Spatial prediction of the geological hazard vulnerability of mountain road network using machine learning algorithms

Abstract

The current assessment index of the geological hazard vulnerability assessment for mountain road network is relatively simple, and the assessment methods used are subjective, complex, and inefficient. This study proposes a prediction model for geological hazard vulnerability assessment of mountain road network incorporating machine learning algorithms. First, based on the quantification of the characteristics of the mountain road network and the local rescue forces, an objective and reasonable index-based system of vulnerability assessment of the mountain road network was constructed by combining the population, economic, and material factors. Second, the FAHP and AHP-TOPSIS were applied for the development of the vulnerability assessment models to carry out the preliminary vulnerability assessment for different road types. Third, the results of the preliminary vulnerability assessment were used as the sample set to build a road vulnerability prediction model using SVM, RF, and BPNN algorithms. Finally, the five-fold cross-validation and statistical parameter accuracy analysis were conducted to determine the most reasonable model with the highest prediction accuracy for geological hazard vulnerability mapping of the mountain road network. The results indicated that the vulnerability prediction model based on the FAHP sample set using the RF algorithm demonstrated the highest accuracy and robustness.

Keywords:

• Mountain roads
• road network features
• machine learning
• vulnerability mapping

1. Introduction

Due to the complex geological environment, human activities, and extreme climatic conditions, geological hazards such as landslides and debris flows frequent occur around mountain roads, seriously threatening road safety and human life. Therefore, it is important to conduct a risk assessment of geological hazards for mountain roads.

At present, several studies on vulnerability and risk assessment for roads have been conducted globally. Alsabhan et al. (2022) performed a landslide susceptibility mapping of roads within the Himalayas based on the comparison of the accuracy of the three methods, namely, weights of evidence, information value, and frequency ratio. Kadi et al. (2021) conducted the analysis and discussion of the best routes for forest roads in the Macka region of Turkey based on the landslide susceptibility mapping. Saravanan et al. (2021) extracted eight factors influencing landslides, and then performed landslide susceptibility mapping for the NH67 road in India using the frequency ratio method (Zayed et al. 2008).

However, the vulnerability assessment of roads involves a broad range of complex influencing factors and cross-cutting disciplines. Therefore, there are only a few research studies on the geological hazards vulnerability assessment of road, which can be mainly divided into the analysis of population vulnerability (Maletta and Mendicino 2022; Zhang et al. 2014) and economic and physical vulnerability (Eidsvig et al. 2014; Hearn and Pongpanya 2021). Moreover, most of these studies only use the possible casualties and direct losses resulting from geological hazards as the vulnerability assessment index. On the whole, the assessment factors used were oversimplified is one of the main problems that need to be solved in geological hazard vulnerability assessment of road.

The construction of the index-based system for assessing vulnerability and the selection of the vulnerability assessment model are the two most important steps in the vulnerability assessment for mountain roads. Among them, the selection of assessment indices has a great influence on the reliability of geological hazards vulnerability assessment of roads. As an important component of the transportation system, the major function of the road is to ensure the normal passage of vehicles. Therefore, the process of selection of factors influencing the vulnerability assessment for the road should initially focus on the characteristics of the road itself and the local disaster relief capacity and then combine them with the local population, economy, material, and other quantitative assessment indices to construct the most suitable index-based assessment system for the vulnerability assessment of mountain road network (Ahmad et al. 2022; Saleh et al. 2022; Sitti et al. 2022).

The assessment methods in the recent road vulnerability studies are mostly based on expert qualitative methods. For example, Zhang et al. (2020) established the Analytical Hierarchy Process (AHP) based on certain assessment factors to analyze the vulnerability of the road network in Oahu, Hawaii. Some researchers (MartínezCarvajal et al. 2018; Petrucci and Gullà 2010) applied mathematical methods in combination with the assessment factors to define landslide susceptibility in a relevant manner and performed the susceptibility zoning calculations for the study area. Although these studies have promoted the development of road vulnerability research to a certain extent, the assessment results of the above studies have the limitation of being strongly subjective. Among them, the selection of evaluation factors and the determination of weights rely on expert rating or empirical formulas, which not only amplify the uncertainty of the assessment, but also tend to be less efficient when dealing with complex data. It has been demonstrated that using algorithm design, and machine learning techniques can be trained to learn from sample data for the assessment of target regions without expert-developed weights, thus, helping in overcoming this limitation.

Over the past 20 years, machine learning techniques have developed rapidly. As an efficient prediction method, machine learning techniques have evolved from initial research in the laboratory to its use in a wide range of commercial applications (Jordan and Mitchell 2015). Especially in the field of susceptibility assessment of geological hazards, machine learning algorithms have gradually become widely accepted assessment models. These mainly include support vector machine models (Chen et al. 2017; Marjanovi et al. 2011; Zhou et al. 2018), logistic regression models (Ayalew and Yamagishi 2005; Bai et al. 2010; Umar et al. 2014), random forest models (Chen et al. 2018; Hong et al. 2016; Kim et al. 2018), artificial neural networks (Pradhan and Lee 2010a; Pradhan and Lee 2010b; Pradhan et al. 2010; Xu et al. 2015), and deep learning algorithms such as multilayer perception models, deep neural networks, and recurrent neural network models (Dong et al. 2020; Lv et al. 2022; Mandal et al. 2021). In addition, many researchers have made successful attempts toward developing machine learning with combinatorial optimization. For example, combined model based on fuzzy theory (Chen et al. 2017), combined model based on random forests (Qiu et al. 2017), and combined model based on heuristic algorithms. The fact that such a large number of studies on geological hazards have been conducted using machine learning models confirms the advantages of machine learning models. However, challenges still exist regarding how machine learning models can be better applied to the vulnerability assessment of geological hazards.

In this context, this study proposed to develop an efficient, objective, and reasonable method for predicting the geological hazards vulnerability of mountain roads. Firstly, based on the targeted construction of the index-based system of vulnerability assessment of the mountain road network, the preliminary vulnerability assessment of the mountain roads was completed. Then, the preliminary results were used as the sample set to construct a road vulnerability prediction model using several machine learning algorithms. Finally, the model with the highest prediction accuracy was selected to complete the geological hazards vulnerability of mountain road network.

