Comparison of two approaches to compute magnetic field in problems with random domains

Int J Numerical Modelling

Beddek

et al. 2013

SUMMARYIn this paper, we analyze the influence of the uncertainties on the behavior constitutive laws of ferromagnetic materials on the behavior of a turboalternator. A simple stochastic model of anhysteretic nonlinear B(H) curve is proposed for the ferromagnetic yokes of the stator and the rotor. The B(H) curve is defined by five random parameters. We quantify the influence of the variability of these five parameters on the flux linkage of one phase of the stator winding depending on the excitation current I. The influence of each parameter is analyzed via the Sobol indices. With this analysis, we can determine the most influential parameters for each state of magnetization (according to the level of I) and investigate where the characterization process of the B(H) curve should focus to improve the accuracy of the computed flux linkage.

Section: Stochastic Magnetostatic Problem With Uncertainties On the Bmentioning

confidence: 99%

Influence of uncertainties on the B(H) curves on the flux linkage of a turboalternator

Mac

Int J Numerical Modelling

Beddek

et al. 2013

“…We have generated two samples of parameter sets of length L equal to 78 and 364 leading to two samples of matrices S To evaluate the quality of the approximation, we have applied the strategy proposed in VII.B by calculating α n DEI (p n ) (see (27)) for each p belonging to P n (see VII.A). We remind that e(p) has been already calculated during the construction of the POD approximation and e r DEI (p) is calculated using the reduced model combining the (D)EI method and the POD method (see (24)) which is very fast. In Fig.8, we give values obtained for 70 snapshots for the four meshes when L=78.…”

Section: Accuracy Of the (D)ei Methodsmentioning

confidence: 99%

“…This technique has been proposed for the stochastic finite element method in [22,23]. Another possibility consists in applying the transformation method proposed in [24,25] which will be used in the following. It can be shown that the parametrization on the geometry can be transferred on a parametrization on the material characteristics [26].…”

Section: A Parametric Finite Element Modelmentioning

confidence: 99%

Error Estimation for Model-Order Reduction of Finite-Element Parametric Problems

Henneron

2016

IEEE Trans. Magn.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. To solve a parametric model in computational electromagnetics, the Finite Element method is often used. To reduce the computational time and the memory requirement, the Finite Element method can be combined with Model Order Reduction Technic like the Proper Orthogonal Decomposition (POD) and the (Discrete) Empirical Interpolation ((D)EI) Methods. These three numerical methods introduce errors of discretisation, reduction and interpolation respectively. The solution of the parametric model will be efficient if the three errors are of the same order and so they need to be evaluated and compared. In this paper, we propose an aposteriori error estimator based on the verification of the constitutive law which estimates the three different errors. An example of application in magnetostatics with 11 parameters is treated where it is shown how the error estimator can be used to control and to improve the accuracy of the solution of the reduced model.

“…The most natural way to account for randomness on the geometry consist in remeshing according to the deformation but the remeshing leads to a discontinuous solution in the space of the input parameters and can create additional numerical noise which can disturb the random solution. Alternatives have been proposed in the literature [5][6][7][8][9] to avoid remeshing. In the following, we will focus mainly on uncertainties on the behaviour laws.…”

Section: Stochastic Problemmentioning

confidence: 99%

Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

Scientific Computing in Electrical Engineering

2016

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. To cite this version :Stephane CLÉNET -Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics -2016Any correspondence concerning this service should be sent to the repository Administrator : archiveouverte@ensam.eu Approximation Methods to solve Stochastic Problems in Computational ElectromagneticsStéphane ClénetAbstract To account for uncertainties on model parameters, the stochastic approach can be used. The model parameters as well as the outputs are then random fields or variables. Several methods are available in the literature to solve stochastic models like sampling methods, perturbation methods or approximation methods. In this paper, we propose an overview on the solution of stochastic problems in computational electromagnetics using approximation methods. Some applications will be presented in order to illustrate the possibilities offered by the approximation methods but also their current limitations due to the curse of dimensionality. Finally, recent numerical techniques proposed in the literature to face the curse of dimensionality are presented for non-intrusive and intrusive approaches.