Adaptive Method for Non-Intrusive Spectral Projection – Application on a Stochastic Eddy Current NDT Problem

Adaptive Method for Non-Intrusive Spectral Projection – Application on a Stochastic Eddy Current NDT Problem. Beddek, K., Clénet, S., Moreau, O., Costan, V., Le Menach, Y., & Benabou, A. IEEE Transactions on Magnetics, 48(2):759–762, IEEE, February, 2012.
doi abstract bibtex

The Non-Intrusive Spectral Projection (NISP) method is widely used for uncertainty quantification in stochastic models. The determination of the expansion of the solution on the polynomial chaos requires the computation of multidimensional integrals. An automatic adaptive algorithm based on nested sparse grids has been developed to evaluate those integrals. The adapted algorithm takes into account the weight of each random variable with respect to the output of the model. To achieve that it constructs anisotropic sparse grid of the mean, leading to a reduction of the number of numerical simulations. Furthermore, the spectral form of the solution is explicitly identified from the constructed quadrature scheme. Numerical results obtained on an industrial application in NDT demonstrate the efficiency of the proposed method.

@Article{         Beddek_2012aa,
  abstract      = {The Non-Intrusive Spectral Projection (NISP) method is widely used for uncertainty quantification in stochastic models. The determination of the expansion of the solution on the polynomial chaos requires the computation of multidimensional integrals. An automatic adaptive algorithm based on nested sparse grids has been developed to evaluate those integrals. The adapted algorithm takes into account the weight of each random variable with respect to the output of the model. To achieve that it constructs anisotropic sparse grid of the mean, leading to a reduction of the number of numerical simulations. Furthermore, the spectral form of the solution is explicitly identified from the constructed quadrature scheme. Numerical results obtained on an industrial application in NDT demonstrate the efficiency of the proposed method.},
  author        = {Beddek, Karim and Clénet, Stéphane and Moreau, Olivier and Costan, Valentin and Le Menach, Yvonnick and Benabou, Abdelkader},
  doi           = {10.1109/TMAG.2011.2175204},
  file          = {Beddek_2012aa.pdf},
  issn          = {0018-9464},
  journal       = {IEEE Transactions on Magnetics},
  keywords      = {fem,uncertainty,magnetics,polynomial-chaos,field,eddy-currents},
  langid        = {english},
  month         = feb,
  number        = {2},
  pages         = {759--762},
  publisher     = {IEEE},
  title         = {Adaptive Method for Non-Intrusive Spectral Projection -- Application on a Stochastic Eddy Current {NDT} Problem},
  volume        = {48},
  year          = {2012},
  shortjournal  = {IEEE Trans. Magn.}
}

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