Antoine Pierquin

Structure preserving model reduction of low frequency electromagnetic problem based on POD and DEIM

The Proper Orthogonal Decomposition (POD) combined with the (Discrete) Empirical Interpolation Method (DEIM) can be used to speed up the solution of a FE model. However, it can lead to numerical instabilities. To increase the robustness, the POD_DEIM model must be constructed by preserving the structure of the full FE model. In this communication, the structure preserving is applied for different potential formulations used to solve electromagnetic problems.

Multirate Coupling of Controlled Rectifier and Non-Linear Finite Element Model Based on Waveform Relaxation Method

To study a multirate system, each subsystem can be solved by a dedicated software with respect to the physical problem and the time constant. Then, the problem is the coupling of the solutions of the subsystems. The waveform relaxation method (WRM) seems to be an interesting solution for the coupling, but until now, it has been mainly applied on academic examples. In this paper, the WRM is applied to perform the coupling of a controlled rectifier and a non-linear finite element model of a transformer.

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

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

Data-Driven Model-Order Reduction for Magnetostatic Problem Coupled With Circuit Equations

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.

Model Order Reduction of Electrical Machines With Multiple Inputs

In this paper, proper orthogonal decomposition (POD) method is employed to build a reduced-order model from a high-order nonlinear permanent magnet synchronous machine model with multiple inputs. Three parameters are selected as the multiple inputs of the machine. These parameters are terminal current, angle of the terminal current, and rotation angle. To produce the lower-rank system, snapshots or instantaneous system states are projected onto a set of orthonormal basis functions with small dimension. The reduced model is then validated by comparing the vector potential, flux density distribution, and torque results of the original model, which indicates the capability of using the POD method in the multivariable input problems. The developed methodology can be used for fast simulations of the machine.

Optimization of the TEAM 22 problem using POD-EIM reduced model

The finite element models are not very used in optimization because of their computation time, in spite of their precision. Model order reduction and matrix interpolation techniques can be applied to a finite element model to obtain a fast and precise model, which can be used in optimization. These techniques are used for the modeling and the optimization of the TEAM 22 workshop problem.

Multidisciplinary Optimization Formulation for the Optimization of Multirate Systems

Multidisciplinary optimization strategies are widely used in the static case and can be extended to a problem with a time-domain model in order to reduce optimization time. The waveform relaxation method is a fixed-point approach applied to waveforms, which allows the coupling of dynamic models. Using the individual discipline feasibility strategy, the coupling is transferred to the optimization problem and leads to a high decrease of the number of model evaluations compared with the multidisciplinary feasibility strategy. The drawback of this approach might be the increased number of optimization variables, but it is coped through an efficient way to compute the derivatives of time-dependent variables.