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Reliability-Based Robust Optimization Applied to Engineering System Design

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Computational Intelligence, Optimization and Inverse Problems with Applications in Engineering

Abstract

Traditionally, concerning the engineering system design, the vector of design variables is considered as being formed by deterministic quantities (free of errors, i.e., without the influence of uncertainties). However, small variations in these quantities can affect the considered objective functions and, consequently, the resulting design of the system. Probabilistic methods have been proposed to deal with this kind of problem. These methodologies can be classified according to two main categories: robust design (RD) and reliability-based design (RBO). In this contribution, reliability and robustness are used simultaneously in engineering system design. The proposed approach is based on the Differential Evolution (DE) algorithm in association with the following strategies: (1) Mean Effective Concept (MEC) (robustness); and (2) Inverse Reliability Analysis (IRA) (reliability-based design). Mathematical and engineering test cases are studied to evaluate the proposed methodology. The obtained results demonstrate that the proposed technique represents an interesting alternative to reliability-based robust design of engineering systems.

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References

  1. Agarwal, H.: Reliability based design optimization: formulations and methodologies. PhD. thesis, University of Notre Dame (2004)

    Google Scholar 

  2. Aoues, Y., Chateauneuf, A.: Benchmark study of numerical methods for reliability-based design. Struct. Multidiscip. Optim. 41, 277–294 (2009)

    Article  MathSciNet  Google Scholar 

  3. Carter, A.D.S.: Mechanical Reliability and Design. Wiley, New York (1997)

    Book  Google Scholar 

  4. Castro, R.E.: Optimization of structures with multi-objective through genetic algorithms. D.Sc. thesis (in Portuguese), COPPE/UFRJ, Rio de Janeiro (2001)

    Google Scholar 

  5. Deb, K., Gupta, H.: Introducing robustness in multiobjective optimization. Evol. Comput. 14(4), 463–494 (2006)

    Article  Google Scholar 

  6. Deb, K., Padmanabhan, D., Gupta, S., Mall, A.K.: Handling uncertainties through reliability-based optimization using evolutionary algorithms. IEEE Trans. Evol. Comput. 13(5), 1054–1074 (2009)

    Article  Google Scholar 

  7. Der-Kiureghian, A., De Stefano, M.: Efficient algorithm for second-order reliability analysis. J. Mech. Eng. ASCE1 17(12), 2904–2923 (1991)

    Article  Google Scholar 

  8. Du, X.: Probabilistic engineering design – first order and second reliability methods. University of Missouri, Rolla (2005)

    Google Scholar 

  9. Du, X., Chen, W.: Sequential optimization and reliability assessment method for efficient probabilistic design. J. Mech. Des. 126, 225–233 (2004)

    Article  Google Scholar 

  10. Fiessler, B., Neumann, H.-J., Rackwitz, R.: Quadratic limit states in structural reliability. J. Mech. Eng. ASCE 105(4), 661–676 (1979)

    Google Scholar 

  11. Gholaminezhad, I., Jamali, A., Assimi, H.: Multi-objective reliability-based robust design optimization of robot gripper mechanism with probabilistically uncertain parameters. Neural Comput. Appl. 1, 1–12 (2016)

    Google Scholar 

  12. Jeong, S.B., Park, G.J.: Reliability-based robust design optimization using the probabilistic robustness index and the enhanced single loop single vector approach. In: 10th World Congress on Structural and Multidisciplinary Optimization, Orlando (2013)

    Google Scholar 

  13. Keshtegar, B., Chakraborty, S.: An efficient-robust structural reliability method by adaptive finite-step length based on Armijo line search. Reliab. Eng. Syst. Saf. 172, 195–206 (2018)

    Article  Google Scholar 

  14. Lagaros, N.D., Plevris, V., Papadrakakis, M.: Reliability based robust design optimization of steel structures. Int. J. Simul. Multidiscip. Des. Optim. 1, 19–29 (2007)

    Article  Google Scholar 

  15. Lee, M.C.W., Mikulik, Z., Kelly, D.W., Thomson, R.S., Degenhardt, R.: Robust design – a concept for imperfection insensitive composite structures. Compos. Struct. 92(6), 1469–1477 (2010)

    Article  Google Scholar 

  16. Leidemer, M.N.: Proposal of evolutionary robust optimization methodology using the unscented transform applicable to circuits for RF circuits/microwave. MSc. Thesis (in Portuguese), University of Brasilia, Brasilia (2009)

    Google Scholar 

  17. Liao, K.W., Ha, C.: Application of reliability-based optimization to earth-moving machine: hydraulic cylinder components design process. Struct. Multidiscip. Optim. 36(5), 523–536 (2008)

    Article  Google Scholar 

  18. Liao, K.W., Ivan, G.: A single loop reliability-based design optimization using EPM and MPP-based PSO. Lat. Am. J. Solids Struct. 11, 826–847 (2014)

    Article  Google Scholar 

  19. Melchers, R.E.: Structural Reliability Analysis and Prediction. Wiley, Chichester (1999)

    Google Scholar 

  20. Moreira, F.R., Lobato, F.S., Cavalini, A.A. Jr., Steffen, V. Jr.: Robust multi-objective optimization applied to engineering systems design. Lat. Am. J. Solids Struct. 13, 1802–1822 (2016)

    Article  Google Scholar 

  21. Paenk, I., Branke, J., Jin, Y.: Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation. IEEE Trans. Evol. Comput. 10, 405–420 (2006)

