Research on SSA-LSTM-Based Slope Monitoring and Early Warning Model

Abstract

For geological disasters such as landslides, active prevention and early avoidance are the main measures to avoid major losses. Therefore, landslide early warning is an effective means to prevent the occurrence of landslide disasters. In this paper, based on geological survey and monitoring data, a landslide monitoring and early warning model based on SSA-LSTM is established for the landslide in Yaoshan Village, Xiping Town, Anxi County, Fujian Province, China. In the early warning model, the hyper parameters of the LSTM neural network are optimized using the SSA algorithm in order to achieve high-accuracy displacement prediction of the LSTM displacement prediction model, and are compared with the unoptimized LSTM, and the results show that the prediction effect of the optimized SSA-LSTM model is significantly improved. Since landslide monitoring and early warning is a long-term work, the model trained by the traditional offline learning method will inevitably have distortion of the prediction effect as the monitoring time becomes longer, so the online migration learning method is used to update the displacement prediction model and combine with the tangent angle model to quantify the warning level. The monitoring and early warning model put forth in this research can be used as a guide for landslide disaster early warning.

1. Introduction

Landslides, as a common natural disaster, often cause great damage [1,2]. The southeast coastal region of China, where Fujian Province is located, is prone to typhoons. As one of the provinces most severely affected by landslides in China, slope instability brought on by typhoons is particularly likely to occur in hilly places. Such rainfall landslides are characterized by clusters, outbreaks, and uncertain locations, which are very likely to cause significant casualties and economic losses. For instance, on 19 November 2011, affected by continuous rainfall, a landslide occurred suddenly in Pengge Village, Penglai Town, Anxi County, Quanzhou City, Fujian Province, causing the collapse of houses and killing one person; on 25 April 2012, a landslide incident occurred in Lundeyang Village, Daqiao Town, Gutian County, Ningde City, Fujian Province, killing six people; on 8 May 2016, a landslide occurred in Taining County, Sanming City, Fujian Province, which washed away a local power plant living camp and office building, eventually causing 35 people to be killed and 14 people to be injured; on 22 April 2017, a landslide occurred in Xibai Bailian Tang, Zhongkeng Village, Chengjiao Town, Yongding District, Longyan City, Fujian Province, due to continuous heavy rainfall, causing the excavator and construction vehicle that was passing by to be buried by a mudslide, and three people on board were killed; on 22 May 2021, a large landslide occurred in Fuan City, Ningde, Fujian Province, on National Highway 104. A large landslide occurred, causing vehicle blockage and seriously affecting traffic. To prevent severe losses brought on by landslides, proactive prevention and early avoidance are the essential strategies. Due to its low cost and great feasibility compared to landslide control, landslide early warning is, therefore, an efficient way to avert the occurrence of landslide disasters.

There are several methods to construct early warning models for landslides: (1) empirical models, (2) theoretical models, (3) artificial intelligence models, etc. The empirical model is a regional rainfall threshold model using the correlation between historical rainfall and landslides in the study area [3,4,5]. This method can realize the monitoring and early warning for large areas, but the early warning effect for specific slopes in small areas is poor, and it cannot realize the accurate monitoring and early warning for specific slopes. Theoretical models are early warning models based on experimental results, and which use theoretical knowledge [6,7,8,9], and the more common ones are the viscous slope model [6], cusp mutation model [8], and improved tangent angle model [9]. The warning time of such early warning models is often more erratic and cannot provide warning within 6–12 h before the occurrence of a landslide, which, in turn, does not provide enough time for the evacuation of the people involved. Among artificial intelligence methods, the commonly used models are recurrent neural network models [10,11,12,13], BP neural network models [14,15], deep belief network (DBN) models [16], support vector machine (SVM) models [17,18,19], and extreme learning machine (ELM) models [20,21,22].

From the above study, it can be seen that artificial intelligence models have achieved a wide application of monitoring and warning of landslides. The artificial intelligence model has a longer warning period than the theoretical model, which can give time for the evacuation of pertinent persons. It can accomplish an accurate early warning for certain slopes when compared to the empirical model. The displacement change of the slope is a time-dependent physical phenomenon, and the Long Short-Term Memory Neural Network (LSTM) has a natural advantage in dealing with the time-dependent change problem [23,24]. Therefore, in this paper, the LSTM neural network in artificial intelligence model is chosen for displacement prediction. However, a single LSTM displacement prediction model cannot quantify the warning level of the slope, so the improved tangent angle model [9] is used to quantify the warning level and, thus, the warning.

