This work introduces a method for plasma state supervision, based on a frequency-modulated continuous wave radar sensor and a suitable signal evaluation enabling a continuous supervision method for the plasma state. Highly precise phase evaluation of the signal allows us to detect and visualize smallest changes in the plasma state. Assuming the plasma to act like a frequency-dependent dielectric material, the propagation of the electromagnetic wave depends on the plasma state and hence, also the measured phase. Broadband measurements are carried out at center frequencies of 80 and 140 GHz in a low-pressure plasma. The radar-based setup can be used for a very flexible application, capable for spatially resolved measurements in the plasma bulk. At the same time, the high measurement rate allows for quasi real-time monitoring, so that transient processes in the plasma are recorded. Due to the simple setup, this approach is most suitable for industrial applications to improve process control. The chosen different frequencies will show a change in the influence of the plasma on the electromagnetic wave demonstrating the advantages of multi-frequency approaches in future applications.

The early detection of gear faults remains a major problem, especially when the gears aresubjected to non stationary phenomena due to defects. In industrial applications, thecrack of tooth is a default very difficult to detect whether using the time descriptors orthe frequency analysis. In this work and based on a numerical model, we prove that thecrack default affects directly the phase of the frequency component of the defective wheel(frequency modulation). To properly estimate the phases, we suggest two high-resolutiontechniques (Estimation of Signal Parameters via Rotational Invariance Techniques ESPRITwith a sliding window and Weighted Least Squares Estimator WLSE). The results of bothmethods are compared to the phase obtained by Hilbert transform. The three techniques arethen applied on a multiplicative signal with a frequency modulation to show the influenceof the amplitude modulation on the quality of phase estimation. We note that the ESPRITmethod is much better in the estimation of frequencies while WLSE shows much efficiency inthe estimation of phases if we keep the frequencies almost stables.