2. Study area

Three distinct road levels were chosen in this study, which included two national roads, three provincial roads, and three county roads, with a total length of 432.479 km, as shown in Table 1.

Table 1. Research road network basic information.

Number	Grade	Length (km)	Number	Grade	Length (km)
G235	National road	91.637	G534	National road	63.627
S215	Provincial road	54.600	S304	Provincial road	36.827
S308	Provincial road	51.095	X731	County road	27.971
X737	County road	28.676	X738	County road	28.046

The road network selected for this study is located in Youxi County, Central Fujian Province, east of Sanming City, China (Figure 1). The geomorphology of the study area is complicated and diverse due to neotectonic uplift, intense erosion, and the cutting effect of flowing water. The study area is characterized by several mountains, hills, basins, valleys, and narrow plains, with the mountains and hills making up around 93% of the entire area. The study area comprises many rivers, with a total watershed area of over 5,000 km² and a total river length of 202 km. The majority of the rock layers in the study area are covered by Quaternary residual soils, resulting in a wide distribution of soil-rock dual structure slope. Youxi County is located in the subtropics, and its climate is affected by alternating continental and oceanic climates, resulting in high precipitation, especially during the spring and summer seasons.

Figure 1. Location map of the study area.

Since the main object of this study is a road, a typical linear project with huge length-to-width ratio, the road is divided into an evaluation unit according to 0.5 km and a total of 758 units, of which the number of units occupied by Chinese roads, provincial roads and county roads are 304, 286 and 168 respectively.

3. Establishment of the index-based vulnerability assessment system

Several objects are threatened by geological hazards, and some of these objects change dynamically with time, such as the buildings in the study area. Meanwhile, different types of geological hazards affect some things differently, for example, a creeping landslide may cause a little damage to moving objects, such as humans, but sudden-onset landslides can be fatal to humans under certain circumstances. Therefore, it is not realistic to include all the objects that may be affected by the geological hazards in the index-based system of vulnerability assessment. When the assessment indices are selected, the objects in the study area that are most likely to be affected by the damage due to geological hazards should be chosen. Moreover, the problem of acquisition is also one of the factors to be considered, and assessment indices that are easy to develop and convenient to quantify should be selected. According to the obtained data and considering the situation in the study area, a hierarchical structure of vulnerability assessment of export network is constructed (Figure 3). Firstly, the vulnerability evaluation of road network was used as the target layer. Then the four major categories of road network characteristics, disaster relief capacity, population, economy and physical characteristics were identified as the criterion layer. Finally, three index factors were used to quantitatively evaluate each major category of the criterion layer, and thus an evaluation system based on 12 indexes was established.

Considering the obtained data and the situation in the study area, this research quantitatively evaluated the characteristics of the road network, disaster relief capacity, population, and economic and material characteristics of the study area and then used them as indices for the vulnerability assessment of the road network.

3.1. Road network characteristics

1. Road grade: The relative grade of the road was determined by the actual local situation based on the Design Specification for Highway Alignment.

2. Road width: Road width is one of the important indices of road capacity, and high-precision remote sensing image identification was used as the method in this study to obtain the road width.

3. Frequency of hidden danger exclusion: Hidden danger exclusion means arranging professional staff to conduct a comprehensive and detailed mapping and survey of the roads as well as the surrounding affiliated facilities, considering the characteristics of geological hazards and the actual situation of road traffic in the study area. This helps to accurately identify the road areas prone to landslides, mudslides, and other geological hazards so that government personnel can take practical and reliable measures for the management of hidden areas before the onset of geological hazards to ensure road safety.

3.2. Disaster relief capability

1. Detour Index: The detour index represents the difference between the detour path and the original travel path when a geological hazard occurs, and the vehicle can choose to bypass the road section affected by the geological hazard before the road is opened for traffic. In this study, the intersection of the boundary of the study area and the road network was defined as the ‘exit’. The road intersection was defined as the ‘node’. The section of road between two adjacent nodes or the road intersection near the exit was known as ‘road section’. As shown in Figure 2, the exits, nodes, and road sections together form the internal road network of the study area. The roads of the study area were divided into different assessment units based on certain road mileage, and the shortest path from the assessment unit to a certain exit was used as the travel path of the valuation unit. If the geological hazards damage the highway, the vehicle can bypass the section affected by the geological hazards to complete the passage of other paths called detour paths.

   In this study, the detour index for each assessment cell is defined as the ratio of the detour path of the road unit at each exit to the original travel path, as given by Equation (1)(1) $$C=\sum _{i=1}^m{C}_x=\sum _{i=1}^m\frac{D_x}{D_y}$$(1) .

(1) $$C=\sum _{i=1}^m{C}_x=\sum _{i=1}^m\frac{D_x}{D_y}$$(1)

where C_x represents the detour index of the road unit at exit x; D_y is the length of the original travel path; and D_x is the length of the detour path.

• Rescue index: If the geological hazards occur somewhere in the region and block or damage the highway, the rescue team starts from the nearest county and moves to the place affected by the geological hazards. If the affected place is far away from the nearest county, it takes a longer time for the rescue team to reach the disaster site. In this study, the rescue index is defined as the ratio of the rescue distance to the design speed of the rescue road.

(2) $$T=\frac{d}{v}$$(2)

where T is the rescue index, d is the rescue distance, and v is the design speed of the rescue road.

• Disaster relief equipment supplies: For geological disaster-prone areas, not only a good emergency plan is needed, but also special equipment to deal with geological disasters is essential. In this study, this index is defined as the density of disaster relief equipment. The following is the specific method of obtaining this index, based on the survey of the number of disaster relief equipped facilities in each township, the density of disaster relief equipped facilities in the study area was calculated by the density analysis tool in the ARCGIS, and the corresponding values were extracted to road units.

