multidiscip Optim 51:1–21. https://doi.org/10.1007/s00158-014-1132-9

    Article  MathSciNet  Google Scholar 

  4. Zhang J, Xiao M, Gao L et al (2018) An improved two-stage framework of evidence-based design optimization. Struct Multidiscip Optim 58:1673–1693. https://doi.org/10.1007/s00158-018-1991-6

    Article  MathSciNet  Google Scholar 

  5. Meng Z, Zhang D, Liu Z, Li G (2018) An adaptive directional boundary sampling method for efficient reliability-based design optimization. J Mech Des 140:121406. https://doi.org/10.1115/1.4040883

    Article  Google Scholar 

  6. Arenbeck H, Missoum S, Basudhar A, Nikravesh P (2010) Reliability-based optimal design and tolerancing for multibody systems using explicit design space decomposition. J Mech Des 132:021010. https://doi.org/10.1115/1.4000760

    Article  Google Scholar 

  7. Huang Y-C, Chan K-Y (2010) A modified efficient global optimization algorithm for maximal reliability in a probabilistic constrained space. J Mech Des 132:061002. https://doi.org/10.1115/1.4001532

    Article  Google Scholar 

  8. Zhao L, Choi KK, Lee I, Gorsich D (2013) Conservative surrogate model using weighted Kriging variance for sampling-based RBDO. J Mech Des 135:091003. https://doi.org/10.1115/1.4024731

    Article  Google Scholar 

  9. Wang Z, Wang P (2013) A maximum confidence enhancement based sequential sampling scheme for simulation-based design. J Mech Des 136:021006. https://doi.org/10.1115/1.4026033

    Article  Google Scholar 

  10. Zhang J, Xiao M, Gao L, Fu J (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 341:32–52. https://doi.org/10.1016/j.cma.2018.06.032

    Article  MathSciNet  MATH  Google Scholar 

  11. Echard B, Gayton N, Lemaire M (2011) AK-MCS: an active learning reliability method combining Kriging and Monte Carlo Simulation. Struct Saf 33:145–154. https://doi.org/10.1016/j.strusafe.2011.01.002

    Article  Google Scholar 

  12. Xiao M, Zhang J, Gao L et al (2019) An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability. Struct Multidiscip Optim 59:2077–2092. https://doi.org/10.1007/s00158-018-2176-z

    Article  MathSciNet  Google Scholar 

  13. Zhang J, Xiao M, Gao L (2019) An active learning reliability method combining Kriging constructed with exploration and exploitation of failure region and subset simulation. Reliab Eng Syst Saf 188:90–102. https://doi.org/10.1016/j.ress.2019.03.002

    Article  Google Scholar 

  14. Xiao N-C, Yuan K, Zhou C (2020) Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables. Comput Methods Appl Mech Eng 359:112649. https://doi.org/10.1016/J.CMA.2019.112649

    Article  MathSciNet  MATH  Google Scholar 

  15. Shi Y, Lu Z, He R et al (2020) A novel learning function based on Kriging for reliability analysis. Reliab Eng Syst Saf 198:106857

    Article  Google Scholar 

  16. Xiao NC, Zuo MJ, Zhou C (2018) A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis. Reliab Eng Syst Saf 169:330–338. https://doi.org/10.1016/j.ress.2017.09.008

    Article  Google Scholar 

  17. Lelièvre N, Beaurepaire P, Mattrand C, Gayton N (2018) AK-MCSi: a Kriging-based method to deal with small failure probabilities and time-consuming models. Struct Saf 73:1–11. https://doi.org/10.1016/j.strusafe.2018.01.002

    Article  Google Scholar 

  18. Yang ZY, Cao ZJ, Feng XB et al (2017) Robustness of subset simulation to functional forms of limit state functions in system reliability analysis: revisiting and improvement. IEEE Trans Reliab 67:66–78

    Article  Google Scholar 

  19. Lee J-O, Yang Y-S, Ruy W-S (2002) A comparative study on reliability-index and target-performance-based probabilistic structural design optimization. Comput Struct 80:257–269. https://doi.org/10.1016/S0045-7949(02)00006-8

