*6.3. Correlation Analysis*

The results of the magnitude-squared coherence (MSC) for three grinding conditions are observed in Figure 6. The coherence was obtained from the raw acoustic emission and piezoelectric time-domain signals. Each of the MSC values indicates how well the PZT signal corresponds to the AE signal for each frequency, with 1 representing an ideal coherence parameter and 0 representing the complete lack of relation between the signals. It can be observed that even in the severe cutting condition, where higher acoustic activity and spectral content is expected, the MSC values were higher than 80%. The successful results presented in Figure 6, directly related to the signals of both sensors under various grinding conditions, reinforce the application of the low-cost piezoelectric diaphragm in the monitoring of the grinding process of advanced ceramics. The lower values of MSC were observed in the frequency range between 200 and 300 kHz; this is due to the attenuation of the PZT sensor, which increases the difference between the signals. The low-cost PZT diaphragm demonstrated a similar response to the AE sensor, being sensitive to the stimulus caused by the grinding processes tested in this test bench.

A linear regression was performed and the coefficient of determination (R) was calculated in order to show the similarity between the measured surface roughness and the signals of each sensor, as shown in Figure 7. The coefficient of determination was 0.90338 for the AE sensor and 0.81068 for the PZT diaphragm. Although the linear fit was better for the AE sensor, there is a high coefficient for both sensors, which is also confirmed by the coherence of Figure 6. Thus, the ROP metric can contribute to the evaluation of the surface quality of the ground ceramic components, as indicated in the results obtained by the linear regression. The linear fit was close to 45◦, i.e., R very close to 1, indicating a high correlation between the signals and the measured roughness, which is the focus of this study. As expected, the AE sensor showed a better response to the acoustic activity generated during the grinding process, which is related to the surface quality of the workpiece, because of the metal housing, filter, and signal unit, which improve the signal conditions. However, the signals from the PZT diaphragm, studied in this work, showed a high degree of correlation (greater than 80%), confirming the feasibility of using the low-cost PZT diaphragm in the monitoring of the surface quality of ground workpieces through the acoustic activity generated during the process. The PZT diaphragm was able to detect the same changes in acoustic activity as the AE sensor.