Figure 2. Original travel path and post-disaster detour path.

Figure 3. A hierarchical structure of vulnerability assessment of road network.

3.3. Population characteristics

This index usually represents the possibility of human casualties in the study area affected by the geological hazards and mainly reflects the resilience of humans to geological hazards in the study area. Based on the characteristics of the study area, three factors, namely, population density, education level, and age structure, were selected as the assessment indices of the population characteristics in the study area.

3.4. Economic and material characteristics

The economic losses caused by the geological hazards are huge. The economic losses can be divided into direct economic losses and indirect economic losses. The direct economic losses include damage to buildings, different equipment, and various production materials. In this study, the two indicators of per capita income and road maintenance cost were selected for economic vulnerability assessment. Meanwhile, material vulnerability leads to losses from damages to fixed structures, such as buildings and roads, during geological hazards. According to the collected information, the building density was selected as the indices of material vulnerability assessment.

Finally, according to the index-based system of road vulnerability assessment, a normalized decision matrix D, as shown below, was constructed. (3) $$D=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{1n}\\ a_{21}& a_{22}& \dots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{m1}& a_{m2}& \dots & a_{mn}\end{array}\right]$$(3) where a_mn represents the normalized value of the nth assessment index of the mth road unit.

4. Preliminary assessment of road vulnerability

4.1. Determination of weights using analytical hierarchy process

In this study, Analytical Hierarchy Process (AHP) was used to calculate the weights of each level of the index in the index-based system of vulnerability assessment. This process uses the 9-point scale proposed by Saaty (Table 2) to construct the judgment matrices for the criterion layer and the index layer and then obtains the comprehensive weights of each assessment index by the product method.

Table 2. Takes values using the 9-point scale.

Value	Explanation
1	The two factors are compared and have the same importance
3	Comparing the two factors, the former is slightly more important than the latter
5	Comparing the two factors, the former is significantly more important than the latter
7	Comparing the two factors, the former is strongly more important than the latter
9	Comparing the two factors, the former is extremely more important than the latter
2, 4, 6, 8	The intermediate value of the above adjacency judgment

As the AHP method is subjective, its judgment matrix was derived based on the data-fitting results of the index-based system of vulnerability assessment of roads, in combination with the opinions of relevant road engineering experts. All the elements in the pairwise comparison matrix passed the consistency test with a certain degree of rationality. The pairwise comparison matrix, the largest eigenvalue, and consistency ratio of layers are shown in Table 3, on this basis we can calculate the comprehensive weight (Table 4).

Table 3. The pairwise comparison matrix, factor weights.

	Pairwise comparison matrix
Criterion and index layers	[1]	[2]	[3]	[4]	Weights
Criterion layer
[1] Road network characteristics (B1)	1	1	3	7	0.416
[2] Disaster relief capability (B2)	1	1	2	6	0.362
[3] Population characteristics (B3)	1/3	1/2	1	3	0.164
[4] Economic and material features (B4)	1/7	1/6	1/3	1	0.058
${\lambda }_{\max }$=4.0157, CR = 0.0060
Index layer
Road network characteristics (B1)
[1] Road grade (C1)	1	4	3		0.634
[2] Road width (C2)	1/4	1	1		0.174
[3] Maintenance intervals (C3)	1/3	1	1		0.192
${\lambda }_{\max }$=3.0092, CR = 0.0088
Disaster relief capability (B2)
[1] Detour index (C4)	1	2	3		0.540
[2] Rescue distances (C5)	1/2	1	2		0.297
[3] Disaster relief equipment density (C6)	1/3	1/2	1		0.163
${\lambda }_{\max }$=3.0092, CR = 0.0088
Population characteristics (B3)
[1] Population density (C7)	1	7	6		0.764
[2] Education level (C8)	1/7	1	1		0.115
[3] Age structure (C9)	1/6	1	1		0.121
${\lambda }_{\max }$=3.0026, CR = 0.0025
Economic and material features (B4)
[1] Per capita income (C10)	1	1	4		0.458
[2] Road maintenance cost (C11)	1	1	3		0.416
[3] Building density (C12)	1/4	1/3	1		0.126
${\lambda }_{\max }$=3.0092, CR = 0.0088

Table 4. Comprehensive weight acquire via the AHP.

Criterion layer	Criterion layer weight W1	Index layer	Index layer weight W2	Comprehensive weight W3 = W1 × W2
B1	0.416	C1	0.634	0.264
		C2	0.174	0.072
		C3	0.192	0.081
B2	0.362	C4	0.540	0.195
		C5	0.297	0.108
		C6	0.163	0.059
B3	0.164	C7	0.764	0.125
		C8	0.115	0.019
		C9	0.121	0.020
B4	0.058	C10	0.458	0.025
		C11	0.416	0.024
		C12	0.126	0.008

At present, the AHP is widely used in risk assessment (Aminbakhsh et al. 2013), geological and environmental assessment (Cengiz and Ercanoglu 2022; Das et al. 2022), and group decision-making because of its simplicity of usage, computational efficiency, and generalizability to multilevel qualitative and quantitative data (Kahraman et al. 2004). However, the decision-makers simplify this strategy to reduce the complexity of the problem or based on the need, resulting in biased judgments. This can lead to a certain degree of inaccuracy and subjectivity in the assessment results, which is the major limitation of this method (Kahraman et al. 2003).

4.2. Determination of vulnerability assessment using FAHP

To overcome the shortcomings of the very subjective traditional hierarchical analysis method, the fuzzy mathematical theory was introduced in combination with the hierarchical analysis to develop Fuzzy-Analytical Hierarchy Process (FAHP). On this basis, the uncertainty in the preferences of decision-makers is quantified to achieve more flexibility in judgment and decision-making. FAHP retains the advantages of simplicity and efficiency of AHP, while the hierarchical structure obtained by this method is easy to decompose and perform a pairwise comparison (Feizizadeh et al. 2014). Moreover, it can reduce inconsistency and generate priority vectors, and reflects the human reasoning of applying approximate information and uncertainty for decision making.

