Evaluation of Landslide Susceptibility of Mangshan Mountain in Zhengzhou Based on GWO-1D CNN Model

Abstract

The Mangshan Mountain is located in the south bank of the Yellow River, which belongs to the typical loess plateau. Landslide disasters occur frequently in this region, so it is urgent to carry out the evaluation of landslide susceptibility. Therefore, this study takes Mangshan Mountain as the research object, selects 13 evaluation factors through multicollinearity diagnostic, Pearson correlation coefficient, and random forest importance analysis, and uses grey wolf optimizer (GWO) algorithm to optimize the initial weights of one-dimensional convolutional neural network model (1D CNN), so as to build a GWO-1D CNN model to carry out the evaluation of landslide susceptibility. The results show that the GWO algorithm can significantly improve the accuracy of 1D CNN model. The final accuracy of the GWO-1D CNN model reaches 0.903, and the accuracy, area under the ROC curve, and kappa coefficients increase by 0.091, 0.098, and 0.187, respectively; The percentage of area of very low, low, medium, high, and very high susceptibility areas in Mangshan Mountain is 40.2%, 23.6%, 14.1%, 12.9%, and 9.2%. The findings of this study provide scientific basis for the prevention and control of landslide disaster in Mangshan Mountain and expand the application of CNN model in the evaluation of landslide susceptibility.

1. Introduction

Located on the south bank of the Yellow River, the Mangshan Mountain is a typical loess plateau area with long gullies and undulating terrain in the region. Landslide disasters are frequent in the region, seriously threatening people’s lives and properties. Therefore, the study of landslide susceptibility evaluation is an urgent need to ensure the ecological protection and development of the region. Landslide susceptibility evaluation is a quantitative evaluation of the probability of occurrence and spatial distribution of landslides based on the conditions of landslide development and the spatial distribution of historical landslides in the study area using susceptibility evaluation methods [1]. Since the mid-1970s, the United States, Italy, Japan, and other countries have carried out landslide susceptibility evaluation studies and have successfully prevented and controlled many landslides [2]. According to the different theoretical basis and prediction means, evaluation methods can be divided into two main categories: deterministic evaluation methods and non-deterministic evaluation methods.

Deterministic methods use traditional physical mechanics as the theoretical basis and establish a slope limit equilibrium model to evaluate the probability of landslides [3]. The typical deterministic models include SHALSTAB and SINMAP [4,5,6]. The deterministic evaluation method usually has a strict and definite mathematical functional equation, and each parameter has a clear explanation, which can reflect the physical substance of landslide occurrence. But the method also has many problems: data collection is difficult, parameters have spatial variability, the complex slope rock mass makes the model’s reliability greatly reduced, and so on. Therefore, the deterministic method can only be applied to the spatial prediction of landslides in individual or small areas, and it is difficult to be applied in a large study area.

The non-deterministic evaluation method does not emphasize the accuracy of each parameter in the evaluation model, but carries out spatial planning of landslides by investigating a series of internal and external influencing factors of landslides such as macroscopic topography and geomorphology, so it is more suitable for the prediction of landslide hazards on a large scale [7]. Non-deterministic evaluation methods mainly contain two categories, knowledge-driven and data-driven, which have gone through a development process from qualitative to quantitative. Knowledge-driven approach is an analytical tool that relies on profound professional knowledge and past experience to assess the likelihood of future landslide events within a region by exhaustively examining the root causes of landslides in that region and their mechanisms of action, and the representative methods are fuzzy logic method [8], hierarchical analysis method [9,10], expert scoring method [11], and so on. Knowledge-driven methods can be well applied in the case of insufficient data, but these kinds of methods rely on professional knowledge, and reliability cannot be guaranteed. With the improved accuracy and reliability of spatial and landslide data, the data-driven methods have shown strong advantages, and their applications are becoming more and more mature [12].

With the vigorous progress of machine learning in recent decades, data-driven methods such as random forest [13,14,15], support vector machine [16,17], neural network [18,19,20], and so on have been widely used. This approach is different from the knowledge-driven approach in that it focuses on automatically extracting laws from a large amount of data, which improves the objectivity and accuracy of predictions. Deep learning, as a hotspot in the field of machine learning nowadays, has stronger expressive ability and accuracy, and has been gradually applied to the field of landslide susceptibility evaluation [21]. Convolution neural network (CNN) can effectively mine the complex relationship between landslides and landslide evaluation factors, greatly improving the accuracy and reliability of evaluation [22,23,24].

However, the current research of landslide susceptibility evaluation based on CNN is still in the exploratory stage, which needs to be further explored and improved. Most of the current landslide susceptibility studies based on CNN models do not fully consider the problem that the accuracy of CNN is easily affected by the initial weights. A suitable method needs to be chosen to optimize the initial weights of the CNN model to improve the model accuracy. Compared with traditional optimization algorithms such as genetic algorithm (GA), the grey wolf optimizer (GWO) algorithm has a stronger global search capability [25,26,27]. Therefore, in order to obtain reliable landslide susceptibility evaluation results for Mangshan Mountain, the GWO algorithm is introduced to search for the best initial weights of the one-dimensional CNN (1D CNN) model. The GWO-1D CNN model is constructed to carry out susceptibility evaluation of Mangshan Mountain to obtain the susceptibility zoning map.

