Hierarchical Metamodeling: Cross Validation and Predictive Uncertainty

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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 ananti-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 atime 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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Periodical:

Key Engineering Materials (Volumes 611-612)

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1519-1527

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May 2014

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[1] L.W. Friedman and I. Pressman. The Metamodel in Simulation Analysis: Can It Be Trusted ?, In: The Journal of the Operational Research Society 39(10) (1988), pp.939-948.

DOI: 10.1057/jors.1988.160

Google Scholar

[2] B. Yu and K. Popplewell. Metamodels in manufacturing: a review,. In: International Journal of Production Research 32(4) (1994), pp.787-796.

DOI: 10.1080/00207549408956970

Google Scholar

[3] L. Baghdasaryan et al. Model Validation Via Uncertainty Propagation Using Response Surface Models,. In: Detc2002/dac-34140. 2002, pp.1-12.

Google Scholar

[4] T.T. Do, L. Fourment, and M. Laroussi. Sensitivity Analysis and Optimization Al- gorithms for 3D Forging Process Design,. In: AIP Conference Proceedings 712. 2004, p.2026-(2031).

Google Scholar

[5] H. Wiebenga, A.H. Boogaard, and G. Klaseboer. Sequential robust optimization of a V bending process using numerical simulations,. In: Structural and Multidisciplinary Opti- mization 46 (2012), pp.137-156.

DOI: 10.1007/s00158-012-0761-0

Google Scholar

[6] R. Hino, F. Yoshida, and V.V. Toropov. Optimum blank design for sheet metal forming based on the interaction of high- and low-fidelity FE models,. In: Archive of Applied Mechanics 75 (2006), pp.679-691.

DOI: 10.1007/s00419-006-0047-3

Google Scholar

[7] D. Huang et al. Sequential kriging optimization using multiple-fidelity evaluations,. In: Structural and Multidisciplinary Optimization 32(5) (2006), pp.369-382.

DOI: 10.1007/s00158-005-0587-0

Google Scholar

[8] G. Sun et al. Multi-fidelity optimization for sheet metal forming process,. In: Structural and Multidisciplinary Optimization 44(1) (2010), pp.111-124.

DOI: 10.1007/s00158-010-0596-5

Google Scholar

[9] Z. Qian et al. Building Surrogate Models Based on Detailed and Approximate Simula- tions,. In: ASME Journal of Mechanical Design 128 (2006), pp.668-677.

Google Scholar

[10] E. Roux and P.O. Bouchard. Kriging metamodel global optimization of clinching joining processes accounting for ductile damage,. In: Journal of Materials Processing Technology 213 (2013), pp.10387-1047.

DOI: 10.1016/j.jmatprotec.2013.01.018

Google Scholar

[11] B.M. Colosimo, L. Pagani, and M. Strano. Metamodeling Based on the Fusion of FEM Simulations Results and Experimental Data,. In: Key Engineering Materials. Vol. 554 - 557. 2013, pp.2487-2498.

DOI: 10.4028/www.scientific.net/kem.554-557.2487

Google Scholar

[12] M. Strano, V. Mussi, and M. Monno. Non-conventional technologies for the manufac- turing of anti-intrusion bars,. In: International Journal of Material Forming 3 (2010), pp.1111-1114.

DOI: 10.1007/s12289-010-0966-y

Google Scholar

[13] S.C.K. Yuen and G.N. Nurick. The Energy-Absorbing Characteristics of Tubular Struc- tures With Geometric and Material Modifications: An Overview,. In: Transactions of the ASME: Applied Mechanics Reviews 61 (2008), pp.1-15.

DOI: 10.1115/1.2885138

Google Scholar

[14] T.J. Santner, B.J. Williams, and W.I. Notz. The Design and Analysis of Computer Ex- periments. Springer Verlag, (2003).

Google Scholar

[15] M. L. Stein. Interpolation of Spatial Data: Some Theory for Kriging. Springer Series in Statistics, (1999).

Google Scholar

[16] D.A. Harville. Maximum likelihood approaches to variance component estimation and to related problems,. In: Journal of the American Statistical Association 72 (1977), pp.320-338.

DOI: 10.1080/01621459.1977.10480998

Google Scholar

[17] O. Shabenberger and C.A. Gotway. Statistical Methods for Spatial Data Analysis. Chap- man and Hall/CRC, (2005).

Google Scholar

[18] M.C. Kennedy and A. O'Hagan. Predicting the Output from a Complex Computer Code When Fast Apporximations Are Available,. In: Biometrika 87 (2000), pp.1-13.

DOI: 10.1093/biomet/87.1.1

Google Scholar

[19] L. Pagani. Multisensor Data Fusion for Quality Inspection of Free-Form Surfaces,. MA thesis. Politecnico di Milano, (2011).

Google Scholar