# Optimization of Reservoir Level Scheduling Based on InSAR-LSTM Deformation Prediction Model for Rockfill Dams

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Obtain the spatial and temporal evolution characteristics of dam surface deformation by constructing a time series model of the Xiaolangdi Dam using SBAS-InSAR.
- (2)
- Analyze the deformation law of the InSAR model and propose an LSTM network model using water storage level data to predict the surface deformation of the dam.
- (3)
- Optimize the prediction model and propose a reservoir level scheduling scheme and finally verify the feasibility of the scheme using the InSAR-LSTM deformation prediction model.

## 2. Materials

#### 2.1. Study Area

^{2}, accounting for 92.3% of the Yellow River.

^{3}, the highest elevation of the dam is 283 m. The normal storage level is 275 m, the heads above and below the dam are approximately 100 m, and the highest historical water storage level was 273.35 m.

#### 2.2. Dataset

## 3. Methods

#### 3.1. InSAR Deformation Model

#### 3.2. Validation of InSAR Deformation Model Reliability

#### 3.3. InSAR Deformation Prediction Model

#### 3.3.1. LSTM Neural Network

#### 3.3.2. Construction of the Prediction Model

## 4. Results and Analysis

#### 4.1. InSAR Deformation Results and Validation

#### 4.2. Analysis of Deformation and Water Storage Level Data

#### 4.3. Prediction of Deformation Based on Reservoir Water Level Data

#### 4.4. Multimodel Comparison and Parameter Optimization

## 5. Discussion

## 6. Conclusions

- The InSAR deformation model shows that there is a gradual weakening in the deformation trend of the dam from the center to the sides and from the top to the bottom. Throughout the 6-year deformation cycle, although there were differences in the deformation trends in different parts of the dam, each region was excessively smooth. The 6-year cumulative deformation in the middle part of the dam near the upstream reached -155 mm, which is within the safe range for large rockfill dams.
- The Xiaolangdi Dam continuously deforms. The satellite platform can continuously and periodically acquire InSAR image data, which helps monitor the overall deformation of the dam over a long period of time and allows more deformation information to be obtained. Theoretically, the combination of InSAR technology and the LSTM model can predict the effects of different storage level planning schemes on the dam and can then adjust storage level planning schemes in a targeted manner, attenuating dam deformation and preventing the risk of possible larger deformations.
- Owing to the inherent limitations of the satellite platform, ground-based measurement data are also required to verify the reliability of the deformation and prediction models. In the future, the launch of satellites with shorter revisit periods and higher resolutions could enable better monitoring of surface deformation. The specific mechanism by which hydrostatic pressure affects the structural stability of dams has not been studied in depth in this work, and this could be the subject of future research.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) The schematic diagram of the location of the Sentinel-1 image. The black box in the figure is the coverage area before the image is cropped. (

**b**) The SAR image of the dam and the red box is the range of the main body of the dam.

**Figure 5.**(

**a**) SBAS-InSAR data processing. (

**b**) Projection of the on–site measurement data of the dam deformation at typical point P.

**Figure 7.**The computation process of the LSTM memory unit, the asterisk in the figure indicates the multiplication operation.

**Figure 9.**The time–series variation in the cumulative deformation of Xiaolangdi Dam from March 2017 to February 2023.

**Figure 10.**(

**a**–

**c**) Cumulative sink value line segments of the upstream slope of the dam, the top of the dam, and on the downstream slope line, which correspond to the points on the red, blue and black lines of (

**d**) respectively. (

**d**) Schematic diagram of the location of the three lines; the serial numbers of the points become larger in the direction of the arrow.

**Figure 11.**(

**a**) Location of on-site data point P. (

**b**,

**c**) Measured data of ground point P; Dx, Dy, and Dz are measured on the ground in each of the three directions, Los is the deformation data Los after the projection of the measured data, and SAR-Los is data from the InSAR deformation model.

**Figure 13.**The time series variation of the cumulative deformation of Xiaolangdi Dam from 2018 to 2019.

**Figure 14.**(

**a**) Comparison of deformation data and water storage level data at point P; (

**b**) Stage diagram of deformation data and water storage level data in 2018–2019, (1)–(4) are the numbering of the different stages based on the trend of the line.

**Figure 15.**(

**a**) Prediction results deformation data. (

**b**) InSAR model deformation data. (

**c**) Error distribution of the MAE in the prediction results. The results of the remaining twelve forecasts are presented in the Supplementary document. (

**d**) Comparison of deformation data and predicted results at point P.

**Figure 16.**(

**a**) Comparison of the prediction data of the three models ANN, RNN and LSTM at typical point P. (

**b**) Comparison of the prediction data before and after the addition of the temperature parameter to the LSTM model.

**Figure 17.**(

**a**) Relationship between on–site deformation data and storage level data at typical point P. (

**b**,

**c**) Comparison of the point P deformation values predicted using the simulated storage level experimental data with the InSAR model deformation values in 2021.

**Table 1.**The characteristics of the water storage level and dam deformation changes at different times.

Stage | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Date | 1 January 2018–6 February 2018 | 6 February 2018–26 March 2018 | 26 March 2018–18 June 2018 | 18 June 2018–8 January 2019 |

Average daily level Average daily level change | 267.2 m +0.01 m | 267.2 m −0.02 m | 253.5 m −0.35 m | 246.5 m +0.15 m |

Cumulative deformation value | −7 mm | −0.7 mm | +14.8 mm | −26.6 mm |

Daily deformation rate | −0.19 mm | −0.01 mm | +0.18 mm | −0.13 mm |

Number | Start Date | End Date | |
---|---|---|---|

Training set | 166/164 | 31 March 2017 | 25 September 2022 |

Prediction set | 15/13 | 7 October 2022 | 28 February 2023 |

MAE | MSE | RMSE | R | |
---|---|---|---|---|

ANN | 3.67 | 19.51 | 4.41 | −0.56 |

RNN | 4.56 | 25.93 | 5.09 | 0.72 |

LSTM | 1.49 | 3.95 | 1.98 | 0.80 |

LSTM-Tem | 1.37 | 3.45 | 1.85 | 0.83 |

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**MDPI and ACS Style**

Fang, Z.; He, R.; Yu, H.; He, Z.; Pan, Y.
Optimization of Reservoir Level Scheduling Based on InSAR-LSTM Deformation Prediction Model for Rockfill Dams. *Water* **2023**, *15*, 3384.
https://doi.org/10.3390/w15193384

**AMA Style**

Fang Z, He R, Yu H, He Z, Pan Y.
Optimization of Reservoir Level Scheduling Based on InSAR-LSTM Deformation Prediction Model for Rockfill Dams. *Water*. 2023; 15(19):3384.
https://doi.org/10.3390/w15193384

**Chicago/Turabian Style**

Fang, Zhigang, Rong He, Haiyang Yu, Zixin He, and Yaming Pan.
2023. "Optimization of Reservoir Level Scheduling Based on InSAR-LSTM Deformation Prediction Model for Rockfill Dams" *Water* 15, no. 19: 3384.
https://doi.org/10.3390/w15193384