# Stress Estimation of Concrete Dams in Service Based on Deformation Data Using SIE–APSO–CNN–LSTM

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

- Data configuration. Observations from dam deformation and stress sensors are collected to provide learning data for the estimation model. The supposed failure time of the target stress sensor is considered to be the splitting point between the training and testing periods. The data samples are then configured via the sliding-window approach.
- Model development. Taking the deformation matrix as the model input and extracting the spatial features among different deformation monitoring points via CNN each day produces the output sequence containing the temporal attributes. Take this sequence as the input of the single-layered LSTM to obtain the temporal representation of the sequence. Finally, set a fully connected (FC) layer to get the model output and take it as the value of concrete stress.
- Tuning and training. The training and validation subset are obtained via the time series cross-validation (CV) technique performed on the training data. Subsequently, taking the average accuracy of the validation set of each fold as the fitness function, the hyperparameter tuning of the estimation model is implemented via the proposed SIE–APSO.
- Evaluation. The estimation performance of the trained model is evaluated by feeding it the configured out-of-training data. Furthermore, the root mean square error (RMSE), average absolute percentage error (MAPE), and average relative variance (ARV) are utilized for model evaluation.

#### 2.1. The CNN–LSTM Estimation Model

**I**is a two-dimensional matrix (n × m) composed of the deformation measured values, where n and m are the number of deformation sequences and the number of monitoring times and represent the spatial and temporal dimensions of the data, respectively. Then, n CNN layers are adopted in parallel to perform convolution processing on the data of the first dimension (spatial dimension) of the matrix

**I**. That is, m deformation data from the same monitoring time participate in the calculation of a convolutional layer. A spatial feature sequence is generated by extracting the spatial association between multiple deformation monitoring points each time. Notably, this sequence contains temporal attributes. The operation of the LSTM is performed subsequently on the temporal dimensions of this sequence and then obtains the spatial–temporal features of the data. The generated spatial–temporal features are connected to target stress values through a single-layer network for estimation. The architectures of CNN and LSTM are briefly introduced as follows.

#### 2.1.1. Convolutional Neural Network

#### 2.1.2. Long Short-Term Memory Network

#### 2.2. Improvement of the Particle Swarm Optimization

- inheritance of its inertia;
- the particle’s cognitive behavior, which represents the thinking of the particle itself;
- the population’s social sharing behavior represents the information sharing and cooperation between particles.

- Reduce the probability of falling into a local optimum. With the preform of iteration, the diversity of particles will continue to decrease, and it is easy to fall into the local optimum. Simulation of particle alienation behavior can reduce the probability of this phenomenon.
- Balance the global and local search capabilities of the algorithm. The particles are uniformly distributed in the early iteration with a larger swarm information entropy. At this stage, the higher alienation rate effectively prevents the particles from moving directly to the current optimal solution, giving it a better global exploration ability. While in the later stage, the particles are gradually concentrated. The decreasing of the alienation rate provides better local development of the particles.

#### 2.3. Time Series Cross-Validation Technique

#### 2.4. Evaluation Metrics

## 3. Case Study

#### 3.1. Project Description

^{3}. The dam is located in a high mountain and valley area, with steep slopes and a relatively complex geological structure. The overall slopes of the terrain on the bank sides are relatively neat and have an asymmetrical "V" shape in the valleys. The monitoring object of the dam monitoring system mainly includes:

- environment variables;
- horizontal and vertical displacement of the dam;
- the inclination of the dam foundation and dam body;
- the stress and strain of the dam concrete.

#### 3.2. Data Configuration

## 4. Results

#### 4.1. Hyperparameter Tuning Result of the Model

#### 4.2. Estimation Stress Results Evaluation

## 5. Discussion

#### 5.1. Estimation Performance Comparison

#### 5.2. Evaluation of Tuning Algorithms SIE–APSO

#### 5.3. Effect Analysis of the Input Sample Length

## 6. Summary and Conclusions

- By comparing three conventional models established with load-stress relationships, this work verified the feasibility of the proposed estimation model based on the data’s spatial–temporal association among the multiple monitoring points of dam deformation and stress.
- The proposed tuning algorithm SIE–APSO, which maintains higher computational accuracy and stability without losing efficiency compared with the standard PSO, is presented and has been tested on the target dataset.
- The estimation method provides reliable data supplements for the strength evaluation of concrete dams under the scenario of sensor failure and data loss, especially dealing with the dam responses under unexperienced conditions.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Layers | Parameters | Domain [Upper Limit, Lower Limit] | Optimization Value |
---|---|---|---|

CNN | filter number of each layer | (2, 64) | (13, 19, 10, 9, 16, 15, 17, 14, 15, 12) |

LSTM | unit number | (2, 32) | 19 |

dropout rate | (0, 0.5) | 0.335 | |

MLP | unit number | (2, 32) | 23 |

Optimizers | algorithms learning rate | - (10 ^{-5}, 10^{-1}) | Adagrad 0.100 |

- | batch size | (32, 256) | 165 |

Layers | Parameters | Domain [Upper Limit, Lower Limit] | Optimization Value |
---|---|---|---|

