# Research on the Uplift Pressure Prediction of Concrete Dams Based on the CNN-GRU Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Problem Description

#### 2.2. Extraction of Uplift Pressure Features Based on the CNN Network

#### 2.3. Prediction Model for Uplift Pressure Based on the GRU Network

_{r}and b

_{r}are reset gate parameters; σ is the nonlinear activation function, where the rule activation function is chosen; and g

_{r}is the gating vector. W

_{z}and b

_{z}are updated gate parameters; all parameters are automatically optimized by the backpropagation algorithm.

#### 2.4. Construction of the CNN-GRU Model for Uplift Pressure Prediction

#### 2.5. Background of a Dam Project

## 3. Results

#### 3.1. Denoising of Uplift Pressure-Monitoring Data

#### 3.2. Impact Factor and Input Data Set Analysis

**H**, (

_{U}**H**)

_{U}^{2},

**H**

_{U}**,**

_{(2–3)}**H**

_{U}**,**

_{(4–7)}**H**,

_{U}_{(8–15}_{)}**H**,

_{U}_{(16–30}_{)}**H**,

_{U}_{(31–60}_{)}**H**), where

_{D}**H**denotes the upstream water level at the current monitoring date,

_{U}**H**denotes the average upstream water level from q to r days before the current monitoring date and

_{U}_{(q-r)}**H**is the downstream water level at the current monitoring date; temperature component (

_{D}**T**,

_{0–1}**T**,

_{2–7}**T**,

_{8–15}**T**,

_{16–30}**T**,

_{31–60}**T**), where

_{61–120}**T**denotes the average temperature from q to r days before the current monitoring date; rainfall component (

_{q-r}**R**,

_{0–1}**R**,

_{2–3}**R**,

_{4–7}**R**,

_{8–15}**R**,

_{16–30}**R**), where

_{31–60}**R**denotes the cumulative value of rainfall from q to r days before the current monitoring date; time effects (

_{q-r}**θ**,

**lnθ**), where

**θ = t/100**,

**t**is the cumulative number of monitoring days from the observation date to the reference date.

**H**,

_{U}_{(8–15}_{)}**H**,

_{U}_{(16–30}_{)}**H**,

_{U}_{(31–60}_{)}**H**) were selected as input factors; the temperature component had a large MIC value, and (

_{D}**T**,

_{16–30}**T**,

_{31–60}**T**) were selected as input factors; the MIC values between rainfall components and uplift pressure were small and had limited effect on the trend of uplift pressure, so they were excluded. The final filtered input factors include: Water pressure component (

_{61–120}**H**,

_{U}_{(8–15}_{)}**H**,

_{U}_{(16–30}_{)}**H**,

_{U}_{(31–60}_{)}**H**), Temperature component (

_{D}**T**,

_{16–30}**T**,

_{31–60}**T**), and Time effects (

_{61–120}**θ**,

**lnθ**).

#### 3.3. Model Prediction

## 4. Discussion

#### 4.1. Analysis of the Denoising Effect of Uplift Pressure-Monitoring Data

#### 4.2. Analysis of the Uplift Pressure Prediction Results

- (1)
- The BP and SVM causal models were considerably weaker than the deep learning models in terms of prediction performance, both in terms of overall trends and local inflection points.
- (2)
- The overall trend of the prediction curves of LSTM and GRU was basically the same as the monitoring value of the uplift pressure, but the trend of the prediction curve in the local inflection point area deviated from the monitoring curve, and the local inflection point could not be accurately predicted.
- (3)
- The fitting effect of the CNN-GRU model on the overall trend and local fluctuations was substantially better than that of the GRU model and the LSTM model, and it could more accurately describe the overall and local inflection points of the uplift pressure, and its prediction curve was closer to the monitoring curve of the uplift pressure.
- (4)
- The CNN-GRU model fits similarly to the CNN-LSTM model on the overall trend and local fluctuations at the UP26, UP35, and UP51 measurement points. However, the CNN-GRU model performs considerably better than the CNN-LSTM model at the UP17 measurement point.