2. Study Area and Dataset

2.1. Study Area

Mangshan Mountain is located on the south bank of the Yellow River about 25 km northwest of Zhengzhou City. The geographic location of Mangshan Mountain is shown in Figure 1. The area is a loess plateau on the transition zone between the Loess Plateau and the North China Plain, with a loess thickness of about 170 m, and with a dense number of ditches in the area, which is characterized by severe soil erosion [28]. The area also develops micro-geomorphic features such as loess columns, loess traps, and loess bridges. Mangshan Mountain mainly contains three kinds of loess strata: Holocene loess, Upper Pleistocene loess, and Lower Pleistocene loess. Among them, the Upper Pleistocene loess is widely distributed on top of the loess plateau of Mangshan Mountain, which is 8.0–15 m thick, with gray-yellow chalk and loose structure, and at the bottom of which there is a layer of light brownish-yellow paleo-soil 0.5–1.0 m thick, with chalky-clay lithology [29].

Its annual precipitation is mostly concentrated in July to September, and strong rainfall often occurs. Its average annual temperature, annual precipitation, and average annual air humidity are 15.7 °C, 406.35 mm, and 54.53%, respectively [30]. Mangshan Mountain belongs to the Yellow River basin. The Yellow River is characterized by little water and much sand and extremely uneven water and sand. Overall, 60% of the water volume and 80% of the sand content of the Yellow River in a year are concentrated in the flood season (June to October). The special geographic and geological environment leads to frequent landslide disasters in Mangshan, and the development of landslide geological disasters is mainly dominated by medium and small landslides.

2.2. Landslide Dataset

Using Sentinel-1 SAR data and Sentinel-2 optical satellite data, the preliminary identification of landslide areas is firstly utilized by double time-phase change detection method [31] and SBAS-InSAR method [32]. The preliminary identification results are then screened and supplemented by combining topographic features and visual interpretation. Finally, 46 landslides were successfully verified through field investigation. The landslide locations are shown in Figure 2. The landslides in the Mangshan Mountain are dominated by small- and medium-sized landslides, most of which are in the shape of cirque and horseshoe. The thickness of the landslides is thin, generally between 0.5 and 5 m, and all of them are shallow landslides.

2.3. Evaluation Factors

At present, there is no uniform specification for the selection of evaluation indicators, so as many indicators as possible should be taken into consideration when constructing the original indicator system. According to the conditions of landslide development and the characteristics of the Mangshan Mountain, from the aspects of topography and geomorphology, geological conditions, hydrological conditions, and human activities, this study initially selects 16 evaluation factors: elevation, slope, aspect, topographic relief, plane curvature, profile curvature, lithology, distance to faults, annual precipitation, distance to water system, stream power index (SPI) [33], topographic wetness index (TWI) [34], distance to road, distance to building, land use type, and normalized difference vegetation index (NDVI) [35]. The data of each factor are shown in Figure 3.

(1)

Elevation. Different elevation areas have different characteristics such as plant type and soil moisture, and different elevation areas are affected by different human activities.

(2)

Slope. Slope is one of the developmental elements of landslides, and generally only slopes are susceptible to landslide hazards. The gravitational and driving forces carried by the material of the slope increase as the slope increases, and the probability of a landslide occurring increases.

(3)

Aspect. Slopes with different slope orientations receive different levels of solar radiation and rainfall, which leads to differences in surface plant types, soil conditions, land use, and other factors affecting slopes, which in turn affect slope stability. Slope orientation data are generally classified into nine categories: flat, north, northeast, east, southeast, south, southwest, west, and northwest.

(4)

Topographic relief. In regional studies, topographic relief is a more objective reflection of topographic features than slope gradient. Differences in topographic relief lead to differences in the internal and external geologic and anthropogenic influences on slopes, which in turn affect the size and distribution of landslides.

(5)

Plane curvature. Curvature is closely related to the internal stress distribution of slopes and influences both runoff flow and soil erosion and accretion, which in turn affects landslide development. Planar curvature is characterized by curvature in the horizontal direction. The greater the planar curvature, the steeper the terrain.

(6)

Profile curvature. Profile curvature is characterized by curvature in the vertical direction, which can better reflect the complexity of the ground.

(7)

Lithology. Rocks and soils are the material basis for landslides. Slopes made up of rock and soil that are soft in structure have low resistance to shear and weathering, and whose properties are prone to change under the action of water are susceptible to landslides.

(8)

Distance to faults. Faults can cause fragmentation of the rock and soil bodies that form slopes, thus affecting the integrity of slopes. Moreover, faults provide a channel for rainfall to enter the slope and for groundwater to flow, thus accelerating the development and sliding of landslides. The more developed the fault that cuts a detached slope, the larger the size of the landslide that forms.

