Karhunen-Loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis.

Authors:
G. Perrin;C. Soize;D. Duhamel;C. Funfschilling
Affiliations:
Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, F-77455 Marne-la-Vallée, France and Université Paris-Est, Modélisation et Simulation Multi-íchell ...;Université Paris-Est, Modélisation et Simulation Multi-íchelle (MSME UMR 8208 CNRS), 5 Bd. Descartes, 77454 Marne-la-Vallée, France;Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, F-77455 Marne-la-Vallée, France;SNCF, Innovation and Research Department, Immeuble Lumière, 40 avenue des Terroirs de France, 75611 Paris, Cedex 12, France
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

Due to scaling effects, when dealing with vector-valued random fields, the classical Karhunen-Loeve expansion, which is optimal with respect to the total mean square error, tends to favorize the components of the random field that have the highest signal energy. When these random fields are to be used in mechanical systems, this phenomenon can introduce undesired biases for the results. This paper presents therefore an adaptation of the Karhunen-Loeve expansion that allows us to control these biases and to minimize them. This original decomposition is first analyzed from a theoretical point of view, and is then illustrated on a numerical example.