A performance measure approach for risk optimization
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In recent years, several approaches have been proposed for solving reliability-based design optimization (RBDO), where the probability of failure is a design constraint. The same cannot be said about risk optimization (RO), where probabilities of failure are part of the objective function. In this work, we propose a performance measure approach (PMA) for RO problems. We first demonstrate that RO problems can be solved as a sequence of RBDO sub-problems. The main idea is to take target reliability indexes (i.e., probabilities of failure) as design variables. This allows the use of existing RBDO algorithms to solve RO problems. The idea also extends the literature concerning RBDO to the context of RO. Here, we solve the resulting RBDO sub-problems using the PMA. Sensitivity expressions required by the proposed approach are also presented. The proposed approach is compared to an algorithm that employs the first-order reliability method (FORM) for evaluation of the probabilities of failure. The numerical examples show that the proposed approach is efficient and more stable than direct employment of FORM. This behavior has also been observed in the context of RBDO, and was the main reason for the development of PMA. Consequently, the proposed approach can be seen as an extension of PMA approaches to RO, which result in more stable optimization algorithms.
KeywordsRisk optimization Reliability-based design optimization Performance measure approach Reliability index Probability of failure
This research was financially supported by CNPq-Brazil.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
Replication of results
The results obtained with the proposed approach are presented in Section 5.
- Chen Z, Qiu H, Gao L, Li P (2013a) An optimal shifting vector approach for efficient probabilistic design. Struct Multidiscip Optim 47:905–920. https://doi.org/10.1007/s00158-012-0873-6
- Chen Z, Qiu H, Gao L, Su L, Li P (2013b) An adaptive decoupling approach for reliability-based design optimization. Compos Struct 117:58–66. https://doi.org/10.1016/j.compstruc.2012.12.001
- Ditlevsen O, Madsen H O (1996) Structural reliability methods. Wiley, ChichesterGoogle Scholar
- Gere J M (2004) Mechanics of materials, 6th edn. Brooks/Cole, BelmontGoogle Scholar
- Haldar A, Mahadevan S (2000) Reliability assessment using stochastic finite element analysis. John Wiley & Sons, New YorkGoogle Scholar
- Jiménez Montoya P, García Meseguer A, Morán Cabré F (2000) Hormignón Armado, 4th edn. Gustavo Gili, BarcelonaGoogle Scholar
- Keshtegar B, Hao P (2018a) 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
- Keshtegar B, Hao P (2018b) 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
- Liu X, Wu Y, Wang B, Yin Q, Zhao J (2018) An efficient RBDO process using adaptive initial point updating method based on sigmoid function. Struct Multidiscip Optim, pp 1–22. https://doi.org/10.1007/s00158-018-2038-8
- Lopez R, Torii A, Miguel L, Cursi JS (2015a) Overcoming the drawbacks of the FORM using a full characterization method. Struct Saf 54:57–63. https://doi.org/10.1016/j.strusafe.2015.02.003
- Lopez RH, Torii AJ, Miguel LFF, de Cursi JES (2015b) An approach for the global reliability based optimization of the size and shape of truss structures. Mec Ind 16(6):603. https://doi.org/10.1051/meca/2015029
- Madsen H O, Krenk S, Lind N C (1986) Methods of structural safety. Prentice Hall, Englewood CliffsGoogle Scholar
- McGuire W, Gallagher R H, Ziemian R D (2000) Matrix structural anlysis, 2nd. Wiley, New YorkGoogle Scholar
- Melchers R E, Beck A T (2018) Structural reliability analysis and prediction, 3rd edn. Wiley, HobokenGoogle Scholar
- Timoshenko S P, Gere J M (1961) Theory of elastic stability, 2nd. McGraw-Hill, New YorkGoogle Scholar
- Torii A J, Lopez R H, Miguel L F F (2017a) A gradient-based polynomial chaos approach for risk and reliability-based design optimization. J Braz Soc Mech Sci Eng 39(7):2905–2915. https://doi.org/10.1007/s40430-017-0815-8
- Torii AJ, Lopez RH, Miguel LFF (2017b) Probability of failure sensitivity analysis using polynomial expansion. Probab Eng Mech 48:76–84. https://doi.org/10.1016/j.probengmech.2017.06.001
- Zhang J, Taflanidis A A (2018) Multi-objective optimization for design under uncertainty problems through surrogate modeling in augmented input space. Struct Multidiscip Optim, pp 1–22Google Scholar