In general, the vulnerability results are taken in the range of [0, 1], and the road network vulnerability assessment results were classified into five levels using the equivalence method (Table 5), i.e. very low, low, medium, high, and very high (Hoque et al. 2019; Tehrany et al. 2014).

Table 5. Vulnerability assessment of earthen sites of road.

Criteria	Very low	Low	Moderate	High	Very high
Scores of criteria	[0, 0.2]	(0.2, 0.4]	(0.4, 0.6]	(0.6, 0.8]	(0.8, 1.0]

In this study, the vulnerability assessment was determined using FAHP in three main steps, as given below:

• Step 1: Determination of the relative membership using the fuzzy set theory

  In the fuzzy set theory, the affiliation degree is used for expressing the fuzzy relation of elements belonging to a certain set, and the affiliation degree quantifies the uncertainty of the affiliation information by some specific functions. Therefore, a fuzzy set can be described as a set containing elements with varying degrees of membership in the set.

  The fuzzy relationship matrix R is represented as, (4) $$R=\left[\begin{array}{c}{R}_1\\ R_2\\ ⋮\\ R_m\end{array}\right]=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1n}\\ r_{21}& r_{22}& \cdots & r_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ r_{m1}& r_{m2}& \dots & r_{mn}\end{array}\right]$$(4)

  where R represents the membership of the ith index belonging to the jth rank. The membership function is established according to the characteristics of the index-based system. When the membership function is comparable to the assessment result, the triangular membership function can be selected, which has been successfully applied by Guo et al. (2017). The triangular membership function (Figure 4) was applied to structure the fuzzy set based on the criteria in Table 5, as represented by Equation (5)(5) $$\begin{array}{c}{r}_{i1}=\{\begin{array}{cc}\begin{array}{c}1\\ \frac{a-0.7}{0.2}\\ 0\end{array}& \begin{array}{c}a\ge 0.9\\ 0.7<a<0.9\\ a<0.7\end{array}\end{array}\\ r_{i2}=\{\begin{array}{cc}\begin{array}{c}0\\ \frac{0.9-a}{0.2}\\ \frac{a-0.5}{0.2}\\ 0\end{array}& \begin{array}{c}a\ge 0.9\\ 0.7\le a<0.9\\ 0.5\le a<0.7\\ a<0.5\end{array}\end{array}\\ r_{i3}=\{\begin{array}{cc}\begin{array}{c}0\\ \frac{0.7-a}{0.2}\\ \frac{a-0.3}{0.2}\\ 0\end{array}& \begin{array}{c}a\ge 0.7\\ 0.5\le a<0.7\\ 0.3\le a<0.5\\ a<0.3\end{array}\end{array}\\ r_{i4}=\{\begin{array}{cc}\begin{array}{c}0\\ \frac{0.5-a}{0.2}\\ \frac{a-0.1}{0.2}\\ 0\end{array}& \begin{array}{c}a\ge 0.5\\ 0.3\le a<0.5\\ 0.1\le a<0.3\\ a<0.1\end{array}\end{array}\\ r_{i5}=\{\begin{array}{cc}\begin{array}{c}1\\ \frac{0.3-a}{0.2}\\ 0\end{array}& \begin{array}{c}a\le 0.1\\ 0.1\le a<0.3\\ a\ge 0.3\end{array}\end{array}\end{array}\}$$(5) : (5) $$\begin{array}{c}{r}_{i1}=\{\begin{array}{cc}\begin{array}{c}1\\ \frac{a-0.7}{0.2}\\ 0\end{array}& \begin{array}{c}a\ge 0.9\\ 0.7<a<0.9\\ a<0.7\end{array}\end{array}\\ r_{i2}=\{\begin{array}{cc}\begin{array}{c}0\\ \frac{0.9-a}{0.2}\\ \frac{a-0.5}{0.2}\\ 0\end{array}& \begin{array}{c}a\ge 0.9\\ 0.7\le a<0.9\\ 0.5\le a<0.7\\ a<0.5\end{array}\end{array}\\ r_{i3}=\{\begin{array}{cc}\begin{array}{c}0\\ \frac{0.7-a}{0.2}\\ \frac{a-0.3}{0.2}\\ 0\end{array}& \begin{array}{c}a\ge 0.7\\ 0.5\le a<0.7\\ 0.3\le a<0.5\\ a<0.3\end{array}\end{array}\\ r_{i4}=\{\begin{array}{cc}\begin{array}{c}0\\ \frac{0.5-a}{0.2}\\ \frac{a-0.1}{0.2}\\ 0\end{array}& \begin{array}{c}a\ge 0.5\\ 0.3\le a<0.5\\ 0.1\le a<0.3\\ a<0.1\end{array}\end{array}\\ r_{i5}=\{\begin{array}{cc}\begin{array}{c}1\\ \frac{0.3-a}{0.2}\\ 0\end{array}& \begin{array}{c}a\le 0.1\\ 0.1\le a<0.3\\ a\ge 0.3\end{array}\end{array}\end{array}\}$$(5)

  where a is the element in the normalized decision matrix D of the index-based system of vulnerability assessment, $i\in 1,2,\dots ,m.$

• Step 2: The integrated weights calculated by AHP were inserted into the fuzzy assessment system, and the comprehensive assessment vector of the goal layer G was calculated, as provided by Equation (6)(6) $$G=w\times R=\left(w_1,w_2,\dots ,w_m\right)\times \left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1n}\\ r_{21}& r_{22}& \cdots & r_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ r_{m1}& r_{m2}& \dots & r_{mn}\end{array}\right]$$(6) . (6) $$G=w\times R=\left(w_1,w_2,\dots ,w_m\right)\times \left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1n}\\ r_{21}& r_{22}& \cdots & r_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ r_{m1}& r_{m2}& \dots & r_{mn}\end{array}\right]$$(6) where w_m is the comprehensive weight calculated by AHP (Table 4).