    Article  Google Scholar 

  20. Ting Lin P, Chang Gea H, Jaluria Y (2011) A modified reliability index approach for reliability-based design optimization. J Mech Des 133:044501

    Article  Google Scholar 

  21. Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121:557. https://doi.org/10.1115/1.2829499

    Article  Google Scholar 

  22. Youn BD, Choi KK, Du L (2008) Enriched performance measure approach for reliability-based design optimization. AIAA J 43:874–884. https://doi.org/10.2514/1.6648

    Article  Google Scholar 

  23. 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

    Article  MathSciNet  MATH  Google Scholar 

  24. Keshtegar B, Hao P (2018) Enriched self-adjusted performance measure approach for reliability-based design optimization of complex engineering problems. Appl Math Model 57:37–51. https://doi.org/10.1016/j.apm.2017.12.030

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhu S-P, Keshtegar B, Trung N-T et al (2019) Reliability-based structural design optimization: hybridized conjugate mean value approach. Eng Comput. https://doi.org/10.1007/s00366-019-00829-7

    Article  Google Scholar 

  26. Keshtegar B, Meng D, Ben Seghier MEA et al (2020) A hybrid sufficient performance measure approach to improve robustness and efficiency of reliability-based design optimization. Eng Comput. https://doi.org/10.1007/s00366-019-00907-w

    Article  Google Scholar 

  27. Yaseen ZM, Keshtegar B (2019) Limited descent-based mean value method for inverse reliability analysis. Eng Comput 35:1237–1249. https://doi.org/10.1007/s00366-018-0661-z

    Article  Google Scholar 

  28. Youn BD, Choi KK, Du L (2005) Adaptive probability analysis using an enhanced hybrid mean value method. Struct Multidiscip Optim 29:134–148. https://doi.org/10.1007/s00158-004-0452-6

    Article  Google Scholar 

  29. Lee I, Choi KK, Du L, Gorsich D (2008) Dimension reduction method for reliability-based robust design optimization. Comput Struct 86:1550–1562. https://doi.org/10.1016/j.compstruc.2007.05.020

    Article  MATH  Google Scholar 

  30. Liang J, Mourelatos ZP, Nikolaidis E (2007) A single-loop approach for system reliability-based design optimization. J Mech Des 129:1215–1224

    Article  Google Scholar 

  31. Keshtegar B, Hao P (2018) Enhanced single-loop method for efficient reliability-based design optimization with complex constraints. Struct Multidiscip Optim 57:1731–1747

    Article  MathSciNet  Google Scholar 

  32. 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

    Article  MathSciNet  Google Scholar 

  33. Huang H, Zhang X, Liu Y et al (2012) Enhanced sequential optimization and reliability assessment for reliability-based design optimization. J Mech Sci Technol 26:2039–2043. https://doi.org/10.1007/s12206-012-0511-7

    Article  Google Scholar 

  34. Youn BD, Choi KK (2004) An investigation of nonlinearity of reliability-based design optimization approaches. J Mech Des 126:403. https://doi.org/10.1115/1.1701880

    Article  Google Scholar 

  35. Papadrakakis M, Lagaros ND (2002) Reliability-based structural optimization using neural networks and Monte Carlo simulation. Comput Methods Appl Mech Eng 191:3491–3507. https://doi.org/10.1016/S0045-7825(02)00287-6

    Article  MATH  Google Scholar 

  36. Basudhar A, Missoum S (2008) Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Comput Struct 86:1904–1917. https://doi.org/10.1016/j.compstruc.2008.02.008

    Article  Google Scholar 

  37. Lee TH, Jung JJ (2008) A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: constraint boundary sampling. Comput Struct 86:1463–1476. https://doi.org/10.1016/j.compstruc.2007.05.023

    Article  Google Scholar 

  38. Zhuang X, Pan R (2012) A sequential sampling strategy to improve reliability-based design optimization with implicit constraint functions. J Mech Des 134:21002

    Article  Google Scholar 

  39. Zhang Y, Gao L, Xiao M (2020) Maximizing natural frequencies of inhomogeneous cellular structures by Kriging-assisted multiscale topology optimization. Comput Struct 230:106197

