Magneto-mechanical resonators (MMRs) are a recently proposed type of passive sensor that allows its own pose as well as further parameters of its environment to be estimated. The sensors are excited by oscillating magnetic fields and are subsequently read out by inductive receiver coils, so that neither a battery nor a wired connection is required at the sensor itself. This makes them attractive for wireless measurements inside process equipment as well as for medical applications such as endoscopy, surgery and vascular interventions.
The sensing technology relies on real-time parameter estimation, which entails the solution of a nonlinear inverse problem with the induced signals and a suitable forward model as inputs. The aim of the work is twofold: first, to introduce a reference model and simplified models for the resonator dynamics and the inductive readout, and second, to provide robust and real-time capable methods to estimate the model parameters.
The effectiveness of the presented methods was evaluated in terms of their real-time potential, precision and accuracy on measurements of two resonators of different size. All methods proved capable of estimating the measured signal. The simplified methods reduced the corresponding parameter estimation time by up to two orders of magnitude, at the expense of a deviation of less than 4 % for large maximum deflection angles.
Since the parameters have to be recovered while the measurement is running, this reduction in computing time is the decisive step towards the use of the resonators as real-time sensors. The models and estimation methods provide the basis for model-based sensing with magneto-mechanical resonators in process engineering and in medical engineering.
The study is a collaboration between the Institute for Biomedical Imaging at Hamburg University of Technology, the Section for Biomedical Imaging at the University Medical Center Hamburg-Eppendorf and the Fraunhofer Research Institution for Individualized Medical Technology and Engineering IMTE in Lübeck, carried out within the Collaborative Research Centre CRC 1615 (SMART Reactors).
Sarah Reiss, Tobias Knopp, Justin Ackers, Jonas Faltinath, Fabian Mohn, Marija Boberg, Nora Timm, Martin Möddel (2026). Parameter Estimation for Model-Based Sensing of Magneto-Mechanical Resonators. arXiv:2602.19965.