• Step 3: The assessment results of the road network vulnerability V were calculated from the weighted average method given by Equation (7)(7) $$V=G\times K^T$$(7) . (7) $$V=G\times K^T$$(7) where K is the mid-score of each level and $K=(0.9,\mathrm{ }0.7,\mathrm{ }0.5,\mathrm{ }0.3,\mathrm{ }0.1)$

4.3. Determination of vulnerability assessment using AHP-TOPSIS

Analytical Hierarchy Process-Technique for Order Preference by Similarity to Ideal Solution (AHP-TOPSIS) computes the weights of each influencing factor, constructs the judgment matrix based on these weights, and determines the posting schedule and the ranking of the judging objects, such that the negotiation result is close to the optimal result (Lixin et al. 2017). In this study, the vulnerability assessment using FAHP was determined by the three main steps as given below:

Figure 4. Triangular membership function.

• Step 1: The first step in the AHP-TOPSIS method includes the decision matrix S given by Equation (8)(8) $$S={\left(s_{ij}\right)}_{m\times n}=\left[\begin{array}{cccc}{w}_1{a}_{11}& w_2{a}_{12}& \dots & w_n{a}_{1n}\\ w_1{a}_{21}& w_2{a}_{22}& \dots & w_n{a}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ w_1{a}_{m1}& w_2{a}_{m2}& \dots & w_n{a}_{mn}\end{array}\right]$$(8) . (8) $$S={\left(s_{ij}\right)}_{m\times n}=\left[\begin{array}{cccc}{w}_1{a}_{11}& w_2{a}_{12}& \dots & w_n{a}_{1n}\\ w_1{a}_{21}& w_2{a}_{22}& \dots & w_n{a}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ w_1{a}_{m1}& w_2{a}_{m2}& \dots & w_n{a}_{mn}\end{array}\right]$$(8) where a is the element in the normalized decision matrix D of the index-based system of vulnerability evaluation, and w_m is the integrated weight calculated by AHP (Table 4).

• Step 2: Determination of relative closeness

  This step produces the positive ideal solution and the negative ideal solution, as given in Equation (9)(9) $$\{\begin{array}{c}{S}^{+}=\left\{\left(\underset{1\le i\le m}{\max s_{ij}}|j\in J_1\right),\left(\underset{1\le i\le m}{\min s_{ij}}|j\in J_2\right)\right\}\\ S^{-}=\left\{\left(\underset{1\le i\le m}{\min s_{ij}}|j\in J_1\right),\left(\underset{1\le i\le m}{\max s_{ij}}|j\in J_2\right)\right\}\end{array}$$(9) . (9) $$\{\begin{array}{c}{S}^{+}=\left\{\left(\underset{1\le i\le m}{\max s_{ij}}|j\in J_1\right),\left(\underset{1\le i\le m}{\min s_{ij}}|j\in J_2\right)\right\}\\ S^{-}=\left\{\left(\underset{1\le i\le m}{\min s_{ij}}|j\in J_1\right),\left(\underset{1\le i\le m}{\max s_{ij}}|j\in J_2\right)\right\}\end{array}$$(9) where S⁺ represents the positive ideal solution, and S^– represents the negative ideal solution. J₁ and J₂ are associated with positive and negative attributes, respectively. In this study, the positive attributes include maintenance intervals, detour index, rescue distances, population density, age structure, road maintenance cost, and building density, while the negative attributes include road grade, road width, disaster relief equipment supplies, education level, and per capita income.

• Step 3: The Euclidean separation distance between each road unit and the ideal solution is calculated as: (10) $$\{\begin{array}{c}{D}_i^{+}=\sqrt{\sum _{j=1}^n{\left(s_{ij}-s_j^{+}\right)}^2}\\ D_i^{-}=\sqrt{\sum _{j=1}^n{\left(s_{ij}-s_j^{-}\right)}^2}\end{array}$$(10) where D_i⁺ and D_i^– are associated with the positive and negative-ideal solutions, respectively. S_ij is each element of the decision matrix S, s_j⁺ is the positive ideal related to each column, and s_j^– is the negative ideal related to each column.

• Step 4: The relative closeness (Bi) value of each alternative of the criterion layer for the ideal solution is determined using Equation (11)(11) $$B_i=\frac{D_i^{-}}{D_i^{+}+D_i^{-}}$$(11) : (11) $$B_i=\frac{D_i^{-}}{D_i^{+}+D_i^{-}}$$(11)

• Step 5: Finally, the comprehensive assessment score V can be calculated according to Equation (12)(12) $$V=w_{1i}\times B$$(12) . (12) $$V=w_{1i}\times B$$(12) where w_1i is the comprehensive weight of the criterion layer calculated by AHP (Table 4), and B is the assessment matrix formed by the relative closeness value of each alternative for the ideal solution.

4.4. Comparison between the vulnerability assessment results using FAHP and AHP-TOPSIS models

The results of the geological hazards vulnerability assessment of road network calculated using the FAHP and AHP-TOPSIS methods are shown in Figure 5a and b. The results indicated that the road vulnerability values calculated by the FAHP method ranged from 0.1746 to 0.6679, while the vulnerability values calculated by the AHP-TOPSIS method ranged from 0.1734 to 0.6608. Thus, the ranges of vulnerability results obtained by the two methods were relatively consistent, which confirmed the accuracy of the vulnerability results to some extent.

Figure 5. Vulnerability assessment results using FAHP and AHP-TOPSIS models: (a) FAHP, (b) AHP-TOPSIS.

The results obtained by the two methods were processed according to the grading criteria in Table 5 for a comprehensive analysis of the vulnerability assessment results using FAHP and AHP-TOPSIS models and represented in Figure 6.

Figure 6. Vulnerability grading results.

As shown in Figure 6, the vulnerability assessment results of the roads in the study area calculated by FAHP and AHP-TOPSIS methods do not indicate ‘very high’ vulnerability levels. According to the grading standard of road network vulnerability (Table 5), a very high road vulnerability grade indicates that the road is under serious threat from geological hazards and the risk to life and property in the area is serious. However, this is contrary to the principles of road design and construction in China. Hence, such a result is in agreement with the actual situation. At the same time, the results of the vulnerability assessment of the road unit indicated that more than 90% of the data were at ‘low’ and ‘medium’ vulnerability levels. Thus, it is evident that the onset of geological hazards can lead to different degrees of damage to most mountain roads. Therefore, urgent steps should be undertaken by the road management departments to formulate and take appropriate protection measures for the safety of roads and surrounding facilities in the study area.