    Article  Google Scholar 

  22. Phadke, M.S.: Quality Engineering Using Robust Design. Prentice Hall, Englewood Cliffs (1989)

    Google Scholar 

  23. Qu, X., Haftka, R.T.: Reliability-based design optimization using probabilistic sufficiency factor. Struct. Multidiscip. Optim. 27(5), 314–325 (2004)

    Article  Google Scholar 

  24. Ramu, P., Qu, X., Youn, B.D., Haftka, R.T., Choi, K.K.: Safety factor and inverse reliability measures. In: Proceeding of 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs (2004)

    Google Scholar 

  25. Ravichandran, G.: Integrated reliable and robust design. Missouri University of Science and Technology (2011)

    Google Scholar 

  26. Ritto, T.G., Sampaio, R., Cataldo, E.: Timoshenko beam with uncertainty on the boundary conditions. J. Braz. Soc. Mech. Sci. Eng. 30(4), 295–303 (2008)

    Article  Google Scholar 

  27. Rosenblatt, M.: Remarks on a multivariate transformation. Ann. Math. Stat. 23, 470–472 (1952)

    Article  MathSciNet  Google Scholar 

  28. Sampaio, R., Soize, C.: On measures of nonlinearity effects for uncertain dynamical systems application to a Vibro-impact system. J. Sound Vib. 303, 659–674 (2007)

    Article  Google Scholar 

  29. Shahraki, A.F., Noorossana, R.: A combined algorithm for solving reliability-based robust design optimization problems. J. Math. Comput. Sci. 7, 54–62 (2013)

    Article  Google Scholar 

  30. Soize, C.: A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics. J. Sound Vib. 288(3), 623–652 (2005)

    Article  MathSciNet  Google Scholar 

  31. Souza, D.L., Lobato, F.S., Gedraite, R.: Robust multiobjective optimization applied to optimal control problems using differential evolution. Chem. Eng. Technol. 1, 1–8 (2015)

    Google Scholar 

  32. Storn, R., Price, K.: Differential evolution – a simple and efficient adaptive scheme for global optimization over continuous spaces. Int. Comput. Sci. Inst. 12, 1–16 (1995)

    Google Scholar 

  33. Taguchi, G.: Taguchi on Robust Technology Development – Bringing Quality Engineering Upstream. ASME Press, New York (1993)

    Book  Google Scholar 

  34. Thanedar, P.B., Kodiyalam, S.: Structural optimization using probabilistic constraints. Struct. Multidiscip. Optim. 4, 236–240 (1992)

    Article  Google Scholar 

  35. Tichy, M.: First-order third-moment reliability method. Struct. Saf. 16(2), 189–200 (1994)

    Article  Google Scholar 

  36. Wang, S., Li, Q., Savage, G.J.: Reliability-based robust design optimization of structures considering uncertainty in design variables. Math. Probl. Eng. 2015, 1–8 (2015)

    MathSciNet  MATH  Google Scholar 

  37. Wang, Y., Tuo, Y., Yang, S.X., Biglarbegian, M., Fu, M.: Reliability-based robust dynamic positioning for a turret-moored floating production storage and offloading vessel with unknown time-varying disturbances and input saturation (2018). https://doi.org/10.1016/j.isatra.2017.12.023

    Article  Google Scholar 

  38. Wu, Y.T., Shin, Y., Sues, R., Cesare, M.: Safety-factor based approach for probability-based design optimization. In: Proceedings of the 42rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2001)

    Google Scholar 

  39. Zhao, Y.G., Ono, T.: A general procedure for first/second-order reliability method (FORM/SORM). Struct. Saf. 21(1), 95–112 (1999)

    Article  Google Scholar 

  40. Zhao, Y.G., Ono, T.: New approximations for SORM: part 2. J. Mech. Eng. ASCE1 25(1), 86–93 (1999)

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the Brazilian research agencies CNPq, FAPEMIG (APQ-02284-15), and CAPES for the financial support of this research work through the National Institute of Science and Technology on Smart Structures in Engineering (INCT-EIE).

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Authors and Affiliations

  1. NUCOP-Laboratory of Modeling, Simulation, Control and Optimization, School of Chemical Engineering, Federal University of Uberlândia, Uberlândia, MG, Brazil

    Fran Sérgio Lobato

  2. LMEst-Structural Mechanics Laboratory, School of Mechanical Engineering, Federal University of Uberlândia, Uberlândia, MG, Brazil

    Márcio Aurelio da Silva, Aldemir Aparecido Cavalini Jr. & Valder Steffen Jr.

Authors
  1. Fran Sérgio Lobato
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  2. Márcio Aurelio da Silva
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  3. Aldemir Aparecido Cavalini Jr.
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  4. Valder Steffen Jr.
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Corresponding author

Correspondence to Fran Sérgio Lobato .

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Editors and Affiliations

  1. Universidade Federal do Rio Grande, Santo Antônio da Patrulha, Rio Grande do Sul, Brazil

    Gustavo Mendes Platt

  2. School of Science and Technology, Middlesex University, London, UK

    Xin-She Yang

  3. Polytechnic Institute, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Rio de Janeiro, Brazil

    Antônio José Silva Neto

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Lobato, F.S., Silva, M.A.d., Cavalini, A.A., Steffen, V. (2019). Reliability-Based Robust Optimization Applied to Engineering System Design. In: Platt, G., Yang, XS., Silva Neto, A. (eds) Computational Intelligence, Optimization and Inverse Problems with Applications in Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-96433-1_2

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