CNN | filter number of each layer | (2, 64) | (27, 35, 21, 12, 24, 33, 26, 31, 20, 23) |

LSTM | unit number | (2, 32) | 11 |

dropout rate | (0, 0.5) | 0.187 | |

MLP | unit number | (2, 32) | 15 |

Optimizers | algorithms learning rate | - (10 ^{-5}, 10^{-1}) | Adagrad 0.300 |

- | batch size | (32, 256) | 76 |

## Appendix B

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**Figure 8.**Instrument schematic of the dam deformation monitoring system (X-direction, Y-direction represent the direction along the river and the direction perpendicular to the river, respectively). (

**a**) Inverted plumb line, (

**b**) Vacuum laser.

**Figure 9.**Time curves of the monitoring data (X-direction, Y-direction represent the direction along the river and the direction perpendicular to the river, respectively). The shaded area is the sensor failure period. (

**a**) Vacuum laser alignment monitoring point LA9, (

**b**) Inverted plumb line monitoring point IP3, and (

**c**) Stress sensor S9.

**Figure 10.**Predictions of the proposed estimation model (lines) versus observed data (circles). The residuals between them are shown in the bar chart. Shaded part is the testing period. (

**a**) Direction along the river. (

**b**) Vertical direction.

**Figure 11.**Error-epoch charts of training and testing sets of the proposed estimation model. (

**a**) Direction along the river. (

**b**) Vertical direction.

**Figure 12.**Time curve of each estimation model and water level. Shaded part is the testing period. (

**a**) HST. (

**b**) SVR. (

**c**) NN. (

**d**) Time curve of water level. HST: hydrostatic-seasonal-time statistical model; SVR: support vector regression; NN: neural network with single hidden layer.

**Figure 13.**Evaluation metrics for each model. The results correspond to the testing period. (

**a**) Direction along the river, (

**b**) Vertical direction.

**Figure 14.**Performance comparison of SIE–APSO (swarm information entropy-based alienation particle swarm optimization), PSO (particle swarm optimization), LDIW–PSO (linear descent inertia weight strategy particle swarm optimization), GSA (gravitational search algorithm), and GWO (standard grey wolf optimizer). Convergence curve of each tuning algorithm. (

**a**) Direction along the river, (

**b**) Vertical direction.

**Figure 15.**Estimation results of proposed model with different input sample lengths. The dashed line is the fitted trend line. (

**a**) Direction along the river, (

**b**) Vertical direction.

Layers | Parameters | Domain (Upper Limit, Lower Limit) | Optimization Value |
---|---|---|---|

CNN | filter number of each layer | (2, 64) | (27, 35, …, 23) |

LSTM | unit number | (2, 32) | 11 |

dropout rate | (0, 0.5) | 0.187 | |

FC | unit number | (2, 32) | 15 |

Optimizers | algorithms learning rate | - (10 ^{−8}, 10^{5}) | Adagrad 0.300 |

- | batch size | (32, 256) | 76 |

Index | RMSE | MAPE | ARV | |||
---|---|---|---|---|---|---|

Direction | Training Period | Testing Period | Training Period | Testing Period | Training Period | Testing Period |

Direction along the river | 0.016 | 0.021 | 1.195% | 1.678% | 0.319 | 0.378 |

Vertical direction | 0.024 | 0.032 | 0.678% | 0.973% | 0.055 | 0.387 |

Direction | SIE–APSO | PSO | LDIW–PSO | GSA | GWO |
---|---|---|---|---|---|

Direction along the river | 1283.1 | 1074.7 | 1473.2 | 6050.2 | 1887.6 |

Vertical direction | 1755.4 | 1236.7 | 963.8 | 6738.8 | 2493.7 |

Average | 1519.2 | 1155.7 | 1218.5 | 6394.5 | 2190.7 |

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**MDPI and ACS Style**

Tao, L.; Zheng, D.; Wu, X.; Chen, X.; Liu, Y.; Chen, Z.; Jiang, H. Stress Estimation of Concrete Dams in Service Based on Deformation Data Using SIE–APSO–CNN–LSTM. *Water* **2023**, *15*, 59.
https://doi.org/10.3390/w15010059

**AMA Style**

Tao L, Zheng D, Wu X, Chen X, Liu Y, Chen Z, Jiang H. Stress Estimation of Concrete Dams in Service Based on Deformation Data Using SIE–APSO–CNN–LSTM. *Water*. 2023; 15(1):59.
https://doi.org/10.3390/w15010059

**Chicago/Turabian Style**

Tao, Liang, Dongjian Zheng, Xin Wu, Xingqiao Chen, Yongtao Liu, Zhuoyan Chen, and Haifeng Jiang. 2023. "Stress Estimation of Concrete Dams in Service Based on Deformation Data Using SIE–APSO–CNN–LSTM" *Water* 15, no. 1: 59.
https://doi.org/10.3390/w15010059