- (1)
- Although causal models, such as BP and SVM, have reasonable prediction results for small sample data, they are unable to learn from data with time series characteristics, resulting in unsatisfactory prediction results for large sample data. In addition, the running time of the model in Table 6 shows that the running time of the SVM model increases exponentially when dealing with large sample data. This is because SVM usually uses the kernel matrix of the dataset to describe the similarity between samples, and when dealing with large sample data, the number of matrix elements increases squarely, resulting in unsatisfactory computational power and operational efficiency.
- (2)
- The LSTM model, GRU model, and CNN-GRU model, which consider the time series characteristics of historical uplift pressure-monitoring data, have obvious advantages over the PSO-BP model and ABC-SVM model. The performance of the LSTM model and GRU model is similar, but because the GRU model integrates the forget gate and input gate of the LSTM model into an update gate, which reduces the parameters required for training the GRU model [29], the training iteration of the GRU model is faster than that of the LSTM model with lower computational cost and higher operational efficiency.
- (3)
- The LSTM model and GRU model do not perform accurately enough on some of the measurement points with more fluctuations due to the inability to mine the potentially hidden information on the local fluctuation features of some of the measurement points. In contrast, CNN is able to extract the continuous and discontinuous features of sequence data and mine the variation characteristics of local fluctuation of uplift pressure, so the CNN-GRU model has better results compared with the LSTM model and GRU model.
- (4)
- The CNN-LSTM model predicts similarly to the CNN-GRU model, but because the model requires too many parameters to be trained and the amount of data is small, overfitting occurs at some prediction points, which makes the prediction results less than ideal.

- (1)
- The model proposed in this study has only been validated for uplift pressure prediction, and its suitability in different scenarios cannot be determined.
- (2)
- There are many hyperparameters involved in the model, and hyperparameters are adjustment knobs that control the structure, function, efficiency, and other functions of the model. These parameters basically have different settings in various scenarios, and currently, there are no uniform selection criteria, so they can only be determined by repeated trials in actual situations. Finding the optimal configuration of hyperparameters in these deep learning models in the high-dimensional data space involved in the field of dam safety monitoring is a major challenge and a difficulty to overcome in the future.
- (3)
- The model established in this study mainly focuses on individual measurement points for prediction while considering the time dimension of monitoring data, but each monitoring point of the dam will also be affected by the spatial dimension, i.e., the changing pattern of each monitoring point will be different under different spatial distribution locations. Therefore, determining the correlation links of each monitoring point of the dam in the spatial dimension, studying the variation law of each point under various spatial distributions, and establishing a dam safety prediction model with coupled spatio-temporal correlation characteristics are directions for future development.

## 5. Conclusions

- (1)
- In this study, the CNN-GRU model is proposed, in which the CNN network is used to extract potential connections and hidden information among the influencing factors of uplift pressure, and the GRU network is used to learn time series correlation features in the monitoring data for uplift pressure.
- (2)
- The CNN-GRU model was used to predict the uplift pressure data: MAE was 0.1554, 0.0398, 0.2306, and 0.1827. RMSE errors were 0.1903, 0.0548, 0.2916, and 0.2127.
- (3)
- In comparison with the CNN-LSTM, LSTM, GRU, PSO-BP, and ABC-SVM models, the CNN-GRU model constructed in this study has a better prediction effect on the overall trend and local fluctuation of the uplift pressure. Based on the accuracy assessment index, the model is more accurate than the other models, and the prediction curves are close to the surveillance data. The model can improve the utilization of dam safety monitoring results and has engineering practicality for safe dam operation.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**The comparison between the denoised data samples and the original uplift pressure data samples.

**Figure 9.**Uplift pressure predicted results. ((

**a**): Prediction results of CNN-GRU model in the UP17 measurement point; (

**b**): Prediction results of CNN-GRU model in the UP26 measurement point; (

**c**): Prediction results of CNN-GRU model in the UP35 measurement point; (

**d**): Prediction results of CNN-GRU model in the UP51 measurement point.)

**Figure 11.**Comparison of uplift pressure prediction results. ((

**a**): The prediction results of each model on the uplift pressure data of the UP17 measuring point; (

**b**): The prediction results of each model on the uplift pressure data of the UP26 measuring point; (

**c**): The prediction results of each model on the uplift pressure data of the UP35 measuring point; (

**d**): The prediction results of each model on the uplift pressure data of the UP51 measuring point.)

Network Structure | Experimental Parameters | Parameter Value |
---|---|---|

Overall Structure | optimization algorithm | Adam |

batch size | 128 | |

epochs | 100 | |

CNN structure (2 layers) | convolution kernels | 16, 32 |

kernel size | 2 | |

strides | 2 | |

activation | $\mathrm{relu}$ | |

pool size | 2 | |

strides | 2 | |

GRU structure (3 layers) | hidden neurons | 64, 64, 64 |

dropout | 0.2 | |

activation | $\mathrm{relu}$ | |

Fully connected layer (1 layer) | units | 1 |

activation | None |

Dam Section | Left Bank Water Blocking Section | Diversion Section | Discharge Section | Spillway Section | Bottom Outlet Section | Ship Lock | Right -Shore Water Blocking Section |
---|---|---|---|---|---|---|---|

