Efficient Calculation of Uncertainty Propagation with an Application in Robust Optimization of Forming Processes

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Abstract

Robust optimization is being used in metal forming processes to select the design which is least sensitive to the presence of uncertainty in the input parameters. In most cases, a mathematical surrogate model is built via input data and resulting output obtained from finite element simulations. The influence of uncertainty in input parameters is then considered using a large number of function evaluations via Monte Carlo analysis with a given probabilistic distribution. Although this method is quite fast and simple, it needs a lot of function evaluations to increase accuracy. This random sampling is neither efficient nor reproducible. A new approach is used to calculate the uncertainty propagation analytically. Compared to conventional Monte Carlo approach this method is accurate, fast, stable, and efficient. In addition, it is possible to employ this method with different types of probability distributions and most commonly-used metamodels. To show the applicability of this method in robust optimization process, a stretch-bending process is investigated with two design and two noise variables. Comparing the results obtained by Monte Carlo and the analytical approach shows that different Monte Carlo runs lead to fluctuations around the exact analytical solution. In addition, the analytical approach reduces the evaluation time of finding the robust optimum to a great extent.
Original languageEnglish
Title of host publicationProceedings of the 20th International ESAFORM Conference on Material Forming
Subtitle of host publicationESAFORM 2017
PublisherAIP Publishing LLC
ISBN (Print)978-0-7354-1580-5
DOIs
Publication statusPublished - 2017
Event20th International ESAFORM Conference on Material Forming - City University Dublin, Dublin, Ireland
Duration: 26 Apr 201728 Apr 2017
Conference number: 20
http://www.esaform2017.com/ehome/index.php?eventid=153382&

Publication series

NameAIP Conference Proceedings
PublisherAIP Publishing
Number1
Volume1896
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference20th International ESAFORM Conference on Material Forming
Abbreviated titleESAFORM 2017
CountryIreland
CityDublin
Period26/04/1728/04/17
Internet address

Fingerprint

Function evaluation
Metal forming
Probability distributions
Mathematical models
Sampling
Uncertainty

Keywords

  • Robust optimization
  • Monte Carlo
  • Analytical uncertainty propagation

Cite this

Nejadseyfi, O., Geijselaers, H. J. M., & van den Boogaard, A. H. (2017). Efficient Calculation of Uncertainty Propagation with an Application in Robust Optimization of Forming Processes. In Proceedings of the 20th International ESAFORM Conference on Material Forming: ESAFORM 2017 [100004] (AIP Conference Proceedings; Vol. 1896, No. 1). AIP Publishing LLC. https://doi.org/10.1063/1.5008122
Nejadseyfi, Omid ; Geijselaers, Hubertus J.M. ; van den Boogaard, Antonius H. / Efficient Calculation of Uncertainty Propagation with an Application in Robust Optimization of Forming Processes. Proceedings of the 20th International ESAFORM Conference on Material Forming: ESAFORM 2017. AIP Publishing LLC, 2017. (AIP Conference Proceedings; 1).
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title = "Efficient Calculation of Uncertainty Propagation with an Application in Robust Optimization of Forming Processes",
abstract = "Robust optimization is being used in metal forming processes to select the design which is least sensitive to the presence of uncertainty in the input parameters. In most cases, a mathematical surrogate model is built via input data and resulting output obtained from finite element simulations. The influence of uncertainty in input parameters is then considered using a large number of function evaluations via Monte Carlo analysis with a given probabilistic distribution. Although this method is quite fast and simple, it needs a lot of function evaluations to increase accuracy. This random sampling is neither efficient nor reproducible. A new approach is used to calculate the uncertainty propagation analytically. Compared to conventional Monte Carlo approach this method is accurate, fast, stable, and efficient. In addition, it is possible to employ this method with different types of probability distributions and most commonly-used metamodels. To show the applicability of this method in robust optimization process, a stretch-bending process is investigated with two design and two noise variables. Comparing the results obtained by Monte Carlo and the analytical approach shows that different Monte Carlo runs lead to fluctuations around the exact analytical solution. In addition, the analytical approach reduces the evaluation time of finding the robust optimum to a great extent.",
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Nejadseyfi, O, Geijselaers, HJM & van den Boogaard, AH 2017, Efficient Calculation of Uncertainty Propagation with an Application in Robust Optimization of Forming Processes. in Proceedings of the 20th International ESAFORM Conference on Material Forming: ESAFORM 2017., 100004, AIP Conference Proceedings, no. 1, vol. 1896, AIP Publishing LLC, 20th International ESAFORM Conference on Material Forming, Dublin, Ireland, 26/04/17. https://doi.org/10.1063/1.5008122

Efficient Calculation of Uncertainty Propagation with an Application in Robust Optimization of Forming Processes. / Nejadseyfi, Omid ; Geijselaers, Hubertus J.M.; van den Boogaard, Antonius H.

Proceedings of the 20th International ESAFORM Conference on Material Forming: ESAFORM 2017. AIP Publishing LLC, 2017. 100004 (AIP Conference Proceedings; Vol. 1896, No. 1).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AB - Robust optimization is being used in metal forming processes to select the design which is least sensitive to the presence of uncertainty in the input parameters. In most cases, a mathematical surrogate model is built via input data and resulting output obtained from finite element simulations. The influence of uncertainty in input parameters is then considered using a large number of function evaluations via Monte Carlo analysis with a given probabilistic distribution. Although this method is quite fast and simple, it needs a lot of function evaluations to increase accuracy. This random sampling is neither efficient nor reproducible. A new approach is used to calculate the uncertainty propagation analytically. Compared to conventional Monte Carlo approach this method is accurate, fast, stable, and efficient. In addition, it is possible to employ this method with different types of probability distributions and most commonly-used metamodels. To show the applicability of this method in robust optimization process, a stretch-bending process is investigated with two design and two noise variables. Comparing the results obtained by Monte Carlo and the analytical approach shows that different Monte Carlo runs lead to fluctuations around the exact analytical solution. In addition, the analytical approach reduces the evaluation time of finding the robust optimum to a great extent.

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Nejadseyfi O, Geijselaers HJM, van den Boogaard AH. Efficient Calculation of Uncertainty Propagation with an Application in Robust Optimization of Forming Processes. In Proceedings of the 20th International ESAFORM Conference on Material Forming: ESAFORM 2017. AIP Publishing LLC. 2017. 100004. (AIP Conference Proceedings; 1). https://doi.org/10.1063/1.5008122