## 3 Analysis and Results  
This section describes and illustrates the EMA and OMA methods, respectively. The overall schematic description, regarding the analysis procedure for regenerating the FRFs from the vibration responses, can be seen in Figure 7. The analysis part started with the pre-processing of the vibration data; an extensive reciprocating coherence analysis was carried out, in order to find out the best measurement points in the structure. The total measured length for each signal was around 768,000 samples. Thereafter, the RD technique procedure was applied to the raw signals, in order to obtain a matrix of 25 \(\times\) 25,600. Figure 5: OMA’s measurement set up for the gearbox with mounted accelerometers. Figure 6: Force and vibration signals in the time-domain: (**a**) the impedance hammer’s force; (**b**) vibration response. To limit the range of interest, a digital low pass filter was used, and a notch filter was also applied to eliminate speed rotation harmonics. Furthermore, in order to eliminate the gear mesh contact frequencies, the cepstrum (filtering) technique was used. CFE, which has ability to extract interesting information about the modal characteristics of the signals, was also applied. Therefore, after the CFE, the obtained vectors were 25 \(\times\) 25 \(\times\) 16,385. Finally, the EITM analysis was performed to obtain the structural resonances, based on Brincker [1]. As it was observed in the development of this research work, to validate the proposed analysis process, we started from the design of an experiment with a simple structure to develop the final process with experiments using complex structures. The structure's natural frequencies of the steel beam, induction motor, and gearbox were obtained through OMA. The measured and regenerated FRFs of the obtained results on the steel bar of the EMA and OMA measurements can be seen in Figure 8. It can be pointed out that the structure resonances are global parameters, which means the resonances do not change in frequency, due to input force placement. It can also be stressed out that the structure regenerate natural frequencies have almost the same frequencies as the measured ones; however, it seems that the anti-resonances have slightly variations or, in some cases, does not exist. Figure 8: Structure natural frequencies of OMA vs. EMA techniques for a steel bar. Figure 7: Flowchart of the overall OMA analysis procedure. The steel bar's regenerate structure natural frequencies for EMA and OMA are shown in Table 1. The obtained results have high accuracy, except at 8 Hz. It was difficult to generate a FRF for that specific resonance frequency with precision. Figure 9 illustrates the obtained results of the regenerated natural frequencies of the induction motor at 1800, 2400, and 3000 rpm, respectively. The obtained results showed an overall consistency. However, it was quite difficult to regenerate the structure's natural frequencies, between 600 to 900 Hz at 1800 rpm, with high precision. Five generated natural structure frequencies for the induction motor were detected. To quantify the precision of the obtained OMA's results, Figure 10 denotes the comparison of the induction motor's FRFs, with five modes at varying speeds (1800, 2400, and 3000 rpm). The highest accuracy was shown by mode one. A typical gearbox's regenerated transfer function at 3000 rpm can be seen in Figure 11.  
Figure 12 illustrates the obtained results of the gearbox structure's natural frequencies with varying speeds. The first three regenerated modes have the highest precision; they can be used for machine diagnostics. In order to reduce the frequency dispersion for higher modes, we could determine a calibration curve to use to adjust the measurement values. An advanced equalization process and scaling of the generated FRFs [14], in order to increase the precision, could be the subject of future research.