Robust formulation for Reliability-based design optimization of structures

RESEARCH PAPER
  • 99 Downloads

Abstract

The reliability-based design optimization (RBDO) has been widely recognized as a powerful optimization tool under probabilistic constraints, through appropriate modeling of uncertainties. However, the drawback of RBDO is that it does not reflect the ability of the structure to comply with large data variations, unforeseen actions or deterioration mechanisms. On the other hand, the robust design optimization (RDO) reduces the variability of the structural performance, in addition to its mean level. However, RDO does not take direct advantage of the interaction between controllable (product design values) and noise variables (environmental random values), and the obtained results do not accurately indicate what parameter has the highest effect on the performance characteristics. The purpose of this paper is to propose a robust formulation for reliability-based design optimization (RRBDO) that combines the advantages of both optimization procedures and overcomes their weaknesses. The optimization model proposed overcomes the limitations of the existing models without compromising the reliability level, by considering a robust convex objective function and a performance variation constraint. The proposed formulation can consider the total cost of structures and can control structural parameter variations. It takes into account uncertainty and variability in the same mathematical formulation. A numerical solution procedure is also developed, for which results are analyzed and compared with RBDO for several examples of concrete and steel structures.

Keywords

Reliability based design Robust design Optimization 

References

  1. Aoues Y, Chateauneuf A (2008) Reliability-based optimization of structural systems by adaptive target safety–Application to RC frames. Struct Saf 30(2):144–161CrossRefGoogle Scholar
  2. Aoues Y, Chateauneuf A (2010) Benchmark study of numerical methods for reliability-based design optimization. Struct Multidiscip Optim 41(2):277–294MathSciNetCrossRefMATHGoogle Scholar
  3. Arora JS (1989) Introduction to Optimum Design. McGraw-Hill, Inc., New YorkGoogle Scholar
  4. Bastidas-Arteaga E, Bressolette P, Chateauneuf A, Sánchez-Silva M (2009) Probabilistic lifetime assessment of RC structures under coupled corrosion–fatigue deterioration processes. Struct Saf 31(1):84–96CrossRefGoogle Scholar
  5. Beck AT, de Santana Gomes WJ (2012) A comparison of deterministic, reliability-based and risk-based structural optimization under uncertainty. Prob Eng Mech 28:18–29CrossRefGoogle Scholar
  6. Beck AT, Gomes WJS, Lopez RH, Miguel LF (2015) A comparison between robust and risk-based optimization under uncertainty. Struct Multidiscip Optim 52:479MathSciNetCrossRefGoogle Scholar
  7. Casas JR (2014) Robustness and life-cycle analysis (LCA) of structures and infrastructures. Proceedings of the 46th ESReDA seminar, Torino, May 29–30Google Scholar
  8. De R S, Karamchandani A, Cornell C A (1989) Study of redundancy in near-ideal parallel structural systems. Structural safety and reliability, ASCE, 975–982Google Scholar
  9. Doltsinis I, Kang Z, Cheng G (2005) Robust design of non-linear structures using optimization methods. Comput Methods Appl Mech Eng 194(12):1779–1795CrossRefMATHGoogle Scholar
  10. El Hassan J, Bressolette P, Chateauneuf A, El Tawil K (2010) Reliability-based assessment of the effect of climatic conditions on the corrosion of RC structures subject to chloride ingress. Eng Struct 32(10):3279–3287CrossRefGoogle Scholar
  11. Frangopol DM, Curley JP (1987) Effects of damage and redundancy on structural reliability. J Struct Eng 113(7):1533–1549CrossRefGoogle Scholar
  12. Guedri M, Cogan S, Bouhaddi N (2012) Robustness of structural reliability analyses to epistemic uncertainties. Mech Syst Signal Process 28:458–469CrossRefGoogle Scholar
  13. Kagho-Gouadjio N, Orcesi A, Cremona C, Marcotte C (2015) Quantification of structural robustness: application to the study of a prestressed concrete beam. Mech Ind 16(1):104CrossRefGoogle Scholar
  14. Kang Z (2005) Robust design optimization of structures under uncertainties. PhD.-Institute of Statics and Dynamics of Aerospace Structures, StuttgartGoogle Scholar