(9)

Annual precipitation. A small amount of rainfall increases the water content of a slope, which increases the weight and at the same time weakens its resistance to sliding. When a large amount of rainfall occurs, the rainfall will wash the slope strongly, thus directly inducing the occurrence of landslides.

(10)

Distance to water system. Soaking of the water system will muddy the softened interlayer of the slope, thus reducing the degree of shear resistance of the slope. At the same time, the scouring of the water flow causes an amount of soil loss of the slope and increases the critical surface.

(11)

SPI. SPI is a good indicator of the potential erosive capacity of slopes from surface runoff [36]. Mangshan Mountain is a loess plateau area, and the loess in the area is mostly chalky, which is affected by runoff erosion. The SPI calculation formula is as follows:

$$SPI=\mathit{ln}(S·\mathit{tan}\theta ),$$

(1)

where S is the catchment area of the upper slope, and $\theta$ is the local gradient of the slope.

(12)

TWI. TWI is a quantitative indicator to evaluate the spatial distribution of soil moisture, and it can also quantitatively characterize runoff trends and runoff convergence locations [37]. TWI is calculated using the following formula:

$$TWI=\mathit{ln}\frac{S}{\mathit{tan}\theta }.$$

(2)

(13)

Distance to road. There is a positive correlation between landslides and the distance from the road. Activities involved in road construction such as slope excavation and hill blasting can seriously affect the stability of slopes.

(14)

Distance to building. Mangshan is a loess plateau with a flat surface and a large number of housing structures. Many of these buildings are close to the edge of the loess surface, which increases the gravitational potential energy of the slope. The construction of houses is often accompanied by excavation and filling of the mountain, which results in a decrease in the stability of the slope.

(15)

Land use type. Land use type can reflect the degree of disturbance and damage to the rock and soil layers caused by human activities, which in turn affects the stability of slopes. The land use types in the study area are divided into six categories: bare soil, buildings, cropland, grassland, woodland, and water.

(16)

NDVI. NDVI can well reflect the degree of plant cover on the surface. Vegetation can improve the shear strength and seepage resistance of slopes, and has an anchoring and reinforcing effect on slopes, thus enhancing the stability of slopes. At the same time, vegetation can inhibit and weaken the scouring effect of slope runoff, thus affecting the development of landslides.

Due to the different sources of evaluation factor data, it is not possible to ensure that all evaluation factor data are at the same time point. In order to reduce the influence of different acquisition times on evaluation factor data, this study tries to avoid too large of a time difference in the process of data collection. And in order to ensure the consistency of spatial resolution, this study resamples all evaluation factor data into 10 × 10 m, which is consistent with the resolution of landslide data. The data sources are shown in

Table 1. The sources of evaluation factor data.

Evaluation Factor	Data Acquisition	Resolution	Data Sources
Elevation	STRM DEM	30 m	NASA
Slope
Aspect
Topographic relief
Plane curvature
Profile curvature
TWI
SPI
Lithology	The Geological map of Zhengzhou city	1:200,000	Geoscientific Data & Discovery Publishing system
Distance to faults
Annual precipitation	Rainfall data	30 s	WorldClim
Distance to water system	The vector data of water system, residential area and traffic [38]	1:250,000	National Catalogue Service for Geographic Information
Distance to road
Distance to building
Land use type	Sentinel-2 optical image	10 m	Copernicus Data Space Ecosystem
NDVI

.

3. Methods

The overall research process is shown in Figure 4. Firstly, the initial evaluation factor data and the spatial distribution information of landslide are collected, and the factors are screened by multicollinearity diagnostic, Pearson correlation coefficient and random forest (RF) algorithm. Secondly, the GWO-1D CNN landslide susceptibility evaluation model is constructed, and its training and accuracy evaluation are carried out. Finally, the model is applied to the landslide susceptibility evaluation of Mangshan Mountain, and the susceptibility zoning map of Mangshan Mountain is completed.

3.1. Factor Screening Method

The initial selection of evaluation factors of Mangshan Mountain is somewhat subjective, which may lead to redundant information between evaluation factors. This prevents the model from accurately determining the true relationship between evaluation factors and landslides, which in turn makes it difficult for the model to accurately evaluate the susceptibility of landslides. Thus, multicollinearity diagnostic, Pearson correlation coefficient, and random forest algorithm are used to analyze the correlation and importance of evaluation factors, which can eliminate the evaluation factors with high correlation and low importance.

Multicollinearity is a highly correlated phenomenon between two or more factors. The factors were tested for multicollinearity using variance inflation factor ($VIF$ and tolerance ($TOL$) [39]. The formulas for $VIF$ and $TOL$ are as follows:

$$VIF=\frac{1}{1-R_i^2},$$

(3)

$$TOL=\frac{1}{VIF},$$

(4)

where $R_i^2$ is the coefficient of determination. If $VIF$ > 10 or $TOL$ < 0.1, the factor is considered to have multicollinearity problems with other factors.