In early warning models constructed by artificial intelligence methods, the selection of hyper parameters has a great impact on the accuracy of their prediction. Currently, the selection of hyper parameters for neural networks is mainly done iteratively by optimization algorithms such as the Particle Swarm Algorithm (PSO) [25,26], Genetic Algorithm (GA) [27], Gray Wolf Algorithm (GWO) [28], and other optimization algorithms for hyper parameters of neural networks. The Sparrow Search Algorithm (SSA) [29] has the advantages of high accuracy, fast convergence, stability, and robustness compared with other optimization algorithms. Therefore, in this paper, SSA is used to optimize the hyper parameter selection of LSTM. The traditional neural network construction method requires a prior given data set for training. This approach is applied to the monitoring and early warning process of the slope, and the neural network model will reduce accuracy tower time and data increase. In order to guarantee the accuracy of the model’s prediction findings, the early warning mechanism in this research updates it using the online migration learning method.

In this paper, the landslide in Yaoshan Village, Xiping Town, Anxi County, Fujian Province, China, is taken as an example, and monitoring equipment, such as displacement meter, moisture meter, osmometer, pore water pressure meter, and rain gauge, are arranged. Based on the monitoring data, the LSTM displacement prediction model was established by optimizing the hyper parameter selection of the LSTM neural network using the SSA algorithm. By combining with the improved tangent angle model, the warning level of the slope was quantified. The displacement prediction model was updated using the online migration learning method to ensure the accuracy of early warning.

2. Background of the Case

2.1. Research Area

Anxi is located in the southeast slope of the Daiyun Mountains. The terrain in the area is mainly mountainous and changes greatly. The highest peak is Taihua tip, 1600 m above sea level, and the lowest place is Chengxiang Jingdou village, only 32 m above sea level; the relative height difference reaches 1568 m. Xiping town is relatively high (the average elevation is 600~700 m) and it is mainly mountainous, with large slope and narrow river valley.

The disaster site is located in Yaoshan Village, Anxi County, Quanzhou City, on the right bank of the Xiaolanxi River (Figure 1), a tectonic erosion low mountain landscape with a maximum elevation of 957 m and a minimum elevation of 290 m, a difference in elevation of 650 m. The overall slope is about 15~20°, and the slope behind the local houses can be 50~70°; the elevation of 470~957 m is a steep slope, with a slope of about 35°~40°. The slope mainly develops three drains. The east and west drains are cut deeper; the ditch width is about 10 m, and the depth is about 5 m. The middle drains are cut shallower; the ditch width is about 2~3 m, the depth is about 1~2 cm, and it is a shallow “U”-shaped valley. The three drains have perennial flowing water; the flow rate is about 150~300 m³/d. The slope is mostly planted with tea, vegetables, and other cash crops. The vegetation is dense, and the coverage rate reaches 70~80%.

The area between the “dotted lines” in Figure 1c is the monitoring area of this paper. According to the “solid line” in the figure, the monitoring area is sampled by boreholes, and a cross-sectional view is drawn (Figure 2). The monitoring area is mainly composed of five types of soil (rock mass): colluvial gravel soil, residual cohesive soil, fully weathered tuff, sandy strongly weathered tuff, and moderately weathered tuff.

2.2. Monitoring Methods

According to the geological survey data on the affected site, monitoring equipment, monitoring content, monitoring parts, and quantities were set up as in

Table 1. Monitoring program.

Monitoring Content	Monitoring Equipment	Monitoring Site	Number of Sensors
Displacement	Guide wheel type fixed measurement	Landslide body	4
Pore water pressure	Pore water pressure gauge	Landslide body	6
Water-level monitoring	Water level gauge	Landslide body	2
Soil water content	Moisture meter	Landslide body	8
Rainfall monitoring	Rain gauge	Side slope area	1

[30]. Displacement monitoring data are shown in Figure 3a, where the first number represents the measurement point, and the second number represents the depth (1 is 4 m from the surface, and 2 is 16 m from the surface). The pore pressure monitoring data are shown in Figure 3b, and six pore pressure monitoring points were deployed, respectively (the first three points are in monitoring point 1, and the last three points are in monitoring point 2). The water level monitoring data are shown in Figure 3c, where SW-1 is 17.5 m from the bottom of the pore, and SW-2 is 16 m from the bottom of the pore. The soil moisture content monitoring data are shown in Figure 3d, and eight moisture content monitoring points are deployed, respectively (the first four points are in monitoring point 1, and the last four points are in monitoring point 2).