Further, a comparison of the results of the two assessment methods indicated certain differences in the vulnerability results calculated by FAHP and AHP-TOPSIS methods. These differences were mainly in terms of the degree of distribution of the vulnerability levels. For example, the vulnerability assessment data values obtained by the FAHP method were mainly at ‘low’ (40.4%) and ‘medium’ (57.7%) vulnerability levels, while the assessment data values obtained by AHP-TOPSIS were very concentrated, with more than 90% of the road units at ‘low’ vulnerability levels. The major reason for the difference in the results may be due to the different judgment matrices applied by the two methods. FAHP mainly applies the fuzzy triangular mathematical function for the construction of the affiliation matrix and then performs a comprehensive assessment of the site vulnerability, while AHP-TOPSIS mainly performs a comprehensive assessment based on the judgment matrix constructed by the relative closeness of each evaluation object to the positive and negative ideal solutions.

Further analysis of the vulnerability character of mountain roads was conducted by dividing the vulnerability results calculated by FAHP and AHP-TOPSIS methods based on the road type (Figure 7). As shown in Figure 7, firstly, the vulnerability assessment results for national roads and county roads obtained by FAHP and AHP-TOPSIS methods were different, with those obtained by FAHP found to be more conservative. However, the results of the two methods for the provincial roads were found to be relatively in agreement. Secondly, the vulnerability results obtained by the FAHP method indicated that the vulnerability severity levels of national roads and county roads were significantly lower than those of provincial roads. However, the assessment results of AHP-TOPSIS demonstrated the vulnerability trend, i.e. national roads > provincial roads > county roads. This phenomenon is observed due to various reasons, one of which may be the influence of AHP assessment weights or the selection of assessment indices. However, in general, the results of the two methods were found to be relatively in agreement, especially for the lower-ranked mountain roads.

Figure 7. Classification of road type vulnerability.

Based on the above analysis and discussion of the FAHP and AHP-TOPSIS results of road vulnerability assessment in the study area, some of the characteristic features of these two methods for vulnerability assessment were identified, and these characteristic features can provide some theoretical basis for the selection of vulnerability assessment methods in other areas. For example, the AHP-TOPSIS method can be used for the evaluation of the vulnerability of some areas or facilities with high-security level requirements, while the FAHP method can be used for calculating the vulnerability assessment in some less important areas.

5. Vulnerability assessment-based machine learning

In the previous section, the results of the vulnerability assessment of geological hazards in combination with the actual situation were analyzed, which validated the rationality of FAHP and AHP-TOPSIS methods to some extent at the subjective level. However, these methods still have some limitations; for example, the calculation of the initial weights is somewhat subjective and involves a high probability of miscalculations in the complex process. Therefore, the study proposed a machine learning algorithm-based geological hazards vulnerability assessment model for mountain road network, which was more rapid, objective, and reliable. The process involved in the model is shown in Figure 8.

Figure 8. Machine learning-based road vulnerability modeling process.

As shown in Figure 8, the machine learning-based vulnerability assessment of the road was divided into four steps. In step 1, the five-fold cross-validation method was used to divide the vulnerability assessment results obtained from the two types of assessment methods into a training set (80%) and a test set (20%). In step 2, the support vector machine (SVM), random forest (RF), and back propagation neural network (BPNN) algorithms were used to conduct the training of the validation model based on the training set and complete the operation of the test set results. In step 3, four statistical metrics, including mean square error (MSE), absolute variance (R²), root mean square error (RMSE) and mean absolute percentage error (MAPE), was introduced for the verification of the accuracy of the test set results. In step 4, the accuracy verification parameters of the results obtained from different vulnerability assessment methods were compared, and the most reasonable method with the highest accuracy was selected and used for carrying out geological hazards vulnerability mapping of mountain road network.

5.1. Models and validation methods

5.1.1. Support vector machine model

Support Vector Machine (SVM) was proposed by Vapnik in 1963 and are novel and promising classification techniques for overcoming the limitations of machine learning methods. This model demonstrated efficient overfitting, under-learning, and local optimality while dealing with insufficient nonlinear and high-dimensional data. It is especially advantageous for less number of samples. Currently, SVM models have become a new research focus for machine learning algorithms following the neural network model and have been successfully applied in several fields, such as image classification, text, handwriting recognition (Campbell et al. 2006; Li et al. 2012; Fanos and Pradhan 2019), etc.

5.1.2. Random forest model

The Random forest (RF) was developed by improving the classification tree model proposed by Breiman in 1984. When compared with the traditional classification tree model, the RF model has the following three advantages. Firstly, it uses random resampling of the original data to effectively restrict over-fitted simulation results. Secondly, the RF model has a high tolerance for data types yielding good classification results even if the input data has anomalies or missing cases. Thirdly, the model can not only solve the classification and regression problems but also has high accuracy in dealing with regression problems.

5.1.3. Back propagation neural network

Back propagation neural network (BPNN) is one of the most widely used artificial neural networks and is a multilayer feedforward neural network trained according to the error backpropagation algorithm. BPNN continuously adjusts the network weights and thresholds by the gradient descent method for error minimization. Nowadays, BPNNs have been widely used because of their advantages, such as simple modeling, efficient extraction of useful information from samples, and high accuracy of output. In addition, BPNN can be trained for automatically acquiring knowledge without assuming functional forms related to input and output variables and effectively model nonlinear problems. Therefore, they have been successfully applied to many fields, such as prediction of mechanics (Wang et al. 2021), road traffic flow prediction (Cui 2010), weather prediction (Kakar et al. 2018), and geological hazard assessment and prediction (Xiong et al. 2019; Rajabi et al. 2022). In this study, the 12–20–1 structure was used as the BP neural network model, i.e. the input layer contained the above 12 assessment metrics, the hidden layer contained 20 neurons, and the output layer contained 1 neuron for the vulnerability score, as shown in Figure 9.

