On the Choice of Basis in Proper Orthogonal Decomposition-Based Surrogate Models

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    Abstract

    To reduce scrap in metal forming processes, one should aim for robustness by means of optimization, control or a combination of both. Due to the high computational costs, a Finite Element (FE) model of a metal forming process cannot be used in optimization routines or control algorithms directly. Alternatively, a surrogate model of the process response to certain variables
    can be created that enables efficient control or optimization algorithms. When the process response is more than a scalar function only, reduction methods such as Proper Orthogonal Decomposition (POD) can be applied to obtain a surrogate model. In this work, the results of a set of FE analyses are decomposed using a single and separated snapshot matrices using different preprocessing methods. Additionally, a new method for projecting in different parts of the snapshot matrix is proposed. The bases obtained using different preprocessing methods are compared. Thereafter, the surrogate models of the process are built by interpolating the amplitudes obtained in different bases. The accuracy of all surrogate models is assessed by comparing the reduced results with the
    results from the FE analyses.
    Original languageEnglish
    Title of host publicationProceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019
    EditorsLander Galdos, Pedro Arrazola, Eneko Saenz de Argandona, Nagore Otegi, Joseba Mendiguren, Aitor Madariaga, Mikel Saez de Buruaga
    PublisherAIP
    Number of pages6
    ISBN (Electronic)978-0-7354-1847-9
    DOIs
    Publication statusPublished - 2 Jul 2019
    Event22nd International Conference on Material Forming 2019 - Votoria-Gasteiz, Spain
    Duration: 8 May 201910 May 2019
    Conference number: 22
    https://esaform2019.mondragon.edu/en/home

    Publication series

    NameAIP Conference Proceedings
    Number010001
    Volume2113

    Conference

    Conference22nd International Conference on Material Forming 2019
    Abbreviated titleESAFORM 2019
    CountrySpain
    CityVotoria-Gasteiz
    Period8/05/1910/05/19
    Internet address

    Fingerprint

    Decomposition
    Metal forming
    Costs

    Keywords

    • Proper orthogonal decomposition
    • snapshot preprocessing
    • Kriging
    • Surrogate model
    • Surrogate Modeling
    • proper orthogonal decomposition (POD)

    Cite this

    de Gooijer, B. M., Hazrati Marangalou, J., Geijselaers, B., & van den Boogaard, A. H. (2019). On the Choice of Basis in Proper Orthogonal Decomposition-Based Surrogate Models. In L. Galdos, P. Arrazola, E. Saenz de Argandona, N. Otegi, J. Mendiguren, A. Madariaga, & M. Saez de Buruaga (Eds.), Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019 (AIP Conference Proceedings; Vol. 2113, No. 010001). AIP. https://doi.org/10.1063/1.5112635
    de Gooijer, Boukje Marije ; Hazrati Marangalou, Javad ; Geijselaers, Bert ; van den Boogaard, Antonius H. / On the Choice of Basis in Proper Orthogonal Decomposition-Based Surrogate Models. Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019. editor / Lander Galdos ; Pedro Arrazola ; Eneko Saenz de Argandona ; Nagore Otegi ; Joseba Mendiguren ; Aitor Madariaga ; Mikel Saez de Buruaga. AIP, 2019. (AIP Conference Proceedings; 010001).
    @inproceedings{5ff1700dda464b63ba38f3bd8d36f4d6,
    title = "On the Choice of Basis in Proper Orthogonal Decomposition-Based Surrogate Models",
    abstract = "To reduce scrap in metal forming processes, one should aim for robustness by means of optimization, control or a combination of both. Due to the high computational costs, a Finite Element (FE) model of a metal forming process cannot be used in optimization routines or control algorithms directly. Alternatively, a surrogate model of the process response to certain variablescan be created that enables efficient control or optimization algorithms. When the process response is more than a scalar function only, reduction methods such as Proper Orthogonal Decomposition (POD) can be applied to obtain a surrogate model. In this work, the results of a set of FE analyses are decomposed using a single and separated snapshot matrices using different preprocessing methods. Additionally, a new method for projecting in different parts of the snapshot matrix is proposed. The bases obtained using different preprocessing methods are compared. Thereafter, the surrogate models of the process are built by interpolating the amplitudes obtained in different bases. The accuracy of all surrogate models is assessed by comparing the reduced results with theresults from the FE analyses.",
    keywords = "Proper orthogonal decomposition, snapshot preprocessing, Kriging, Surrogate model, Surrogate Modeling, proper orthogonal decomposition (POD)",
    author = "{de Gooijer}, {Boukje Marije} and {Hazrati Marangalou}, Javad and Bert Geijselaers and {van den Boogaard}, {Antonius H.}",
    year = "2019",
    month = "7",
    day = "2",
    doi = "10.1063/1.5112635",
    language = "English",
    series = "AIP Conference Proceedings",
    publisher = "AIP",
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    editor = "Lander Galdos and Pedro Arrazola and {Saenz de Argandona}, Eneko and Nagore Otegi and Joseba Mendiguren and Aitor Madariaga and {Saez de Buruaga}, Mikel",
    booktitle = "Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019",