3. Displacement Prediction Model

3.1. SSA

The sparrow search algorithm is an algorithm that imitates bird foraging in nature. It has the advantages of high accuracy, fast convergence speed, strong stability, and good robustness in practical applications [29]. Each sparrow position in SSA corresponds to a solution. There are three behaviors of sparrows when foraging: (1) foraging as discoverers; (2) foraging as joiners following discoverers; and (3) foraging as scouts deciding whether to abandon food in the population. Among them, discoverers and joiners can switch between each other, but the proportion remains constant, with discoverers generally accounting for 10% to 20% of the population. The discoverer acts as a foraging guide, searching a wide range and constantly updating its position by memory to obtain food sources. The joiners, on the other hand, follow the discoverers to continuously forage for a higher level of adaptation. However, due to the threat of predators at all times, the population randomly selects 10–20% of sparrows as scouts to monitor, in order to alert the whole population to anti-predatory behavior in time when predators appear.

During each iteration, the position update of the discoverer is described as shown in Equation (1):

$$X_{i,j}^{t+1}=\{\begin{array}{c}{X}_{i,j}^{t+1}·e^{\left(-\frac{i}{\alpha ·ite{r}_{max}}\right)},R_2<ST\\ X_{i,j}^t+QL,R_2\ge ST\end{array}$$

(1)

where $t$ is the number of current iterations; $ite{r}_{max}$ is the maximum number of iterations; $X_{i,j}^{t+1}$ is the position information of the $i-th$ sparrow in the $j-th$ dimension; $\alpha \in (0,1]$ is a random number; $R_2$ and $ST$ denote the warning and safety values, respectively, where $R_2\in \left[0,1\right]$ and $ST\in \left[0.5,1\right]$; $L$ is a $1\times d$ matrix, and each element in this matrix is 1. when $R_2<ST$, it means that there are no predators around the foraging environment at this time and the finder can perform extensive search operations; when $R_2\le ST$, it means that some sparrows in the population have spotted the predator and alerted the rest of the population, at which point, all sparrows need to quickly fly to other safe places to forage.

The update of the joiner is described as shown in Equation (2):

$$X_{i,j}^{t+1}=\{\begin{array}{c}Q·e^{\left(\frac{X_{worst}^t-X_{i,j}^t}{i^2}\right)},i>\frac{n}{2}\\ X_P^{t+1}+\left|X_{i,j}^t-X_P^{t+1}\right|A^{+}·L,Other\end{array}$$

(2)

where $X_P$ is the optimal position currently occupied by the discoverer; $X_{worst}$ is the current global worst position; $A$ is a $1\times d$ matrix with random magnitude of 1 or −1 for each element within this matrix and $A^{+}=A^T{\left(A{A}^T\right)}^{-1}$. When $i>\frac{n}{2}$, it indicates that the $i-th$ joiner with a lower fitness value is not getting food and is in a very hungry state, and needs to fly to other places to forage for more energy.

When aware of danger, sparrow populations engage in anti-predatory behavior, the mathematical expression of which is shown in Equation (3):

$$X_{i,j}^{t+1}=\{\begin{array}{c}{X}_{best}^t+\beta \left|X_{i,j}^t-X_{best}^t\right|,f_i>f_g\\ X_{i,j}^t+K\left[\frac{\left|X_{i,j}^t-X_{worst}^t\right|}{\left(f_i-f_w\right)+\epsilon }\right],f_i=f_g\end{array}$$

(3)

where $X_{best}$ is the current global optimal position; $\beta$ is the step control parameter, which obeys a normal random distribution number with a mean of 0 and a variance of 1; $K$ is a random number that represents the direction of sparrow movement along with the control parameter of the step size, and $K\in \left[-1,1\right]$; $f_i$ is the current fitness value of the individual sparrow; $f_g$ and $f_w$ are the current global best and worst fitness values, respectively; $\epsilon$ is the smallest constant to avoid 0 in the denominator.

