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

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

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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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    author = "Omid Nejadseyfi and Geijselaers, {Hubertus J.M.} and {van den Boogaard}, {Antonius H.}",
    year = "2017",
    doi = "10.1063/1.5008122",
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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