Volume 13, Issue 4
An Efficient Sampling Method for Regression-based Polynomial Chaos Expansion

Samih Zein, Benoît Colson & François Glineur

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

Published online: 2013-08

Preview Full PDF 129 666
Export citation
  • 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 approximationcanbe 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 exchangealgorithm. The efficiency of our approachinterms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.


  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

  • BibTex
  • RIS
  • TXT
@Article{CiCP-13-1173, author = {Samih Zein, Benoît Colson and François Glineur}, title = {An Efficient Sampling Method for Regression-based Polynomial Chaos Expansion}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {4}, pages = {1173--1188}, 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 approximationcanbe 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 exchangealgorithm. The efficiency of our approachinterms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.020911.200412a}, url = {http://global-sci.org/intro/article_detail/cicp/7269.html} }
TY - JOUR T1 - An Efficient Sampling Method for Regression-based Polynomial Chaos Expansion AU - Samih Zein, Benoît Colson & François Glineur JO - Communications in Computational Physics VL - 4 SP - 1173 EP - 1188 PY - 2013 DA - 2013/08 SN - 13 DO - http://dor.org/10.4208/cicp.020911.200412a UR - https://global-sci.org/intro/cicp/7269.html KW - AB -

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 approximationcanbe 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 exchangealgorithm. The efficiency of our approachinterms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.


Samih Zein, Benoît Colson & François Glineur. (1970). An Efficient Sampling Method for Regression-based Polynomial Chaos Expansion. Communications in Computational Physics. 13 (4). 1173-1188. doi:10.4208/cicp.020911.200412a
Copy to clipboard
The citation has been copied to your clipboard