3.2. LSTM

LSTM neural networks are a variant of recurrent neural networks [31,32]. In traditional RNN neural networks, the input is a set of associated sequential data, and recursive computation is used in the sequence forward direction, and all neurons are linked by chaining, so that the previous historical information can be integrated with the current moment’s information to work together in the next moment, which, thus, ensures the advantageousness of RNNs to achieve the role of memory and to process time sequences. Compared to other ordinary neural networks, an additional feedback input is used as a dynamic recurrent system, which can pass the results of the previous neuron computation to the new neuron computation according to a certain weighting [33].

RNN neural networks are similar to the structure of the human brain, which can compute and analyze the input of historical information to produce prediction results. Due to the limitations of the memory capacity of RNN neural networks, the historical information features of earlier moments will be retained less, whereas the information features of the nearer moments will be retained more, and in the training process, a large number of repetitions make the information decay in the process of going through the loop body, so RNN neural networks have certain shortcomings in the actual use process; namely, there is a gradient disappearance [34]. Figure 4a shows the internal structure of the RNN neural network, whose recurrent body is simply through a tanh function. The LSTM neural network [35] is able to store the older information features to be utilized by accumulating the historical information input during each training process, and the advantage of the RNN neural network of processing time series is still retained because only the internal structure is changed.

The LSTM neural network is also a recurrent neural network of time series, and its internal structure is shown in Figure 4b. The neural network structure of traditional neurons is improved by introducing memory cells. The state of the memory cells and the information transfer and processing between memory cells are the special features of the LSTM neural network architecture, and the historical information is also well preserved in the memory cells, and the input gate mechanism inside the memory cells can feasibly operate the value preservation time by itself, so that the important information can be well predicted based on it.

The LSTM neural network relies on the forgetting gate, input gate, and output gate in the memory cell structure to realize its memory function, which is the dashed part in Figure 4b. The state of the memory unit will be updated with the input of new data, and the operation of refining and judging the original information is mainly realized through the neural network layer and the multiplication operation algorithm; that is, the “gate” structure.

Taking the input value $x_t$ of the LSTM network of moment $t$ and the output values $h_{t-1}$ at moment $t-1$ as the input information on the model, it relies on the structural action of the three gates to update the information $C_t$ in the memory cell and the memory cell output $h_t$ at that moment. The working mechanism of its three gates is as follows:

(1)

Forgetting gate: used to determine whether to retain the value of the memory unit through the sigmoid function to determine the input information and the previous moment of information forgotten or retained. Its formula is shown in (4):

$$f_t=\sigma \left(W\left[h_{t-1},x_t\right]+b\right)$$

(4)

where $h_{t-1},x_t$ is the output value of the previous moment and the input value of the current moment; $\sigma$ is the sigmoid activation function; $W$ is the weight matrix; and $b$ is the bias value.

(2)

Input gates: used to control the addition of new information on the training process to obtain the cell state at that moment. The sigmoid layer in the input gate determines the content of the information update, and the tanh layer generates a new vector of candidate values to be added to the current state. The formulas are shown in (5) and (6):

$$i_t=\sigma \left(W\left[h_{t-1},x_t\right]+b\right)$$

(5)

$$\widetilde{C_t}=tanh\left(W\left[h_{t-1},x_t\right]+b\right)$$

(6)

By multiplying the previous moment state with $f_t$ to determine the forgotten information while adding the new information on training, the formula is shown in (7):

$$C_t=f_t{C}_{t-1}+i_t\widetilde{C_t}$$

(7)