The Pearson correlation coefficient calculation is shown in Equation (5):

$$r=\frac{1}{n-1}\sum _{i=1}^n\left(\frac{X_i-\bar{X}}{\sqrt{X_i-\bar{X}}}\right)\left(\frac{Y_i-\bar{Y}}{\sqrt{Y_i-\bar{Y}}}\right),$$

(5)

where $n$ is the number of samples; $X_i$ and $Y_i$ are the values of the two evaluation factors for calculating the correlation, respectively; $\bar{X}$ and $\bar{Y}$ are the mean values of the corresponding evaluation factors. When |$r$| > 0.5, it is recognized that there is a serious correlation between two evaluation factors [40].

Random forest is an integrated learning algorithm that quantitatively describes the extent to which evaluation factors contribute to the model [41,42]. It uses the bootstrap resampling method to draw multiple samples from the original sample and performs decision tree modeling on each bootstrap sample. Then, combining multiple decision trees for prediction and voting to arrive at the final classification result [43]. The core idea behind the importance of random forests is to compare the average of the sum of the contributions of each feature in each tree of RF, which is generally measured using the Gini index (Equation (6)) for each evaluation factor [44,45].

$$Gini\left(p\right)=1-\sum _{i=1}^K{p}_i^2,$$

(6)

where $i$ denotes the evaluation factor, and $p_i$ is the weight of the factor.

3.2. Convolution Neural Network

CNN is a special feed-forward neural network model proposed by LeCun et al. in 1989, which is essentially a multilayer perceptron [46]. In the study of landslide susceptibility evaluation, data are usually one-dimensional structures. Therefore, this study constructs a one-dimensional CNN (1D CNN) model, which is mainly composed of convolutional layers, pooling layers, and fully connected layers. A series of factor vectors are convolved by the convolution layer and pooled by the maximum pooling layer, and then, the extracted high-dimensional feature information is mapped into the low-dimensional feature space by using the fully connected layer. Finally, the landslide and non-landslide classification results and their probabilities are obtained by nonlinear activation function. The model is shown in Figure 5.

The convolutional layer uses a convolutional kernel to perform feature extraction and feature mapping on the input data. The convolution formula is shown in Equation (7):

$$X_j=f\left(\sum _i^N{w}_j\cdot x_i+b_j\right),j=\mathrm{1,2},\cdot \cdot \cdot ,k,$$

(7)

where $X_j$ is the output result; $f$ is the nonlinear activation function; $x_i$ is the local input data; $w_j$ and $b_j$ are the weight and bias coefficient. After the convolution operation, the output dimension is generally reduced. In order to keep the output dimension unchanged, this study chooses to fill first and then convolve.

The direct connection of the convolutional module to the classification layer can easily lead to the problem of dimension explosion and overfitting. To solve this problem, the pooling layer is usually connected behind the convolutional layer for feature sampling. This reduces the number of parameters and decreases the feature dimensionality while allowing the CNN to remain undeformed to small local morphological changes. In this study, the maximum pooling layer is used for pooling. The calculation formula of maximum pooling layer is shown in Equation (8):

$$p_i=\underset{i\in N}{max}\left(a_i\right),$$

(8)

where $p_i$ is the pooling operation output; $i$ is the pooling location; $a_i$ is the input data corresponding to the pooling window.

3.3. Grey Wolf Optimizer

The accuracy of the 1D CNN model will be affected by the initial weights: if the initial weights are too small, the model cannot fit the dataset adequately; if the initial weights are too large, the model may suffer from the problem of gradient explosion, which leads to the model failing to converge [47]. The training of 1D CNN model by back propagation algorithm and gradient descent algorithm will make the model fall into the local optimal solution. Therefore, this study introduces the GWO algorithm to search for the best initial weights. The GWO algorithm will search for weight-optimal solutions from different sets of initial weights.

The GWO is an intelligence optimization algorithm proposed by Mirjalilil et al. to achieve the purpose of optimal search by simulating the gray wolf hierarchy and group hunting behavior [48]. There are four classes of gray wolves: $\alpha$ wolves, $\beta$ wolves, $\delta$ wolves, and $\omega$ wolves. In the GWO algorithm, the wolves complete the hunting by searching for the prey, surrounding the prey and attacking the prey, and the process of the wolves searching for the prey is the algorithm’s process of searching for the optimal solution. The encircling prey process is shown in Equation (9):

$$X^{t+1}=X_p^t-A\cdot \left|C\cdot X_p^t-X^t\right|,$$

(9)

where $X_p$ and $X$ are the position vectors of the prey and the gray wolf; $A$ and $C$ are the coefficient vectors, as shown in Equation (10):

$$\left\{\begin{array}{l} A=2a\cdot r_1-a\\ C=2\cdot r_2\end{array}\right.,$$

(10)

where $a$ is a vector of convergence factors that decreases linearly from 2 to 0 during the iteration; $r_1$ and $r_2$ are random vectors in [0, 1]. When |$A$| ≤ 1, the algorithm converges, and the prey position is obtained. The $\alpha$ wolves, $\beta$ wolves, and $\delta$ wolves will estimate the prey position and guide the $\omega$ wolf to update the position. The process is shown in Equation (11):

$$\left\{\begin{array}{l}{ X}_1=X_{\alpha }^t-A_1\cdot |C_1\cdot X_{\alpha }^t-X^t|\\ { X}_2=X_{\beta }^t-A_2\cdot |C_2\cdot X_{\beta }^t-X^t|\\ { X}_3=X_{\delta }^t-A_3\cdot |C_3\cdot X_{\delta }^t-X^t|\\ { X}^{t+1}=(X_1+X_2+X_3)/3\end{array}\right.,$$

