[Krigeage et amélioration attendue à visée industrielle - Prédiction de nouvelles géométrie de système de ventilation améliorant le rendement]
Cette étude résulte d’une collaboration avec Valeo, partenaire industriel. Dans l’industrie automobile, les besoins du marché évoluent très rapidement dans un contexte où la concurrence est forte et tout particulièrement concernant les systèmes de ventilation qui jouent un rôle clef dans le système de refroidissement du moteur. Les ingénieurs doivent dans ce contexte proposer des géométries de pales “optimales” dans des délais très courts. Malheureusement, les codes numériques sont coûteux à évaluer et des méthodes d’approximations et des techniques d’optimisation spécifiques doivent être developpées. Nous proposons de combiner l’interpolation par krigeage et l’algorithme d’optimisation d’amélioration attendue pour déterminer des géométries de pales ayant de bonnes performances en termes de rendement. Une telle application industrielle basée sur le krigeage et l’amélioration attendue semble inédite et fournit d’excellents résultats.
This study has been done in cooperation with the automotive supplier Valeo. In automotive industry, client needs evolve quickly in a competitiveness context, particularly, regarding the fan involved in the engine cooling module. The practitioners are asked to propose “optimal” new fans in short times. Unfortunately, each evaluation of the underlying computer code may be expensive whence the need of approximated models and specific, parsimonious, and efficient global optimization strategies. In this paper, we propose to use the Kriging interpolation combined with the expected improvement algorithm to provide new fan designs with high performances in terms of efficiency. As far as we know, such a use of Kriging interpolation together with the expected improvement methodology is unique in an industrial context and provide really promising results.
Keywords: Kriging, expected improvement, optimization
Mot clés : Krigeage, amélioration attendue, optimisation
@article{JSFS_2021__162_1_22_0,
author = {Lagnoux, Agn\`es and Nguyen, Thi Mong Ngoc and Demory, Bruno and Henner, Manuel},
title = {Kriging and expected improvement combined to an industrial context - {Prediction} of new geometries increasing the efficiency of fans},
journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
pages = {22--45},
publisher = {Soci\'et\'e fran\c{c}aise de statistique},
volume = {162},
number = {1},
year = {2021},
mrnumber = {4286848},
zbl = {07371756},
language = {en},
url = {http://archive.numdam.org/item/JSFS_2021__162_1_22_0/}
}
TY - JOUR AU - Lagnoux, Agnès AU - Nguyen, Thi Mong Ngoc AU - Demory, Bruno AU - Henner, Manuel TI - Kriging and expected improvement combined to an industrial context - Prediction of new geometries increasing the efficiency of fans JO - Journal de la société française de statistique PY - 2021 SP - 22 EP - 45 VL - 162 IS - 1 PB - Société française de statistique UR - http://archive.numdam.org/item/JSFS_2021__162_1_22_0/ LA - en ID - JSFS_2021__162_1_22_0 ER -
%0 Journal Article %A Lagnoux, Agnès %A Nguyen, Thi Mong Ngoc %A Demory, Bruno %A Henner, Manuel %T Kriging and expected improvement combined to an industrial context - Prediction of new geometries increasing the efficiency of fans %J Journal de la société française de statistique %D 2021 %P 22-45 %V 162 %N 1 %I Société française de statistique %U http://archive.numdam.org/item/JSFS_2021__162_1_22_0/ %G en %F JSFS_2021__162_1_22_0
Lagnoux, Agnès; Nguyen, Thi Mong Ngoc; Demory, Bruno; Henner, Manuel. Kriging and expected improvement combined to an industrial context - Prediction of new geometries increasing the efficiency of fans. Journal de la société française de statistique, Tome 162 (2021) no. 1, pp. 22-45. http://archive.numdam.org/item/JSFS_2021__162_1_22_0/
[1] Finite-time Analysis of the Multiarmed Bandit Problem, Machine Learning, Volume 47 (2002) no. 2, pp. 235-256 | DOI | Zbl
[2] Estimation et interpolation spatiale: méthodes déterministes et méthodes géostatistiques, Hermès, 2000
[3] Three-dimensional neurointerpolation of annual mean precipitation and temperature surfaces for China, Geographical Analysis, Volume 34 (2002) no. 2, pp. 93-111 | DOI
[4] Cross validation and maximum likelihood estimations of hyper-parameters of Gaussian processes with model misspecification, Comput. Statist. Data Anal., Volume 66 (2013), pp. 55-69 | DOI | MR | Zbl
[5] Le krigeage: revue de la théorie et application à l’interpolation spatiale de données de précipitations (2005)
