Optimization and inverse problems

The optimal design of electromagnetic devices and the solution of inverse problems are in the focus of this research area.

Optimal design means, that, for instance, some physical quantities like the torque of a motor or the starting power of an actuator should be within a certain range while keeping the dimension of the devices and the cost of production as small or as low as possible. In the early stage of the design process, when there is little or even no knowledge about feasible or unfeasible regions in the design space or about the principle appearance of the device, stochastic optimization methods like evolution strategies or population based swarm methods can be applied to investigate as many feasible designs as possible. On the other hand, once the most promising set up has been detected, gradient based methods or other deterministic optimization strategies can be used to finally tune the features of the device.

Topology optimization, as another method, is used to allocate different types of material without defining a rigid geometry in advance.

In most cases optimizing a technical device leads to a multi-objective optimization problem, where the individual objectives or goals are conflicting each other. Among others, this can be taken into account by solving for pareto optimal solutions.

Especially for devices or systems with higher production tolerances and uncertainties, considering robustness of the solution is crucial. Worst case as well as probabilistic approaches are used to ensure the quality of the desired objective.

Projects in the field of shape and topology optimization:

  • Magneto-rheologic fluid clutch
  • Electromagnetic and eddy current emergency rail brakes
  • Antennas (NFC, Yagi-Uda)
  • Shielding of power devices by magnetic shunts

Optimized shape of a magneto-rheologic clutch (left), electromagnetic track brake optimization (right)

Inverse problems deal with the determination of inaccessible information like material parameters or the spatial distribution of parts by exploiting measurements outside the space under investigation. In general, this leads to ill posed problems, which need special mathematical treatment. Deterministic, stochastic and hybrid strategies are used to solve this special class of optimization problems. Problem specific regularization methods, like the Tikhonov regularization, as well as the probabilistic approach following the Bayes’ theorem (Markov Chain Monte Carlo method) can be applied. From the latter one the uncertainties can be obtained without further simulation, which is in particular advantageously for biomedical applications.

Projects in the field of inverse problems:

  • Non-invasive biomedical applications (electrical impedance tomography, impedance cardiography for aortic dissection identification)
  • Source reconstruction in acoustics
  • Identification of hidden conductive materials
  • Network parameter identification

Simulation model of a human thorax for the identification of an aortic dissection (left), identification of the hidden drill holes by eddy current testing (right)

In any case, one is forced to solve numerous electromagnetic or coupled field problems with varying parameters, which can lead to a disproportional computational effort. Therefore, model order reduction is also part of this research area. Surrogate models, like multi quadrics or neural networks replace the costly numerical simulation of the field problem while maintaining an adequate accuracy.