Debris Flow Classification and Risk Assessment Based on Combination Weighting Method and Cluster Analysis: A Case Study of Debris Flow Clusters in Longmenshan Town, Pengzhou, China

Abstract

Debris flows can damage infrastructure and threaten human life and property safety, especially in tourist attractions. Therefore, it is crucial to classify and evaluate the risk of debris flows. This article takes 14 debris flows in Longmenshan Town, Pengzhou, Sichuan, China, as the research object. Based on on-site geological surveys, combined with drone images and multiple remote sensing images, the essential characteristics of each debris flow are comprehensively determined. A total of nine factors are used as the primary indicators affecting the risk of debris flow: drainage density, roundness, the average gradient of the main channel, maximum elevation difference, bending coefficient of the main channel, the loose-material supply length ratio, vegetation area ratio, population density, and loose-material volume of unit area. The subjective weights of each indicator are obtained using the Analytic Hierarchy Process, while the objective weights are obtained using the CRITIC method. Based on this, the distance function is introduced to couple the subjective and objective weights, determine each indicator’s combined weights, and obtain the integrated evaluation score values of different debris flow hazards. Considering the integrated evaluation score of debris flow, cluster analysis was used to classify 14 debris flows and cluster effectiveness indicators were introduced to determine the effectiveness of debris flow classification. A quantitative standard for the risk of debris flow within the study area was proposed, and finally, a risk assessment of debris flow in the study area was made. Comparing the results of this paper with the gray correlation method, the coupled synergistic method, and the geological field survey results, proves that the proposed method is feasible and provides a reasonable scientific basis for the study of the hazard assessment of regional debris flow clusters and other related issues within the scope of the Jianjiang River basin and other areas.

1. Introduction

Debris flow is a common geological hazard widely distributed in mountainous areas. It is a debris flow composed of water, rock, soil, and steam, and its formation process is highly complex. Its eruption is sudden and short-lived [1,2,3]. Due to the characteristics of high density, strong fluidity, and fast flow velocity, debris flows are highly destructive. In recent years, frequent debris flows have significantly harmed human life, property, the economy, and the environment, especially in mountainous areas’ seismic and geological active zones [4,5,6]. The CMLR (Chinese Ministry of Land and Resources) reports that thousands of disasters occur yearly in China, and mountainous hazards threaten 74 million people. Specifically, during the decade between 2001 and 2010, mountain hazards caused 9933 deaths and missing persons, excluding approximately 25,000 deaths caused by landslides, collapses, and mudslides during the Wenchuan earthquake [7]. Especially for the debris flow group located in the active seismic zone and scenic area, because of the dense population and numerous road networks, if the debris flow disaster occurs, it will cause incalculable losses, so it is essential to classify debris flow in particular areas and assess the risk of debris flow in special areas [8,9].

In recent years, research on the risk assessment of debris flows has been divided into numerical simulation [10], empirical analysis [11], and artificial intelligence [12]. Among them, numerical simulation can not only simulate the movement process of debris flows but also calculate flow velocity and movement distance. However, the parameters required for numerical simulation calculation are generally difficult to obtain. The simulation process is also relatively complex, making the obtained results not necessarily consistent with the actual situation. Moreover, simulating and calculating each debris flow is impractical for regional debris flow clusters [13,14]. The empirical analysis mainly depends on the geological engineering scientists’ on-site survey results. Human subjectivity plays a leading role. Different researchers may have different evaluation criteria for the same debris flow risk, leading to the need for empirical analysis methods to combine other methods to determine the debris flow risk comprehensively [15].

With the development of artificial intelligence, extension theory [16], artificial neural networks [17], Bayesian theory [18], genetic algorithms [19], evidence weight method [20], grey correlation method, and other methods have been widely used in debris flow risk assessment [21]. When most algorithms are applied to debris flow risk assessment, complex risk assessment indicators need to be selected, indicator weights need to be calculated, and the final evaluation model needs to be determined. However, things could still be improved in the current method of determining the weight of evaluation indicators. Researchers often pay more attention to the influence of objective indicators or subjective factors, and it is necessary to consider the collective impact of the two comprehensively. Some evaluation models require manual scoring and determination of grading boundaries, leading to certain deficiencies in the evaluation results of debris flow risk. Therefore, understanding how to combine the influence of subjective and objective weights and establish a scientific evaluation model based on this has practical significance for the risk assessment of debris flows.

Through an on-site geological survey, combined with UAV images and remote sensing images, 14 debris flows were found in Longmenshan Town, Pengzhou City, Sichuan Province, China, distributed on both sides of Baishui River and Jianjiang River, with 5 on both sides of Jianjiang River, and 9 on both sides of Baishui River. Considering the rapid and sudden occurrence of debris flows and many surrounding villages and tourists, it is essential to classify and evaluate the risk of debris flows in this area.

