From solutions of finite element (FE) simulations depending on parameters, a surrogate model of the FE solution can be built based on the proper orthogonal decomposition (POD) combined with the ...radial basis functions (RBFs) interpolation. Then, a fast approximation of an FE solution can be computed for any parameter set. In order to optimize the number of FE solutions required for the construction of the surrogate model and to control the error between the FE and surrogate models, a hierarchical multilevel approach based on an iterative algorithm is investigated. In this article, a hierarchical multilevel (H-POD-RBF) approach is developed for a nonlinear magnetostatic problem. In terms of application, a 3-D three-phase inductance is considered. The results obtained from the surrogate model are compared with those given from the FE model for a current or voltage supply.
In order to reduce the computational time induced by solving a finite element (FE) model for a magnetostatic problem with varying geometric parameters, a parametric geometric metamodel is defined ...using the proper generalized decomposition (PGD) approach. The mesh deformation associated with the geometric variation is implemented using the radial basis functions (RBFs) interpolation method. The proposed approach is applied to a variable inductance and then to a permanent magnet synchronous machine (PMSM). The results show that the PGD metamodel can accurately approximate the FE solution for the case of parametric geometric problems.
The proper orthogonal decomposition (POD) approach is applied to a linear finite element (FE) model of a squirrel cage induction machine. In order to obtain a reduced model valid on the whole ...operating range, snapshots are extracted from the simulation of typical tests, such as at the locked rotor and the synchronous speed. Then, the reduced model of the induction machine is used to simulate different operating points with variable rotation speed, and the results are compared to the full FE model to show the effectiveness of the proposed approach.
In an industrial context of electrical device design or expertise, it is common for engineers to use models based on the finite element (FE) method. In the case of nonlinear magneto-quasistatic ...problems, it can lead to prohibitive computational times. Then, model order reduction (MOR) approaches based on the proper orthogonal decomposition (POD) combined with a hyper-reduction (HR) method can be employed to reduce the computational time but often leads to numerical instabilities. In this article, we aim to compare two HR methods that were developed to improve the stability of the nonlinear reduced model: the Gaussian Newton augmented tensors (GNAT) method and the energy-conserving mesh sampling and weighting (ECSW) method. The reduced models are evaluated in terms of accuracy on global and local quantities of interest and in terms of speedup, with application to a squirrel cage induction machine. Improvement of the ECSW method has been proposed such that it appears that this method is more competitive than the GNAT method and enables to obtain very good results both in terms of accuracy and time computation, which was reduced by a factor of 40 compared to the FE model.
The proper orthogonal decomposition (POD) is an interesting approach to compress into a reduced basis numerous solutions obtained from a parametrized finite-element (FE) model. In order to obtain a ...fast approximation of an FE solution, the POD can be combined with an interpolation method based on radial basis functions (RBFs) to interpolate the coordinates of the solution into the reduced basis. In this article, this POD-RBF approach is applied to a nonlinear magnetostatic problem and is used with a single-phase transformer and a three-phase inductance.
In this article, a finite element (FE) modeling of the punching effect on the magnetic properties of electrical steel sheet is carried out. For that, the modified anhysteretic Sablik model is applied ...together with the plastic strain distribution obtained from a punching process simulation performed using the software ABAQUS. First, a synchronous electrical machine is simulated including the effect of the punching process, and it shows the degradation of the magnetic flux density at the lamination edges and an increase of the iron losses. Then, results obtained from the magneto-mechanical simulation are investigated in terms of the method used to implement the plastic strain distribution in the FE computation. Two examples have been investigated: a square steel sheet and a tooth of an electrical machine.
A method is proposed in this article to place sensors in an electrical machine in order to be able to reconstruct the magnetic field distribution. This method is based on the empirical interpolation ...method combined with the Maxvol technique. The results applied on a surface-mounted permanent magnet machine at no load show that the field distribution can be accurately reconstructed even when the sensor location is imposed in the airgap of the rotating machine.
Among the model order reduction techniques, the proper generalized decomposition (PGD) has shown its efficiency to solve static and quasistatic problems in the time domain. However, the introduction ...of non-linearity due to ferromagnetic materials, for example, has never been addressed. In this paper, the PGD technique combined with the discrete empirical interpolation method (DEIM) is applied to solve a non-linear magnetostatic problem coupled with the circuit equations. To evaluate the reduction technique, the transient state of a three-phase transformer at no load is studied using the full finite-element model and the PGD-DEIM model.
Among the model order reduction techniques, the proper generalized decomposition (PGD) has shown its efficiency to solve a large number of engineering problems. In this paper, the PGD approach is ...applied to solve a multi-physics problem based on a magnetoelectric device. A reduced model is developed to study the device in its environment based on an offline/online approach. In the offline step, two specific simulations are performed in order to build a PGD reduced model. Then, we obtain a model very well fitted to study in the online stage the influence of parameters like the frequency or the load. The reduced model of the device is coupled with an electric load (<inline-formula> <tex-math notation="LaTeX">R </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>) to illustrate the possibility offered by the PGD.
Among the model-order reduction techniques, the proper orthogonal decomposition (POD) has shown its efficiency to solve magnetostatic and magnetoquasistatic problems in the time domain. However, the ...POD is intrusive in the sense that it requires the extraction of the matrix system of the full model to build the reduced model. To avoid this extraction, nonintrusive approaches like the data-driven (DD) methods enable to approximate the reduced model without the access to the full matrix system. In this paper, the DD-POD method is applied to build a low-dimensional system to solve a magnetostatic problem coupled with electric circuit equations.
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