Figure 9. Structure of back propagation neural network model.

5.1.4. Precision assessment indices

Mean Square Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE), Absolute Variance (R²) were the four precision assessment indices introduced to monitor the accuracy of the prediction results of the machine learning model. These indices can be calculated by Equations (13)(13) $$\mathit{MSE}=\frac{1}{N}\sum _{i=1}^N{\left(O_i-T_i\right)}^2$$(13) to (16)(16) $$R^2=1-\left(\frac{\sum _{i=1}^N{\left(O_i-T_i\right)}^2}{\sum _{i=1}^N{T}_i{}^2}\right)$$(16) . (13) $$\mathit{MSE}=\frac{1}{N}\sum _{i=1}^N{\left(O_i-T_i\right)}^2$$(13) (14) $$\mathit{RMSE}=\sqrt{\frac{\sum _{i=1}^N{\left(O_i-T_i\right)}^2}{N}}$$(14) (15) $$\mathit{MAPE}=\frac{1}{N}\sum _{i=1}^{N}100\times \left|\frac{O_i-T_i}{O_i}\right|$$(15) (16) $$R^2=1-\left(\frac{\sum _{i=1}^N{\left(O_i-T_i\right)}^2}{\sum _{i=1}^N{T}_i{}^2}\right)$$(16) where O represents the actual vulnerability result calculated by the two assessment methods in the previous section, T represents the vulnerability value of each road unit calculated by the machine learning model, and N is the number of input samples in the training or testing phase. The model accuracy was higher at lower values of MSE, RMSE, and MAPE, and R² closer to 1.

5.2. Results and discussion

5.2.1. Comparative analysis

Taking the preliminary evaluation data as the training set, conduct predictive training based on the machine learning model, and complete the calculation of the test set results, so as to obtain the results of the vulnerability assessment of the road network in the study area. Figures 10a–f show the vulnerability zones obtained from six different machine learning models.

Figure 10. Results of vulnerability obtained based on machine learning models: (a) FAHP-SVM, (b) FAHP-RF, (c) FAHP-BPNN, (d) AHP-TOPSIS-SVM, (e) AHP-TOPSIS-RF, (f) AHP-TOPSIS-BPNN.

In order to intuitively compare the differences between the results of vulnerability zoning based on different preliminary evaluation data and machine learning algorithms, the results of the six road network vulnerability prediction models are presented in the form of box plots in Figure 11.

Figure 11. Box plot of vulnerability results.

The following points can be draw from the analysis of Figure 11: (I) the prediction results based on AHP-TOPSIS preliminary evaluation data training all have outliers, while those based on FAHP preliminary evaluation data training have no outliers. (II) the boxes of the evaluation results obtained from training based on the preliminary evaluation data of AHP-TOPSIS are flatter, which indicates the presence of exceptionally large or small outliers. (III) the means of the evaluation results obtained from the FAHP preliminary evaluation data training are smaller than the median, indicating that all three machine learning models obey the left-skewed distribution and the obtained prediction results are relatively conservative. (IV) comparing the evaluation results obtained from the FAHP-based preliminary evaluation data training, it can be found that the evaluation results using the SVM prediction model have a smaller value domain compared to the other two machine learning models. This indicates to a certain extent that the model constructed using the SVM algorithm is less capable of digging into the differences existing between complex data.

The corresponding vulnerability prediction results were obtained by training and testing the machine learning models established in the previous section, and the statistical parameter index of each model in the five-fold cross-validation process was calculated. Based on these indices, the rationality and accuracy of the three types of machine learning models were analyzed in detail.

The statistical parameters of the accuracy of the vulnerability assessment results of the three types of machine learning models are presented in Table 6. First, the MSE values of the models constructed using the RF and BPNN algorithms were found to be less than 1 × 10³, and the values of R² ranged from 0.94 to 1 in either stage, indicating that the models using both machine learning algorithms exhibited high prediction accuracy. In contrast, the model constructed using the SVM algorithm demonstrated poor accuracy, which may be because the SVM model was less suitable for situations with a large number of factors and samples. Second, a comparison of the statistical parameters of the three types of machine learning models in the training and testing phases indicated that all the values of the statistical parameters in the testing phase decreased when compared to those in the training phase. Third, the prediction accuracy of the RF model was higher than that of the BPNN model in both FAHP or AHP-TOPSIS sample sets, which may be due to a large number of parameters and threshold settings in the BPNN model affecting the subsequent model fitting and generalization of the prediction results. Fourth, the combined sample set, as well as the prediction model, indicated that the model based on the FAHP sample set using the RF algorithm had the highest prediction accuracy, while the model based on the AHP-TOPSIS sample set using the SVM algorithm showed the lowest prediction accuracy.

Table 6. Prediction accuracy of three types of machine learning models.

Method	Index	FAHP		AHP-TOPSIS
		Training	Validating	Training	Validating
SVM	MSE	1.736 × 10^-3	1.858 × 10^-3	5.235 × 10^-3	5.461 × 10^-3
	RMSE	4.167 × 10^-2	4.310 × 10^-2	7.235 × 10^-2	7.390 × 10^-2
	MAEP	8.856	9.157	18.828	19.206
	R^2	0.798	0.791	0.717	0.705
RF	MSE	0.384 × 10^-4	1.250 × 10^-4	0.412 × 10^-4	1.600 × 10^-4
	RMSE	0.620 × 10^-2	1.182 × 10^-2	0.641 × 10^-2	1.265 × 10^-2
	MAEP	1.276	2.051	1.527	2.563
	R^2	0.995	0.984	0.992	0.966
BPNN	MSE	1.690 × 10^-4	1.825 × 10^-4	2.496 × 10^-4	2.876 × 10^-4
	RMSE	1.300 × 10^-2	1.351 × 10^-2	1.580 × 10^-2	1.696 × 10^-2
	MAEP	2.483	2.561	3.793	3.974
	R^2	0.981	0.979	0.949	0.941

The rationality of the selected samples and methods was further verified by processing the FAHP and AHP-TOPSIS sample sets using five-fold cross-validation, and the corresponding machine-learning models were constructed. The MSE values of these models were calculated for the model training as well as prediction results and are provided in Table 7.