[6] A supermartingale approach to Gaussian process based sequential design of experiments (2018) (working paper or preprint) | HAL | MR
[7] Fast Computation of the Multi-Points Expected Improvement with Applications in Batch Selection, Learning and Intelligent Optimization (Nicosia, Giuseppe; Pardalos, Panos, eds.), Springer Berlin Heidelberg, Berlin, Heidelberg (2013), pp. 59-69 | DOI
[8] Statistics for spatial data, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, Inc., New York, 1993, xxii+900 pages (Revised reprint of the 1991 edition, A Wiley-Interscience Publication) | DOI | MR
[9] Practical methods of optimization, Wiley-Interscience publication, Wiley, 1987 no. vol. 1 https://books.google.fr/books?id=3EzvAAAAMAAJ
[10] A knowledge-gradient policy for sequential information collection, SIAM J. Control Optim., Volume 47 (2008) no. 5, pp. 2410-2439 | DOI | MR | Zbl
[11] Robust design and parametric performance study of an automotive fan blade by coupling multi-objective genetic optimization and flow parameterization, Proc. of the International Congress on Fluid Dynamics Applications in Ground Transportation, Lyon, France (2005)
[12] Bayesian spatial prediction, Environmental and Ecological Statistics, Volume 6 (1999) no. 2, pp. 147-171 | DOI
[13] A Multi-points Criterion for Deterministic Parallel Global Optimization based on Gaussian Processes (2008) ( Technical report ) | HAL
[14] Sequential kriging optimization using multiple-fidelity evaluations, Structural and Multidisciplinary Optimization, Volume 32 (2006) no. 5, pp. 369-382 | DOI
[15] An efficient algorithm for constructing optimal design of computer experiments, J. Statist. Plann. Inference, Volume 134 (2005) no. 1, pp. 268-287 | DOI | MR | Zbl
[16] A taxonomy of global optimization methods based on response surfaces, Journal of global optimization, Volume 21 (2001) no. 4, pp. 345-383 | DOI | MR | Zbl
[17] Efficient Global Optimization of Expensive Black-Box Functions, Journal of Global Optimization, Volume 13 (1998) no. 4, pp. 455-492 | DOI | MR | Zbl
[18] A statistical approach to some basic mine valuation problems on the Witwatersrand, Journal of the Chemical, Metallurgical and Mining Society of South Africa, Volume 52 (1951), pp. 119-139
[19] Geometric Parametric Study of a Fan Blade Cascade Using the New Parametric Flow Solver Turb’Opty, ASME 2004 Heat Transfer/Fluids Engineering Summer Conference, American Society of Mechanical Engineers Digital Collection (2004), pp. 1293-1298 | DOI
[20] Traité de géostatistique appliquée, Tome I, Editions Technip, Paris, 14, Mémoires du Bureau de Recherches Géologiques et Minières, 1962
[21] Principles of geostatistics, Economic Geology, Volume 58 (1963), pp. 1246-1266 | DOI
[22] On bayesian methods for seeking the extremum, Optimization Techniques IFIP Technical Conference Novosibirsk, July 1–7, 1974 (Marchuk, G. I., ed.), Springer Berlin Heidelberg, Berlin, Heidelberg (1975), pp. 400-404 | DOI
[23] ORTHOGONAL ARRAYS FOR COMPUTER EXPERIMENTS, INTEGRATION AND VISUALIZATION, Statistica Sinica, Volume 2 (1992) no. 2, pp. 439-452 http://www.jstor.org/stable/24304869 | MR | Zbl
[24] Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction, Stat. Comput., Volume 25 (2015) no. 6, pp. 1265-1280 | DOI | MR | Zbl
[25] DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization, Journal of Statistical Software, Articles, Volume 51 (2012) no. 1, pp. 1-55 https://www.jstatsoft.org/v051/i01 | DOI
[26] Mathematical statistics and data analysis, Cengage Learning, 2006
[27] Spatial statistics, John Wiley & Sons, Inc., New York, 1981, x+252 pages (Wiley Series in Probability and Mathematical Statistics) | DOI | MR
[28] Gaussian Processes for Machine Learning, The MIT Press, Cambridge, 2006 | MR
[29] Computer experiments and global optimization (1997) | MR
[30] The correlated knowledge gradient for simulation optimization of continuous parameters using Gaussian process regression, SIAM J. Optim., Volume 21 (2011) no. 3, pp. 996-1026 | DOI | MR | Zbl
[31] Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting, IEEE Transactions on Information Theory, Volume 58 (2012) no. 5, pp. 3250-3265 | DOI | MR | Zbl
[32] Exploration of metamodeling sampling criteria for constrained global optimization, Engineering optimization, Volume 34 (2002) no. 3, pp. 263-278 | DOI
[33] Interpolation of Spatial Data: Some Theory for Kriging, Springer, New York, 1999 | DOI | MR
[34] The design and analysis of computer experiments, 1, Springer, 2003 | DOI | MR
[35] Convergence properties of the expected improvement algorithm with fixed mean and covariance functions, J. Statist. Plann. Inference, Volume 140 (2010) no. 11, pp. 3088-3095 | DOI | MR | Zbl
