Implementation of an Eigenfrequency-Based Deformation Identification for RF Cavities

Proseminar, Projektseminar, Studienarbeit, Bachelorarbeit

Due to the growing importance of e-mobility, the efficient simulation and optimization of electric energy converters, in particular electric machines, is becoming increasingly important. In the manufacturing process of these electric machines imperfections and small deviations from the nominal design can occur. In the worst case, these imperfections can lead to a significant decrease in quality or even failure of the machine. To avoid this, the machine can be optimized robustly, i.e., considering the deviations in the machine design. Robust optimization aims to find a machine design which is robust in terms of deviations from the nominal design, i.e., to find an optimum in terms of a goal function J which does not deteriorate significantly for small changes in the design parameters p, compare Fig. 2. In this project an electric machine is simulated using isogeometric analysis and the shape of the machine shall be optimized robustly considering uncertainties, using uncertainty quantification methods like the Monte Carlo method.

Work plan

  • Literature study on robust optimization
  • Modelling an uncertain deviation, e.g. uncertain magnetization or shape
  • Implementation of robust optimization given code for nominal shape optimization
  • Application of the robust shape optimization to a machine model


Basic knowledge of the finite element method, interest in numerical methods and Matlab programming


  • Corno, Jacopo; Georg, Niklas et al.: Uncertainty modeling and analysis of the European X-ray free electron laser cavities manufacturing process. Nuclear Inst. and Methods in Physics Research, 2020, Vol. 971
  • Georg, Niklas; Ackermann, Wolfgang; Corno, Jacopo; Schöps, Sebastian: Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking. Comput. Meth. Appl. Mech. Eng., 2023, Vol. 350, pp. 228-244
  • Ziegler, Anna; Hahn, Robert; Isensee, Victoria; Nguyen, Anh Duc; Schöps, Sebastian: Gradient-Based Eigenvalue Optimization for Electromagnetic Cavities with Built-in Mode Matching. Cornell University, ARXIV: 2310.15751. 2023. Preprint