Table 7. MSE result values for 5-fold cross-validation (×10⁻⁵).

Method	Statistical index	Training							Validating
		K = 1	K = 2	K = 3	K = 4	K = 5	Mean	Standard deviation	K = 1	K = 2	K = 3	K = 4	K = 5	Mean	Standard deviation
SVM	FAHP	186	185	184	194	176	185	5.47	194	181	174	189	191	186	7.38
	A-T	533	529	548	563	518	538	15.4	541	537	524	559	529	538	12.0
RF	FAHP	4.91	3.61	3.60	3.61	3.63	3.87	0.52	14.7	12.8	9.01	20.8	13.9	14.2	3.80
	A-T	3.59	4.89	3.61	3.58	4.92	4.12	0.64	14.4	15.9	18.5	15.3	15.9	16.0	1.36
BPNN	FAHP	14.4	14.3	14.5	16.9	25.6	17.1	4.34	17.5	15.1	14.0	18.1	28.0	18.5	4.97
	A-T	24.6	19.6	25.6	32.5	22.5	24.9	4.27	40.4	19.2	24.1	33.9	28.3	29.2	7.42

Table 7 indicates that the average MSE of the vulnerability prediction model based on the FAHP sample set using the RF algorithm was 3.87 × 10⁻⁵ in the five-fold cross-validation process, which was higher than that of the other three types of models, indicating differences in the accuracy levels. The standard deviation of the MSE of the model was 0.52 × 10⁻⁵, which was much lower than 0.05. This indicated that the model also has good robustness and can provide strong technical support for the vulnerability assessment of other roads in the future.

Although the above multi-level assessment process has greatly reduced the subjective error in the vulnerability assessment of mountain road networks, it is worth mentioning that there is still no way to verify the results of the vulnerability zoning in the current studies(Hossein, et,al 2021). This is because vulnerability is the social attribute of natural disasters, not the natural attribute, so it is inappropriate to use historical disaster data to verify the vulnerability assessment results. But this does not mean that vulnerability research is meaningless and unreasonable. On the contrary, it is very important to carry out spatio-temporal prediction of the vulnerability of hazard-affected bodies to mitigate the impact of natural disasters.

5.2.2. Road vulnerability mapping

Based on the machine learning model established in the previous section to carry out the study area road network geological hazards vulnerability mapping work, the mapping work was completed using the FAHP-RF model with smaller MSE and MAPE values in the five-fold cross-validation process, and the final geo-hazard vulnerability map of the mountain road network obtained is provided in Figure 12.

Figure 12. Geological hazard vulnerability map of the mountain road network.

As shown in Figure 12, the results of the geological hazard vulnerability assessment of the mountain road network indicated that the vulnerability of the road network was governed by a combination of factors, and the following are the major characteristics of its distribution. First, the areas with higher road vulnerability are located at the junction of the study area and other counties because these areas are farther away from the central urban area and need to pay more for road management as well as maintenance and repair. Second, the road units located in remote mountainous areas are generally at a higher level of threat from geological hazards than those in the central urban areas. Third, road units in the vicinity of emergency management points are significantly less vulnerable than those away from emergency management points.

Based on the above analysis, the actual situation of the road network in the study area, and expert opinions, some targeted disaster prevention, and mitigation suggestions can be put forward. (1) The road sections with higher transport frequency have high traffic flow, greater population density, and high vulnerability to road disasters. Therefore, the road slopes in these areas should be inspected in a focused manner to exclude dangerous rock bodies and eliminate the hidden dangers of rock fall and collapse. (2) Fujian area is affected by frequent typhoons and rainstorms, which are highly likely to cause rainfall-type landslides. If conditions permit, the highway department should set up several disaster monitoring stations in disaster-prone areas to issue safety notices and evacuate residents before the onset of disasters, as well as carry out the corresponding de-risking strategy. (3) According to the actual situation of the road network in the study area, the highway department, together with the disaster management department, should draw up a targeted disaster prevention and management plan. Local government should invest more human and material resources for carrying out the maintenance and repair of the road network, improving the protection facilities of the roadbed and road surface, improving the disaster resistance and prevention capacity of the highway, and reducing the vulnerability of the highway to disasters.

6. Conclusions

1. Considering the oversimplification of assessment index for the geological hazards vulnerability of mountain road network, this study takes into account the quantitative indices of road characteristics and rescue capacity and combines them with the vulnerability of the population, economic and material characteristics to objectively and reasonably construct an index-based system of vulnerability assessment for the mountain road.

2. Two combined models (FAHP and AHP-TOPSIS) were applied to perform a preliminary assessment of the geological hazards vulnerability of mountain roads in the study area, and to a certain extent, the negative influence of the subjective factors on the assessment results was reduced. Moreover, the applicability of the two combined models was compared and analyzed based on the vulnerability results.

3. The preliminary assessment results of the geological hazards vulnerability of mountain road network derived from the FAHP and AHP-TOPSIS models were used as the sample sets, and machine learning algorithms (SVM, RF, and BPNN) were used to build a geological hazards vulnerability prediction model for mountain road network. The results indicated that the model based on the FAHP sample set and using the RF model demonstrated the highest prediction accuracy, and its robustness was significantly better than that of other models.

Acknowledgements

The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (No. U2005205, No. 42007235), Natural Science Foundation of Shandong Province (ZR2021QE259) and the Science and Technology Innovation Platform Project of Fuzhou Science and Technology Bureau (No. 2021-P-032).

Disclosure statement

All authors disclosed no relevant relationships, and authors have no conflict of interest to declare.

Data availability

Data will be made available on request.