## 3 Results and Discussion
### Effect of Double Uncertainties  
In the generator rotor system, uncertainty may not occur alone. Thus, the uncertain gravity responses with double uncertainties are analyzed in this section. Firstly, to validate the accuracy and efficiency of the proposed method, the case with uncertainties in both the bearing's stiffness and Young's modulus is analyzed by the proposed method and the scanning method. The deviations in the bearing's stiffness and Young's modulus are 10% and 5%, respectively. Thus, the corresponding interval variables are \(\varepsilon_{k}^{I}=\left[4.5\times 10^{8},5.5\times 10^{8}\right]\) N/m and \(\varepsilon_{E}^{I}=\left[199.5,220.5\right]\) GPa, respectively. The number of samples in the application of the scanning method is 2500. The number of samples when adopting a 10-order CIM is 121.  
Figures 8 and 9 show the uncertain gravity response amplitude versus rotational speed by using the scanning method and the proposed method, respectively. As shown in Figure 8, at the antiresonance position (near 1500 rpm), unexpected spurious oscillation can be found. It means that the scanning method with 2500 samples cannot give an accurate estimation of the uncertain gravity response with double uncertainties. To gain a better evaluation of the uncertain response, more samples are needed, which shows the drawback of the scanning method. As shown in Figure 9, a good agreement can be seen between the bounds obtained by the proposed method and the scanning method. Fewer samples in the proposed method can give more smooth results than those in Figure 8, which shows the  
Figure 7: The bounds of uncertain gravity response versus rotational speed by the CIM with a 5% deviation in density.  
efficiency and the accuracy of the proposed method. It can be found that the bounds influenced by two uncertainties are wider than those influenced by each of them individually.  
Figure 10 shows the uncertain gravity response amplitudes versus rotational speed with uncertainties in the Young's modulus and density. The deviations in Young's modulus and density are both equal to 5%, which means \(\varepsilon_{E}^{I}=[199.5,220.5]\) GPa and \(\varepsilon_{p}^{I}=[7410,8190]\) kg/m\({}^{3}\). The number of samples used in the proposed method is equal to that of the last case. Unlike the results shown in Figure 9, the uncertainties in [PERSON]'s modulus and density lead to two obvious local large-amplitude bands in the third resonance peak. Comparing with the results shown in Figures 6 and 7, the first local large-amplitude band is dominated by Young's modulus, and the second one is dominated by density. Moreover, two local small-amplitude bands in the antiresonance peak can be found. The first and the  
Figure 8: The bounds of uncertain gravity response versus rotational speed by the scanning method with a 10% deviation in bearing’s stiffness and a 5% deviation in [PERSON]’s modulus.  
Figure 9: The bounds of uncertain gravity response versus rotational speed by CIM with a 10% deviation in bearing’s stiffness and a 5% deviation in Young’s modulus.  
second local small-amplitude bands are dominated by density and Young's modulus, respectively. As can be seen in the above analysis, the uncertain gravity responses of the generator rotor system with different types of double uncertainties are different from each other.