2. Study Area

Pengzhou City is located in the northwest of Sichuan Basin and the northwest edge of Chengdu Plain, 36 km away from the urban area of Chengdu, spanning 103°40′~104°10′ east longitude and 30°54′~31°26′ north latitude. The city covers an area of 1421 km². Longmenshan Town is located in the north of Pengzhou, upstream of Jianjiang River, 55 km away from the Pengzhou urban area, connecting Shifang City in the east, Cifeng Town in the south, Dujiangyan Irrigation Project in the west, and Wenchuan County in the north. The research area is located in the core area of the Longmenshan Fault, with the Yingxiu Beichuan Fault passing through the right bank of the Baishui River and the Guanxian Anxian Fault passing through the downstream Xiaoyudong Town, which belongs to a controlled structure. The base tectonic layer in the study area is the Huangshuihe Group stratum, and the main rock types of the group is the “Pengguan Complex”, which has experienced many strong orogenies (Himalayan movement, Indosinian movement, Chengjiang movement). Finally, neotectonics led to the formation of typical mountain canyon geomorphic features. Longmenshan Town has a humid subtropical climate, with the highest temperature of 24.8 °C in summer and the coldest temperature of 5.2 °C in January in winter. The average annual rainfall for many years is 932.5 mm. There is a significant amount of rainfall in summer, primarily rainstorms. Due to the humid subtropical climate, the plants in the study area are mainly subtropical alpine forest vegetation. Before the 2008 earthquake, the vegetation coverage rate exceeded about 60%. The “Longmen Mountain National Scenic Area” is located here and is a famous tourist resort. After the Wenchuan earthquake, geological disasters frequently occurred in the area, with different numbers and scales of debris flow occurring in 2008, 2009, 2010, 2012, and 2022, causing significant property losses and casualties. The distribution of multiple remote sensing images and debris flows in the study area is shown in the following figure (Figure 1, Figure 2 and Figure 3).

3. Materials and Methods

The calculation of the weight of debris flow indicators mainly adopts a single subjective and objective weighting method. The subjective weighting method obtains weights based on individuals’ subjective experiences, such as AHP. This has unique advantages in determining the weights of various indicators at different levels in an extensive system and can fully utilize the expert experience in the corresponding field. The objective weighting rule entirely relies on the laws of the data, such as the CRITIC method, which can reflect the relative importance of various factors. Combining the AHP and CRITIC methods can reflect researchers’ intuitive understanding of debris flow in the geological field survey stage and consider the regularity of objective data, making the weight obtained more scientific.

The classification of debris flow is a straightforward guide to prevent the occurrence of debris flow disasters, and the classification method is well established [22]. However, because there are many classification methods, the same debris flow has different classification results under different criteria. The affinity propagation cluster analysis method, which applies to analyzing various geostatistical data, is applied to classify debris flows in this paper [23,24]. The final result of debris flow hazard evaluation is obtained based on the calculation results of debris flow index weights combined with the classification of debris flow hazard. The risk assessment process is shown in Figure 4:

3.1. Indicator Selection

The selection of risk assessment indicators for debris flow mainly considers the primary conditions for forming and developing debris flow disasters. From the quantitative evaluation requirements perspective, specific indicators need to reflect the debris flow risk. Geological conditions, material conditions, and trigger conditions play a crucial role in the distribution and activity of debris flows. When selecting debris flow indicators, it is necessary to consider the scientific, representative, comprehensive, and regional differences between the indicators.

Table 1. Factors frequently used in risk assessment of debris flow.

Factors	[25]	[26]	[27]	[28]	[29]	[30]	[31]	[32]	[33]	Time
Rainfall intensity		√	√					√		3
Daily rainfall			√						√	2
Cumulative rainfall		√	√					√		3
Main channel length	√	√	√				√	√	√	6
Gully slope angle	√	√	√			√	√	√		6
Drainage density	√	√	√				√	√	√	6
Soil particle size		√	√					√		3
Basin area	√	√	√	√	√	√	√	√	√	9
Average gradient of main channel	√			√	√	√			√	5
Slope direction					√					1
Vegetation coverage	√			√		√	√			4
Loose material volume	√						√			2
Population density	√							√		2
Maximum elevation difference	√				√	√	√	√		5
Bengding coefficient of main channel	√				√			√		3
Fault length						√				1
Frequency						√	√		√	3

shows the indicators selected by researchers worldwide in recent years in the study of debris flow risk assessment. Table 1 shows specific differences in the selection of evaluation indicators in different regions. Considering that rainfall within the study area is the same, it is difficult to accurately obtain the debris flow frequency and soil particle size. At the same time, the lithology and fault length of the strata can be reflected to a certain extent by the amount of material sources. The study area is located in a scenic area with a relatively dense population. Therefore, based on on-site geological surveys, combined with the analysis results of drone images and multiple remote sensing images, there are nine specific factors that are important and closely related to the occurrence of debris flow in the research area and can be used as essential indicators for debris flow risk assessment. These are drainage density, roundness, average gradient of main channel, maximum elevation difference, Bengding coefficient of main channel, loose-material supply length ratio, vegetation area ratio, population density, and loose-material volume of unit area. This article utilizes multiple remote sensing images, digital elevation models (DEM), drone stereo aerial photography, and field investigations (Figure 1, Figure 2, Figure 3 and Figure 5) (

Table 2. Data Description.

Data Type	Date	Resolution	Source
Remote sensing image (Figure 1)	2020.9	2 m	GF-6
Remote sensing image (Figure 2)	2020.8	0.5 m	Pleiades
Remote sensing image (Figure 3)	2020.11	0.8 m	GF-2
DEM (Figure 5)	2020.11	0.8 m	GF-2

) to ultimately obtain the size of various risk assessment indicators for debris flow in the study area through calculations and depictions.

Drainage density (F1) (km/km²): The ratio of the total length of gullies developed within the debris flow basin area to the basin area, comprehensively reflecting the engineering geological conditions within the watershed. This value is calculated using ArcGIS geometry from remote sensing images.

Roundness (F2) (km/km²): This refers to the ratio of the length of the main gully of a debris flow to the basin area. In general, at different stages of debris flow development, the flat form of valleys varies, and the degree of danger also varies. This value is calculated using ArcGIS geometry from remote sensing images.

