Surrogate models for optimization in high dimension using a mixed Kriging/PLS method

M. Bouhlel (1) , N. Bartoli (1) , J. Morlier (2) , A. Otsmane (3)

1 ONERA - The French Aerospace Lab [Toulouse]
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace
3 SNECMA [Paris]

Kriging is a popular metamodel used to replace a computationally expensive simulation model. However, with the development of modern scientific codes in the field of engineering, the number of variables increases in order to capture the physical behaviour and it is well known that Kriging performances are degraded in this condition. In order to overcome this problem, several methods for reducing the dimension are available, particularly the Partial Least Squares method (PLS) [2]. PLS creates new variables (latent variables or principal components) by modelling the relationship between input and output variables while maintaining most of information in the input variables. In this work, a new method is developed by combining Kriging and PLS. This method consists in using information from the PLS in order to build an efficient Kriging metamodel adapted to high dimension. Numerical experiments on both academic and industrial test cases show the efficiency of such method in terms of accuracy and CPU time up to dimension 60.

Keywords: KRIGING; PLS; DESIGN OF EXPERIMENT

Domains: Mathematics [math]; Statistics [math.ST]; Statistics [stat]; Statistics Theory [stat.TH]

M. Bouhlel, N. Bartoli, J. Morlier, A. Otsmane. Surrogate models for optimization in high dimension using a mixed Kriging/PLS method. 8th international Conference on Partial Least Squares and Related Methods (PLS2014), May 2014, PARIS, France. ⟨hal-01071553⟩