Risk Prediction Model for Tailings Ponds Based on EEMD-DA-LSTM Model

Abstract

With the passage of time, the constant changes in relevant factors, and the daily maintenance of tailings ponds, the difficulty of tailings pond safety management is increasing day by day. In order to systematically improve the early warning ability for tailings pond dam break risk, the relationship between and influence of various related dam break risk factors of tailings ponds are utilised and the combination with dual attention is innovatively proposed. The risk prediction model for tailings ponds, EEMD-DA-LSTM, is improved. First, Pearson correlation coefficients are used to analyse the correlation between risk factors of tailings ponds. Then, the EEMD method is used to decompose the nonlinear displacement sequence, and the weights of input features are dynamically adjusted by double attention (DA). Finally, the LSTM network model is constructed to predict the displacement change. Taking valley-type tailings pond WKB-1 and mountainside tailings pond WKB-2 as examples, the dam break risk prediction models for tailings ponds are constructed based on three different models, the prediction results of different models are compared and analysed, and the prediction accuracy of the models is evaluated by three different evaluation criteria. The research results show that the integration of the EEMD-LSTM model with the DA model, that is, the EEMD-DA-LSTM model, has a better prediction effect for the dam break risk of tailings ponds WKB-1 and WKB-2 than other models through experimental verification. Therefore, the EEMD-DA-LSTM model is of great significance for preventing and resolving the safety risks of tailings ponds. It is valuable for practitioners in the mining industry and environmentally sustainable development.

1. Introduction

Tailings reservoirs are an indispensable and important part of mining activities and they exist widely. However, there are some potential safety hazards, such as dam break, leakage, environmental pollution, and so on. These hidden dangers not only threaten the balance of the surrounding ecological environment but also pose serious threats to the safety of residents and environmental protection. Once the dam breaks, it will affect the health of residents and pose a huge burden on the economy [1]. Therefore, it is particularly urgent and important to carry out research on risk prediction models for tailings ponds, which is of great significance to people’s lives and environmental protection.

In recent years, there are many scholars experimenting on risk prediction of various tailings ponds. Yang Yuhao et al. [2] proposed a combination method of a one-dimensional convolutional neural network (1DCNN) and long short-term memory neural network (LSTM) to predict the infiltration line. Taking the main dam of the Fengshuigou tailings pond in Qidashan, Liaoning Province, as an example, five main factors, namely, the historical infiltration line, reservoir water level, internal and external displacement of the dam, and length of the dry beach, were used as model input data to predict the location of the infiltration line in the future in 1D and the future in 3D. Huang Taiyu et al. [3] combined Flow-3D numerical simulation technology to conduct an in-depth study on the evolution process of tailings sand flow after the diffuse roof breach of a tailings pond. Lv Shi-Wei et al. [4] proposed a kriging space prediction algorithm based on the particle swarm algorithm to optimise the kriging model to fit the internal parameter data of tailings ponds, aiming to improve the fitting accuracy of the internal parameter information of tailings ponds and reduce the error. Xunxi et al. [5] constructed a BWOA-SVM model to predict the risk level of tailings ponds. Tang Yufeng et al. [6] proposed a tailings dam displacement prediction method based on temporal decomposition and the sparrow search algorithm-long and short-term memory-attention mechanism (SSA-LSTM-Attention) model. Ruan Shunling et al. [7] proposed a method to predict the safety situation of tailing reservoir infiltration line by integrating convolutional neural network (CNN) and gated cycle unit (GRU), so as to grasp the stability and safety development situation of the dam body. Huang S et al. [8] proposed to forecast the runoff of irrigated rice fields in southern China based on the EEMD-LSTM model, which also simulated and predicted the multi-factor correlation analysis and achieved good results.Yingkang Lu et al. [9], owing to the nonlinearity and uncertainty of workshop power consumption data, reported that it is very difficult to establish an accurate energy consumption prediction model. They proposed an energy consumption prediction model based on Prophet-EEMD-LSTM and predicted the final energy consumption value using LSTM’s excellent prediction performance on time series data. The effect was good. Jiwei Z et al. [10] used the coupling model to fit and forecast different data related to precipitation series and used multiple evaluation indicators to evaluate the prediction performance. The experimental results showed that the model had a good effect and had high confidence in future precipitation prediction results.