(3)

output gate: the output value determined by the sigmoid function is multiplied with the tanh functions to obtain the final output value. The formula is shown in (8):

$$O_t=\sigma \left(W\left[h_{t-1},x_t\right]+b\right)$$

(8)

$$h_t=O_{t}tanh\left(C_t\right)$$

3.3. SSA-LSTM

In the process of slope monitoring, the monitoring data will inevitably be affected by noise due to the influence of the instrument itself and natural conditions. The noise in the monitoring data will have a great influence on the prediction result of slope displacement, so the monitoring displacement data of the slope will be filtered and the noise will be reduced before the displacement prediction. At present, the main methodological studies on noise-containing signal processing in various fields include Kalman filtering [36,37,38], wavelet noise reduction [39,40,41], and Savitzky–Golay filtering [42,43,44]. Since Savitzky–Golay filtering can ensure that the shape and width of the signal remains unchanged while filtering the noise, and its required time cost and computational cost are low, Savitzky–Golay filtering is chosen here to filter the monitoring data of the slope. Because the complex structure of the LSTM data network and the weights between different structural layer connections make the data features more sensitive, in order to eliminate the odd sample data, we need to generalize the same sample data statistical distribution characteristics and accelerate the network learning and computational convergence efficiency. Therefore, the data set needs to be normalized before the training process. Similarly, the prediction results need to be to reverse-normalized, and the processed data are the real results, as shown in Equations (9) and (10):

$$p_n=\frac{p-p_{min}}{p_{max}-p_{min}}$$

(9)

where $p_n$ is the normalized processing of; $p$ is the original value of the sample; $p_{max}$ and $p_{min}$ are the original maximum and minimum values of the sample, respectively;

$$q=q_n\left(q_{max}-q_{min}\right)+q_{min}$$

(10)

where $q_n$ is the original value of the prediction result; $q$ is the normalized processing value; $q_{max}$ and $q_{min}$ are the original maximum and minimum values of the prediction, respectively.

The construction process of the SSA-LSTM displacement prediction model is shown in Figure 5, with the following six steps:

• Reading of monitoring data;
• Data pre-processing, including filtering and normalization of monitoring data;
• Population initialization, including population size, maximum number of iterations, percentage of discoverers and scouts, and optimization parameters of LSTM;
• Execution of SSA algorithm;
• If the algorithm reaches the preset maximum number of iterations or the best fitness is continuously maintained at 10% of the total number of iterations, the algorithm search ends and returns the sparrow location information of the best fitness, which is the best optimization parameter of the LSTM; otherwise, skip to 4;
• The optimization results are used to build the LSTM model and saved.

3.4. Comparison of Predicted Results

In order to compare the traditional LSTM model and the SSA-LSTM model, the prediction effect of the monitoring data on the disaster site was compared. The monitored data on the first 300 days were used to build a model (that is, from 20 November 2020 to 15 September 2021), and the training set and test set were divided according to 8:2. The prediction results are shown in Figure 6. As can be seen in Figure 6, although both the LSTM model and the SSA-LSTM model can accurately predict the displacement trend, the SSA-LSTM has a higher degree of overlap between the real data, so the prediction of the LSTM model optimized by the SSA algorithm is considered to have a higher accuracy compared to the traditional LSTM.

In order to quantitatively to analyze the prediction effect of the LSTM neural network of this slope displacement monitoring data, and to compare the performance difference in this model at different points of different prediction times, in this paper, three metrics commonly used in regression problems of deep learning are chosen for comparison and analysis; namely, Mean Absolute Error (MAE), Root-Mean Squared Error (RMSE), and Coefficient of Determination (R²). MAE is the mean value of the absolute error between the predicted and true values; RMSE represents the deviation between the predicted and true values; and R² is a statistical indicator used to measure the strength of the linear relationship between the true and predicted data. The formulae for calculating the three indicators are shown in Equations (11)–(13):

$$MAE=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\left|F_i-g_i\right|$$

(11)

$$RMSE=\sqrt{\frac{1}{N}{\displaystyle \sum }_{i=1}^N(F_i-g_i{)}^2}$$

(12)

$$R^2=1-\frac{{{\displaystyle \sum }}_{i=1}^N(g_i-F_i{)}^2}{{{\displaystyle \sum }}_{i=1}^N(g_i-\overline{g}{)}^2}$$

(13)

where $g_i$ is the specific value of the $i_{th}$ real data; $\overline{g}$ is the average value of the real data; $F_i$ is the specific value of the $i_{th}$ predicted data.

The MAE, RMSE, and R² calculation results of the four monitoring point prediction model test sets are shown in

Table 2. Comparison of predicted effects of monitoring points of WY1-1.

