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Zeger Bontinck

Publications and source records attributed to Zeger Bontinck.

9 recordsLinked to original sources
arXiv2020

A multilevel Monte Carlo method for high-dimensional uncertainty quantification of low-frequency electromagnetic devices

This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized in space by the finite element method. Both methods yield numerical approximations such that the total errors is split into stochastic and spatial contributions. We propose a particular implementation where the spatial error is controlled based on a Richardson-extrapolation-based error indicator. The stochastic error in turn is efficiently reduced in the MLMC approach by distributing the samples on multiple grids. The method is applied to a toy problem with closed-form solution and a permanent magnet synchronous machine with uncertainties. The uncertainties under consideration are related to the material properties in the stator and the magnets in the rotor. The examples show that the error indicator works reliably, the meshes used for the different levels do not have to be nested and, most importantly, MLMC reduces the computational cost by at least one order of magnitude compared to standard Monte Carlo.

cs.CE↗
arXiv2018

Robust Optimization Approaches for the Design of an Electric Machine

In this paper two formulations for the robust optimization of the size of the permanent magnet in a synchronous machine are discussed. The optimization is constrained by a partial differential equation to describe the electromagnetic behavior of the machine. The need for a robust optimization procedure originates from the fact that optimization parameters have deviations. The first approach, i.e., \textcolor{red}{worst-case} optimization, makes use of local sensitivities. The second approach takes into account expectation values and standard deviations. The latter are associated with global sensitivities. The geometry parametrization is elegantly handled thanks to the introduction of an affine decomposition. Since the stochastic quantities are determined by tools from uncertainty quantification (UQ) and thus require a lot of finite element evaluations, model order reduction is used in order to increase the efficiency of the procedure. It is shown that both approaches are equivalent if a linearization is carried out. \textcolor{blue}{This finding is supported by the application on an electric machine. The optimization algorithms used are sequential quadratic programming, particle swarm optimization and genetic algorithm}. While both formulations reduce the size of the magnets, the UQ based optimization approach is less pessimistic with respect to deviations and yields smaller magnets.

math.OC↗
arXiv2018

Robust Shape Optimization of Electric Devices Based on Deterministic Optimization Methods and Finite Element Analysis With Affine Decomposition and Design Elements

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element approach, both of which avoid remeshing. Furthermore, it is shown how to robustify the optimization procedure, i.e., how to deal with uncertainties on the design parameters. The overall procedure is illustrated by an academic example and by the example of a permanent-magnet synchronous machine. The examples show the advantages of deterministic optimization compared to standard and popular stochastic optimization procedures such as, e.g., particle swarm optimization.

math.OC↗
arXiv2017

Recent Advances of Isogeometric Analysis in Computational Electromagnetics

In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite Element Method (FEM). While identical to FEM with Nédélec's basis functions in the lowest order case, it is based on B-spline and Non-Uniform Rational B-spline basis functions. The main benefit of this is the exact representation of the geometry in the language of computer aided design (CAD) tools. This simplifies the meshing as the computational mesh is implicitly created by the engineer using the CAD tool. The curl- and div-conforming spline function spaces are recapitulated and the available software is discussed. Finally, several non-academic benchmark examples in two and three dimensions are shown which are used in optimization and uncertainty quantification workflows.

cs.CE↗
arXiv2017

Isogeometric Analysis and Harmonic Stator-Rotor Coupling for Simulating Electric Machines

This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby avoiding any geometrical error in the representation of the air gap where a high accuracy is mandatory. To increase the generality of the method, and to allow rotation, the rotor and the stator computational domains are constructed independently as multipatch entities. The two subdomains are then coupled using harmonic basis functions at the interface which gives rise to a saddle-point problem. The properties of Isogeometric Analysis combined with harmonic stator-rotor coupling are presented. The results and performance of the new approach are compared to the ones for a classical finite element method using a permanent magnet synchronous machine as an example.

math.NA↗
arXiv2017

Modelling of a Permanent Magnet Synchronous Machine Using Isogeometric Analysis

Isogeometric analysis (IGA) is used to simulate a permanent magnet synchronous machine. IGA uses non-uniform rational B-splines to parametrise the domain and to approximate the solution space, thus allowing for the exact description of the geometries even on the coarsest level of mesh refinement. Given the properties of the isogeometric basis functions, this choice guarantees a higher accuracy than the classical finite element method. For dealing with the different stator and rotor topologies, the domain is split into two non-overlapping parts on which Maxwell's equations are solved independently in the context of a classical Dirichlet-to-Neumann domain decomposition scheme. The results show good agreement with the ones obtained by the classical finite element approach.

cs.CE↗
arXiv2017

Model Order Reduction for Rotating Electrical Machines

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that contain non-symmetric components. These are usually introduced during the mass production process and are modeled by small perturbations in the geometry (e.g., eccentricity) or the material parameters. While model order reduction for symmetric machines is clear and does not need special treatment, the non-symmetric setting adds additional challenges. An adaptive strategy based on proper orthogonal decomposition is developed to overcome these difficulties. Equipped with an a posteriori error estimator the obtained solution is certified. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

math.NA↗