The above research has achieved certain results, but there is still a gap that needs to be supplemented and further studied. For example, the Fengshuigou tailings pond in Qidashan, Liaoning Province, is a valley-type tailings pond, which can be extended by a mountainside tailings pond. Five main factors were used for the analysis and simulation and more related influencing factors can be studied for comparative analysis. For example, more kinds of relevant data, such as the infiltration line, rainfall, reservoir water level, and displacement, are widely used. For another example, although the LSTM model is widely used in this aspect, it is recognised that it can better handle nonlinear data with time series characteristics. The algorithm can be used to scientifically and reasonably analyse the related risk factors of tailings pond dam breaks and build a tailings pond risk prediction model for fitting predictions. Therefore, an improved EEMD-DA-LSTM prediction model is proposed in this paper, taking valley-type tailings pond WKB-1 and mountainside tailings pond WKB-2 as examples.

2. Research Methods

2.1. Collective Empirical Modal Decomposition

The empirical mode decomposition (EMD) method can adaptively smooth nonlinear and non-smooth signals, but the Intrinsic Mode Function (IMF) obtained by EMD decomposition is prone to waveform aliasing. Therefore, this paper introduces ensemble empirical mode decomposition (EEMD), which can adaptively smooth nonlinear data. The specific decomposition steps of EEMD are as follows:

(1) To the original displacement sequence $w(t)$, add Gaussian white noise sequence $y_i(t)~N(0,{\sigma }^2)$ to obtain the new sequence $w_i(t)$, as shown in Equation (1).

$$w_i\left(t\right)=w\left(t\right)+{\mathbf{y}}_i\left(t\right)$$

(1)

(2) EMD decomposition of the sequence $w_i\left(t\right)$ yields the decomposition result shown in Equation (2).

$$w_i\left(t\right)={\displaystyle \sum _{j=1}^{N}IM{F}_j^i\left(t\right)}+q_i\left(t\right)$$

(2)

In the equation, N denotes the number of IMF components obtained by EMD decomposition, $IM{F}_j^i(t)$ denotes the jth order IMF component obtained by the ith EMD decomposition, and $q_i(t)$ denotes the trend term obtained by the ith EMD decomposition.

(3) Repeat steps (1) and (2) a total of M times to obtain the corresponding IMF components and residual sequences by adding different white noise to the original displacement signal.

(4) Calculate the mean value of the IMF component obtained from M decompositions as the final IMF component, as shown in Equation (3).

$$IM{F}_j\left(t\right)={\displaystyle \frac{1}{M}}{\displaystyle \sum _{i=1}^{M}IM{F}_j^i\left(t\right)}$$

(3)

In the equation, $IM{F}_j(t)$ denotes the jth IMF component extracted from M decompositions.

(5) The representation of the original displacement sequence is shown in Equation (4).

$$w\left(t\right)={\displaystyle \sum _{j=1}^{N}IM{F}_j(t)+}q(t)$$

(4)

In the equation, $q(t)$ indicates the trend term.

2.2. Dual Attention

Dual attention (DA) can be used to highlight the influence of important historical information on the prediction results and improve model prediction accuracy by reasonably allocating the input sequence information of the neural network and assigning different weights to the hidden layer states in the neural network [11]. The equations for the weight assignment calculation are shown in Equations (5) and (6).

$$p_t=v_j\tanh (w_j{h}_t+b_j)$$

(5)

In the equation, $h_t$ denotes the neural network hidden layer state vector; $p_t$ denotes the attention weight matrix; $v_j$ and $w_j$ denote attention weight matrices; and $b_j$ denotes the attention bias vector.

$${\alpha }_t={\displaystyle \frac{\exp (p_t)}{{\displaystyle \sum _{j=1}^t\exp (p_t)}}}$$

(6)

In the equation, ${\alpha }_t$ indicates the attention score.

Dual attention consists of two parts, feature attention (FA) and temporal attention (TA). Feature attention assigns different weights to the input sequences to determine the most relevant aspects affecting the deformation of the tailings dam, thus improving the prediction accuracy of the model. Temporal attention replaces random assignment with probabilistic assignment, which can effectively improve the neural network model’s tendency to lose information during long time series predictions.

2.3. Long Short-Term Memory Neural Network

A long short-term memory (LSTM) neural network is a special kind of recurrent neural network (RNN). The LSTM neural network can achieve selective memory of historical information and fully capture the long time-dependent information of nonlinear time series data.

