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

Boukje Marije de Gooijer; Javad  Hazrati Marangalou; Bert Geijselaers; Antonius H. van den Boogaard

doi:10.1063/1.5112635

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

Boukje Marije de Gooijer, Javad Hazrati Marangalou, Bert Geijselaers, Antonius H. van den Boogaard

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

2 Citations (Scopus)

10 Downloads (Pure)

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 language	English
Title of host publication	Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019
Editors	Pedro Arrazola, Eneko Saenz de Argandona, Nagore Otegi, Joseba Mendiguren, Mikel Saez de Buruaga, Aitor Madariaga, Lander Galdos
Publisher	American Institute of Physics
Number of pages	6
ISBN (Electronic)	978-0-7354-1847-9
DOIs	https://doi.org/10.1063/1.5112635
Publication status	Published - 2 Jul 2019
Event	22nd International Conference on Material Forming 2019 - Votoria-Gasteiz, Spain Duration: 8 May 2019 → 10 May 2019 Conference number: 22 https://esaform2019.mondragon.edu/en/home

Publication series

Name	AIP Conference Proceedings
Number	010001
Volume	2113

Conference

Conference	22nd International Conference on Material Forming 2019
Abbreviated title	ESAFORM 2019
Country/Territory	Spain
City	Votoria-Gasteiz
Period	8/05/19 → 10/05/19
Internet address	https://esaform2019.mondragon.edu/en/home

Keywords

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

Access to Document

10.1063/1.5112635

On the choice of basis in POD-based surrogate models
de Gooijer, B. M. (Speaker)
8 May 2019
Activity: Talk or presentation › Oral presentation

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 P. Arrazola, E. Saenz de Argandona, N. Otegi, J. Mendiguren, M. Saez de Buruaga, A. Madariaga, & L. Galdos (Eds.), Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019 Article 100002 (AIP Conference Proceedings; Vol. 2113, No. 010001). American Institute of Physics. https://doi.org/10.1063/1.5112635

de Gooijer, Boukje Marije ; Hazrati Marangalou, Javad ; Geijselaers, Bert et al. / 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 / Pedro Arrazola ; Eneko Saenz de Argandona ; Nagore Otegi ; Joseba Mendiguren ; Mikel Saez de Buruaga ; Aitor Madariaga ; Lander Galdos. American Institute of Physics, 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.}",

note = "Funding Information: This research project is part of the {\textquoteleft}Region of Smart Factories{\textquoteright} project and is partially funded by the {\textquoteleft}Samenwerk-ingsverband Noord-Nederland (SNN){\textquoteright}, Ruimtelijk Economisch Programma{\textquoteright}. Publisher Copyright: {\textcopyright} 2019 Author(s).; 22nd International Conference on Material Forming 2019, ESAFORM 2019 ; Conference date: 08-05-2019 Through 10-05-2019",

year = "2019",

month = jul,

day = "2",

doi = "10.1063/1.5112635",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

number = "010001",

editor = "Pedro Arrazola and {Saenz de Argandona}, Eneko and Nagore Otegi and Joseba Mendiguren and {Saez de Buruaga}, Mikel and Aitor Madariaga and Lander Galdos",

booktitle = "Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019",

address = "United States",

url = "https://esaform2019.mondragon.edu/en/home",

}

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 P Arrazola, E Saenz de Argandona, N Otegi, J Mendiguren, M Saez de Buruaga, A Madariaga & L Galdos (eds), Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019., 100002, AIP Conference Proceedings, no. 010001, vol. 2113, American Institute of Physics, 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 et al.
Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019. ed. / Pedro Arrazola; Eneko Saenz de Argandona; Nagore Otegi; Joseba Mendiguren; Mikel Saez de Buruaga; Aitor Madariaga; Lander Galdos. American Institute of Physics, 2019. 100002 (AIP Conference Proceedings; Vol. 2113, No. 010001).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-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.

N1 - Conference code: 22

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 - Arrazola, Pedro

A2 - Saenz de Argandona, Eneko

A2 - Otegi, Nagore

A2 - Mendiguren, Joseba

A2 - Saez de Buruaga, Mikel

A2 - Madariaga, Aitor

A2 - Galdos, Lander

PB - American Institute of Physics

T2 - 22nd International Conference on Material Forming 2019

Y2 - 8 May 2019 through 10 May 2019

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 Arrazola P, Saenz de Argandona E, Otegi N, Mendiguren J, Saez de Buruaga M, Madariaga A, Galdos L, editors, Proceedings of the 22nd International ESAFORM Conference on Material Forming: ESAFORM 2019. American Institute of Physics. 2019. 100002. (AIP Conference Proceedings; 010001). doi: 10.1063/1.5112635

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

Abstract

Publication series

Conference

Keywords

Access to Document

Fingerprint

Activities

On the choice of basis in POD-based surrogate models

Cite this