(11)

where $X_1$, $X_2$, and $X_3$ are the updated vectors of the positions of the candidate solutions relative to the three preferred solutions; $X^{t+1}$ is the position of the selected solution after the update.

3.4. Model Evaluation

The GWO-1D CNN landslide susceptibility evaluation model is a binary classification model. There are four general scenarios for the prediction results of the binary classification model (

Table 2. The prediction results of binary classification model.

		Predicted Value
		Landslide	Non-Landslide
True value	Landslide	True Positive (TP)	False Positive (FP)
	Non-landslide	False Negative (FN)	True Negative (TN)

).

For binary classification problems, the most commonly used evaluation metrics are the receiver operating characteristic curve (ROC) [49,50] and the area under the ROC curve (AUC) [51,52]. When the AUC value is greater than 0.7, it means that the model has high accuracy.

In order to better evaluate accuracy, this study also selects accuracy ($ACC$), Kappa coefficient, sensitivity ($SEN$), and specificity ($SPE$) as evaluation indicators. The corresponding formula is as follows:

$$ACC=\frac{TP+TN}{TP+TN+FP+FN},$$

(12)

$$\left\{\begin{array}{l}Kappa=\frac{ACC-p_e}{1-p_e}\\ p_e=\frac{(TP+FN)\cdot (TP+FP)+(FP+TN)\cdot (FN+TN)}{(TP+FP+FN+TN{)}^2}\end{array}\right. ,$$

(13)

$$SEN=\frac{TP}{TP+FN},$$

(14)

$$SPE=\frac{TN}{TN+FP} .$$

(15)

Among them, the values of $ACC$, $SEN$, and $SPE$ range from 0 to 1, and the closer the value is to 1, the higher the model is. The Kappa coefficient value is between −1 and 1, and the value is greater than 0.6, which indicates that the model has high accuracy.

4. Results

4.1. Evaluation Factor Screening

According to

Table 3. The results of multicollinearity diagnostic for 16 factors (the meaning of the letters is consistent with Figure 3).

Factors	A	B	C	D	E	F	G	H	L	J	K	I	M	N	O	P
VIF	1.53	24.01	1.72	23.34	1.50	1.44	1.35	1.65	1.28	1.81	2.11	2.67	1.22	1.28	1.13	1.20
TOL	0.65	0.04	0.58	0.04	0.67	0.69	0.74	0.61	0.78	0.55	0.47	0.38	0.82	0.78	0.89	0.84

, the TOL and VIF values of slope and terrain relief are 0.04 and 24.01 and 0.04 and 24.34, which do not satisfy the conditions of VIF < 10 and TOL > 0.1. There is a problem of multicollinearity between slope and terrain relief and other landslide evaluation factors. However, slope and terrain relief are important topographic and geomorphic factors, which cannot be removed completely. Therefore, it is necessary to combine correlation analysis and importance analysis to remove other factors to solve the multicollinearity problem.

As can be seen from Figure 6, the landslide evaluation factors with high correlation are slope and topographic relief (0.973), aspect and topographic relief (0.508), plane curvature and profile curvature (0.534), SPI and slope (0.64), SPI and topographic relief (0.617), TWI and slope (0.718), TWI and topographic relief (0.71), and TWI and SPI (0.552). Mangshan Mountain is a typical loess tableland landform. The tableland surface is flat, and the gully is developed on the edge of the tableland. Therefore, the area with large slope is also the area with large topographic relief, which results in a serious correlation between slope and topographic relief. The aspect is the only factor describing the orientation, which needs to be retained. The same parameters (including slope) are used in the calculation of SPI and TWI, so there is a strong correlation between them and between them and slope. However, SPI and TWI are indexes describing the erosion capacity of slope runoff and the spatial distribution of soil water, which should be considered separately from slope. In summary, it is necessary to remove one evaluation factor from each of the three groups of factors: slope and terrain relief, plan curvature and profile curvature, and TWI and SPI.

The removal of evaluation factors should refer to the results of the importance analysis. The results of the RF importance analysis are shown in Figure 7. Slope has the highest importance, with a value of 0.285, and lithology has the lowest importance, with a value of 0.004. In the group of slope and topographic relief, the importance of slope (0.285) is slightly greater than that of topographic relief (0.216), so the evaluation factor of topographic relief is excluded. Similarly, the two evaluation factors of plane curvature and TWI are excluded. So far, the three evaluation factors of topographic relief, planar curvature, and TWI were excluded. The remaining 13 landslide susceptibility evaluation factors included elevation, slope, aspect, annual rainfall, and so on.

