# A Tailings Dam Long-Term Deformation Prediction Method Based on Empirical Mode Decomposition and LSTM Model Combined with Attention Mechanism

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dam Displacement Prediction Process

- (1)
- Data preprocessing: elimination of outliers and missing value interpolation.
- (2)
- The decomposition and reconstruction of multi-factor time series data through the EMD method.
- (3)
- Determining the input sequence by the lag autocorrelation coefficient method.
- (4)
- Parameter adjustment of lagging LSTM network based on attention mechanism.
- (5)
- Results prediction and accuracy evaluation.

#### 2.1.1. Principle of EMD Method

#### 2.1.2. Lagged Autocorrelation Coefficient

#### 2.1.3. LSTM Network

#### 2.1.4. Attention Mechanism

#### 2.1.5. Prediction Model Structure

#### 2.2. A Tailing Dam Study

#### 2.2.1. Introduction of Background

#### 2.2.2. The Outlier Data Processing

#### 2.2.3. Missing Value Date Processing

#### 2.2.4. Data Normalization

## 3. Results

#### 3.1. Data Analysis and Processing

#### 3.2. EMD Reorganization of Absolute Deformation of the Tailings Dam

#### 3.2.1. Stationarity Test

_{1}to IMF

_{5}and the residual term. The ADF test can determine whether unit roots exist in the sequence. Under a stationary sequence, there is no unit root, and vice versa [57]. It is specified here that the sequence can be considered as stationary when the p-value of the ADF test is lower than 0.05; otherwise, it is nonstationary. After the ADF test, the test statistic and p-value of IMF

_{1}to IMF

_{5}and the residual term are as shown in Table 1. Y represents the sequence is stationary, and N represents the sequence is nonstationary. Because the original displacement data is nonstationary, the residual term and the original sequence are nonstationary after EMD, and IMF

_{1}~IMF

_{5}are all stationary sequences.

#### 3.2.2. Component Identification

_{1,}IMF

_{5}and the residual term are more correlated with the original series, which indicates that the IMF

_{1}and IMF

_{5}components and the residual term are more correlated with the original data. While the rest of the IMF

_{2}, IMF

_{3}and IMF

_{4}components are less correlated with that. After comprehensive consideration of the two methods, the ADF test and component identification, the IMF

_{1}-IMF

_{5}components and the residual term are combined as follows.

_{1}, IMF

_{5}and the residual term, which are higher correlated with the original time series or have the same stationarity as that, as independent components and combine the remaining three components (IMF

_{2}, IMF

_{3}and IMF

_{4}) to form a new component IMF

_{6}. IMF

_{1}, IMF

_{5}, the residual term and the newly formed component IMF

_{6}are input are into the attention-mechanism-based LSTM network model for prediction, respectively. Then the predicted value of each group of components and the predicted value of the trend are added with equal weight. Finally, the prediction result of the deformation of the tailings dam is obtained.

#### 3.3. Input Sequence

#### 3.4. Model Parameter Setting

## 4. Discussion

#### 4.1. Factor Analysis

#### 4.2. Model Application

## 5. Conclusions

- (1)
- In this study, the EMD-attention-LSTM neural network model is proposed. Compared with the control models, this model achieves higher accuracy in the prediction of tailings dam deformation under the influence of rainfall and phreatic line, and also has good performance in multiple directions. The prediction effect reflects the universality of this model in the prediction of tailings dam deformation. This method is suitable for dam deformation prediction under the influence of rainfall and phreatic line and has engineering significance.
- (2)
- The LSTM model used in this study effectively avoids the problem of gradient disappearance and gradient explosion, while the model considers the lag to better reflect the delayed impact of external factors on the dam deformation in real situations.
- (3)
- Compared with a single LSTM model, the addition of the attention mechanism takes into account the characteristics of the input variables and the long-term dependence of the time series, which improves the prediction accuracy of the dam displacement.
- (4)
- The significance test reveals that atmospheric rainfall and the change of phreatic line in the tailings dam will accelerate the tailings dam deformation process, and the change of phreatic line has a more significant effect on tailings dam deformation.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flow chart of dam displacement prediction. ((

**a**): decomposition of tailings dam displacement data using EMD and reorganization using statistical methods; (

**b**): perform outlier and missing value processing and determine lag order, and input each component into the Attention-LSTM model for prediction; (