The LSTM network unit includes the forgetting gate, input gate, output gate, and unit state. The first step of LSTM computation is to selectively discard the previous moment state information through the forgetting gate. First, the input vector $p_t$ at moment t is extracted and combined with the output vector $h_{t-1}$ at moment t − 1 to obtain the splice vector, $\left[h_{t-1},p_t\right]$. Then, the proportion of retainable information through the activation function $\sigma$ is calculated, and the specific calculation is shown in Equation (7).

$$f_t=\sigma \left(w_f\cdot \left[h_{t-1},p_t\right]+b_f\right)$$

(7)

In the equation, $f_t\in \left[0,1\right]$ denotes the output vector of the oblivion gate at time t, and $w_f \mathrm{and} b_f$ denote the weight matrix and bias vector corresponding to the forgetting gate, respectively.

In the second step, the information of the current moment is selectively updated through an input gate to decide which information can enter the cell state of the current moment. First, the output of the previous moment and the input of the current moment are transformed into a vector of candidate memory cells ${\tilde{c}}_t$ using the tanh function. Then, the proportion added to the unit state ${\tilde{c}}_t$ is calculated by the activation function $\sigma$, as shown in Equations (8) and (9).

$${\tilde{c}}_t=\tanh \left(w_c\cdot \left[h_{t-1},p_t\right]+b_c\right)$$

(8)

In the equation, $w_c \mathrm{and} b_c$ denote the weight matrix and bias vector corresponding to the cell state, respectively.

$$i_t=\sigma \left(w_i\cdot \left[h_{t-1},p_t\right]+b_i\right)$$

(9)

In the equation, $i_t\in \left[0,1\right]$ denotes the output vector of the input gate at time t; and $w_i \mathrm{and} b_i$ denote the weight matrix and bias vector corresponding to the input gate, respectively. Based on the calculation results of the forgetting gate and the input gate and the unit state of the previous moment, the unit state information of the current moment is updated, and the calculation equation is shown in Equation (10).

$$c_t=f_t·c_{t-1}{+\mathbf{i}}_t\cdot {\tilde{c}}_t$$

(10)

In the equation, $c_{t-1} \mathrm{and} c_t$ denote the unit state vectors at moments t − 1 and t, respectively.

Finally, the information of the state of the control unit is output through the output gate. Based on the output at moment t − 1 and the input at moment t, the activation function $\sigma$ is used to calculate the output of the output gate at the moment t. Then, the tanh function is used to process the unit state information at the current moment and finally, the output $h_t$ at the moment t is obtained. The calculations are shown in Equations (11) and (12).

$$o_t=\sigma \left(w_o\cdot \left[h_{t-1},p_t\right]+b_o\right)$$

(11)

In the equation, $o_t$ denotes the output vector of the output gate at time t; and $w_o \mathrm{and} b_o$ denote the weight matrix and bias vector corresponding to the output gate, respectively.

$$h_t=o_t\ast \tanh \left(c_t\right)$$

(12)

3. Risk Prediction Model for Tailings Ponds

Based on the EEMD-LSTM model [12], combined with dual attention, the tailings dam failure risk prediction method of EEMD-DA-LSTM is proposed to achieve the quantisation of the input features, select the most relevant tailings dam failure risk factors, and predict the deformation of the tailings dam. Aiming at the different degrees of influence of tailings pond failure risk factors on tailings pond deformation and the problem that LSTM is prone to losing some information in long time series prediction, a tailings pond failure risk prediction method based on EEMD-DA-LSTM is proposed. The method takes into account the strong nonlinear characteristics of the data, temporal characteristics, and multifactor coupling and uses dual attention to fully explore the correlation between the deformation of the tailings pond and its influencing factors, as well as the correlation between the risk factors of tailings pond dam failure in the historical time series. The prediction results of each model are analysed by experimental comparison and the prediction accuracy of each model is assessed according to the error evaluation index. The weights of the input features are dynamically adjusted through dual attention to improve the memory ability of the LSTM network for temporal information, thus improving the accuracy and credibility of the LSTM model prediction. The specific prediction flow of the tailings dam failure risk prediction method based on EEMD-DA-LSTM is shown in Figure 1.

The process of tailings pond dam failure risk prediction based on EEMD-DA-LSTM is described as follows:

(1) Pearson correlation coefficients are used to analyse the correlation between the time series data of tailings pond dam failure risk factors, screen the main influence factors of tailings dam deformation (F₁, F₂, …, F_k), and reduce the dimensionality of model input features.

(2) An ensemble empirical modal decomposition method was used to smooth the tailings pond displacement time series data and decompose it into a number of J1 measurement point displacement components, [IMF₁, IMF₂, …, IMF_N, Res].