Average gradient of main channel (F3) (°): This is the ratio of the maximum elevation difference of the main channel to its linear length. The larger the value, the better the hydrodynamic condition is. The value is obtained through DEM.

Maximum elevation difference (F4) (m): The difference between the highest and lowest elevations in the basin provides kinetic conditions for the occurrence of debris flow disasters. The value is obtained through DEM.

Bengding coefficient of main channel (F5): This refers to the ratio of the main channel length to its linear length, which reflects the degree of channel blockage. The size of the bending coefficient is positively correlated with the blockage coefficient and is related to the flow rate and scale of the debris flow. This value is calculated using ArcGIS geometry from remote sensing images.

The loose-material supply length ratio (F6) (%): This refers to the ratio of loose-material length along a channel to total channel length, which reflects the successive supplied sediments. This value is obtained through on-site geological surveys and remote sensing images.

Vegetation area ratio (F7) (%): Low vegetation coverage can cause severe soil erosion in the basin. The value is obtained through drone aerial photography and remote sensing images, and the vegetation coverage is estimated based on the depth of the color. The lighter the color, the lower the vegetation coverage, and this is corrected through drone aerial photography.

Population density (F8) (number of people per km²): With the development of the economy and technology, human activities have become one of the essential factors affecting mudslides, and population density can reflect the intensity of human activities. This value is estimated based on the number of buildings using remote sensing images and confirmed through on-site investigations.

Loose-material volume of unit area (F9) (×10⁴ m³/km²): The ratio of the source quantity of a single debris flow to the basin area. The source of materials in the ditch is one of the basic factors that cause debris flow disasters, and the size of the unit area loose material volume is directly proportional to the risk of debris flow. The value is obtained by combining a Laser rangefinder with a remote-sensing image, and the thickness is obtained by combining field estimation and drilling data.

Table 3. Evaluation index values of debris flow risk in the research area.

Number	Debris Flow	F1	F2	F3	F4	F5	F6	F7	F8	F9
1	Xiaoniuquan	1.11	0.66	16.20	2350	1.1711	39.46	70	5	119.5
2	Lianshan	2.15	1.36	33.56	1430	1.1250	11.06	60	5	25.50
3	Feishuiyan	2.20	1.52	33.66	1420	1.1620	12.32	60	5	21.33
4	Huilong	1.25	0.49	20.09	2130	1.1535	38.72	70	5	122.70
5	Yanzidong	1.19	0.58	14.28	2245	1.1816	40.90	70	5	113.20
6	Shiliangzi	1.47	0.78	30.26	1500	1.2731	21.66	55	1	35.16
7	Machang	1.92	1.33	35.58	1430	1.1947	19.71	55	1	38.99
8	Manban	1.73	1.40	29.02	1400	1.0588	22.72	55	1	36.47
9	Henghe	0.80	0.50	18.53	2137	1.1615	39.13	50	1	135.30
10	Yushi	0.94	0.45	15.57	2500	1.2020	44.05	80	150	259.34
11	Longcao	1.80	0.75	16.62	2300	1.2160	42.45	80	150	277.80
12	Meizilin	0.80	0.33	15.59	1700	1.2429	43.22	80	150	252.57
13	Xujia	1.70	1.22	18.48	1130	1.1236	14.66	60	50	35.16
14	Baiyan	2.53	2.19	33.98	1320	1.1841	13.45	60	30	24.86

shows the evaluation index values of debris flow risk in the study area.

3.2. Combination Weighting Method

3.2.1. CRITIC Method

The CRITIC method is an objective weighting method that reflects the discreteness and factor conflict between samples through standard deviation and correlation coefficient. The size of the standard deviation is directly proportional to the degree of discreteness and factor weight, and the size of the correlation coefficient is also directly proportional to the conflict between factors. The larger the correlation coefficient, the smaller the weight [34]. The CRITIC method takes into account sample information and factor correlation. Also, it utilizes the coefficient of variation to make the dispersion reflected by standard deviation more realistic, with significant advantages [35,36,37]. The specific calculation steps are as follows:

(1) Assuming m samples containing n indicators, construct the original data matrix using the indicators:

$$X=\left[\begin{array}{cccc}{\alpha }_{11}& {\alpha }_{12}& \dots & {\alpha }_{1n}\\ {\alpha }_{21}& {\alpha }_{22}& \dots & {\alpha }_{2n}\\ \dots & \dots & \dots & \dots \\ {\alpha }_{m1}& {\alpha }_{m2}& \dots & {\alpha }_{mn}\end{array}\right]$$

(1)

(2) Normalization of indicators:

$$q_{ij}=\frac{{\alpha }_{ij}-{\min }_j({\alpha }_{ij})}{{\max }_j({\alpha }_{ij})-{\min }_j({\alpha }_{ij})}$$

(2)

(3) Calculate coefficient of variation:

$$\overline{{\alpha }_j}=\frac{{\displaystyle {\sum }_{i=1}^m{\alpha }_{ij}}}{m}$$

(3)

$$S_j=\sqrt{\frac{1}{m}{\displaystyle {\sum }_{i=1}^m{({\alpha }_{ij}-\overline{{\alpha }_j})}^2}}$$

(4)

$${\mu }_j=\frac{S_j}{\overline{{\alpha }_j}}$$

(5)

In the formula, $\overline{{\alpha }_j}$ is the average value of each indicator; $S_j$ is the standard deviation; ${\mu }_j$ is the coefficient of variation.

