## 3 Numerical Simulations and Discussion
### Effect of Sensor Resolution  
#### 3.4.1 Results  
The unbalance responses calculated by CRDAM contaminating three kinds of typical sensor resolution, which are 0.1 mn, 1 nm, and 1 um, respectively, are the input data to the two algorithms  
Figure 7: Statistical results of the amount of the frequencies, at which the related error is less than 10%: (**a**) #1 bearing; (**b**) #2 bearing; (**c**) #3 bearing; (**d**) #4 bearing; (**e**) #5 bearing; (**f**) #6 bearing; (**g**) #7 bearing; (**h**) #8 bearing. Figure 8: _Cont._  
Figure 8: Statistical results of the amount of the frequencies, at which the related error is less than 10% or the absolute value is less than 10: (**a**) #1 bearing; (**b**) #2 bearing; (**c**) #3 bearing; (**d**) #4 bearing; (**e**) #5 bearing; (**f**) #6 bearing; (**g**) #7 bearing; (**h**) #8 bearing. Figure 9: _Cont._  
Simulations Results Based on Algorithm I  
According to Figure 7, the following can be obtained. 1. 0.1 nm resolution. Most identification errors of the main stiffness coefficients are smaller than 10% and there are some identification errors of the main damping coefficients smaller than 10%. In the x direction, the amounts of LEFPs of k1.xx, k2.xx,..., k8.xx are 1000, 999, 999, 998, 992, 993, 996 and 1000, respectively. While for c1.xx, c2.xx,..., c8.xx, the amounts are 885, 494, 433, 455, 347, 451, 499 and 929, respectively. In the y direction, there are 1000, 999, 999, 995, 995, 996, 998 and 1000 LEFPs of k1.yy, k2.yy,..., k8.yy, respectively. While for c1.yy, c2.yy,..., c8.yy, the amounts are 882, 472, 407, 437, 288, 457, 487 and 931, respectively. (2) 1 nm resolution. Most identification errors of the main stiffness coefficients are smaller than 10%. Some identification errors are smaller than 10% for the main damping coefficients. Figure 9: Statistical results of the amount of the frequencies, at which the related error is less than 10% or the absolute value is less than 10: (**a**) #1 bearing; (**b**) #2 bearing; (**c**) #3 bearing; (**d**) #4 bearing; (**e**) #5 bearing; (**f**) #6 bearing; (**g**) #7 bearing; (**h**) #8 bearing. In the x direction, the amounts of LEFPs of k1.xx, k2.xx,..., k8.xx are 999, 994, 992, 987, 979, 982, 986 and 996, respectively. While for c1.xx, c2.xx,..., c8.xx, the amounts are 886, 495, 437, 460, 331, 452, 497 and 920, respectively. In the y direction, there are 999, 993, 989, 984, 983, 985, 990 and 996 LEFPs of k1.yy, k2.yy,..., k8.yy, respectively. While for c1.yy, c2.yy,..., c8.yy, the amounts are 878, 471, 421, 51, 296, 447, 484 and 924, respectively. 1 um resolution. Most identification errors of the main stiffness coefficients are smaller than 10%. While for the main damping coefficients, only some identification errors are smaller than 10%. In the x direction, the amounts of LEFPs of k1.xx, k2.xx,..., k8.xx are 927, 758, 681, 615, 462, 494, 588 and 835, respectively. While for c1.xx, c2.xx,..., c8.xx, the amounts are 457, 143, 87, 68, 13, 27, 38 and 500, respectively. In the y direction, there are 927, 765, 686, 615, 435, 477, 596 and 831 LEFPs of k1.yy, k2.yy,..., k8.yy, respectively. While for c1.yy, c2.yy,..., c8.yy, the amounts are 455, 134, 84, 64, 18, 13, 32 and 495, respectively. Other simulations results are obtained as follows. 1. The maximum relative error of the identified coefficient is very big and it appears at low frequency. 2. The main stiffness coefficients cannot be identified at 1 Hz when 1 nm resolution is used and the main stiffness coefficients cannot be identified from 1 to 33 Hz when 1 um resolution is applied. Similar results can be obtained from the simulations of g1.4 and g1.1, whose results are shown in Figures A1-A8 in Appendix A.  
Simulations Results Based on Algorithm II  
According to Figure 8, the following can be obtained. 1. 0.1 nm resolution. Most of the identification errors of the main stiffness coefficients are smaller than 10%, but there are only several identification errors smaller than 10% for the main damping coefficients.