(3) The displacement subsequence of the J1 measurement point obtained from the EEMD decomposition was combined with the time series data of the main influence factors of tailings dam deformation, respectively, [IMF_i, F₁, F₂, …, F_k], as model inputs. DA-LSTM prediction models are constructed respectively and parameters such as learning rate, iteration number, and training batch of the model are set for model training to seek the optimal network structure and predict the change in the displacement component of the J1 measurement point.

(4) The DA-LSTM model prediction results are superimposed and reconstructed, and the FA-LSTM layer adopts feature attention to encode the quantitative weights and extract the feature information related to the output displacement at each time step in the LSTM network. The TA-LSTM layer adopts the temporal attention to fully excavate the historical temporal sequence state information related to the displacement change at the current moment and obtains the corresponding hidden state weights and the degree of influence on the tailings dam deformation at the current moment. The final tailings dam deformation prediction result is obtained. The superposition and summation equation is shown in Equation (13).

$$y={\displaystyle \sum _{i=1}^{N+1}{y}_i}$$

(13)

In the equation, N denotes the number of IMF subsequences; y denotes the final prediction of the displacement sequence; and $y$_i denotes the prediction result of the displacement component sequence.

(5) Root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are selected as the evaluation metrics to assess the prediction accuracy of the EEMD-DA-LSTM model. They are calculated as shown in Equations (14)–(16):

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}}$$

(14)

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|y_i-{\widehat{y}}_i\right|}$$

(15)

$$MAPE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|1-\frac{{\widehat{y}}_i}{y_i}\right|}$$

(16)

In Equations (14)–(16), n denotes the total number of samples in the test set, and $y_i \mathrm{and} {\widehat{y}}_i$ denote the measured and predicted values of the ith displacement data, respectively.

4. Empirical Analysis

4.1. Data Preprocessing

The safety monitoring data, such as the dip line, rainfall, reservoir level, and displacement, of valley-type tailings pond WKB-1 from September 2020 to October 2020, totalling 997 data points, were selected as the dataset. Compared with valley-type tailings impoundments, the initial dams of evening hill-type tailings impoundments are relatively long and have smaller reservoir capacities. In order to further verify the applicability of the EEMD-DA-LSTM-based tailings impoundment dam failure risk prediction method proposed in this paper, according to the different types of tailings impoundments and the variability of the impact of dam failure influencing factors on tailings impoundment dam deformation, the safety monitoring data of Pongsan-type tailings impoundment WKB-2 for the period of 4 March 2021–18 April 2021, including the displacement, reservoir level, and dry beach length, were selected, with a total of 620 data points as the dataset. In order to improve the reliability of the data and the continuity of the time scale, isolation forest (IF) was used for outlier detection, and the outliers and nulls in the original data were interpolated as missing values. The min–max normalisation method was used to scale the original data to eliminate the differences between features of different dimensions.

4.2. Risk Factor Correlation Analysis

Tailings pond dam failure accidents are affected by various risk factors, such as rainfall, dip line, reservoir water level, and dry beach length. The safety monitoring data of tailings pond WKB-1 were used as sample data to analyse the trends of tailings pond dam failure risk factors. Tailings pond WKB-1 is equipped with the J1 measuring point, J2 measuring point, and J3 measuring point, which are three displacement monitoring points. Scatterplots were used to show the trends of tailings pond dam failure risk factors in the same time period and to analyse the trends of the displacement of the tailings pond at measurement point J1 with the displacement of measurement point J2, displacement of measurement point J3, horizontal displacement in the x-direction of measurement point J1, horizontal displacement in the y-direction of measurement point J1, settlement displacement in the z-direction of measurement point J1, rainfall, height of the infiltration line, height of the reservoir water level, and length of the dry beach. The changes in risk factors for tailings pond failure in a certain time period are shown in Figure 2.

Pearson’s correlation coefficients were used to explore the correlation between dam failure risk factors, to quantify the influence of each dam failure factor on the displacement change in the J1 measurement point of tailings pond WKB-1, and to screen the main characteristic factors of tailings dam deformation. The equation for calculating the Pearson’s correlation coefficient is shown in Equation (17).

$$r={\displaystyle \frac{{\displaystyle \sum _{i=1}^n\left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)}}{\sqrt{{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}}\sqrt{{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}}}\in \left[-1,1\right]$$

(17)