(4) Calculate the correlation coefficient matrix:

$${\kappa }_{ij}=\frac{cov(y_k,y_l)}{(s_k{s}_j)},k=1,2,\dots ,n;l=1,2,\dots ,n$$

(6)

In the formula, ${\kappa }_{ij}$ represents the correlation coefficient between indicators, and cov(y_k, y_l) represents the covariance between indicators.

(5) Calculation of indicator information quantity:

$${\omega }_j={\mu }_j{\displaystyle \sum {}_{i=1}^n(1-{\kappa }_{ij}),}j=1,2,\dots ,n$$

(7)

The weights of each indicator are:

$$y_j=\frac{{\omega }_j}{{\displaystyle \sum {}_{i=1}^n{\omega }_j}}j=1,2,\dots ,n$$

(8)

3.2.2. Analytic Hierarchy Process (AHP)

The Analytic Hierarchy Process (AHP) was proposed by renowned mathematician Saaty and is a simple and feasible decision-making method with significant subjectivity [38]. The main advantage lies in the ability to determine the weights of various indicators at different levels in the system, which has unique advantages and is simple and convenient to calculate; therefore, it is widely used [39,40]. The specific calculation steps are as follows:

(1) Establish a tiered hierarchical structure model. The hierarchical structure is generally divided into three layers: target layer, criterion layer, and scheme layer.

(2) Establish the judgement matrix. For different factors at the same level, establish a judgment matrix by comparing their impact on the target factors. The formula for constructing the judgment matrix is as follows:

$$A={(a_{ij})}_{n\times n},a_{ij}>0,a_{ij}=\frac{1}{a_{ij}},(i,j=1,2,\dots n)$$

(9)

Among them, a_ij is the ratio of the influence degree of elements B_i and B_j, usually represented by a scoring method of one to nine, as shown in the

Table 4. Definition of comparative importance.

1	Two decision factors (e.g., indicators) are equally important
3	Two decision factors (e.g., indicators) are equally important
5	Two decision factors (e.g., indicators) are equally important
7	One decision factor is very strongly more important
9	One decision factor is extremely more important
2, 4, 6, 8	Intermediate values
Reciprocals	If ij is the judgement value when i is compared to j, then Uji = 1/Uji is the judgement value when j is compared to i

below.

(3) Calculate consistency indicator CI. By calculating the eigenvalues and eigenvectors of the judgment matrix, it can be represented as:

$$CI=\frac{{\lambda }_{\max }-n}{n-1}$$

(10)

Among λ_max is the eigenvalue of matrix A.

(4) Calculate consistency ratio CR

$$CR=\frac{CI}{RI}$$

(11)

Among them, RI is the consistency indicator of the judgment matrix (

Table 5. The random average consistency index.

n	1	2	3	4	5	6	7	8	9	10	11	12
RI	0	0	0.52	0.89	1.12	1.26	1.36	1.41	1.46	1.49	1.52	1.54

). When CR < 0.1, it is judged that the matrix meets the consistency requirement. Otherwise, it is considered that the matrix does not meet the consistency requirement, and further adjustments are needed until the consistency check is met.

3.2.3. Combination Weighting Rule

The Analytic Hierarchy Process determines the judgment matrix mainly based on the subjective experience of experts. In contrast, the evaluation process of the CRITIC method relies entirely on the own laws of objective data. In order to reflect both the researchers’ intuitive understanding of debris flow in the field geological investigation stage and to take into account the regularity of objective data, the degree of difference between the weights obtained by the two methods is consistent with the degree of difference between their corresponding distribution coefficients, this paper introduces a distance function, which couples the weights obtained by the two methods together to determine the index weights comprehensively.

Suppose the weight vector obtained by the Analytic Hierarchy Process method is ω_i^c, the weight vector obtained by the CRITIC method is ω_i^y, and the distance function between them is denoted as d(ω_i^c, ω_i^y) [33]:

$$d({\omega }_i{}^c,{\omega }_i{}^y)={\left[\frac{1}{2}{\displaystyle \sum _{i=1}^n{({\omega }_i{}^c-{\omega }_i{}^y)}^2}\right]}^{\frac{1}{2}}$$

(12)

Assuming that the combined weights are ω_i^z and the linear weighting method is used to obtain ω_i^z, and assuming that the distribution coefficients of the two weights are a and b, respectively, then ω_i^z can be expressed as:

$${\omega }_i{}^z=a{\omega }_i{}^c+b{\omega }_i{}^y$$

(13)

To ensure a consistent degree of variation in the magnitude of the weights and the distribution coefficients, make the distance function and the distribution coefficients the same:

$$d{({\omega }_i{}^c,{\omega }_i{}^y)}^2={(a-b)}^2$$

(14)

The two weight assignment coefficients also have to satisfy Equation (15). Combining Equations (14) and (15) yields the assignment coefficients a and b. Substituting a and b into Equation (13) yields ω_i^z.

$$a+b=1$$

(15)

3.3. Cluster Analysis

As an essential method for studying classification problems, cluster analysis groups similar things together as much as possible and separates things that are more different (Figure 6). The fundamental laws within things can be more clearly recognized by cluster analysis, which plays an essential role in several scientific fields [41,42,43,44,45,46]. There are certain drawbacks to the traditional clustering method: (1) artificially determining the number of groups and (2) artificially selecting the clustering center. However, the result of such division is mainly affected by human factors, which makes the final division unreliable [47,48,49,50,51].

