# Research on an Evaluation Method of Snowdrift Hazard for Railway Subgrades
## 2 Methods
### Establishment of the FCE Model  
The FCE model establishes the process introduced in [14] based on a five-step process. 1. Step 1: Establish the factor set, U. It can be determined that snowdrift on railway subgrades is primarily influenced by factors such as maximum wind speed, snowfall amount, average snow depth, and embankment height. Based on preliminary analysis and considering the comprehensive assessment of contributing factors to existing risk evaluations, four main indicators were ultimately selected: on-site environmental characteristics, on-site snowfield characteristics, on-site windfield characteristics, and subgrade design parameters, denoted as U1, U2, U3, and U4, respectively. Based on these main indicators, 11 secondary indicators were further divided, denoted as U1i, U2j, U3k, and U4l, corresponding to their respective main indicators. Thereby, a risk assessment system for snowdrift disasters on railway subgrades was established (Figure 2). Figure 2: Analytic Hierarchy Process (AHP) model. Step 2: Establish the annotation set V  
The hazard level is an index used to assess the risk level of snowdrift disasters. In order to provide a more comprehensive evaluation of the risk levels of snowdrift disasters, this paper, based on an extensive literature review and expert opinions, categorizes the hazard levels of snowdrift disasters on railway subgrades into five levels. \[V=\{V_{1},V_{2},V_{3},V_{4},V_{5}\}=\{\text{I},\text{II},\text{III},\text{IV}, \text{V}\} \tag{1}\]  
where \(V\) is the set of evaluation comments and \(V_{i}(i=1,2,3,\ldots,l)\) represents the overall evaluation of the \(i\)-th possibility. A level I risk grade indicates a low risk of snowdrift disasters occurring on the railway subgrade; a level II risk grade indicates a relatively low risk of snowdrift disasters; a level III risk grade indicates a moderate risk of snowdrift disasters; a level IV risk grade indicates a high risk of snowdrift disasters; and a level V risk grade indicates a very high risk of snowdrift disasters on the railway subgrade. After summarizing and generalizing the research findings of scholars at home and abroad, and combining extensive field research, expert brainstorming, experiments, and the conclusions of numerical simulations, the paper has provided the range of values for each secondary influencing factor and the indicators of these factors in Table 1.  
3. Step 3: Determine the weight vector W.  
The weight of risk factors measured by the hierarchical analysis (AHP) method can be attributed to the quantitative and qualitative analysis and the quantification of the constructed hierarchical model. The evaluation exponential weight vector is determined as shown in Formulas (2)-(4). The importance of evaluation indicator factors is represented by solving the eigenvector of the judgment matrix. This paper mainly introduces the method of calculating the eigenvector using the product method, as follows. (1) Normalize the column elements of the matrix  
\[\overline{u}_{ij}=\frac{u_{ij}}{\sum\limits_{i=1}^{n}u_{ij}} \tag{2}\]
2. Sum the elements of each normalized column \[\overline{W}_{i}=\sum\limits_{j=1}^{n}\overline{u}_{ij}\] (3)
3. Normalize the vector \(\overline{W}=\left(\overline{W}_{1},\overline{W}_{2},\cdots,\overline{W}_{n} \right)^{\text{T}}\) obtained from the previous step \[W_{i}=\frac{\overline{W}_{i}}{\sum\limits_{i=1}^{n}\overline{W}_{i}}\] (4)  
Through Equations (2)-(4), the eigenvector \(W=\left(W_{1},W_{2},\cdots,W_{n}\right)^{\text{T}}\) of the corresponding judgment matrix, i.e., the weight value of each evaluation indicator, can be obtained. 4. Step 4: Calculate the single-factor membership degree  
Since the fuzzy statistical method requires large sample data statistics, the process is relatively complex and difficult to implement. Therefore, this paper will select an appropriate fuzzy distribution as the membership function for the evaluation index and use the fuzzy distribution method for calculation.