Commun. Comput. Phys., 13 (2013), pp. 1173-1188.


An Efficient Sampling Method for Regression-Based Polynomial Chaos Expansion

Samih Zein 1*, Benoit Colson 1, Francois Glineur 2

1 Samtech H.Q., LMS International, 8 rue des chasseurs ardennais Angleur, Belgium.
2 Center for Operations Research and Econometrics & Information and Communication Technologies, Electronics and Applied Mathematics Institute, Universite catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium.

Received 2 September 2011; Accepted (in revised version) 20 April 2012
Available online 21 September 2012
doi:10.4208/cicp.020911.200412a

Abstract

The polynomial chaos expansion (PCE) is an efficient numerical method for performing a reliability analysis. It relates the output of a nonlinear system with the uncertainty in its input parameters using a multidimensional polynomial approximation (the so-called PCE). Numerically, such an approximation can be obtained by using a regression method with a suitable design of experiments. The cost of this approximation depends on the size of the design of experiments. If the design of experiments is large and the system is modeled with a computationally expensive FEA (Finite Element Analysis) model, the PCE approximation becomes unfeasible. The aim of this work is to propose an algorithm that generates efficiently a design of experiments of a size defined by the user, in order to make the PCE approximation computationally feasible. It is an optimization algorithm that seeks to find the best design of experiments in the D-optimal sense for the PCE. This algorithm is a coupling between genetic algorithms and the Fedorov exchange algorithm. The efficiency of our approach in terms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.

AMS subject classifications: 60H15, 62K20, 62K05

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Key words: Polynomial chaos expansion, regression, D-optimal design, Fedorov Algorithm, genetic algorithms.

*Corresponding author.
Email: samih.zein@lmsintl.com (S. Zein), benoit.colson@lmsintl.com (B. Colson), Francois.Glineur@uclouvain.be (F. Glineur)
 

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