The affinity propagation clustering algorithm overcomes the shortcomings of traditional clustering analysis. Its principle is to achieve efficient and accurate data clustering by iteratively transmitting attraction and attribution information between data points in a given data set. It is a clustering algorithm based on the “information transfer” between data points. It takes the similarity between a pair of data points as input and exchanges accurate and valuable information between data points until an optimal set of class representative points and clustering are gradually formed. The main advantages include: (1) the number of clusters and the cluster center can be obtained by calculation, which does not need to be specified manually; (2) each data point can be used as a potential cluster center; (3) the clustering results are unique; (4) the starting condition of the algorithm is the input correlation matrix, and (5) there is no requirement for the symmetry of the matrix. The specific algorithm flow is as follows [52,53].

(1)

Calculate data point correlation matrix.

(2)

Determining the size of p (Preference) and the number of iterations.

(3)

Calculate the responsibility information and the availability information between monitoring points.

(4)

Update the responsibility information and availability information.

(5)

Calculate the cluster center.

(6)

The maximum number of cycles is reached, and the final result is obtained.

In the study of debris flow classification, traditional clustering analysis methods require the manual determination of classification numbers, which is subjective. However, using the affinity propagation clustering algorithm to classify debris flows can be completed without specifying the number of classifications and clustering centers in advance. The calculation results are unique and reasonable. However, an essential parameter in the affinity propagation algorithm is the reference p-value, which refers to the reliability of using data points as clustering centers. The size of the reference p-value directly affects the clustering results, and its size is directly proportional to the number of clusters. Improper selection of p-values can lead to poor clustering results [54]. In general, when there is no prior knowledge, the p-value is set as the median of the similarity matrix and remains unchanged during the clustering process. However, selecting the median of the similarity matrix may not necessarily result in the optimal result [55]. Considering that the basis of algorithm startup is a correlation matrix, and different p-values input in the calculation process will also lead to different calculation results, therefore, determine the correlation between debris flows before calculation, and use quantum particle swarm optimization (QPSO) [56] to optimize the p-value, find the p-value under the optimization condition of the objective function, and obtain the classification result of debris flows under the optimization p-value condition.

3.3.1. Correlation Calculation

They assumed that for any two debris flows, i and j, each has z evaluation indicators. The k_th evaluation indicator of the two debris flows can be expressed as i_k and j_k. The evaluation indicators of debris flow i and j can be combined into a set of data pairs (i_k, j_k) (1 ≤ k ≤ z). For any two data pairs (i_k, j_k) and (i_l, j_l) in a set, when i_k > i_l and j_k > j_l, or i_k < i_l and j_k < j_l, the data pair is said to be consistent; when i_k > i_l and j_k < j_l, or i_k < i_l and j_k > j_l, the data pair is said to be inconsistent; when i_k = i_l and j_k = j_l, this data pair is neither consistent nor inconsistent. If correlation analysis is conducted on the evaluation indicators between two debris flows, the correlation between any two evaluation indicators can be expressed as [57]:

$${\tau }_{ij}=\frac{2C}{\frac{1}{2}z(z-1)}-1=\frac{4C}{z(z-1)}-1$$

(16)

Among them, C is the number of identical order pairs. The value range of τ_ij is [−1, +1], and when τ_ij = 1, it indicates that the two debris flows have the exact level correlation; when τ_ij = −1, it indicates that two debris flows have opposite level correlations; when τ_ij = 0, it indicates that the two debris flows are independent of each other. For the risk assessment indicators of debris flow, due to the different dimensions of each indicator, correlation calculation can not only eliminate the impact of different dimensions of each evaluation indicator but also serve as a prerequisite for establishing a correlation matrix [58].

3.3.2. Classification and Risk Assessment of Debris Flow

Assuming there are n debris flows in total, for a particular debris flow i, it is necessary to calculate the correlation between debris flow i and n − 1 debris flow other than debris flow i and establish a debris flow correlation matrix S_ij:

$$S_{ij}=\left[\begin{array}{cccc}{\tau }_{11}& {\tau }_{12}& \dots & {\tau }_{1n}\\ {\tau }_{21}& {\tau }_{22}& \dots & {\tau }_{2n}\\ \dots & \dots & \dots & \dots \\ {\tau }_{n1}& {\tau }_{n2}& \dots & {\tau }_{nn}\end{array}\right]$$

(17)

Based on the correlation matrix of debris flow, affinity propagation clustering analysis is conducted because selecting different p-values will result in different classification results. However, too many or too few classification numbers do not match debris flow’s actual risk classification results. Therefore, the optimal classification results need to be determined through the clustering effectiveness function. Among many clustering indicators, the Silhouette indicator is widely used, which can not only reflect the intra-class tightness and inter-class separateness of clustering results but also assess the optimal number of clusters and evaluate the quality of clustering, so the Silhouette indicator is chosen to judge the optimal debris flow classification.

Suppose there is a data set with n data points, which is divided into K clusters C_i (i = 1, 2, … K). a(t) denotes the average dissimilarity of data point t in cluster C_j to all other data points within C_j, and d(t, C_i) is the average dissimilarity of data point t in C_j to all data points in another class C_i, then b(t) = min{d(t, C_i }, where i = 1, 2, … K, i ≠ j. Therefore, the Silhouette index of a data point is [59,60,61]:

$$S(t)=\frac{b(t)-a(t)}{\max \left\{a(t),b(t)\right\}}$$

(18)

The average S(t) value S_avg(C_i) of all data points in cluster C_i can be obtained from S(t), which reflects the compactness and separation of cluster C_i. The average S(t) value S_avg of all data points in a dataset can reflect the quality of clustering results. The larger S_avg, the better the clustering quality, and the optimal number of clusters must correspond to the maximum S_avg value. The formula is as follows:

$$S_{avg}=\frac{{\displaystyle {\sum }_{t=1}^{n}S(t)}}{n}$$

(19)

According to the above description, when the quantum particle swarm optimization (QPSO) algorithm is used to optimize the p-value, assuming that the number of p-values to be optimized is N, the p-values to be optimized are P₁, P₂, P₃, … P_N and the total number of variables to be solved are N, which can be transformed into an N-dimensional optimization problem [62,63]. The optimization calculation process is as follows:

Step 1: Calculate the correlation matrix S_ij of debris flow.

