Efficient Pareto-Front Generation for Electric Machines using IGA and Second Order Derivatives

The multiobjective optimization of electric machines always involves a trade-off caused by various competing objectives such as performance and cost.

A suitable design is usually determined by comparing variants from the Pareto front, which has been generated by a large number of simulation runs.

This paper addresses the efficient generation of the Pareto front using a continuation method based on a homotopy method that exploits second-order derivative information to achieve superlinear convergence, enabling the fast generation of new Pareto-optimal points within only a few iterations.

A key contribution is the derivation of formulas to compute the Hessian with respect to geometry parameters and shape, thus enabling direct modifications of the motor geometry in the context of Isogeometric Analysis.

We apply our method to nonlinear 2D magnetostatic simulations of a permanent magnet synchronous motor and demonstrate its effectiveness by optimizing the cost, mean torque and torque ripple of the motor.

Compared to a first-order optimization method, this approach reduces the number of iterations and function evaluations needed, making the pareto optimization fast and efficient.