In the equation, r denotes the correlation coefficient between two characteristic factors; n indicates the number of samples; $x_i$ and $y_i$ denote the ith sample value of the two eigenfactors, respectively; and $\overline{x}$ and $\overline{y}$ denote the sample means of the two eigenfactors, respectively. Generally when $\left|r\right|>0.4$, the two sets of samples can be considered to be linearly correlated. The three-dimensional displacements of the J1, J2, and J3 measuring points of tailings pond WKB-1 are denoted as D₁, D₂, and D₃, respectively; the horizontal displacements in the x-direction and y-direction of the J1 measuring point are denoted as X_D and Y_D, respectively; and the settlement displacements in the z-direction are denoted as Z_D. The internal displacement, reservoir level height, rainfall, dry beach length, and dip line height are denoted as I_D, K, F, B, and L, respectively. The Pearson’s correlation coefficients between D₁ and D₂, D₃, X_D, Y_D, and L were calculated and the results are shown in

Table 1. Correlation coefficients of D₁.

Variable	D2/mm	D3/mm	XD/mm	YD/mm	ID/mm	ZD/mm	K/m	F/mm	B/m	L/m
correlation coefficient	0.904	0.893	0.754	−0.621	0.355	−0.519	0.645	−0.341	0.273	0.764

and Figure 3.

From the results of the D₁ correlation coefficient calculations in Table 1 and Figure 3, it can be seen that the correlation coefficients between the displacement of the J1 measuring point of tailings pond WKB-1 and the displacement of the J2 measuring point, the displacement of the J3 measuring point, the horizontal displacement in the x-direction of the J1 measuring point, and the height of the dip line are more than 0.75, which has a strong positive correlation, positive correlation with the change in the reservoir water level height, and negative correlation with the horizontal displacement in the y-direction of the J1 measuring point and the vertical displacement. It has a negative correlation with the horizontal displacement and vertical displacement in the y-direction of the J1 measurement point. In summary, the main influencing factors of tailings dam failure of tailings pond WKB-1 are identified as displacement, horizontal displacement, vertical displacement, infiltration line, and reservoir water level, in which the change in the displacement of each measuring point has high consistency, which reflects the overall structural change of the tailings dam and can reflect the deformation of the tailings dam. Therefore, the dam failure risk prediction method proposed in this paper is to predict the displacement change in the J1 measurement point of the tailings pond and judge the stability of the tailings pond dam body.

4.3. EEMD-LSTM Modelling

Tailings pond dam failure accidents are affected by a variety of risk factors, such as rainfall, infiltration line, reservoir water level, and dry beach length. The safety monitoring data of tailings pond WKB-1 were selected as the experimental data, the data were subjected to outlier detection and missing value filling to reduce the influence of noisy data, and then the displacement sequence was decomposed using the EEMD method to obtain the IMF components and the trend terms of different characteristic scales Res Figure 4.

An LSTM network model was used for predictive modelling of the risk data of tailings ponds. Horizontal displacement, vertical displacement, infiltration line, and reservoir water level were taken as input features and trained on the LSTM network model. The activation function was rectified linear unit (ReLU), the loss function was MSE, and the optimisation algorithm was adaptive moment estimation (Adam). After model training, the relevant parameter settings of the EEMD-LSTM network model are shown in

Table 2. EEMD-LSTM model parameter settings.

Parameter Name	Parameter Value
Number of iterations	100
Learning rate	0.02
Time series segmentation scale	10
Number of neurons in LSTM layer	(100, 32)
Number of neurons in the fully connected layer	(50, 1)

.

Table 3. Prediction error of EEMD-LSTM model.

Phase	Measured Value/mm	Predicted Value/mm	Residual Value/mm	Phase/Phase	Measured Value/mm	Predicted Value/mm	Residual Value/mm
807	2.124	1.748	0.376	818	1.508	1.734	−0.226
808	1.435	1.459	−0.024	…	…	…	…
809	1.763	1.517	0.246	988	1.453	1.542	−0.089
810	1.072	1.052	0.020	989	1.695	1.503	0.192
811	2.278	1.756	0.522	990	1.693	1.511	0.182
812	1.886	2.001	−0.115	991	2.279	1.610	0.669
813	2.187	1.998	0.189	992	2.203	2.076	0.127
814	1.473	2.075	−0.602	993	1.386	1.587	−0.201
815	2.221	1.583	0.638	994	2.148	2.165	−0.017
816	1.389	1.842	−0.453	995	1.483	1.432	0.051
817	1.465	1.841	−0.376	996	1.747	2.176	−0.429

shows the partial prediction error results of the EEMD-LSTM model.