Type of Error	SSA-LSTM	LSTM
MAE	0.875	3.276
RMSE	1.307	3.393
R2	0.965	0.766

,

Table 3. Comparison of predicted effects of monitoring points of WY1-2.

Type of Error	SSA-LSTM	LSTM
MAE	9.063	5.997
RMSE	9.439	7.563
R2	0.880	0.923

,

Table 4. Comparison of predicted effects of monitoring points of WY2-1.

Type of Error	SSA-LSTM	LSTM
MAE	1.200	1.421
RMSE	1.269	1.700
R2	0.922	0.860

and

Table 5. Comparison of predicted effects of monitoring points of WY2-2.

Type of Error	SSA-LSTM	LSTM
MAE	2.168	2.927
RMSE	2.375	3.612
R2	0.978	0.949

. It can be seen from the table that, except the monitoring point, WY1-2, the other three monitoring points had obvious improvement, especially at the monitoring point, WY1-1: the MAE value decreased by 2.401, the RMSE value decreased by 2.086, and the R² value increased by 0.199. Except for WY1-2, the R² values of the other three monitoring points were all above 0.9. Therefore, it is considered that the prediction effect of the SSA-LSTM displacement prediction model is better than that of the LSTM displacement prediction model.

4. Building Early Warning Models

4.1. Model Updates

In traditional neural network training, offline learning is generally used; that is, both source data and target data are already fixed. However, in the monitoring and early warning of slopes, the data are gradually increased with the passage of monitoring time. Therefore, although the traditional offline learning method can obtain good results in the training set and test set, it will inevitably fail to adapt to its application environment in time with the increase in data. In this regard, using the online migration learning method whenever new monitoring data are added, the SSA-LSTM displacement prediction model established in the previous subsection of this paper is used as the basis, and the 300 most recent data are selected to update the model once, and the SSA algorithm is also used to optimize the corresponding hyper parameters during the model update. For a total of 60 days, from 16 September 2021 to 14 November 2021, data were used to validate the model’s predictions. This is shown in Figure 7. From the figures, it can be seen that the prediction effect of the model updated by online migration learning is significantly better than that of the initial model, which is closer to the real data. In order to quantify the prediction effect of the two models more clearly, the maximum percentage error and the average error of the two models are calculated and listed in

Table 6. WY1-1 monitoring point online learning and offline learning effect comparison.

Type of Error	Online Learning	Off-Line Learning	Upgraded
Average error	0.935	5.057	4.122
Maximum Error	5.859	12.701	6.842

,

Table 7. WY1-2 monitoring point online learning and offline learning effect comparison.

Type of Error	Online Learning	Off-Line Learning	Upgraded
Average error	2.275	10.304	8.030
Maximum Error	4.489	14.235	9.746

,

Table 8. WY2-1 monitoring point online learning and offline learning effect comparison.

Type of Error	Online Learning	Off-Line Learning	Upgraded
Average error	1.530	9.550	8.021
Maximum Error	5.838	14.522	8.683

and

Table 9. WY2-2 monitoring point online learning and offline learning effect comparison.

Type of Error	Online Learning	Off-Line Learning	Upgraded
Average error	0.765	8.063	7.298
Maximum Error	1.727	9.562	7.835

. The online migration learning model’s prediction effect greatly increased, particularly for the monitoring locations, WY1-2 and WY2-1, where the improvement is over 8%.

4.2. Early Warning Level Classification

In this early warning model, the improved tangent angles model [9] is used to quantify the early warning level of the slope. The improved tangent angle model realizes the same dimension of the horizontal and vertical coordinate by transforming the cumulative displacement–time curve of the slope, and then obtains the tangent angle method. This method can reasonably convert the displacement value of the landslide into an angle value, thereby realizing the division of the warning level, and has achieved good results in many cases [45]. However, in the previous research, the early warning was mainly based on the tangent angle value obtained from the monitoring data, and the early warning time was unstable. The landslide displacement prediction method proposed in this paper can accurately predict the displacement in the next 24 h. Therefore, it cooperates with the landslide displacement prediction model proposed in this paper. The definition of the improved tangent angle model is shown in Equation (14):

$${\mathsf{\alpha }}_i=arctan\frac{T\left(i\right)-T\left(i-1\right)}{t_i-t_{i-1}}$$

(14)

where $t_i$ is the monitoring moment, $t_i$; ${\mathsf{\alpha }}_i$ is the improved tangent angle value at the requested monitoring moment; $T\left(i\right)$ is calculated according to Equation (15), and is the longitudinal coordinate value of the cumulative displacement–time curve with the same dimension as time after transformation:

$$T\left(i\right)=\frac{S_i}{\overline{v}}$$

(15)

where $S_i$ is the displacement change of the slope in a certain time period; $\overline{v}$ is the displacement rate of the equal deformation phase.

