Abstract
Reliability-based methods have been established to take into account, in a rigorous manner, the uncertainties involved in analysis of engineering systems. The failure probability and reliability index are used to quantify risks and therefore evaluate the consequences of failure. First/second-order reliability method (FORM/SORM) is considered to be one of the most reliable computational methods to deal with reliability in engineering systems. Basically, the idea is to overcome the computational difficulties in determination of the reliability index and approximating the constraints. In this contribution, a new methodology to deal with uncertainties in engineering systems is proposed. This approach, called Second-Order Inverse Reliability Analysis (SOIRA), consists in the use of first and second order derivatives to find the solution associated with the highest probability value (inverse reliability analysis). In order to evaluate the proposed methodology, three reliability approaches (FORM, SORM and IRA - Inverse Reliability Analysis) are applied in two test cases: (i) W16X31 steel beam problem and (ii) beam problem. The obtained results demonstrated that the proposed strategy represents an interesting alternative to reliability design of engineering systems.
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References
Breitung, K.: Asymptotic approximations for multinormal integrals. J. Eng. Mech. 110(3), 357–366 (1984). https://doi.org/10.1061/(ASCE)0733-9399(1984)110:3(357)
Du, X.: Probabilistic Engineering Design, 1st edn. University of Missouri, Rolla (2005)
Fletcher, R.: Practical Methods of Optimization, 2nd edn. Wiley-Interscience, New York (1987)
Hjerager, P.: Methods for structural reliability computations. In: Casciati, F., Roberts, J.B. (eds.) Reliability Problems: General Principles and Applications in Mechanics of Solids and Structures, CISM International Centre for Mechanical Sciences, vol. 317, 1 edn., pp. 89–135. Springer, Wien (1991). Chapter 3
Huang, C., El Hami, A., Radi, B.: Overview of structural reliability analysis methods—Part I: local reliability methods. Uncertainties Reliab. Multiphys. Syst. 1 (2017). https://doi.org/10.21494/ISTE.OP.2017.0115
Huang, C., El Hami, A., Radi, B.: Overview of structural reliability analysis methods—Part II: sampling methods. Uncertainties Reliab. Multiphys. Syst. 1 (2017). https://doi.org/10.21494/ISTE.OP.2017.0116
Huang, C., El Hami, A., Radi, B.: Overview of structural reliability analysis methods—Part III: global reliability methods. Uncertainties Reliab. Multiphys. Syst. 1 (2017). https://doi.org/10.21494/ISTE.OP.2017.0117
Keshtegar, B., Baharom, S., El-Shafie, A.: Self-adaptive conjugate method for a robust and efficient performance measure approach for reliability-based design optimization. Eng. Comput. 34(1), 187–202 (2018). https://doi.org/10.1007/s00366-017-0529-7
Kiureghian, A.D., Lin, H., Hwang, S.: Second-order reliability approximations. J. Eng. Mech. 113(8), 1208–1225 (1987). https://doi.org/10.1061/(ASCE)0733-9399(1987)113:8(1208)
Lobato, F.S., Gonçalves, M.S., Jahn, B., Cavalini, A.A., Steffen, V.: Reliability-based optimization using differential evolution and inverse reliability analysis for engineering system design. J. Optim. Theor. Appl. 174(3), 894–926 (2017). https://doi.org/10.1007/s10957-017-1063-x
Ritto, T.G., Sampaio, R., Cataldo, E.: Timoshenko beam with uncertainty on the boundary conditions. J. Braz. Soc. Mech. Sci. Eng. 30, 295–303 (2008). https://doi.org/10.1590/S1678-58782008000400005
Rosenblatt, M.: Remarks on a multivariate transformation. Ann. Math. Statist. 23(3), 470–472 (1952). https://doi.org/10.1214/aoms/1177729394
Sohouli, A., Yildiz, M., Suleman, A.: Efficient strategies for reliability-based design optimization of variable stiffness composite structures. Struct. Multidiscip. Optim. 57(2), 689–704 (2018). https://doi.org/10.1007/s00158-017-1771-8
Sundararajan, C.R.: Probabilistic Structural Mechanics Handbook: Theory and Industrial Applications, 1st edn. Springer, Boston (1995)
Tichý, M.: First-order third-moment reliability method. Struct. Saf. 16(3), 189–200 (1994). https://doi.org/10.1016/0167-4730(94)00021-H
van Eekelen, A.J.: Review and Selection of Methods for Structural Reliability Analysis. Aerospace Structures and Computational Mechanic, 1st edn. Delft University Press, Delft (1997)
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Libotte, G.B., Neto, F.D.M., Lobato, F.S., Platt, G.M. (2019). Second-Order Inverse Reliability Analysis: A New Methodology to the Treatment of Reliability in Engineering System. In: Rodrigues, H., et al. EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization. EngOpt 2018. Springer, Cham. https://doi.org/10.1007/978-3-319-97773-7_74
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