**c**): accuracy evaluation using RMSE and MAE.).

Original Data | IMF_{1} | IMF_{2} | IMF_{3} | IMF_{4} | IMF_{5} | Residual Term | |
---|---|---|---|---|---|---|---|

Test Statistic | 0.900 | −8.065 | −7.577 | −7.348 | −4.637 | −4.225 | −0.641 |

p-value | 0.788 | 0.000 | 0.000 | 0.000 | 0.000 | 0.001 | 0.861 |

Stationarity | N | Y | Y | Y | Y | Y | N |

**Table 2.**Pearson correlation coefficient between IMF

_{1}~IMF

_{5}, residual term and the original data.

IMFs and Residual Term | IMF_{1} | IMF_{2} | IMF_{3} | IMF_{4} | IMF_{5} | Residual Term |
---|---|---|---|---|---|---|

Pearson Correlation Coefficient | 0.2077 | 0.1264 | 0.1453 | 0.1470 | 0.4599 | 0.9122 |

Day | EMD-Attention-LSTM | EMD-LSTM | EMD-ARIMA | Multiple Regression | LSTM | SVM | |
---|---|---|---|---|---|---|---|

RMSE | 1 | 0.144 | 0.371 | 0.529 | 4.760 | 0.470 | 0.296 |

5 | 0.183 | 0.351 | 0.410 | 4.398 | 0.411 | 0.496 | |

10 | 0.549 | 0.934 | 1.049 | 4.673 | 0.945 | 1.167 | |

15 | 0.553 | 0.835 | 0.992 | 4.675 | 0.907 | 1.129 | |

20 | 0.607 | 0.865 | 1.010 | 4.844 | 0.893 | 1.222 | |

25 | 0.625 | 0.898 | 1.053 | 5.237 | 0.908 | 1.208 | |

30 | 0.729 | 0.955 | 1.120 | 4.937 | 0.970 | 1.285 | |

MAE | 1 | 0.157 | 0.524 | 0.676 | 6.731 | 0.642 | 0.384 |

5 | 0.215 | 0.439 | 0.536 | 6.080 | 0.462 | 0.573 | |

10 | 0.509 | 0.992 | 1.059 | 6.455 | 0.955 | 1.078 | |

15 | 0.555 | 0.906 | 1.035 | 6.455 | 0.950 | 1.145 | |

20 | 0.636 | 0.945 | 1.054 | 6.668 | 0.934 | 1.274 | |

25 | 0.664 | 0.996 | 1.111 | 6.747 | 0.965 | 1.294 | |

30 | 0.770 | 1.068 | 1.207 | 6.801 | 1.063 | 1.394 |

Multiple Regression Model | Unstandardized Coefficient B | Standard Error | t | Significance |
---|---|---|---|---|

Constant | −22.890 | 5.631 | −4.065 | 0.000 |

Phreatic line | 0.524 | 0.263 | 1.991 | 0.047 |

rainfall | −0.392 | 0.152 | −2.588 | 0.010 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, Y.; Gao, Y.; Wang, Z.; Cao, G.; Wang, R.; Lu, S.; Li, W.; Nie, W.; Zhang, Z. A Tailings Dam Long-Term Deformation Prediction Method Based on Empirical Mode Decomposition and LSTM Model Combined with Attention Mechanism. *Water* **2022**, *14*, 1229.
https://doi.org/10.3390/w14081229

**AMA Style**

Zhu Y, Gao Y, Wang Z, Cao G, Wang R, Lu S, Li W, Nie W, Zhang Z. A Tailings Dam Long-Term Deformation Prediction Method Based on Empirical Mode Decomposition and LSTM Model Combined with Attention Mechanism. *Water*. 2022; 14(8):1229.
https://doi.org/10.3390/w14081229

**Chicago/Turabian Style**

Zhu, Yang, Yijun Gao, Zhenhao Wang, Guansen Cao, Renjie Wang, Song Lu, Wei Li, Wen Nie, and Zhongrong Zhang. 2022. "A Tailings Dam Long-Term Deformation Prediction Method Based on Empirical Mode Decomposition and LSTM Model Combined with Attention Mechanism" *Water* 14, no. 8: 1229.
https://doi.org/10.3390/w14081229