Top

Published in:

2021 | OriginalPaper | Chapter

Stochastic Gradient Descent for Risk Optimization

Authors : André Gustavo Carlon, André Jacomel Torii, Rafael Holdorf Lopez, José Eduardo Souza de Cursi

Published in: Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper presents an approach for the use of stochastic gradient descent methods for the solution of risk optimization problems. The first challenge is to avoid the high-cost evaluation of the failure probability and its gradient at each iteration of the optimization process. We propose here that it is accomplished by employing a stochastic gradient descent algorithm for the minimization of the Chernoff bound of the limit state function associated with the probabilistic constraint. The employed stochastic gradient descent algorithm, the Adam algorithm, is a robust method used in machine learning training. A numerical example is presented to illustrate the advantages and potential drawbacks of the proposed approach.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Robust Design of Stochastic Dynamic Systems Based on Fatigue Damage

next chapter Time-Variant Reliability-Based Optimization with Double-Loop Kriging Surrogates

Lopez, R.H., Beck, A.T.: RBDO methods based on form: a review. J. Braz. Soc. Mech. Sci. Eng. 34(4), 506–514 (2012). https://doi.org/10.1590/S1678-58782012000400012CrossRef

Beck, A.T., Gomes, W.J.: A comparison of deterministic, reliability-based and risk-based structural optimization under uncertainty. Probab. Eng. Mech. 28, 18–29 (2012)CrossRef

Gomes, W.J.S., Beck, A.T.: Global structural optimization considering expected consequences of failure and using ann surrogates. Comput. Struct. 126, 56–68 (2013). https://doi.org/10.1016/j.compstruc.2012.10.013CrossRef

Beck, A.T., Gomes, W.J.S., Lopez, R.H., Miguel, L.F.F.: A comparison between robust and risk-based optimization under uncertainty. Struct. Multidisc. Optim. 52(3), 479–492 (2015). https://doi.org/10.1007/s00158-015-1253-9MathSciNetCrossRef

Gomes, W.J.S., Beck, A.T.: The design space root finding method for efficient risk optimization by simulation. Probab. Eng. Mech. 44, 99–110 (2016). https://doi.org/10.1016/j.probengmech.2015.09.019CrossRef

Torii, A., Lopez, R., Miguel, L.: A gradient-based polynomial chaos approach for risk and reliability-based design optimization. J. Braz. Soc. Mech. Sci. Eng. 39(7), 2905–2915 (2017)CrossRef

Torii, A.J., Lopez, R.H., Beck, A.T., Miguel, L.F.F.: A performance measure approach for risk optimization. Struct. Multidisc. Optim. 60(3), 927–947 (2019)MathSciNetCrossRef

Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 22, 400–407 (1951)MathSciNetCrossRef

Carlon, A.G., Dia, B.M., Espath, L.F., Lopez, R.H., Tempone, R.: Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization. arXiv preprint arXiv:1807.00653

10.

Carlon, A.G., Lopez, R.H., da Espath Rosa, L.F., Miguel, L.F.F., Beck, A.T.: A stochastic gradient approach for the reliability maximization of passively controlled structures. Eng. Struct. 186, 1–12 (2019)CrossRef

11.

Kingma, D.P., Ba, J., Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980

12.

Melchers, R.E., Beck, A.T.: Structural Reliability Analysis and Prediction. Wiley, Hoboken (2018)

13.

Lehman, E., Leighton, T., Meyer, A.R.: Mathematics for computer science, Technical report, 2006. Lecture notes (2010)

14.

Gere, J.M.: Mechanics of Materials, 6th edn. Cengage Learning, Boston (2004)

15.

Timoshenko, S.P., Gere, J.M.: Theory of Elastic Stability, Courier Corporation. Dover Publication, New York (2009)

Title: Stochastic Gradient Descent for Risk Optimization
Authors: André Gustavo Carlon
André Jacomel Torii
Rafael Holdorf Lopez
José Eduardo Souza de Cursi
Publisher: Springer International Publishing
Book: Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling
Print ISBN: 978-3-030-53668-8

Electronic ISBN: 978-3-030-53669-5

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-53669-5_31