4.2. Dataset Construction and Processing

Before the landslide susceptibility evaluation, it is necessary to construct a dataset composed of landslide samples and non-landslide samples. There are only 46 landslide points used in this study. However, CNN requires a large number of sample datasets, so it is necessary to expand the landslide sample data. Thus, visual interpretation is carried out based on Google Earth images to obtain the approximate range of each landslide. A total of 5–15 sample points were randomly selected at each landslide, and a total of 345 sample points were obtained. In order to obtain non-landslide data with large discrimination from landslide data, this study establishes a 100 m buffer area with landslide points, and randomly selects 345 non-landslide points in the area outside the water area and buffer area according to the ratio of 1:1 (Figure 8). In order to reduce the discreteness of the data and the influence of different dimensions, the maximum and minimum normalizations of the continuous factor data are performed, and the unordered category factor data are dummy coded.

4.3. GWO-1D CNN Model Construction

In this study, Python language is utilized to develop the GWO-1D CNN landslide susceptibility model using the Keras deep learning library. The model comprises three main components: construction of the 1D CNN base model, optimization of initial weights using the GWO algorithm, and training and prediction of the optimized 1D CNN model. The algorithmic workflow is illustrated in Figure 9.

There is no complete set of methods to solve the problem of hyperparameter selection for GWO and 1D CNN models, which are generally adjusted according to the tuning experience and experimental effects [22]. Following numerous experiments, the study establishes that the optimal structure of the 1D CNN model consists of nine layers: one input layer, three convolutional layers with a kernel size of 3, three maximum pooling layers with a pool size of 2, one fully connected layer, and one output layer. Subsequently, relative optimal hyperparameters are determined, as detailed in

Table 4. 1D CNN model parameter settings.

Model Parameter	Parameter Setting
Size of convolution kernel (kernel_size)	3 × 1
Number of convolution kernels (filters)	15, 30, 60
Size of pooling kernel (pool_size)	2 × 1
Activation function (activation)	Tanh
Optimizer (optimizer)	Adam
Loss function (loss)	binary_crossentroy
Neuronal inactivation ratio (dropout)	0.2
Learning rate (learning_rate)	0.01
Batch size (batch_size)	32
Number of iterations (epoches)	100

. The GWO algorithm is employed with a population size of 15 and 200 iterations. Upon the completion of the iterations, the optimal solution is assigned to the 1D CNN model. Subsequently, the sample dataset is input into the optimized model for training and testing. The specific optimization steps are as follows:

Step 1. 1D CNN basic model building: build the 1D CNN model structure and set up the loss function, excitation function, and other hyperparameters.

Step 2. Setting the basic parameters of the GWO algorithm: determine the size of the gray wolf population and initialize the parameters a, A, and C (coefficient vectors) based on the constructed 1D CNN base model.

Step 3. Setting the fitness function and calculating the fitness: the loss function of the 1D CNN is used as the fitness function of the GWO algorithm, and each iteration splits the gray wolf individual into the weights of the 1D CNN. Subsequently, the loss value is calculated according to the loss function, and this value is used as the value of the fitness, according to which the optimal solution, the suboptimal solution, and the position of the third are selected, and the position of the gray wolf individual is the optimal solution when the fitness value is the largest.

Step 4. Update Individuals: update the position of individual gray wolves based on the position of the three head wolves, and update the values of the parameters a, A, and C at the same time.

Step 5. Iteration and output: keep repeating steps (3) and (4) until the maximum number of iterations is reached or the set accuracy is achieved. The optimal solution is passed into the 1D CNN model as initial weights.

In order to avoid the optimal 1D CNN model from falling into an overfitting or underfitting state, its training loss and testing loss are monitored at each training. The specific results are shown in Figure 10. From Figure 10, it can be seen that both show a rapid decline in the early stage of training. With the growth in the number of iterations, the training loss gradually stabilizes around 0.2561, while the testing loss stabilizes at about 0.2608, and the difference between the two is small. This proves that the constructed model has good fitting ability and generalization performance without overfitting or underfitting problems.

4.4. Evaluation of Model Accuracy

In addition to constructing 1D CNN and GWO-1D CNN models, this study also constructed GA-1D CNN and GWO -SVM models. The test sample set is fed into the trained four models for prediction, resulting in the generation of ROC (Figure 11) and confusion matrices (Figure 12) for four models. Upon examining Figure 11, the farthest point from the reference line on the ROC curves of the 1D CNN, GA-1D CNN, and GWO-1D CNN is close to the upper left corner, while the AUC values are 0.845, 0.902, and 0.943, which are greater than 0.7. This indicates that three models demonstrate favorable fitting and predictive accuracy. The ROC curve of GWO-SVM is furthest away from the upper left corner, and its AUC value (0.720) is the smallest. The AUC value of GWO-SVM is smaller than the 1D CNN base model, demonstrating that the 1D CNN model has a stronger expressive ability and evaluation accuracy in landslide susceptibility research. Both GA algorithm and GWO algorithm have an optimization effect on 1D CNN model, and the accuracy is significantly improved. However, the optimization effect of GWO is more obvious, and its AUC value is improved by 0.098.