The MAE of the EEMD-LSTM model is 0.181 mm, the MAPE is 6.330%, and the RMSE is 0.228 mm. The experimental results show that Figure 5, in response to the strong nonlinear and non-stationary characteristics of the tailings pond displacement changes, the performance of the LSTM prediction model is enhanced and the prediction accuracy is improved after smoothing the displacement time series data using the EEMD approach. In this paper, considering the complex coupling effect between the risk factors of tailings pond dam failure and the problem that LSTM is prone to losing part of the information in long time series prediction, we combined dual attention with EEMD-LSTM to further improve the prediction accuracy of the EEMD-LSTM model on the basis of EEMD-LSTM and carried out modelling experiments and comparative analyses based on the engineering examples to validate the validity of the proposed method in this paper.

4.4. EEMD-DA-LSTM Modelling

Tailings dam failure is a strongly nonlinear dynamic process and the tailings dam failure risk prediction model was constructed based on ensemble empirical modal decomposition (EEMD) and long short-term memory neural network (LSTM) to predict tailings dam displacement changes. The model makes full use of EEMD’s smoothing ability for nonlinear data and LSTM’s long-term memory ability for nonlinear data. The basic prediction process of tailings pond dam failure risk based on EEMD-LSTM is shown below:

(1) Displacement time series data smoothing: Based on the results of outlier detection and missing value processing of the displacement of the J1 measurement point of tailings pond WKB-1, the displacement time series data with strong nonlinear characteristics are decomposed into a number of relatively smooth components using the EEMD method, [IMF₁, IMF₂, …, IMF_N, Res].

(2) Feature downscaling: Based on the pre-processing results of the risk monitoring data, such as displacement, reservoir level, and dip line, of tailings pond WKB-1, Pearson correlation coefficients are used to screen the tailings dam deformation impact factor (F₁, F₂, …, F_k).

(3) LSTM model prediction: Each component obtained from the EEMD decomposition is separately combined with the deformation impact factor as a model input, [IMF_i, F₁, F₂, …, F_k], the LSTM model is constructed separately, the parameters such as learning rate, iteration number, and training batch of the model are set, model training is carried out, the optimal network structure is sought, and the change in the displacement component is predicted.

(4) Superposition reconstruction: the prediction results of the displacement components are superimposed and summed as the displacement sequence prediction results. The superposition and summing equation is shown in Equation (18).

$$y={\displaystyle \sum _{i=1}^{N+1}{y}_i}$$

(18)

In the equation, N denotes the number of IMF subsequences; $y$ denotes the prediction result of the displacement sequence; and $y_i$ denotes the prediction result of the displacement component sequence.

Tailings pond J1 point displacement monitoring data and deformation influencing factor data, such as reservoir water level, dip line, and horizontal displacement, of valley-type tailings pond WKB-1 were selected as samples and combined with the J1 point displacement component obtained from EEMD decomposition as well as the main influencing factors of deformation to predict the risk of tailings pond dam failure. The preprocessed dataset was divided into the 80% training set and 20% test set. The EEMD-DA-LSTM model had three hidden layers. Among them, the FA-LSTM layer had two hidden layers and the TA-LSTM layer had one hidden layer. The parameter settings of the EEMD-DA-LSTM model are shown in

Table 4. EEMD-DA-LSTM model parameter settings.

Parameter Name	Parameter Value
Number of iterations	256
batches	32
Learning rate	0.001
Time series segmentation scale	10
Number of neurons in the hidden layer	(200, 50, 25)
Number of neurons in the fully connected layer	(50, 1)

and the activation function of this model was the ReLU function during training. At this time, the EEMD-DA-LSTM prediction model has the best performance.

4.5. Comparative Analysis of Tailings Pond Risk Prediction Experiments

In this experiment, tailings pond dam failure risk prediction models were constructed based on EEMD-DA-LSTM, EEMD-LSTM, and DA-LSTM, respectively, the prediction results of different models were compared and analysed for the relevant data of valley-type tailings pond WKB-1 and the relevant data of mountain adjacent-type tailings pond WKB-2, and the mean absolute error, the root mean square error, and the mean absolute percentage error were used to assess the prediction accuracy of the models. The average absolute error, root mean square error, and average absolute percentage error were used to verify the reliability of the method proposed in this chapter.

The safety monitoring data, such as dip line, rainfall, reservoir level, and displacement, from September 2020 to October 2020 of valley-type tailings pond WKB-1 were selected as a dataset with a total of 997 data points. The change curve of displacement in dataset WKB-1 is shown in Figure 6.

Comparisons of the prediction results of each prediction model based on dataset WKB-1 for the displacement of measurement point J1 are shown in Figure 7 and Figure 8.

