## 4 Development of LR Liquefaction Probability Model
### Feature Selection and Parameter Setting  
In constructing the model, \(V_{s}\) serves as the primary parameter for the liquefaction assessment, necessitating the inclusion of suitable auxiliary parameters to ensure the method's efficacy. This study employs machine learning techniques to identify the key parameters. Specifically, the random forest feature importance ranking algorithm in MATLAB evaluates the significance of various parameters influencing earthquake-induced liquefaction.  
Feature importance measures the extent to which each parameter influences the liquefaction outcome and its contribution to the model's predictive performance. In this study, feature importance is calculated based on the Out-of-Bag (OOB) error. The OOB data refer to the approximately one-third of the data that are not used in the construction of a decision tree during the bootstrap sampling. These data are used to calculate the model's prediction error rate, known as the OOB error.  
Specifically, feature importance is determined by randomly permuting the values of a feature \(X\) in the OOB data and calculating the resulting increase in the prediction error for each tree. The average of these increases is then divided by the standard deviation of the entire ensemble to compute the importance value of the feature. In summary, the feature  
Figure 6: Flowchart of the construction process.  
importance is estimated based on the change in the OOB error before and after introducing noise to the feature values in the OOB data.  
The analysis encompassed all the collected independent variables, including \(V_{s}\), \(V_{s1}\), \(V_{s1,cs}\), groundwater level (\(d_{w}\)), \(CSR\), \(CSR_{7.5}\), peak ground acceleration (\(a_{\text{max}}\)), \(M_{W}\), \(FC\), depth (Z), vertical total stress (\(\sigma_{\text{v}}\)), and \(\sigma_{\text{v}}\)', with the liquefaction outcomes as the dependent variable. The raw data were cleaned and normalized, with any duplicates being checked and removed. The parameters such as \(a_{\text{max}}\) and \(CSR\) were recalculated and validated. Additionally, the missing values of various feature parameters were compared and addressed. The final parameter importance ranking, illustrated in Figure 7, highlights that \(FC\) is the most critical parameter, followed by those representing the site's seismic intensity.  
The ranking of certain similar parameters in Figure 7 requires careful differentiation. For example, although parameters such as \(V_{s}\), \(V_{s1}\), and \(V_{s1,cs}\) may have reduced individual importance due to their similar mechanisms, it is more critical to compare the importance among these primary parameters than to compare them with other distinct parameters. Similarly, the primary parameters representing seismic intensity (\(a_{\text{max}}\) and \(CSR\)) and the auxiliary parameters representing depth and groundwater level should be analyzed using the same approach. Therefore, the impact of the parameters' similarity on their importance needs to be discerned through engineering experience. Based on these findings, \(V_{s1}\), \(CSR_{7.5}\), \(M_{W}\), \(Z\), and \(FC\) were selected as the parameters for the liquefaction probability model.  
Among these parameters, the fines content (\(FC\)) has garnered significant attention in recent liquefaction studies. Researchers have widely recognized the influence of fines content on liquefaction and have incorporated this parameter into the development of liquefaction probability assessment methods in recent years [15; 28]. This paper confirms the critical impact of fines content on liquefaction assessment from a statistical data analysis perspective.