## 4 Conclusions
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sensor Resolution** & **Low Frequency (1 Hz)** & **First Order (269 Hz)** & **Second Order** & **Third Order** \\  & **(1 Hz)** & **(645 Hz)** & **(1267 Hz)** \\ \hline
0.1 nm & (10.84\%, 1 Hz) & (2.02\%, 271 Hz) & (0.31\%, 643 Hz) & (0.42\%, 1267 Hz) \\  & (2.12\({}^{\circ}\), 1 Hz) & (1.47\({}^{\circ}\), 271 Hz) & (0.32\%, 645 Hz) & (0.32\%, 1267 Hz) \\
1 nm & (83.36\%, 1 Hz) & (1.92\%, 269 Hz) & (0.31\%, 643 Hz) & (0.42\%, 1267 Hz) \\  & (8.77\({}^{\circ}\), 1 Hz) & (1.45\({}^{\circ}\), 271 Hz) & (0.32\%, 645 Hz) & (0.32\%, 1267 Hz) \\
0.1 um & (695.26\%, 4 Hz) & (19.45\%, 268 Hz) & (0.65\%, 646 Hz) & (0.62\%, 1266 Hz) \\  & (140.04\({}^{\circ}\), 4 Hz) & (10.86\({}^{\circ}\), 268 Hz) & (0.55\({}^{\circ}\), 646 Hz) & (0.45\({}^{\circ}\), 1262 Hz) \\  & \multicolumn{2}{c}{Cannot be} & \multicolumn{1}{c}{Cannot be} & \multicolumn{1}{c}{Cannot be} & \multicolumn{1}{c}{(0.63\%, 1266 Hz)} \\
1 um & \multicolumn{2}{c}{identified} & \multicolumn{1}{c}{identified} & \multicolumn{1}{c}{identified} & \multicolumn{1}{c}{(0.45\({}^{\circ}\), 1262 Hz)} \\  & \multicolumn{2}{c}{Cannot be} & \multicolumn{1}{c}{Cannot be} & \multicolumn{1}{c}{Cannot be} & \multicolumn{1}{c}{(0.45\({}^{\circ}\), 1262 Hz)} \\  & \multicolumn{2}{c}{identified} & \multicolumn{1}{c}{identified} & \multicolumn{1}{c}{identified} & \multicolumn{1}{c}{(0.45\({}^{\circ}\), 1262 Hz)} \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Statistical results of peak values of identification errors of rotor unbalance for #1 disc in g1.4. For future research, there are various possible directions. Experiments should be conducted to validate the proposed methods. The limitation of the proposed algorithms is that they are not suitable for low-speed rotors and a high accuracy of measurement of unbalance responses is strongly demanded. Therefore, sensors and instruments with high accuracy and good resolutions for measuring unbalance responses should be developed. Moreover, further investigations could focus on decreasing the high requirements on measurement accuracy. Sensors with a resolution of 1 um can be used for the identification. The Timoshenko model, in which gyroscopic moments are considered, could be taken into consideration based on CRDAM when modelling a continuous shaft. The research method of this paper can be regarded as a tool for future study. Conceptualization, A.W. ; methodology, A.W. ; software, A.W., Y.B. and Y.F. ; formal analysis, A.W. ; investigation, Y.F., X.C. and J.Y. ; writing--original draft preparation, A.W. and Y.B. ; writing--review and editing, A.W. and Y.B. ; supervision, G.M. ; funding acquisition, G.M. All authors have read and agreed to the published version of the manuscript. This research was funded by the Fundamental Research Funds for the Central Universities, grant number 8000150A084, and the Yue Qi Young Scholar Project, China University of Mining & Technology, Beijing. Not applicable. The study did not report any data. The authors  
Simulation results for rotor g1.4  
In this simulation, #20 is used as one of the required measuring points and the other measuring points are #15, #90, #21, #41, #61, and #81, which are the locations of the two bearings and the four discs. Figure 14: The maximum identification error for each rotor unbalance in g1.4 based on TODA using #20 point as one of the required measuring points: (**a**) relative error for rotor unbalance amplitude; (**b**) absolute error for rotor unbalance angle. Figure 13: The maximum identification error for each rotor unbalance in g1.4 based on SDA using #20 point as one of the required measuring points: (**a**) relative error for the rotor unbalance amplitude; (**b**) absolute error for the rotor unbalance angle. \[TODA\_M1_{g44}=\left[