  15. Lee K, Park G (2001) Robust optimization considering tolerances of design variables. Comput Struct 79(1):77–86CrossRefGoogle Scholar
  16. Lee I, Choi K, Du L, Gorsich D (2008) Dimension reduction method for reliability-based robust design optimization. Comput Struct 86(13):1550–1562CrossRefMATHGoogle Scholar
  17. Madsen H, Krenk L S (1986) Methods of structural safety. Englewood Cliff, Dover publications, United StatesGoogle Scholar
  18. Parks J (2001) On stochastic optimization: Taguchi Methods™ demystified; its limitations and fallacy clarified. Prob Eng Mech 16(1):87–101MathSciNetCrossRefGoogle Scholar
  19. Pendola M, Mohamed A, Lemaire M, Hornet P (2000) Combination of finite element and reliability methods in nonlinear fracture mechanics. Reliab Eng Syst Saf 70(1):15–27CrossRefGoogle Scholar
  20. Rathod V, Yadav OP, Rathore A, Jain R (2013) Optimizing reliability-based robust design model using multi-objective genetic algorithm. Comput Ind Eng 66(2):301–310CrossRefGoogle Scholar
  21. Rizzuti S, De Napoli L, Giampà F, Lofranco F (2009) Axiomatic design as a means to find contradiction in an integrated approach for product design. Fifth International Conference on Axiomatic Design, ICAD, 25–27Google Scholar
  22. Saad L, Aissani A, Chateauneuf A, Raphael W (2016) Reliability-based optimization of direct and indirect LCC of RC bridge elements under coupled fatigue-corrosion deterioration processes. Eng Fail Anal 58:570–587CrossRefGoogle Scholar
  23. Sandgren E, Cameron T (2002) Robust design optimization of structures through consideration of variation. Comput Struct 80(20):1605–1613CrossRefGoogle Scholar
  24. Saydam D, Frangopol DM (2011) Time-dependent performance indicators of damaged bridge superstructures. Eng Struct 33(9):2458–2471CrossRefGoogle Scholar
  25. Shahraki AF, Noorossana R (2014) Reliability-based robust design optimization: A general methodology using genetic algorithm. Comput Ind Eng 74:199–207CrossRefGoogle Scholar
  26. Spence S M, Gioffrè M, Kareem A (2015) An efficient framework for the reliability-based design optimization of large-scale uncertain and stochastic linear systems. Prob Eng MechGoogle Scholar
  27. Stewart MG (2004) Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure. Struct Saf 26(4):453–470CrossRefGoogle Scholar
  28. Sundaresan S, Ishii K, Houser DR (1995) A robust optimization procedure with variations on design variables and constraints. Eng Opt A35 24(2):101–117CrossRefGoogle Scholar
  29. Taguchi G, Rafanelli A J (1994) Taguchi on robust technology development: bringing quality engineering upstreamGoogle Scholar
  30. Thoft-Christensen P (1998) Assessment of the reliability profiles for concrete bridges. Eng Struct 20(11):1004–1009CrossRefGoogle Scholar
  31. Tovo R (2001) On the fatigue reliability evaluation of structural components under service loading. Int J Fatigue 23(7):587–598CrossRefGoogle Scholar
  32. Tsompanakis Y, Lagaros N D, Papadrakakis M (2008) Structural Design Optimization Considering Uncertainties: Structures & Infrastructures Book, Vol. 1, Series, Series Editor: Dan M. Frangopol. CRC PressGoogle Scholar
  33. Val DV, Melchers RE (1997) Reliability of deteriorating RC slab bridges. J Struct Eng 123(12):1638–1644CrossRefGoogle Scholar
  34. Val DV, Stewart MG (2003) Life-cycle cost analysis of reinforced concrete structures in marine environments. Struct Saf 25(4):343–362CrossRefGoogle Scholar
  35. Val DV, Stewart MG, Melchers RE (1998) Effect of reinforcement corrosion on reliability of highway bridges. Eng Struct 20(11):1010–1019CrossRefGoogle Scholar
  36. Van Belle G (2011) Statistical rules of thumb. WileyGoogle Scholar
  37. Youn BD, Choi KK, Yi K (2005) Performance moment integration (PMI) method for quality assessment in reliability-based robust design optimization. Mech Based Des Struct Mach 33(2):185–213CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Université Blaise Pascal, Institut PascalUniversité Clermont AuvergneClermont-FerrandFrance
  2. 2.Ecole Supérieure d’Ingénieurs de Beyrouth (ESIB)Saint-Joseph University, CST Mkalles Mar RoukosBeirutLebanon
  3. 3.CNRS, UMR 6602Institut PascalAubièreFrance

Personalised recommendations