## 3 Numerical Simulations and Discussion
### Affect of Sensor Resolution  
#### 3.4.1 Results  
According to the result in the third kind of simulation, the maximum identification error of TODA was too big. Hence, the fourth kind of simulation was conducted based on SDA. The simulated unbalance responses calculated by CRDAM containing different sensor resolutions (0.1 nm, 1 nm, 0.1 um, and 1 um) were used as input data to the method. The computational example g1.4 is used. In the simulation, the measuring points for the  
Figure 19: Identification error changed with frequency based on TODA for the first kind of g.4.4 simulation in which the proposed adjustment points (#60 and #80 points) are applied: (**a**) rotor unbalance amplitude of #3 disc; (**b**) rotor unbalance angle of #3 disc; (**c**) rotor unbalance amplitude of #4 disc; (**d**) rotor unbalance angle of #4 disc. two discs and the four bearings are utilized and #20, #40, #60, and #80 points are used as the respective adjustment points in order to obtain good identification results. The curves for the identification errors, which were obtained when the sensor resolutions were 0.1 nm, 1 nm, 0.1 um, and 1 um, are shown in Figures 21-24. According to the figures, the identified rotor unbalance changes with the rotating frequencies and there are several peak values for the identified rotor unbalance. The results are as follows:  
(1) Sensor resolution of 0.1 nm  
According to Figure 21, for #1 disc, the peak values of the amplitude of the identified rotor unbalance are 10.84%, 2.02%, 0.31%, and 0.42% at frequencies of 1 Hz, 271 Hz, 643 Hz, and 1267 Hz, respectively. The peak values of the absolute error for the angle are 2.12\({}^  
respectively. The peak values of the absolute error for the angle are 16.259\({}^{\circ}\), 1.88\({}^{\circ}\), 1.39\({}^{\circ}\), and 4.15\({}^{\circ}\) at 269 Hz, 645 Hz, 809 Hz, and 1265 Hz, respectively. Figure 21: Identified rotor unbalance changing with frequency in g1.4 using a 0.1 nm resolution: (**a**) obtained rotor unbalance amplitude; (**b**) obtained rotor unbalance angle. Figure 22: Identified rotor unbalance changing with frequency in g1.4 using a 1 nm resolution: (**a**) obtained rotor unbalance amplitude; (**b**) obtained rotor unbalance angle. Figure 23: Identified rotor unbalance changing with frequency in g1.4 using a 0.1 um resolution: (**a**) obtained rotor unbalance amplitude; (**b**) obtained rotor unbalance angle. Figure 24: Identified rotor unbalance with frequency in g1.4 using a 1 um resolution: (**a**) obtained rotor unbalance amplitude; (**b**) obtained rotor unbalance angle. 2. Sensor resolution of 1 nm According to Figure 22, for #1 disc, the peak values of the amplitude of identified rotor unbalance are 83.36%, 1.92%, 0.31%, and 0.42% at frequencies of 1 Hz, 269 Hz, 643 Hz, and 1267 Hz, respectively. The peak values of the absolute error for the angle are 8.7\({}^{\circ}\), 1.45\({}^{\circ}\), 0.32\({}^{\circ}\), and 0.32\({}^{\circ}\)at 1 Hz, 271 Hz, 645 Hz, and 1267 Hz, respectively. For #2 disc, the peak values of the amplitude of identified rotor unbalance are 95.6%, 42.54%, 4.33%, and 1.42% at frequencies of 1 Hz, 269 Hz, 645 Hz, and 1263 Hz, respectively. The peak values of the absolute error for the angle are 32.5\({}^{\circ}\), 8.6\({}^{\circ}\), and 0.8\({}^{\circ}\) at 1 Hz, 267 Hz, and 1265 Hz, respectively. For #3 disc, the peak values of the amplitude of identified rotor unbalance are 242.24%, 257.23%, 11.64%, and 20.64% at frequencies of 1 Hz, 269 Hz, 645 Hz, and 1265 Hz, respectively. The peak values of the absolute error for the angle are 108.42\({}^{\circ}\), 57.41\({}^{\circ}\), 11.72\({}^{\circ}\), and 7.76\({}^{\circ}\)at 1 Hz, 271 Hz, 645 Hz, and 1267 Hz, respectively. For #4 disc, the peak values of the amplitudes of identified rotor unbalance are 17.48%, 6.46%, 0.82%, 0.66%, and 7.61% at frequencies of 1 Hz, 267 Hz, 645 Hz, 809 Hz, and 1267 Hz, respectively. The peak values of the absolute error for the angle are 165.08\({}^{\circ}\), 16.25\({}^{\circ}\), and 4.15\({}^{\circ}\)at 1 Hz, 269 Hz, and 1265 Hz, respectively.