A posteriori error estimation for stochastic static problems

To solve stochastic static field problems, a discretization by the Finite Element Method can be used. A system of equations is obtained with the unknowns (scalar potential at nodes for example) being random variables. To solve this stochastic system, the random variables can be approximated in a finite dimension functional space - a truncated polynomial chaos expansion. The error between the exact solution and the approximated one depends not only on the spatial mesh but also on the discretization along the stochastic dimension. In this paper, we propose an a posteriori estimation of the error due to the discretization along the stochastic dimension.This work is supported by the program MEDEE funded by the Nord Pas de Calais council and the European Community

Model Order Reduction of Non-Linear Magnetostatic Problems Based on POD and DEI Methods

In the domain of numerical computation, Model Order Reduction approaches are more and more frequently applied in mechanics and have shown their efficiency in terms of reduction of computation time and memory storage requirements. One of these approaches, the Proper Orthogonal Decomposition (POD), can be very efficient in solving linear problems but encounters limitations in the non-linear case. In this paper, the Discret Empirical Interpolation Method coupled with the POD method is presented. This is an interesting alternative to reduce large-scale systems deriving from the discretization of non-linear magnetostatic problems coupled with an external electrical circuit

Benefits of Waveform Relaxation Method and Output Space Mapping for the Optimization of Multirate Systems

We present an optimization problem that requires to model a multirate system, composed of subsystems with different time constants. We use waveform relaxation method in order to simulate such a system. But computation time can be penalizing in an optimization context. Thus we apply output space mapping which uses several models of the system to accelerate optimization. Waveform relaxation method is one of the models used in output space mapping

Non Linear Proper Generalized Decomposition method applied to the magnetic simulation of a SMC microstructure

Improvement of the magnetic performances of Soft Magnetic Composites (SMC) materials requires to link the microstructures to the macroscopic magnetic behavior law. This can be achieved with the FE method using the geometry reconstruction from images of the microstructure. Nevertheless, it can lead to large computational times. In that context, the Proper Generalized Decomposition (PGD), that is an approximation method originally developed in mechanics, and based on a finite sum of separable functions, can be of interest in our case. In this work, we propose to apply the PGD method to the SMC microstructure magnetic simulation. A non-linear magnetostatic problem with the scalar potential formulation is then solved

Error estimation of a proper orthogonal decomposition reduced model of a permanent magnet synchronous machine

Model order reduction methods, like the proper orthogonal decomposition (POD), enable to reduce dramatically the size of a finite element (FE) model. The price to pay is a loss of accuracy compared with the original FE model that should be of course controlled. In this study, the authors apply an error estimator based on the verification of the constitutive relationship to compare the reduced model accuracy with the full model accuracy when POD is applied. This estimator is tested on an example of a permanent magnet synchronous machine.This work is supported by the IAP7/M2E2S (Belgium state) and MEDEE pole supported by the region council of Nord Pas de Calais (France) and the European Community

Investigations on the performances of the electrical generator of a rim-driven marine current turbine”

In this paper, the electrical generator of a rim-driven horizontal-axis current turbine is modeled in detail. Its main characteristics and performances are evaluated (efficiency, mass, cost, etc). This generator is of permanent magnet direct-driven synchronous type and is connected to a variable speed power electronics drive. It is then compared to a more traditional technology (a pod generator) in terms of mass and cost for a common set of specification. In addition, due to the specific geometry of the machine, the use of low-cost ferrite magnets is investigated in place of NdFeB magnets

Comparizon of Conventional and Unconventional 5-phase PM Motor Structures for Naval Applications

Multi-phase motors are widely used in marine propulsion. In this paper, a Multi-machine modeling of Surface Mounted PM motors is presented and applied to a 5-phase one. The latter is proved to be equivalent to a set of two-phase fictitious machines each ones being characterized by a set of specific harmonic rank. A simple control consists in supplying each fictitious machine by a current which contains only one harmonic. A five phase machine is then supplied by currents with only both first and third harmonics. Considering this kind of control, it is proved that for given stator resistance and average torque the Joule losses and the torque ripple are minimized if a simple criterion on the harmonics of electromotive force at constant speed is fullfilled. Different structures of rotor are then compared to examine numerically which improvements can be practically obtaine

Stochastic post-processing calculation of iron losses – application to a PMSM

To take account of the uncertainties introduced on the magnetic properties during the manufacturing process, the present work aims to focus on the stochastic modelling of iron losses in electrical machine stators. The investigated samples are composed of 28 slinky stators, coming from the same production chain. The stochastic modelling approach is first described. Thereafter, the Monte-Carlo sampling method is used to calculate, in post-processing, the iron loss density in a PMSM that is modelled by the finite element method. The interest of such an approach is emphasized by calculating the main statistical characteristics associated to the losses variability, which are Gaussian distributed for A and O formulations. The originality of the approach is due to the fact that the global influence of the manufacturing process (cutting, assembly, …) on magnetic properties of the considered samples is taken into account in the way of computing the iron losses.This work is supported by the program MEDEE (Nord Pas-de-Calais Region, France

A priori error indicator in the transformation method for problems with geometric uncertainties

Version éditeur de cette publication à l'adresse suivante : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6514655To solve stochastic problems with geometric uncertainties, one can transform the original problem in a domain with stochastic boundaries and interfaces to a problem defined in a deterministic domain with uncertainties in the material behavior. The latter problem is then discretized. There exist infinitely many random mappings that lead to identical results in the continuous domain but not in the discretized domain. In this paper, an a priori error indicator is proposed for electromagnetic problems with scalar and vector potential formulations. This leads to criteria for selecting random mappings that reduce the numerical error. In an illustrative numerical example, the proposed a priori error indicator is compared with an a posteriori estimator for both potential formulationsThis work is supported by the program MEDEE funded by the Nord Pas de Calais council and the European Community and supported in part by the National Science Foundation under Grant No. 1216927

A coupled electromagnetic / hydrodynamic model for the design of an integrated rim - driven naval propulsion system

This paper presents an analytical multi-physic modeling tool for the design optimization of a new kind of naval propulsion system. This innovative technology consists in an electrical permanent magnet motor that is integrated into a duct and surrounds a propeller. Compared with more conventional systems such as pods, the electrical machine and the propeller have the same diameter. Thus, their geometries, in addition to speed and torque, are closely related and a multidisciplinary design approach is relevant. Two disciplines are considered in this analytical model: electromagnetism and hydrodynamics. An example of systematic design for a typical application (a rim-driven thruster for a patrol boat) is then presented for a set of different design objectives (efficiency, mass, etc). The effects of each model are commente