From the prediction results of the DA-LSTM model in Figure 7 and the EEMD-DA-LSTM model, it can be seen that the prediction effect of the DA-LSTM model is poorer, although it can achieve the basic fitting of the trend of the displacement change, but the prediction effect is not good compared with the EEMD-DA-LSTM model when the displacement changes suddenly. Compared with the prediction results of the DA-LSTM model in Figure 7, the prediction effect of the EEMD-LSTM model in Figure 8 is better and it can accurately predict the change in the risk of tailings pond failure when the displacement undergoes a strong nonlinear change, but the prediction accuracy still needs to be further improved. Therefore, the combination of the EEMD method and DA-LSTM model was considered to predict the risk of tailings pond dam failure. From the prediction results of the EEMD-DA-LSTM model in Figure 8, it can be seen that the EEMD-DA-LSTM model can well capture the strong nonlinear changes in the displacement of the tailings dam and the error between the model predicted value and the measured value of the displacement is small.

As shown in

Table 5. WKB-1 model error evaluation index calculation results.

Model	Evaluation Indicators
	MAE/mm	MAPE/%	RMSE/mm
EEMD-DA-LSTM	0.159	5.587	0.197
EEMD-LSTM	0.192	6.324	0.275
DA-LSTM	0.269	9.793	0.364

, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) of the DA-LSTM model are reduced by 0.076 mm, 1.072%, and 0.044 mm, respectively, compared to the LSTM model, and the combination of dual attention and the LSTM network model can reduce the prediction error of the LSTM model and improve model prediction accuracy. Compared with the LSTM model, the various error indicators of the EEMD-LSTM model are reduced by 0.153 mm, 4.541%, and 0.133 mm, respectively, which indicates that the smoothing of the displacement time series data using EEMD can effectively improve the reliability of LSTM model prediction. Compared with the single LSTM model, the combined DA-LSTM model, and the combined EEMD-LSTM model, the mean absolute error (MAE) of the EEMD-DA-LSTM model is 0.159 mm, which is a decrease of 0.186 mm, 0.110 mm, and 0.033 mm, respectively; the mean absolute percentage error (MAPE) is 5.587%, which is a decrease of 5.278%, 4.206%, and 0.737%, respectively; and the root mean square error (RMSE) is 0.197 mm, decreasing by 51.7%, 45.9%, and 28.4%, respectively. The results show that for the strong nonlinearity and random volatility of tailings dam deformation and the complex coupling between dam failure risk factors, the dam failure risk prediction method based on EEMD-DA-LSTM proposed in this paper is able to reduce the prediction error of the LSTM model for tailings dam failure risk and effectively improve the prediction accuracy of the EEMD-LSTM model.

The safety monitoring data of displacement, reservoir water level, and dry beach length from 4 March 2021 to 18 April 2021 for certain side hill-type tailings pond WKB-2 were selected, with a total of 620 data points. The variation curves of displacement in dataset WKB-2 are shown in Figure 9.

The deformation data of tailings pond WKB-2 were also characterised by strong nonlinearity and frequent fluctuations. In this experiment, dataset WKB-2 was divided into the 80% training set and 20% test set. The single LSTM model, the DA-LSTM combined model, and the EEMD-LSTM combined model were compared and analysed with the EEMD-DA-LSTM model constructed in this paper, respectively. The relevant parameter settings of each model are shown in

Table 6. Parameter settings for each model.

Model	Parameters
	Number of Iterations	Learning Rate	Number of Hidden Layers	Number of Neurons in LSTM Layer
LSTM	200	0.001	1	100
DA-LSTM	256	0.005	2	(128, 50)
EEMD-LSTM	200	0.001	1	128
EEMD-DA-LSTM	100	0.02	3	(100, 50, 20)

. At this time, the prediction performance of each model is the best.

A comparison of the results of the model for predicting the dam failure risk of tailings pond WKB-2 is shown in Figure 9. As can be seen from Figure 10a, the LSTM model also suffers from poor prediction of strong nonlinear displacement variations when predicting the risk of dam failure for the Pongshan-type tailings pond. From Figure 10b, it can be seen that the DA-LSTM model is able to fit the tailings impoundment displacement changes better, capturing most of the strong nonlinear changes in the displacement sequence. From Figure 10a,c, it can be seen that the EEMD-LSTM model is able to better fit the variation of tailings pond displacement compared to the LSTM model. From Figure 10b,c, it can be seen that the prediction results of the DA-LSTM model are better than the EEMD-LSTM model compared to the experimental results on dataset WKB-1, which may be due to the fact that the amount of data in dataset WKB-2 had been reduced compared to that in dataset WKB-1, which improved the learning ability of the DA-LSTM model for the strong nonlinear displacement series. From Figure 10, it can be seen that the prediction results of the combined EEMD-DA-LSTM model are basically consistent with the displacement variations, and the fitting effect on displacement variations is better than that of the single LSTM model, the combined DA-LSTM prediction model, and the combined EEMD-LSTM prediction model.

