## 4 Results and Discussions
### Comparison of the Deviation of the Computed Demands  
The deviation between the seismic demands by different IGM selection procedures and the benchmark demands was calculated to quantitatively compare the reliability and reasonability of the seismic demands of NLRHA with a diverse selection of IGMs. The deviation \(\delta_{N}^{ij}\) shows the relative difference between the benchmark demands of motion set \(j\) and demands computed using IGMs from IGM selection method \(N\) at the \(i\)th story, respectively, which are calculated as:  
\[\delta_{N}^{ij}=\left|\frac{d_{N}^{ij}-\overline{d^{ij}}}{\overline{d^{ij}}} \right|\times 100\% \tag{12}\]  
where \(N\) is the IGM selection methods, namely the MGMS method, UW-CM method and VW-CM method; \(d_{N}^{ij}\) is the \(i\)-th story's seismic demands calculated using IGMs selected by method \(N\) for motion set \(j\); \(\overline{d^{ij}}\) is the benchmark demands \(i\)th story for motion set j, which are the means demand of NLRHA with all IGMs of the set. The statistics of the deviations are presented using box plots in Figure 8. Deviations of MGMS procedure and CM procedures are compared for motion sets containing seed IGMs selected and scaled concerning design spectra and conditional mean spectra. For each plot, the highest and lowest edges of the cirrus stand for the largest and lowest deviation. The horizontal axial value of the line inside the box is the mean deviation. The horizontal axial values of the upper and lower box edges are the deviation value of 75 th and 25 th percentiles, respectively. The mean deviation value shows the reliability of the IGM selection procedure. Additionally, as the smaller the difference between the 75 th percentile deviation and 25 th percentile deviation (75 th-25 th deviation difference) is, the trend of distribution of computed seismic demands along the height of the structure is closer to that of the benchmark seismic demands. Therefore, the 75 th-25 th deviation difference reveals the reasonability of the IGMs selected by the different selection methods. Comparing the mean deviation of the seismic demands, it is evident that the MGMS-IGMs and VW-CM-IGMs can achieve a much lower mean deviation than that of the UW-CM selected IGMs, except for computing shear forces with IGMs selected with DSs being the target spectra. Therefore, the reliability of NLRHA with UW-CM-IGMs is lower than that of NLRHA with IGMs chosen by the other two IGM selection methods. The mean deviation of seismic deformation, including inter-story drift ratio and floor displacement, by MGMS-IGMs and VW-CM-IGMs is similar when using the DS as the target spectra. Meanwhile, a more than 27% lower mean deviation of seismic deformation by IGMs selected by MGMS procedure is noticed when selecting and scaling IGMs referring to CMSs. Considering the seismically induced forces, the MGMS selected IGMs, and the VW-CM selected IGMs have a higher mean deviation of shear force and bending moment, respectively, but the difference is insignificant. The 75 th-25 th deviation difference of most seismic demands of the UW-CM method is much higher than that of MGMS and VW-CM methods, indicating lower reasonability of the UW-CM selected IGMs. Comparing the 75 th-25 th deviation difference of seismic deformation of the VW-CM and MGMS methods, it is found that the deviation difference of the MGMS procedure is over 38% and 54% lower than that of the VW-CM method when the target spectrum is DSs and CMSs, respectively. Compared with the VW-CM method, the MGMS procedure tends to have a slightly lower and higher 75 th-25 th deviation difference of seismically induced forces, when the target spectra for selecting and scaling the IGMs are DSs and CMs, respectively. Based on the comparison of deviation of the computed demands, it is clear that considering the modal contribution in the IGM selection procedure, the VW-CM procedure can select more reliable and reasonable IGMs, compared with the UW-CM procedure.