# Prediction of Dam Deformation Using SSA-LSTM Model Based on Empirical Mode Decomposition Method and Wavelet Threshold Noise Reduction

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## Abstract

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^{2}of 0.9533 being closer to 1 and a better fit than the other two models. This can effectively mine the relationship in the measured deformation data, and reduce the influence of high-frequency components on the dam prediction accuracy.

## 1. Introduction

## 2. Selection of Statistical Models for Dam Deformation Prediction

## 3. Wavelet Threshold-EMD-Based Data Noise Reduction Method

#### 3.1. Empirical Mode Decomposition

#### 3.2. Wavelet Threshold Noise Reduction

## 4. The Prediction Model Based on Optimized LSTM Model with Sparrow Search Algorithm

#### 4.1. Sparrow Search Algorithm

#### 4.2. LSTM Neural Networks

## 5. Construction of the Model

- Step 1: The monitored raw data are decomposed by EMD, and the IMF components obtained from the decomposition are distributed from high to low. Perform wavelet threshold noise reduction on high-frequency IMF components, reconstruct the high-frequency IMF components after noise reduction and low-frequency IMF components, and obtain the data after noise reduction;
- Step 2: Initialize and normalize the denoised data. Determine the following parameters: length of LSTM time window, number of hidden layer cells, sparrow population size and the number of iterations. Subsequently, initial safety threshold and sparrow position;
- Step 3: Use the predicted value of the LSTM algorithm and the root mean square of the sample data to determine the fitness value of each sparrow;
- Step 4: Update the sparrow position, get a new fitness value, and search for the optimal position of the population and the global optimal value;
- Step 5: Perform iterations, determine whether the maximum number of iterations is reached, and obtain the optimal individual solution. Stop the iteration if the maximum value is reached and determine the optimal parameters of the LSTM. If not, repeat the loop step;
- Step 6: Substitute the obtained LSTM parameters into the training grid to make predictions.

## 6. Case Study

#### 6.1. Factsheet

#### 6.2. Data Noise Reduction Based on EMD Combined with Wavelet Threshold

#### 6.3. Model Analysis

^{2}: SSA-LSTM model has a value of 0.9533, LSTM model has a value of 0.9036, and PSO-SVM model has a value of 0.885 at this measurement point. It can be seen that for the selected measurement point C4-A22-PL-05, SSA-LSTM > LSTM > PSO-SVM, where the SSA-LSTM model had the highest actual fit.

## 7. Conclusions

- This paper proposes a noise reduction method based on EMD combined with wavelet threshold, using the EDM method to decompose the original monitoring data of the dam, and applying wavelet threshold noise reduction to the decomposed high- frequency IMF components. The high-frequency IMF components after noise reduction are obtained, and the low-frequency IMF components obtained by decomposition are combined for reconstruction. A prediction model is constructed from the denoised data, which improves the prediction accuracy of the SAA-LSTM model.
- This paper uses the Sparrow Search Algorithm to optimize the long short-term memory (LSTM), and uses the good stability, convergence speed, scalability, and robustness of the Sparrow Search Algorithm to perform grid training and parameter optimization of the LSTM. The global optimal location and fitness values are updated, and the optimized LSTM model is optimized in terms of the number of hidden layer nodes and learning rate using grid search to effectively mine the complex functional relationship between the dam deformation and its influence factors.
- The two deformation prediction models of LSVM and PSO-SVM are compared by using the example verification analysis. Compared with the other three models, the multiple correlation coefficient R
^{2}of the SSA-LSTM model is 0.9533, which is closer to 1 and has better fitting accuracy. The mean absolute error and root mean square error are 0.05345 and 0.06358, which are smaller than the other two models. It can be seen that the prediction accuracy and convergence speed of the SSA-LSTM model have been significantly improved, which provides a new method for high-precision prediction of dam deformation and is more suitable for practical engineering.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Concrete arch dam prediction process based on EMD combined with wavelet threshold noise reduction coupled with SSA-LSTM.

**Figure 8.**IMF components after noise reduction based on EMD combined with wavelet thresholds. (

**a**) IMF1 components after noise reduction based on EMD combined with wavelet thresholds; (

**b**) IMF2 components after noise reduction based on EMD combined with wavelet thresholds; (

**c**) IMF3 components after noise reduction based on EMD combined with wavelet thresholds; (

**d**) IMF4 components after noise reduction based on EMD combined with wavelet thresholds; (

**e**) IMF5 components after noise reduction based on EMD combined with wavelet thresholds.

Measuring Points | Predictive Models | RMSE/mm | MAE/mm^{2} | MSE/mm | R^{2} |
---|---|---|---|---|---|

C4-A22-PL-05 | SSA-LSTM | 0.06358 | 0.05345 | 0.00404 | 0.9533 |

LSTM | 0.0913 | 0.07611 | 0.00835 | 0.9036 | |

PSO-SVM | 0.1293 | 0.09564 | 0.01096 | 0.8852 |

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**MDPI and ACS Style**

Zhang, C.; Fu, S.; Ou, B.; Liu, Z.; Hu, M.
Prediction of Dam Deformation Using SSA-LSTM Model Based on Empirical Mode Decomposition Method and Wavelet Threshold Noise Reduction. *Water* **2022**, *14*, 3380.
https://doi.org/10.3390/w14213380

**AMA Style**

Zhang C, Fu S, Ou B, Liu Z, Hu M.
Prediction of Dam Deformation Using SSA-LSTM Model Based on Empirical Mode Decomposition Method and Wavelet Threshold Noise Reduction. *Water*. 2022; 14(21):3380.
https://doi.org/10.3390/w14213380

**Chicago/Turabian Style**

Zhang, Caiyi, Shuyan Fu, Bin Ou, Zhenyu Liu, and Mengfan Hu.
2022. "Prediction of Dam Deformation Using SSA-LSTM Model Based on Empirical Mode Decomposition Method and Wavelet Threshold Noise Reduction" *Water* 14, no. 21: 3380.
https://doi.org/10.3390/w14213380