Robust shape optimization of electric devices based on deterministic optimization methods and finite-element analysis with affine parametrization and design elements

Abstract

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by piecewise affine parametrizations of the geometry or by the design element approach, both of which avoid remeshing. Furthermore, it is shown how to robustify the optimization procedure, that is, 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 particle swarm optimization.

A space-time certified reduced basis method for quasilinear parabolic partial differential equations

“…We note that we performed the series of numerical approximations in order to provide a computable bound for the right-hand side of (31). In particular, the residual (30) coincides with the residual (38) for the Crank-Nicolson time-marching scheme (12) after application of the trapezoidal quadrature rule. However, in order to invoke the definition of the residual (30), u δ must be the solution to our reference problem (9).…”

“…The non-linear reluctivity function ν 1 is reconstructed from the real B − H measurements using monotonicity-preserving cubic spline interpolation and ν 2 value is chosen as the reluctivity of air. We then solve the problem with the Crank-Nicolson scheme (12), while applying Newton's method, described in Section 2.2, on each time step for the numerical computation of the time snapshots. We iterate the Newton's method unless the norm of the residual ( 13) is less than the tolerance level, which we set to 10 −8 .…”

“…We initiate the algorithm with the choice of the initial basis vector ξ 1 := u 0 δ / u 0 δ V ; this choice is motivated by the assumption in Proposition 1. The snapshots u k δ (μ) for the procedure are provided by the Crank-Nicolson scheme (12). Next, we proceed as stated in the following Algorithm 2.…”

“…This equation finds its place in important applications, such as the computation of magnetic fields in the presence of eddy currents in electrical machines [17]. The development of fast and accurate simulation methods for such problems is of great importance in the optimization and design of electrical machines and other devices [1,12]. Therefore, there is a demand for reduced order models (see, e.g.…”

A Neural Solver for Variational Problems on CAD Geometries with Application to Electric Machine Simulation

“…The neural solver developed in this work is first verified on a toy problem from computational electromagnetics and then applied to a real-world engineering test case, namely, for the simulation of a permanent magnet synchronous machine (PMSM) (Bhat et al, 2018;Bontinck et al, 2018a,b;Ion et al, 2018;Merkel et al, 2019). The real-world test case features all problems that this work aims to address, in particular, a complicated, multi-patch CAD geometry described by means of NURBS, upon which materials with different electromagnetic (EM) properties coexist.…”