# Explainable Machine-Learning Predictions for Peak Ground Acceleration
## 3 Establishment of the Machine Learning Model
### Feature Selection  
The main factors that influence the site amplification effect include three aspects. One is the ground motion characteristics, including amplitude, spectral characteristics and duration. Another one is site characteristics, such as site class, the equivalent shear wave velocity of the site, the thickness of the overburden layer, and the site's fundamental period. The third one is soil layer characteristics, including physical properties, shear wave velocity, and depth of soil. In this paper, PBA and FP were selected to describe the characteristics of the input ground motion, and there are many parameters used to describe the site characteristics. For example, for the description of the equivalent shear wave velocity of the site, there are not only the equivalent shear wave velocity (\(V_{\text{se}}\)) commonly used for site classification in Chinese code, but also the average shear wave velocity within 20 m and 30 m below the site surface (\(V_{\text{s20}}\) and \(V_{\text{s30}}\)). We use these factors as original input features and perform feature selection to select features that have a greater influence on the model. The following 11 factors are initial input features:  
(1) Peak Bedrock Acceleration (PBA/g). (2) Predominant Frequency (FP/Hz): Input the predominant frequency corresponding to the Fourier spectrum of the seismic acceleration time history. (3) Site Fundamental Period (SFP/s): The calculation formula is given in Equation (8) [44]:  
\[T=\sum_{i=1}^{N}\frac{4h_{i}}{v_{i}}, \tag{8}\]  
where \(T\) is the basic period of the site; \(h_{i}\) and \(v_{i}\) are the thickness and the shear wave velocity, respectively, of the \(i\)th soil layer; and \(N\) is the total number of calculated soil layers. (4) Overburden Thickness (OBT/m): This is determined according to the OBT in the site classification in \"GB 50011-2010: Code for seismic design of buildings\" [41]. Generally, the OBT is the distance from the ground to the top of the soil layer with shear wave velocity greater than 500 m/s and the shear wave velocity of each underlying layer of rock and soil is not less than 500 m/s. (5) The depth of the soil when the shear wave velocity reaches 800 m/s (D800/m): For the section where the shear wave velocity of the soil layer is less than 800 m/s, the buried depth of the ground motion input surface is taken as D800. (6) Profile Depth (Depth/m): This is the buried depth of the downhole recorder. (7) Surface shear wave velocity (Surface \(V_{\text{s}}\)/(m/s)): This is the shear wave velocity where the uppermost layer of the site is located. (8) Bedrock shear wave velocity (Bedrock \(V_{\text{s}}\)/(m/s)): This is the shear wave velocity of the bedrock where the input ground motion is located. (9) Equivalent shear wave velocity (\(V_{\text{se}}\)/(m/s)): This is determined according to the calculation formula of equivalent shear wave velocity in site classification in \"GB 50011-2010: Code for seismic design of buildings\" [41]. Its calculation formula is given in Equation (9):  
\[V_{\text{se}}=\frac{d_{0}}{\sum\limits_{i=1}^{n}(d_{i}/v_{\text{si}})}, \tag{9}\]where \(d_{0}\) is the smaller value between OBT and 20 m, \(d_{\text{i}}\) and \(v_{\text{si}}\) are the thickness and shear wave velocity of soil layer \(i\) within the \(d_{0}\), respectively, and \(n\) is the number of layers of soil layer within the \(d_{0}\). (10) Average shear wave velocity within 20 m below the site surface (\(V_{\text{s20}}\)/(m/s)): According to the previous numerical simulation and measured records, the amplification effect of the site is mainly reflected in the upper soil layer, and the soil structure near the surface has a great influence on the amplification effect. When the depth of the borehole and wave velocity measurement is less than 20 m, it can be calculated according to the velocity extrapolation formula established by [PERSON] et al. [45].