    }

    de Gooijer, BM, Hazrati Marangalou, J, Geijselaers, B & van den Boogaard, AH 2019, On the Choice of Basis in Proper Orthogonal Decomposition-Based Surrogate Models. in L Galdos, P Arrazola, E Saenz de Argandona, N Otegi, J Mendiguren, A Madariaga & M Saez de Buruaga (eds), Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019. AIP Conference Proceedings, no. 010001, vol. 2113, AIP, 22nd International Conference on Material Forming 2019, Votoria-Gasteiz, Spain, 8/05/19. https://doi.org/10.1063/1.5112635

    On the Choice of Basis in Proper Orthogonal Decomposition-Based Surrogate Models. / de Gooijer, Boukje Marije; Hazrati Marangalou, Javad ; Geijselaers, Bert; van den Boogaard, Antonius H.

    Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019. ed. / Lander Galdos; Pedro Arrazola; Eneko Saenz de Argandona; Nagore Otegi; Joseba Mendiguren; Aitor Madariaga; Mikel Saez de Buruaga. AIP, 2019. (AIP Conference Proceedings; Vol. 2113, No. 010001).

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

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    AU - de Gooijer, Boukje Marije

    AU - Hazrati Marangalou, Javad

    AU - Geijselaers, Bert

    AU - van den Boogaard, Antonius H.

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    N2 - To reduce scrap in metal forming processes, one should aim for robustness by means of optimization, control or a combination of both. Due to the high computational costs, a Finite Element (FE) model of a metal forming process cannot be used in optimization routines or control algorithms directly. Alternatively, a surrogate model of the process response to certain variablescan be created that enables efficient control or optimization algorithms. When the process response is more than a scalar function only, reduction methods such as Proper Orthogonal Decomposition (POD) can be applied to obtain a surrogate model. In this work, the results of a set of FE analyses are decomposed using a single and separated snapshot matrices using different preprocessing methods. Additionally, a new method for projecting in different parts of the snapshot matrix is proposed. The bases obtained using different preprocessing methods are compared. Thereafter, the surrogate models of the process are built by interpolating the amplitudes obtained in different bases. The accuracy of all surrogate models is assessed by comparing the reduced results with theresults from the FE analyses.

    AB - To reduce scrap in metal forming processes, one should aim for robustness by means of optimization, control or a combination of both. Due to the high computational costs, a Finite Element (FE) model of a metal forming process cannot be used in optimization routines or control algorithms directly. Alternatively, a surrogate model of the process response to certain variablescan be created that enables efficient control or optimization algorithms. When the process response is more than a scalar function only, reduction methods such as Proper Orthogonal Decomposition (POD) can be applied to obtain a surrogate model. In this work, the results of a set of FE analyses are decomposed using a single and separated snapshot matrices using different preprocessing methods. Additionally, a new method for projecting in different parts of the snapshot matrix is proposed. The bases obtained using different preprocessing methods are compared. Thereafter, the surrogate models of the process are built by interpolating the amplitudes obtained in different bases. The accuracy of all surrogate models is assessed by comparing the reduced results with theresults from the FE analyses.

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    KW - snapshot preprocessing

    KW - Kriging

    KW - Surrogate model

    KW - Surrogate Modeling

    KW - proper orthogonal decomposition (POD)

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    T3 - AIP Conference Proceedings

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    A2 - Arrazola, Pedro

    A2 - Saenz de Argandona, Eneko

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    A2 - Mendiguren, Joseba

    A2 - Madariaga, Aitor

    A2 - Saez de Buruaga, Mikel

    PB - AIP

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    de Gooijer BM, Hazrati Marangalou J, Geijselaers B, van den Boogaard AH. On the Choice of Basis in Proper Orthogonal Decomposition-Based Surrogate Models. In Galdos L, Arrazola P, Saenz de Argandona E, Otegi N, Mendiguren J, Madariaga A, Saez de Buruaga M, editors, Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019. AIP. 2019. (AIP Conference Proceedings; 010001). https://doi.org/10.1063/1.5112635