Hierarchical metamodeling: Cross validation and predictive uncertainty

Bianca M. Colosimo, Luca Pagani, Matteo Strano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

At Esaform 2013 a hierarchical metamodeling approach had been presented, able to combine the results of numerical simulations and physical experiments into a unique response surface, which is a "fusion'' of both data sets. The method had been presented with respect to the structural optimization of a steel tube, filled with an aluminium foam, intended as an anti-intrusion bar. The prediction yielded by a conventional way of metamodeling the results of FEM simulations can be considered trustworthy only if the accuracy of numerical models have been thoroughly tested and the simulation parameters have been sufficiently calibrated. On the contrary, the main advantage of a hierarchical metamodel is to yield a reliable prediction of a response variable to be optimized, even in the presence of non-completely calibrated or accurate FEM models. In order to demonstrate these statements, in this paper the authors wish to compare the prediction ability of a "fusion'' metamodel based on under-calibrated simulations, with a conventional approach based on calibrated FEM results. Both metamodels will be cross validated with a "leave-one- out'' technique, i.e. by excluding one experimental observation at a time and assessing the predictive ability of the model. Furthermore, the paper will demonstrate how the hierarchical metamodel is able to provide not only an average estimated value for each excluded experimental observation, but also an estimation of uncertainty of the prediction of the average value.

LanguageEnglish
Title of host publicationMaterial Forming ESAFORM 2014
PublisherTrans Tech Publications Ltd
Pages1519-1527
Number of pages9
Volume611-612
ISBN (Print)9783038351061
DOIs
Publication statusPublished - 2014
Externally publishedYes
Event17th Conference of the European Scientific Association on Material Forming - Dipoli Congress Centre, Espoo, Finland
Duration: 7 May 20149 May 2014
Conference number: 17
https://www.vtt.fi/sites/esaform/en/17th-esaform-conference-7-9-may-2014 (Link to Conference Details )

Publication series

NameKey Engineering Materials
Volume611-612
ISSN (Print)1013-9826

Conference

Conference17th Conference of the European Scientific Association on Material Forming
Abbreviated titleESAFORM 2014
CountryFinland
CityEspoo
Period7/05/149/05/14
Internet address

Fingerprint

Finite element method
Fusion reactions
Structural optimization
Steel
Aluminum
Foams
Numerical models
Uncertainty
Computer simulation
Experiments

Cite this

Colosimo, B. M., Pagani, L., & Strano, M. (2014). Hierarchical metamodeling: Cross validation and predictive uncertainty. In Material Forming ESAFORM 2014 (Vol. 611-612, pp. 1519-1527). (Key Engineering Materials; Vol. 611-612). Trans Tech Publications Ltd. https://doi.org/10.4028/www.scientific.net/KEM.611-612.1519
Colosimo, Bianca M. ; Pagani, Luca ; Strano, Matteo. / Hierarchical metamodeling : Cross validation and predictive uncertainty. Material Forming ESAFORM 2014. Vol. 611-612 Trans Tech Publications Ltd, 2014. pp. 1519-1527 (Key Engineering Materials).
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Colosimo, BM, Pagani, L & Strano, M 2014, Hierarchical metamodeling: Cross validation and predictive uncertainty. in Material Forming ESAFORM 2014. vol. 611-612, Key Engineering Materials, vol. 611-612, Trans Tech Publications Ltd, pp. 1519-1527, 17th Conference of the European Scientific Association on Material Forming, Espoo, Finland, 7/05/14. https://doi.org/10.4028/www.scientific.net/KEM.611-612.1519

Hierarchical metamodeling : Cross validation and predictive uncertainty. / Colosimo, Bianca M.; Pagani, Luca; Strano, Matteo.

Material Forming ESAFORM 2014. Vol. 611-612 Trans Tech Publications Ltd, 2014. p. 1519-1527 (Key Engineering Materials; Vol. 611-612).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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T1 - Hierarchical metamodeling

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AU - Colosimo, Bianca M.

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AU - Strano, Matteo

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PY - 2014

Y1 - 2014

N2 - At Esaform 2013 a hierarchical metamodeling approach had been presented, able to combine the results of numerical simulations and physical experiments into a unique response surface, which is a "fusion'' of both data sets. The method had been presented with respect to the structural optimization of a steel tube, filled with an aluminium foam, intended as an anti-intrusion bar. The prediction yielded by a conventional way of metamodeling the results of FEM simulations can be considered trustworthy only if the accuracy of numerical models have been thoroughly tested and the simulation parameters have been sufficiently calibrated. On the contrary, the main advantage of a hierarchical metamodel is to yield a reliable prediction of a response variable to be optimized, even in the presence of non-completely calibrated or accurate FEM models. In order to demonstrate these statements, in this paper the authors wish to compare the prediction ability of a "fusion'' metamodel based on under-calibrated simulations, with a conventional approach based on calibrated FEM results. Both metamodels will be cross validated with a "leave-one- out'' technique, i.e. by excluding one experimental observation at a time and assessing the predictive ability of the model. Furthermore, the paper will demonstrate how the hierarchical metamodel is able to provide not only an average estimated value for each excluded experimental observation, but also an estimation of uncertainty of the prediction of the average value.

AB - At Esaform 2013 a hierarchical metamodeling approach had been presented, able to combine the results of numerical simulations and physical experiments into a unique response surface, which is a "fusion'' of both data sets. The method had been presented with respect to the structural optimization of a steel tube, filled with an aluminium foam, intended as an anti-intrusion bar. The prediction yielded by a conventional way of metamodeling the results of FEM simulations can be considered trustworthy only if the accuracy of numerical models have been thoroughly tested and the simulation parameters have been sufficiently calibrated. On the contrary, the main advantage of a hierarchical metamodel is to yield a reliable prediction of a response variable to be optimized, even in the presence of non-completely calibrated or accurate FEM models. In order to demonstrate these statements, in this paper the authors wish to compare the prediction ability of a "fusion'' metamodel based on under-calibrated simulations, with a conventional approach based on calibrated FEM results. Both metamodels will be cross validated with a "leave-one- out'' technique, i.e. by excluding one experimental observation at a time and assessing the predictive ability of the model. Furthermore, the paper will demonstrate how the hierarchical metamodel is able to provide not only an average estimated value for each excluded experimental observation, but also an estimation of uncertainty of the prediction of the average value.

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M3 - Conference contribution

SN - 9783038351061

VL - 611-612

T3 - Key Engineering Materials

SP - 1519

EP - 1527

BT - Material Forming ESAFORM 2014

PB - Trans Tech Publications Ltd

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Colosimo BM, Pagani L, Strano M. Hierarchical metamodeling: Cross validation and predictive uncertainty. In Material Forming ESAFORM 2014. Vol. 611-612. Trans Tech Publications Ltd. 2014. p. 1519-1527. (Key Engineering Materials). https://doi.org/10.4028/www.scientific.net/KEM.611-612.1519