Step 2: Initialization. The qubit phase plays the role of the random initial population, which is in the range of [0, 2π] calculated by random number function. Then, combined with the upper and lower limits of p-values variables, by solving the solution space transformation formula, the probability amplitude is converted to the variable space.

Step 3: The correlation matrix S_ij and p-value variables were used for affinity propagation clustering calculation, and the Silhouette index value was obtained from the output classification results. The average Silhouette index value is taken as the fitness value of the QPSO algorithm. Considering the comprehensive evaluation of classification results, the average Silhouette index value (S_avg) is selected as the objective function.

Step 4: Nonlinear adjustment of inertia weight.

Step 5: Update particle state (update qubit depression angle and qubit probability amplitude)

Step 6: Adaptive adjustment of mutation operator and mutation processing. The quantum nongate is used to mutate particles.

Step 7: The correlation matrix S_ij and p-value variables were used for affinity propagation clustering calculation, and the average value of the Silhouette index was calculated. If the average value of Silhouette index meets the stopping condition, or if the number of iterations has reached the maximum, the clustering results under the optimized p-value will be output; otherwise, return to Step 3 to continue the cyclic calculation.

Figure 7 shows the flowchart of the debris flow classification algorithm:

Based on the clustering analysis method proposed above, debris flows can be divided into different types. However, the clustering analysis results only classify debris flows into different categories, and another judgment is needed regarding which risk level corresponds to different categories of debris flows.

This article calculates the synthetic evaluation score (D_i) for each debris flow risk based on the combined weight values obtained by the combination weighting method (Equation (20)) [33]. The larger D_i, the greater the probability of the debris flow occurring and the more dangerous it is. Select indicators and synthetic evaluation scores to calculate the correlation between debris flows. Based on correlation calculation (τ_ij), establish a correlation matrix (S_ij) and perform cluster analysis. Based on the clustering results and synthetic evaluation scores, classify the risk of debris flow.

$$D_i={\displaystyle \sum _{j=1}^n{\omega }_z(j)q_{ij}}$$

(20)

4. Classification and Risk Assessment Results of Debris Flow in the Study Area

4.1. Weight Calculation

4.1.1. Results of the AHP

Based on the selection of evaluation indicators for debris flow, a hierarchical structure model for evaluating the risk of debris flow groups in Longmenshan Town is constructed (Figure 8).

According to the hierarchical structure model of debris flow evaluation indicators, each evaluation indicator is graded using the 1–9 scale method, a judgment matrix is constructed (

Table 6. Criterion layer judgment matrix for goal layer.

Criterion Level	Material Condition	Geology Condition	Trigger Condition	CI	RI	CR
Material condition	1	1/3	2	0.0268	0.52	0.0516
Geology condition	3	1	3
Trigger condition	1/2	1/3	1

,

Table 7. Criterion layer judgment matrix for geology condition.

Geology Condition	F1	F3	F5	F4	F2	CI	RI	CR
F1	1	1/2	3	1/3	2	0.0709	1.12	0.0633
F3	2	1	3	1/4	3
F5	1/3	1/3	1	1/4	2
F4	3	4	4	1	4
F2	1/2	1/3	1/2	1/4	1

,

Table 8. Criterion layer judgment matrix for material condition.

Material Condition	F9	F6	CI	RI	CR
F9	1	3	0	0	0
F6	1/3	1

and

Table 9. Criterion layer judgment matrix for trigger condition.

Trigger Condition	F8	F7	CI	RI	CR
F8	1	2	0	0	0
F7	1/2	1

), and consistency testing is conducted. Finally, the weights of each evaluation indicator are obtained (

Table 10. The weighted values of the factors obtained by AHP.

Evaluation Index	F1	F2	F3	F4	F5	F6	F7	F8	F9
Weight	0.1	0.04	0.13	0.28	0.05	0.06	0.05	0.10	0.19

). During the evaluation process, a total of 15 experts were selected for scoring, all of whom were from the Sichuan Province Sudden Major Geological Disaster Expert Database.

4.1.2. Results of CRITIC Method

Using the data in Table 4, establish the original evaluation index matrix using the CRITIC method, normalize the indicators, calculate the information content, and finally use Equation (8) to obtain the objective weight value (

Table 11. CRITIC method evaluation index weight.

Evaluation Index	F1	F2	F3	F4	F5	F6	F7	F8	F9
Amount of information	1.07	0.83	1.09	1.04	1.32	0.80	1.05	1.67	0.80
Weight	0.11	0.09	0.11	0.11	0.14	0.08	0.11	0.17	0.08

).

4.1.3. Results of the Combination Weighting Method

Based on the weight results obtained by the Analytic Hierarchy Process and CRITIC method, the combined weights of each evaluation index are calculated using Equations (12)–(15) (

Table 12. Combination weighting method for evaluating indicator weight results.

