## 2 Methodology Framework
### Finite Element Model  
This paper focuses on the prediction of seismic damage for multi-story RC frame buildings. In order to build a training set for the MI-CNN model, 40 building models with different attribute data, including 10 fundamental periods (0.1-1 s) and 4 seismic fortification levels (levels 6, 7, 8, and 9), were set up. The aforementioned 40 building models with different attribute data are modeled using a nonlinear multi-degree-of-freedom (MDOF) shear model, as shown in Figure 3a. This model concentrates the mass of each story in a mass point and adjacent stories are connected by shear springs, which can reflect the nonlinear seismic performance of multi-story RC frame buildings [26]. The fundamental period of a building will change when entering nonlinear state. Nevertheless, the extent of fundamental period variation is difficult to characterize, which can be influenced by many factors, such as the intensity of a ground motion and the seismic performance of a building. In this study, the fundamental period of a building in the elastic state is used to characterize the elastic property of a  
Figure 2: Schematic diagram of the MI-CNN model. building. According to Chinese code [27], the elastic fundamental period is proportional to the number of stories (Equation (1) [27]), which can be used to predict the fundamental period of low- to mid-rise buildings. The damping ratio of the building model is taken as 0.05 [27]. \[T_{1}=0.1\ n \tag{1}\]  
where \(T_{1}\) is fundamental period (unit: s) and \(n\) is the number of stories. The story mass is determined based on the area of each story \(A_{1}\) and the mass per unit area \(m_{1}\) (Equation (2)), and the international unit is adopted for all the following equations. \(m_{1}\) can be estimated according to the occupancy of each story. In this study, the \(A_{1}\) and \(m_{1}\) were set to 1000 m\({}^{2}\) and 1000 kg/m\({}^{2}\) for all building models. \[m=m_{1}A_{1} \tag{2}\]  
The stiffness of each story is assumed uniformly distributed along the height. Given the fundamental period \(T_{1}\) and the mass of each story, the shear stiffness \(k\) of each story can be calculated through modal analysis. From the above procedure, the elastic parameters of a MDOF model can be obtained. Although only the fundamental period \(T_{1}\) is used to determine the elastic parameters, the MDOF model can consider a higher mode vibration. Moreover, considering that the elastic performance of low- to mid-rise buildings is primarily controlled by the fundamental period \(T_{1}\), it is also adopted as a building attribute for the following machine learning model. The MDOF model can also capture the nonlinear performance of RC frame buildings. The tri-linear backbone curve model, as shown in Figure 3b, is adopted to simulate the seismic capacity of each story. The yield strength \(V_{\text{d}}\) and peak strength \(V_{\text{p}}\) of each story of a building can be determined by Equations (3) and (4). \[V_{\text{y}}=\Omega_{1}V_{\text{d}} \tag{3}\]  
\[V_{\text{p}}=\Omega_{2}V_{\text{d}} \tag{4}\]  
\[\Omega_{2}=K_{1}K_{2} \tag{5}\]  
\[K_{1}=0.1671 FL^{2}-3.1062 FL+16.399 \tag{6}\]  
\[K_{2}=1-(0.0099n-0.0197) \tag{7}\]  
where \(V_{\text{d}}\) is the design shear force, which can be calculated through the equivalent static load method [22]. \(\Omega_{1}\) and \(\Omega_{2}\) are yield and peak overstrength ratios of RC frame, respectively, and the \(\Omega_{1}\) is set to 1.1 [26] and \(\Omega_{2}\) can be calculated through Equations (5)-(7). \(FL\) and \(n\) are the fortification level and the number of stories. Equations (6) and (7) were obtained through the statistical analysis of 155 pushover results of RC frames designed following the Chinese seismic design code [22]. More details on the MDOF shear model can be found in the former study of [PERSON] et al. [26]. Five damage states were adopted, which are none, slight, moderate, extensive, and complete damages. The damage state of each story was determined according to the damage limits shown in Figure 3b.