From the confusion matrix diagram (Figure 12), it is evident that out of 115 landslide samples, the 1D CNN, GA-1D CNN, GWO-1D CNN, and GWO-SVM accurately predicted 98, 103, 109, and 84 samples, respectively; and out of 92 non-landslide samples, the four models accurately predicted 70, 73, 78, and 61, respectively. Based on the confusion matrix, various accuracy indicators such as accuracy (ACC) and Kappa coefficient are computed, as summarized in

Table 5. Accuracy evaluation of the two models.

Model	ACC	AUC	Kappa	SEN	SPE
1D CNN	0.812	0.845	0.616	0.852	0.761
GA-1D CNN	0.850	0.902	0.694	0.896	0.793
GWO–1D CNN	0.903	0.943	0.803	0.947	0.847
GWO-SVM	0.700	0.720	0.393	0.730	0.663

. The accuracy of GWO-SVM is obviously smaller than that of GWO-1D CNN model, and it is hereby argued that 1D CNN model has a greater application value in landslide susceptibility evaluation research. And the optimization effect of GWO is better than GA, so the comprehensive consideration is to use GWO-1D CNN model for evaluation. Notably, the SEN of GWO-1D CNN model significantly surpasses the SPE, indicating a tendency to predict some non-landslides as landslides. It could result in the misallocation of human, material, and financial resources, but this may mitigate potential landslide disasters. The accuracy of 1D CNN model is calculated as 0.812, with a Kappa coefficient of 0.616. In contrast, the GWO-1D CNN model achieves an accuracy of 0.903, along with a Kappa coefficient of 0.803. These values exceed 0.8 for accuracy and 0.6 for the Kappa coefficient, suggesting high accuracy levels and effective application in landslide susceptibility evaluation for Mangshan Mountain. Furthermore, the precision of 1D CNN model optimized by GWO algorithm demonstrates significant improvement. Notably, its ACC, AUC, Kappa coefficient, SEN, and SPE increase by 0.091, 0.098, 0.187, 0.095, and 0.086, respectively.

4.5. Susceptibility Evaluation and Mapping

The 13 filtered landslide susceptibility evaluation factors undergo normalization or coding and are integrated into a multi-channel image, where each grid unit represents a one-dimensional feature vector. Subsequently, the GWO-1D CNN model calculates the probability of landslide occurrence in each grid unit. The landslide susceptibility of Mangshan Mountain is classified into five grades: very low, low, medium, high, and very high. Finally, the landslide susceptibility zoning map of Mangshan Mountain is generated, as depicted in Figure 13.

From Figure 13, it is evident that the majority of the Mangshan Mountain falls within the categories of very low and low landslide susceptibility, predominantly situated in internal regions characterized by gentle slopes. Conversely, high and very high susceptibility areas are concentrated along the periphery of Mangshan Mountain, particularly near the Yellow River, exhibiting undulating terrain and steep slope. To further comprehend the distribution of landslide sample points across different susceptibility grades, the number of grid units within each susceptibility area and the corresponding count of landslide samples are tabulated. Additionally, the density of landslide samples is calculated and summarized in

Table 6. Proportion of different susceptibility levels.

Susceptibility Grade	Number of Grids (Unit)	Area Ratio (%)	Number of Landslides (Unit)	Landslide Ratio (%)	Landslide Density (Unit/km2)
Very low	236,668	40.2	1	2.2	0.04
Low	138,693	23.6	4	8.7	0.29
Medium	83,185	14.1	8	17.4	0.96
High	76,019	12.9	14	30.4	1.84
Very high	53,846	9.2	19	41.3	3.52
Total	588,411	100	46	100	—

.

Table 6 reveals the proportion and total area of each susceptibility grade in Mangshan Mountain, as follows: very low 40.2% (23.7 square kilometers), low 23.6% (13.9 square kilometers), medium 14.1% (8.3 square kilometers), high 12.9% (7.6 square kilometers), and very high 9.2% (5.4 square kilometers). Overall, the proportion of landslides increases with higher susceptibility levels, with landslide density positively correlated with susceptibility levels. Specifically, 71.7% of landslide points are concentrated in high and very high susceptibility areas, occupying 22.1% of the grid ratio. Conversely, only 10.9% of landslide points are distributed across more than 50% of the low and very low susceptibility areas.

