## 5 Experimental Verification  
The safety domain was determined by the data of two normally operating flywheels. Firstly, the noise data was collected for a time period of 60 s under the working conditions of 3000 r/min and 4600 r/min, respectively. Secondly, the root-mean-square value \(R\), kurtosis \(K\), and sharpness \(S\) were calculated and the clustering fusion of them was performed on the signals under the two working conditions according to the proposed method. The clustering center points of the normalized samples were (0.6246, 0.3988, 0.3667) and (0.4032, 0.2270, 0.4479) for the two different conditions. Finally, the scopes of the safety domain obtained by applying the 5\(\sigma\) rule are 0.7790 and 0.8826, respectively. Taking the centers as the origin and the safety scopes as the radius, the schematic diagrams of the established safety domain are shown in Figure 11. The method established in this paper was used to evaluate the condition of other flywheels (#1-#7). The seven flywheels were tested products for long life experiments. In order to verify the effectiveness of the monitoring method, these flywheels were noise tested several times separately. The parameters distribution of test flywheels #1-#7 is shown in Figures 12-18 (each red star in the figure represents a sample), and the monitoring results can be found in Table 2.  
Figure 11: The security domain under normal operating conditions: (**a**) 3000 r/min; (**b**) 4600 r/min. Figure 10: The state monitoring approach for the MWA’s bearings based on multi-acoustic parameter fusion. Figure 14: Flywheel #3 test noise sample point and security domain: (**a**) 3000 r/min; (**b**) 4600 r/min. Figure 12: Flywheel #1 test noise sample point and security domain: (**a**) 3000 r/min; (**b**) 4600 r/min. Figure 13: Flywheel #2 test noise sample point and security domain; (**a**) 3000 r/min; (**b**)4600 r/min. Figure 15: Flywheel #4 test noise sample point and security domain: (**a**) 3000 r/min; (**b**) 4600 r/min. It can be found out from Table 2 that the excess rates of #3 and #4 were equal or less than 20% under the speed of 3000 r/min, while both were 0 under the speed of 4600 r/min. Moreover, the abnormal rate of 4600 r/min is higher than 1.000 r/min. Figure 16: Flywheel #5 test noise sample point and security domain: (**a**) 3000 r/min; (**b**) 4600 r/min. Figure 17: Flywheel #6 test noise sample point and security domain: (**a**) 3000 r/min; (**b**) 4600 r/min. Table 2.0 Flywheel #7 test noise sample point and security domain: (**a**) 3000 r/min; (**b**) 4600 r/min. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**MWA** & \multicolumn{2}{c}{**Excess Rate (\%)**} & \multicolumn{2}{c}{**Excess Distance (\%)**} & \multicolumn{2}{c}{**Abnormal Index \(I_{a}\)**} \\ \cline{2-7}
**Number** & **3000 r/min** & **4600 r/min** & **3000 r/min** & **4600 r/min** & **3000 r/min** & **4600 r/min** \\ \hline \#1 & 100 & 43.3 & 2.717 & 1.160 & 2.717 & 0.502 \\ \#2 & 50 & 13.3 & 1.772 & 0.430 & 0.886 & 0.057 \\ \#3 & 20 & 0 & 1.843 & 0 & 0.369 & 0 \\ \#4 & 16.7 & 0 & 0.991 & 0 & 0.165 & 0 \\ \#5 & 100 & 83.3 & 1.812 & 2.052 & 1.182 & 1.710 \\ \#6 & 20 & 56.7 & 0.256 & 0.115 & 0.051 & 0.065 \\ \#7 & 66.7 & 100 & 5.298 & 33.91 & 3.532 & 33.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Excess rates of seven tested MWAs with the same structural parameters at a rotating speed of 3000 r/min. index was small at both speeds, so it can be considered that the two flywheels were basically normal. Flywheel #6 had a higher excess rate, but the excess distance was not large, and the abnormal index under both conditions was also small. A careful analysis of Figure 17 shows that the main excess reason is due to the small root mean square value. We know that the mean square value represents energy, and the low energy indicates that the bearing worked under normal condition; hence, flywheel #6 is a normal flywheel, too. Due to the original differences among MWAs, these three MWAs were recognized as in a normal state.