## 4 Validation of the Rotational Speed Estimation Principle Using GAD
### Speed Estimation Result Comparisons  
**(i)** **Test 01: startup working condition**  
The acquired acceleration signals from the tangential in situ accelerometer are illustrated in Figure 5. As can be seen from the original plot and the zoomed-in one, there exists a big sinusoidal periodic signal in the tangential accelerometer. The frequency of the sinusoidal periodic component grows over time, with a period similar to the rotational frequency of the disc. According to the signal composition analyzation in Equation (2), the sinusoidal periodic signal is caused by the time-varying gravity acceleration component. Hence, the rotational speed can be estimated by decoupling the gravity acceleration component from the acquired acceleration signal. However, it is obvious there are lots of noise components and interferences that need to be suppressed, as shown in Figure 5.  
Figure 4: The established experimental setup: (**a**) sketch diagram; (**b**) photograph. According to Equation (6) and the rated speed of the experimental setup, the cutoff frequency of the linear-phase low-pass filter is set as 100 Hz. The filtered local embedded acceleration signals are then obtained, as shown in Figure 6. Compared to the raw signals in Figure 5, lots of high-frequency components are suppressed based on the linear-phase low-pass filter, so the period of the gravity acceleration component becomes clearer. However, there are still lots of oscillations in both the low-speed range and high-speed range of the startup working condition, which is not conducive to the accurate estimation of the speed. Then, the CEEMDAN method, ICEEMDAN method and EWT method are applied to the filtered local embedded acceleration signals to decouple the gravity acceleration components. The decomposed IMFs of the filtered acceleration signals based on the three methods are shown in Figure 7; there are 18, 15 and 15 decomposed IMFs in the three methods, the desired IMFs are highlighted by the red dashed frame in Figure 7. In the CEEMDAN method, it is found that the noise components are mainly decomposed into the first 8 IMFs, while the time-varying gravity components are decomposed into IMF 9 to 11, as shown in Figure 7a,b. But it seems there are still some high-frequency noises in IMF 9. In the ICEEMDAN method, the noise components are mainly located at the first 5 IMFs, while the time-varying gravity components are decomposed into IMF 6 to 10, and it seems the high-frequency noise suppression performance in IMF 6 to 10 is better, as shown in Figure 7c,d. In the EWT method, clearly decomposition of the vibration signal in the time and frequency dimension can be observed; the noise components are mainly located at the first 7 IMFs, while the time-varying gravity components are decomposed into IMF 8 to 14. The noise suppression performance based on the EWT method seems to be the best among the three methods, as depicted in Figure 7e,f. Figure 5: The (**a**) acquired local embedded acceleration signals under the Test 01 working condition and (**b**) the zoomed-in plot. Figure 6: The (**a**) filtered local embedded acceleration signals and (**b**) the zoomed-in plot. The Pearson correlation coefficients between each IMF and the filtered local embedded acceleration signals are calculated for the three methods, as illustrated by the blue solid line in Figure 8. In this paper, the average value of all IMF correlation coefficients is used as the threshold to select sensitive IMFs, as shown by the red dotted line in Figure 8. It is found that the IMFs containing more time-varying gravity acceleration components are well selected based on the three methods. The reconstructed gravity acceleration components under the Test 01 working condition based on the three methods are then obtained and compared, as shown in Figure 9. Most of the oscillations are suppressed in all of the three methods, especially in the high-speed range. And the magnitude of the reconstructed sinusoidal periodic component approximately equals the gravity in all of the three methods.