5. Discussion

5.1. GWO Algorithm Optimization Effect

CNN models have great potential for application in landslide susceptibility evaluation [24,52]. The accuracy of classical 1D CNN can reach 81.2% when the accuracy of traditional GWO-SVM is 70.0%, and the accuracy of GA-1D CNN and GWO-1D CNN models can even reach 85.0% and 90.3%. However, the model of 1D CNN also faces the problem of initial weight selection, and the initial weight will directly affect the classification accuracy of the model. The classical 1D CNN model will reduce the model error by backpropagation and gradient descent algorithms, which can easily cause the model to fall into the local optimal solution [47]. Therefore, this study uses the GWO algorithm to globally search for the optimal initial weights. The global search of the GWO algorithm can well make up for the shortcomings of the classical 1D CNN model. The global search ability of the GWO algorithm and the local optimization ability of the gradient descent algorithm can be well combined to make the selection of the initial weights more reasonable, which substantially improves the classification accuracy of the 1D CNN model. The accuracy of the model is improved by 9.1%. And the GWO algorithm has a better optimization effect compared to the GA algorithm. In summary, the GWO-1D CNN model used in this study explores the problem of the initial weight selection of the CNN model. However, the CNN model currently still has problems in landslide susceptibility evaluation research, such as how to reasonably select non-landslide samples, difficulties in selecting hyperparameters of the CNN model, and large training samples [22]. These problems need to be further explored in future landslide susceptibility research based on the CNN model.

5.2. Analysis of Landslide Susceptibility for Mangshan Mountain

The susceptibility of Mangshan Mountain escalates with increasing slope. Given the relatively small research scope, factors such as annual precipitation and lithology exhibit minimal influence on the overall landslide susceptibility division, aligning with the importance analysis results. The landslide susceptibility evaluation results obtained from the GWO-1D CNN model are specifically analyzed as follows:

(1)

Higher susceptibility areas. The higher susceptibility zone consists of the very high susceptibility zone, which covers 9.2%, and the high susceptibility zone, which covers 12.9%. A total of 33 landslides fell in this area, accounting for 71.7%. This area is concentrated at the edge and is distributed along gullies, roads, and lakes. These areas have steeper slopes, lower NDVI, and are closer to the Yellow River, and slope protection should be strengthened in these areas. In addition to slope, river, and vegetation, roads and human buildings also have a greater impact on this region, while other factors have relatively less prominent impacts and mostly interact with each other.

(2)

Medium susceptibility areas. The medium susceptibility zone accounts for 14.1% of the total study area, which contains eight landslides with a landslide share of 17.4%. This type of area is a buffer zone between the higher and lower susceptibility zones, with most of them distributed around the higher susceptibility zone and a few sporadically situated in the lower susceptibility zone.

(3)

Lower susceptibility areas. The lower susceptibility zone consists of the very low susceptibility zone, which covers 40.2% of the study area, and the low susceptibility zone, which covers 23.6%. This type of area covers the largest area and is concentrated within the study, mostly located on loess plateau surfaces and gully bottoms with gentle slopes and lush vegetation. The main controlling factors for this type of area are slope and vegetation, but factors such as rivers, lakes, roads, and human construction have less influence on it than on the higher susceptibility areas.

6. Conclusions

Aiming at the problem that the classical 1D CNN model is easily affected by the initial weights, this study introduces the GWO algorithm to optimize the initial weights. In this study, Mangshan Mountain was taken as the research object, and 13 factors were screened for evaluation from 16 factors by multicollinearity test, Pearson correlation analysis, and RF importance analysis. Then, the GWO-1D CNN model was constructed and analyzed for accuracy comparison with the 1D CNN, GA-1D CNN, and GWO-SVM models. Finally, the GWO-1D CNN model was used to evaluate the landslide susceptibility of Mangshan Mountain, and the landslide susceptibility zoning map of the area was obtained. The key findings of this study are as follows:

(1)

The GWO-1D CNN model can effectively mine the complex relationship between landslides and landslide evaluation factors, greatly improving the accuracy and reliability of evaluation. The accuracies of 1D CNN, GA-1D CNN, GWO-1D CNN, and GWO-SVM are 0.812, 0.850, 0.903 and 0.700, respectively. The GWO-1D CNN model has the highest accuracy.

(2)

Utilizing the 1D CNN model as a foundation, the GWO algorithm is integrated to optimize its initial weights, leading to the development of the GWO-1D CNN model. Accuracy evaluation results demonstrate that the GWO algorithm markedly enhances the performance of the 1D CNN model. Specifically, its ACC, AUC, Kappa, SEN, and SPE exhibit notable improvements, increasing by 0.091, 0.098, 0.187, 0.095, and 0.086.

(3)

The susceptibility grades and respective area proportions of Mangshan Mountain are as follows: very low 40.2%, low 23.6%, medium 14.1%, high 12.9%, and very high 9.2%. The landslide susceptibility of Mangshan Mountain correlates positively with slope inclination, while annual precipitation and lithology exhibit minimal influence. High and extremely high susceptibility areas predominantly cluster along the periphery of the study area, adjacent to rivers, lakes, valleys, and roads. These regions are characterized by steep slopes, low NDVI values, and proximity to the Yellow River. Enhanced slope protection measures are recommended for such areas.