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

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

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",
number = "010001",
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

TY - GEN

T1 - On the Choice of Basis in Proper Orthogonal Decomposition-Based Surrogate Models

AU - de Gooijer, Boukje Marije

AU - Hazrati Marangalou, Javad

AU - Geijselaers, Bert

AU - van den Boogaard, Antonius H.

PY - 2019/7/2

Y1 - 2019/7/2

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.

KW - Proper orthogonal decomposition

KW - snapshot preprocessing

KW - Kriging

KW - Surrogate model

KW - Surrogate Modeling

KW - proper orthogonal decomposition (POD)

U2 - 10.1063/1.5112635

DO - 10.1063/1.5112635

M3 - Conference contribution

T3 - AIP Conference Proceedings

BT - Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019

A2 - Galdos, Lander

A2 - Arrazola, Pedro

A2 - Saenz de Argandona, Eneko

A2 - Otegi, Nagore

A2 - Mendiguren, Joseba

A2 - Madariaga, Aitor

A2 - Saez de Buruaga, Mikel

PB - AIP

ER -

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