To further evaluate the accuracy of the prediction of each model, the prediction error of each model was calculated, and the results are shown in

Table 7. Prediction error results for each model for dataset WKB-2.

Model	Evaluation Indicators
	MAE/mm	MAPE/%	RMSE/mm
EEMD-DA-LSTM	0.162	5.594	0.213
LSTM	0.455	12.384	0.561
DA-LSTM	0.197	5.883	0.265
EEMD-LSTM	0.218	7.351	0.273

. As can be seen from the table, compared with the LSTM model, the MAE of the EEMD-DA-LSTM model is 0.162 mm, which is a reduction of 0.293 mm, the MAPE is reduced by 6.790%, and the RMSE is reduced by 62.0%. Compared with the DA-LSTM model, the MAE of the EEMD-DA-LSTM model is reduced by 17.8%, the MAPE is 5.594%, a reduction of 0.289%, and the RMSE is reduced by 19.6%, which indicates that the displacement was smoothed using the EEMD method. The DA-LSTM model was constructed to predict each displacement component separately and the predicted results were superimposed and reconstructed to obtain the predicted value of the displacement, which made the prediction effect of tailings pond dam failure risk significantly improved. Compared with the EEMD-LSTM model, the MAE of the EEMD-DA-LSTM model is reduced by 0.056 mm, the MAPE is reduced by 1.757%, and the RMSE is reduced by 21.9%, which indicates that combining dual attention on the basis of the EEMD-LSTM model can improve the ability of the LSTM network model to memorise the information of the long time series and the memory of the EEMD-LSTM combined model for the extreme points and inflection points. The combined models have better ability to predict extreme points and inflection points.

Based on the two sets of sample data, the EEMD-DA-LSTM model was experimentally compared with the single LSTM model, the combined DA-LSTM model, and the combined EEMD-LSTM model, etc., to analyse the results of model prediction and the calculation of error indicators. The experiments proved that compared with other models, the prediction effect of this model for valley-type tailings ponds and mountainside-type tailings ponds is significantly improved and the prediction accuracy is significantly improved, which is suitable for the prediction of tailings pond dam failure risk.

5. Conclusions

In summary, considering the complex coupling between the risk factors of tailings pond dam failure and the problem that LSTM easily loses part of the information in long time series prediction, this paper innovatively proposes a tailings pond dam failure risk prediction method based on EEMD-DA-LSTM by improving EEMD-LSTM. The experiment proves that the EEMD-DA-LSTM model constructed in this paper is more effective in predicting the dam failure risk of tailings pond WKB-1 and tailings pond WKB-2 compared with other models, which proves that the dam failure risk prediction method proposed in this chapter is not only applicable to valley-type tailings ponds, but also applicable to tailings ponds on the sides of mountains. Dual attention can quantify the weights of the input features and explore the dependence relationship between the historical time series information of the tailings pond dam failure risk factors, which achieves better performance in tailings pond dam failure risk prediction. The combined EEMD-DA-LSTM prediction model takes into full consideration the different impacts of multi-factors on tailings pond dam failure and the problem that the LSTM is prone to losing part of the information in long time series prediction, which is a good solution to the problem. The prediction error of strongly nonlinear tailings dam deformation data is small. It is proved through experiments that the method proposed in this paper is suitable for the prediction of tailings pond dam failure risk changes with complex and strong nonlinear characteristics and it is suitable for the prediction of tailings pond dam failure risk changes.

This paper has reference value for practitioners in the mining industry and environmentally sustainable development. Tailings ponds are related to the mining industry and early warning of tailings pond dam break risk is conducive to environmentally sustainable development. This paper proposes that the model achieves good prediction results in short-term prediction, but it may reduce the model training speed due to the increase in the amount of data. In the future, studying the method of parallelisation of the model will be considered to improve the running speed of the model. This model is feasible for predicting the risk of tailings pond failure in the mining field and in the future, we will consider studying the feasibility of this method in the deformation prediction of reservoir dams or landslide prediction.