Evaluation Index	F1	F2	F3	F4	F5	F6	F7	F8	F9
AHP	0.10	0.04	0.13	0.28	0.05	0.06	0.05	0.10	0.19
CRITIC	0.11	0.09	0.11	0.11	0.14	0.08	0.11	0.17	0.08
Combination weighting method	0.10	0.06	0.12	0.21	0.09	0.07	0.07	0.13	0.14

). According to Equation (12), this is calculated as:

$$d({\omega }_i{}^c,{\omega }_i{}^y)={\left[\frac{1}{2}{\displaystyle \sum _{i=1}^n{({\omega }_i{}^c-{\omega }_i{}^y)}^2}\right]}^{\frac{1}{2}}=0.1746$$

(21)

By combining Equations (13) and (14), it can be concluded that:

$$\begin{array}{l}a-b=0.1746\\ a+b=1\end{array}$$

(22)

Solved:

$$\begin{array}{l}a=0.5873\\ b=0.4127\end{array}$$

(23)

Therefore, the combination weight value obtained by the combination weighting method can be expressed as:

$${\omega }_i{}^z=0.5873{\omega }_i{}^c+0.4127{\omega }_i{}^y$$

(24)

4.2. Classification Results of Debris Flow

Considering the synthetic weight values obtained by the combination weighting method, the synthetic evaluation score (D_i) for each debris flow risk degree is calculated (

Table 13. Synthetic evaluation score (D_i) of debris flow in the research area.

Number	Debris Flow	Di	Number	Debris Flow	Di
1	Xiaoniuquan	0.5359	8	Manban	0.2113
2	Lianshan	0.2660	9	Henghe	0.3963
3	Feishuiyan	0.2692	10	Yushi	0.7948
4	Huilong	0.4727	11	Longcao	0.8301
5	Yanzidong	0.5210	12	Meizilin	0.6718
6	Shiliangzi	0.2716	13	Xujia	0.2856
7	Machang	0.2397	14	Baiyan	0.3064

).

This study selected 9 evaluation index values (F1~F9) from 14 debris flows in the research area as well as the synthetic evaluation score of each debris flow (D_i). Using these 10 indicators, Equation (16) was used to calculate the correlation between the 14 debris flows τ_ij. Based on the correlation calculation, the correlation matrix of debris flow in the study area was established according to Equation (17) (Figure 9).

According to the previous description of S_avg, the larger the calculated S_avg value, the more scientific and reasonable the classification results are. The correlation matrix shown in Figure 9 is used as the basis for starting the algorithm, and the QPSO-optimized affinity propagation clustering is used to compute the matrix. The calculation results showed that, when the debris flow is divided into four types, the S_avg index value is the highest, reaching 0.66. Therefore, the classification result is the optimal number of classifications (

Table 14. The optimal classification results of debris flow in the research area.

Classification	Number of Categories	Debris Flow
I	3	Longcao, Meizilin, Yushi
II	4	Xiaoniuquan, Yanzidong, Huilong, Henghe
III	3	Shiliangzi, Baiyan, Xujia
IV	4	Feishuiyan, Lianshan, Machang, Manban

).

4.3. Risk Assessment Based on Classification Results

Based on the above clustering analysis results, debris flows are divided into four categories. However, the clustering analysis results only classify debris flows into different categories and which risk level corresponds to each of the four categories of debris flows. The clustering results are not provided, and another judgment is needed.

Table 15. Debris flow risk assessment in study area.

Classification	Number of Categories	Debris Flow	max (Di)	min (Di)	Debris Flow Risk Degree
I	3	Longcao, Meizilin, Yushi	0.8301	0.6718	extreme risk
II	4	Xiaoniuquan, Yanzidong, Huilong, Henghe	0.5359	0.3963	high risk
III	3	Shiliangzi, Baiyan, Xujia	0.2692	0.2113	moderate risk
IV	4	Feishuiyan, Lianshan, Machang, Manban	0.3064	0.2716	low risk

shows that, among Class I debris flows, Longcao Gully has the highest synthetic evaluation score of 0.8301, while Meizilin Gully has the lowest synthetic evaluation score of 0.6718. Among Class II debris flows, the synthetic evaluation score of Xiaoniuquan Gully debris flow is the highest at 0.5359, while the synthetic evaluation score of Henghe Gully is the lowest at 0.3963. Among Class III debris flows, Baiyan Gully has the highest synthetic evaluation score of 0.3064, while Shiliangzi Gully has the lowest synthetic evaluation score of 0.2716. Among Class IV debris flows, Feishui Rock Gully has the highest synthetic evaluation score of 0.2692, while Manban Gully has the lowest synthetic evaluation score of 0.2113. Therefore, based on the calculation results, the Class I debris flow in the study area is classified as extremely dangerous (0.6718 ≤ D_i ≤ 0.8301), the Class II debris flow is classified as highly dangerous (0.3963 ≤ D_i ≤ 0.5359), the Class III debris flow is classified as moderately dangerous (0.2716 ≤ D_i ≤ 0.3064), and the Class IV debris flow is classified as low-risk (0.2113 ≤ D_i ≤ 0.2692).

This article compared and analyzed the debris flow risk assessment results with those obtained by the grey correlation and collaborative coupling methods (

Table 16. Comparative analysis of risk assessment results using different methods.