    Article  Google Scholar 

  40. Xiao M, Zhang J, Gao L (2020) A system active learning Kriging method for system reliability-based design optimization with a multiple response model. Reliab Eng Syst Saf. https://doi.org/10.1016/j.ress.2020.106935

    Article  Google Scholar 

  41. Zhang Y, Xiao M, Gao L et al (2020) Multiscale topology optimization for minimizing frequency responses of cellular composites with connectable graded microstructures. Mech Syst Signal Process 135:106369. https://doi.org/10.1016/J.YMSSP.2019.106369

    Article  Google Scholar 

  42. Zhang Y, Xiao M, Zhang X, Gao L (2020) Topological design of sandwich structures with graded cellular cores by multiscale optimization. Comput Methods Appl Mech Eng 361:112749. https://doi.org/10.1016/J.CMA.2019.112749

    Article  MathSciNet  MATH  Google Scholar 

  43. Zhang J, Xiao M, Gao L, Chu S (2019) A combined projection-outline-based active learning Kriging and adaptive importance sampling method for hybrid reliability analysis with small failure probabilities. Comput Methods Appl Mech Eng 344:13–33. https://doi.org/10.1016/j.cma.2018.10.003

    Article  MathSciNet  MATH  Google Scholar 

  44. Qian J, Yi J, Cheng Y et al (2019) A sequential constraints updating approach for Kriging surrogate model-assisted engineering optimization design problem. Eng Comput. https://doi.org/10.1007/s00366-019-00745-w

    Article  Google Scholar 

  45. Chen Z, Qiu H, Gao L et al (2014) A local adaptive sampling method for reliability-based design optimization using Kriging model. Struct Multidiscip Optim 49:401–416. https://doi.org/10.1007/s00158-013-0988-4

    Article  MathSciNet  Google Scholar 

  46. Chen Z, Peng S, Li X et al (2015) An important boundary sampling method for reliability-based design optimization using Kriging model. Struct Multidiscip Optim 52:55–70. https://doi.org/10.1007/s00158-014-1173-0

    Article  MathSciNet  Google Scholar 

  47. Li X, Qiu H, Chen Z et al (2016) A local Kriging approximation method using MPP for reliability-based design optimization. Comput Struct 162:102–115. https://doi.org/10.1016/j.compstruc.2015.09.004

    Article  Google Scholar 

  48. Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492. https://doi.org/10.1023/A:1008306431147

    Article  MathSciNet  MATH  Google Scholar 

  49. Rosenblatt M (2007) Remarks on a multivariate transformation. Ann Math Stat 23:470–472. https://doi.org/10.1214/aoms/1177729394

    Article  MathSciNet  MATH  Google Scholar 

  50. Liu PL, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probab Eng Mech 1:105–112. https://doi.org/10.1016/0266-8920(86)90033-0

    Article  Google Scholar 

  51. Zhang D, Han X, Jiang C et al (2017) Time-dependent reliability analysis through response surface method. J Mech Des 139:41404

    Article  Google Scholar 

  52. Chen Z, Qiu H, Gao L et al (2013) An adaptive decoupling approach for reliability-based design optimization. Comput Struct 117:58–66. https://doi.org/10.1016/j.compstruc.2012.12.001

    Article  Google Scholar 

  53. Li W, Peng X, Xiao M et al (2019) Multi-objective design optimization for mini-channel cooling battery thermal management system in an electric vehicle. Int J Energy Res 43:3668–3680

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant Nos. 51675196 and 51721092), the Natural Science Foundation of Hubei Province (Grant No. 2019CFA059), the Program for HUST Academic Frontier Youth Team (Grant No. 2017QYTD04).

Author information

Authors and Affiliations

  1. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jinhao Zhang, Mi Xiao & Liang Gao

Authors
  1. Jinhao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mi Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liang Gao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Xiao, M. & Gao, L. A new local update-based method for reliability-based design optimization. Engineering with Computers 37, 3591–3603 (2021). https://doi.org/10.1007/s00366-020-01019-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-020-01019-6

Keywords

Search

Navigation