Generally speaking, it is difficult to accurately delineate the isokinetic deformation phase in the landslide deformation process, especially for sudden-onset landslides [45], where the rate of the early isokinetic deformation phase is small or the isokinetic deformation phase is not obvious, so the average rate of the whole process $B$ is used instead of the deformation rate of the uniform deformation phase, as shown in Equation (16):

$$B=\frac{S_n-S_0}{t_n-t_0}$$

(16)

Referring to the early warning thresholds set in the application of the improved tangent angle to several slopes, the thresholds, as in

Table 10. Early warning threshold setting for early warning model.

Early Warning Thresholds	$\mathit{\alpha }<45°$	$45°\le \mathit{\alpha }<65°$	$65°\le \mathit{\alpha }<80°$	$\mathit{\alpha }\ge 80°$
Early warning level	None	Green alert	Yellow alert	Red alert

, are set for the slopes described in this paper. The effect of the division of the early warning level in the application of real monitoring data is shown in Figure 8.

4.3. Early Warning Model Workflow

The early warning model constructed in this paper mainly uses the constructed landslide displacement prediction model to predict the displacement in the next 24 h, combined with the improved tangent angle model for early warning. The workflow mainly includes the following four steps:

• Data pre-processing, including noise reduction, normalization, and extraction of the first 300 data;
• Optimize the online migration learning of the initial model using the SSA algorithm to update the weights within the initial model to adapt it to the latest monitoring data using the 300 most recent data monitored;
• Predict the displacement value for the coming day and obtain the warning level of displacement for that day using the improved tangent angle model;
• Transmission of alert levels to the server side for alerting.

5. Discussion

In this research, we provide a slope monitoring early warning model based on SSA and LSTM. We show that the prediction outcomes of the LSTM model improved by the SSA approach have a considerable improvement in Figure 4 and Table 2, Table 3, Table 4 and Table 5. Additionally, since slope monitoring and early warning is a long-term project, the standard offline learning approach may produce inaccurate predictions as more data become available. In this context, the online migration method is used to update the displacement prediction model. It is demonstrated in Figure 5 and Table 6, Table 7, Table 8 and Table 9 that this method has higher accuracy and stability than the conventional method.

In summary, we optimize the LSTM displacement prediction model using the SSA algorithm to establish a preliminary displacement prediction model for the corresponding case series. The displacement prediction model was updated using the online migration learning method to ensure its long-term prediction accuracy. According to the displacement prediction results, four warning levels were quantified using the improved tangent angle model, as shown in Table 10, and the warning effects of the warning levels are shown in Figure 8.

6. Conclusions

The monitoring data are the basis for establishing the landslide displacement prediction model, and the landslide displacement prediction results are the basis for the landslide warning model. The displacement prediction model of this slope is established in this paper using the SSA algorithm and the LSTM neural network, and the model is updated using the migration learning method in the actual monitoring process to ensure its calculation accuracy in the early warning process. This paper uses the landslide in Yaoshan Village, Xiping Town, Anxi County, Fujian Province, China, as an example. The main conclusions are as follows: (1) the optimization of the LSTM model using the SSA algorithm can significantly improve the performance of the model in the data set; (2) the LSTM model with the traditional offline learning method will gradually distort with the increase of monitoring data in the monitoring and warning process of the landslide; (3) updating the model using the online migration learning method can ensure the prediction accuracy in the overall monitoring process.

In general, the landslide monitoring and early warning model proposed in this paper can accurately predict the displacement development process of the landslide, and it can be combined with the improved tangent angles model for early warning. In the early warning model, we use the SSA-LSTM displacement prediction model to predict the displacement in the next 24 h, and use the improved tangent angle model to quantify the displacement prediction results of four levels. Therefore, the monitoring and early warning of landslides in the next 24 h are realized.