Number	Debris Flow	Results of This Article	Results of Grey Correlation Method	Results of Synergistic Coupling Method
1	Xiaoniuquan	High risk degree	Moderate risk degree	High risk degree
2	Lianshan	Low risk degree	Low risk degree	Low risk degree
3	Feishuiyan	Low risk degree	Low risk degree	Low risk degree
4	Huilong	High risk degree	Moderate risk degree	High risk degree
5	Yanzidong	High risk degree	Moderate risk degree	High risk degree
6	Shiliangzi	Moderate risk degree	Low risk degree	Moderate risk degree
7	Machang	Low risk degree	Low risk degree	Low risk degree
8	Manban	Low risk degree	Low risk degree	Low risk degree
9	Henghe	High risk degree	Moderate risk degree	High risk degree
10	Yushi	Extreme risk degree	High risk degree	Extreme risk degree
11	Longcao	Extreme risk degree	High risk degree	Extreme risk degree
12	Meizilin	Extremely risk degree	High risk degree	Extreme risk degree
13	Xujia	Moderate risk degree	Low risk degree	Moderate risk degree
14	Baiyan	Moderate risk degree	Moderate risk degree	Extreme risk degree

). Table 16 shows that the results obtained in this article are consistent with those obtained by the coupling synergy method, generally one level higher than the risk obtained by the grey correlation method. The results obtained by the grey correlation method are mainly medium to low, with a small amount being hazardous, and there is no extreme risk. Compared to the results obtained in this article, they tend to be conservative. The results of the grey correlation method indicate that the possibility of debris flow outbreaks in the study area is minimal. However, the results obtained by the grey correlation method do not match the actual situation of multiple debris flows that have already erupted in the research area. For example, in July 2009, a debris flow broke out in Yushi Gully, depositing some houses (Figure 10 and Figure 11). In 2012, a significant debris flow disaster occurred on August 18th in Longmenshan Town [64]. In August 2022, a debris flow disaster broke out in Longcao Gully, and on-site investigations also showed that there were multiple stages of debris flow accumulation in most debris flow channels (Figure 12). The evaluation criteria of the grey correlation method are significantly too low, so the evaluation results obtained in this article can better reflect the actual situation of debris flow outbreaks in the study area.

5. Discussion

The accuracy of classification and risk assessment of debris flows is crucial for preventing and controlling debris flows. According to different classification standards, the same debris flow can belong to different categories simultaneously. The traditional classification standards for debris flows have a certain lag in preventing and controlling current debris flows [25]. For regional debris flows, different regions of debris flows have different impact factors, which need to be comprehensively selected based on the actual situation of different research regions [65]. At the same time, there are also areas for improvement in calculating the weight of the selected influencing factors. For current debris flow risk assessment models, most require manual determination of risk classification standards, which results in the inability of debris flow risk assessment results to escape the influence of human subjectivity [33]. This article proposes associating the combination weighting method with affinity propagation clustering analysis to obtain combination weights scientifically and, based on this, use clustering analysis to obtain accurate classification standards.

In this article, the reasonable and correct selection of debris flow evaluation indicators and the calculation of indicator weights are prerequisites for using cluster analysis methods for debris flow classification and risk assessment [66]. This article uses various methods, such as on-site geological surveys, multiple remote sensing images, and drone images, to select nine influencing factors based on the essential characteristics of the debris flow clusters in Longmenshan Town. These influencing factors reflect the various geological, material, and trigger conditions of the debris flows within the study area and calculate the weight of the selected factors. The CRITIC method is an objective weight calculation method, but objective methods cannot reasonably exclude singular data in data processing, which may result in incorrect results. The AHP can fully utilize the experience of experts in the corresponding field to calculate weights, which is a subjective method. However, different experts judge different factors, which can cause incorrect results. Therefore, using the combination weighting method to combine the advantages of the two methods can obtain more scientific indicator weights, which is superior to applying a single method.

Compared with traditional clustering analysis, affinity propagation clustering analysis does not require manually specifying the number of clusters and cluster centers, and the clustering results are unique, with obvious advantages. When using affinity propagation clustering analysis to classify and evaluate the risk of debris flows, optimizing the affinity propagation clustering algorithm, further optimizing the algorithm performance, scientifically obtaining the classification results of debris flows, quantifying the classification standards, and correctly evaluating the risk of debris flows. However, this classification and evaluation method has limitations: (1) it does not apply to the risk assessment of individual debris flows; (2) when the number of debris flows is small, this method cannot be applied; and (3) a certain number of evaluation indicators need to be selected, and this method cannot be applied when the number of evaluation indicators is too small.

As the results of this article are based on the primary data of 14 debris flows in Longmenshan Town, Pengzhou City, China, with significant regional significance, considering the different development characteristics of debris flows in different regions, when applying this method to debris flows in other regions, the differences in regional conditions should be considered.

6. Conclusions

(1)

Based on on-site geological surveys, drone images, and multiple remote sensing images, 9 debris flow risk assessment indicators were selected from 14 debris flows in Longmenshan Town, Pengzhou, China. Each indicator’s subjective and objective weights were calculated using hierarchical analysis and CRITIC methods, and the two weights were coupled to obtain the synthetic weights of the evaluation indicators. Based on this, the synthetic evaluation score D_i was calculated for each debris flow so that the obtained synthetic evaluation score could scientifically reflect the risk level of each debris flow gully.

(2)

This study conducted cluster analysis of 14 debris flows, established the classification model, and classified the debris flows in the study area into four categories. By combining the classification results with synthetic evaluation scores, it was ultimately determined that, among the 14 debris flows in the study area, 3 were extremely dangerous (0.6718 ≤ D_i ≤ 0.8301), 4 were highly dangerous (0.3963 ≤ D_i ≤ 0.5359), 3 were moderately dangerous (0.2716 ≤ D_i ≤ 0.3064), and 4 were low-risk (0.2113 ≤ D_i ≤ 0.2692).