Number | 1#~7# | 8#~21# | 22# | 23#~35# | 36# | 37#~38# | 39#~42# |

Subsequences | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 |
---|---|---|---|---|---|---|

SE | 0.0111 | 0.0438 | 0.2094 | 0.4050 | 0.5324 | 0.4856 |

Component Name | Factors | ${\mathit{C}}_{\mathbf{MIC}}$ | Whether to Be Selected |
---|---|---|---|

Time effects | θ | 0.8995 | Y |

lnθ | 0.8995 | Y | |

Water pressure component | H_{U} | 0.1945 | N |

(H_{U})^{2} | 0.1945 | N | |

H_{U(2–3)} | 0.2078 | N | |

H_{U(4–7)} | 0.2175 | N | |

H_{(U8–15)} | 0.2487 | Y | |

H_{U(16–30)} | 0.2675 | Y | |

H_{U(31–60)} | 0.2537 | Y | |

H_{D} | 0.2451 | Y | |

Temperature component | T_{0–1} | 0.4725 | N |

T_{2–7} | 0.5147 | N | |

T_{8–15} | 0.5253 | N | |

T_{16–30} | 0.6071 | Y | |

T_{31–60} | 0.6064 | Y | |

T_{61–120} | 0.7076 | Y | |

Rainfall component | R_{0–1} | 0.1908 | N |

R_{2–3} | 0.1562 | N | |

R_{4–7} | 0.1723 | N | |

R_{8–15} | 0.1804 | N | |

R_{16–30} | 0.1912 | N | |

R_{31–60} | 0.1984 | N |

**Table 5.**Statistics of prediction evaluation indexes for original and denoised data of UP17 measurement points.

UP17 | RMSE | MAE |
---|---|---|

Original data | 1.3614 | 1.2890 |

denoised data | 0.1903 | 0.1554 |

Points | UP17 | UP26 | ||||

Models | RMSE/(m) | MAE/(m) | Time/s | RMSE/(m) | MAE/(m) | Time/s |

LSTM | 0.3312 | 0.2309 | 325.12 | 0.0605 | 0.0429 | 353.95 |

GRU | 0.3638 | 0.3321 | 199.23 | 0.0629 | 0.0426 | 277.76 |

CNN-GRU | 0.1903 | 0.1554 | 276.38 | 0.0548 | 0.0398 | 291.83 |

PSO-BP | 1.0973 | 0.8919 | 215.43 | 0.1674 | 0.1416 | 212.69 |

ABC-SVM | 1.0165 | 0.8303 | 464.51 | 0.1438 | 0.1225 | 582.21 |

Points | UP35 | UP51 | ||||

Models | RMSE/(m) | MAE/(m) | Time/s | RMSE/(m) | MAE/(m) | Time/s |

LSTM | 0.5650 | 0.5305 | 382.02 | 0.3549 | 0.3059 | 321.54 |

GRU | 0.7577 | 0.6967 | 300.28 | 0.4484 | 0.3602 | 183.03 |

CNN-GRU | 0.2916 | 0.2306 | 310.53 | 0.2127 | 0.1827 | 222.77 |

PSO-BP | 1.1081 | 0.8951 | 154.85 | 1.2607 | 1.0787 | 186 |

ABC-SVM | 1.2673 | 0.9972 | 569.27 | 1.6306 | 1.3256 | 523.13 |

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## Share and Cite

**MDPI and ACS Style**

Hua, G.; Wang, S.; Xiao, M.; Hu, S.
Research on the Uplift Pressure Prediction of Concrete Dams Based on the CNN-GRU Model. *Water* **2023**, *15*, 319.
https://doi.org/10.3390/w15020319

**AMA Style**

Hua G, Wang S, Xiao M, Hu S.
Research on the Uplift Pressure Prediction of Concrete Dams Based on the CNN-GRU Model. *Water*. 2023; 15(2):319.
https://doi.org/10.3390/w15020319

**Chicago/Turabian Style**

Hua, Guowei, Shijie Wang, Meng Xiao, and Shaohua Hu.
2023. "Research on the Uplift Pressure Prediction of Concrete Dams Based on the CNN-GRU Model" *Water* 15, no. 2: 319.
https://doi.org/10.3390/w15020319