Hierarchical metamodeling: Cross validation and predictive uncertainty

Bianca M. Colosimo, Luca Pagani, Matteo Strano

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


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.

Original languageEnglish
Title of host publicationMaterial Forming ESAFORM 2014
PublisherTrans Tech Publications Ltd
Number of pages9
ISBN (Print)9783038351061
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
ISSN (Print)1013-9826


Conference17th Conference of the European Scientific Association on Material Forming
Abbreviated titleESAFORM 2014
Internet address


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