# Prediction for the Settlement of Concrete Face Rockfill Dams Using Optimized LSTM Model via Correlated Monitoring Data

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## Abstract

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## 1. Introduction

## 2. The Interpretation Model for the Settlement of CFRD

## 3. LSTM-CS MMP Prediction Model for the Settlement of CFRD

#### 3.1. Data Clustering Based on K-Means++ Algorithm

#### 3.2. CS Algorithm Optimized LSTM

#### 3.2.1. Long Short-Term Memory Structure

#### 3.2.2. Cuckoo Search Algorithm

## 4. Project Overview

## 5. Results and Discussion

#### 5.1. Clustering Results of Monitoring Data Series

#### 5.2. Optimization of Parameters in LSTM

#### 5.3. Fitting and Prediction Results

#### 5.3.1. Selection of the Input Variables in the Model

#### 5.3.2. Fitting and Prediction Performance of M–LSTM Model

#### 5.3.3. Comparison between Different Models

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Fitting and Predicting Results

**Figure A1.**Fitting and prediction results of M–LSTM model based on the training datasets in Cluster 1 (LD1-2 in red lines and LD3-5 in green lines).

**Figure A2.**Fitting and prediction results of M–LSTM model based on the training datasets in Cluster 2 (LD2-2 in red, LD3-3 in green, LD5-4 in blue, and LD6-3 in purple lines, respectively).

**Figure A3.**Fitting and prediction results of M–LSTM model based on the training datasets in Cluster 3 (LD2-3 in red, LD3-4 in green, LD5-5 in blue, and LD6-4 in purple lines, respectively).

**Figure A4.**Fitting and prediction results of M–LSTM model based on the training datasets in Cluster 4 (LD3-2, LD4-2, LD4-3, LD5-2, LD5-3, and LD6-2).

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**Figure 1.**Schematic diagram of the CFRD and the main components of the settlements: (

**a**) sketch of the CFRD, (

**b**) structure of the main body of the CFRD, (

**c**) creep deformation component, (

**d**) consolidation of soil particles, (

**e**) hydrostatic load component, (

**f**) frost heave of soil particles.

**Figure 3.**Schematics for typical searching process of Lévy flights and random walk in 2000 iterations.

**Figure 5.**Schematic of: (

**a**) location, (

**b**) structure, (

**c**) distribution of monitoring points of settlement, of the CFRD for Langyashan PSPS.

**Figure 7.**Ambient data series of Langyashan dam: (

**a**) upstream water level, (

**b**) environmental temperature.

**Figure 15.**Results of: (

**a**) AMSE of M–LSTM, LSTM, BPNN, and HST models under different prediction lengths, (

**b**) ASMAPE of M–LSTM, LSTM, BPNN, and HST models under different prediction lengths, (

**c**) AMAPE of M–LSTM, LSTM, BPNN, and HST models under different prediction lengths.

**Table 1.**Upper bound and lower bound of the parameters set in the CS algorithm, and the results of optimized parameters of the NN structure in LSTM model.

Hidden Layers | Hidden Nodes | Learning Rate | |
---|---|---|---|

Upper bound | 10 | 20 | $1\times {10}^{-1}$ |

Lower bound | 1 | 1 | $1\times {10}^{-5}$ |

Optimized parameters | 2 | 7 | $3\times {10}^{-2}$ |

Monitoring Point | M–LSTM | LSTM | BPNN | HST |
---|---|---|---|---|

LD1-2 | 0.843 | 0.985 | 0.754 | 0.576 |

LD2-2 | 0.987 | 0.807 | 0.971 | 0.918 |

LD2-3 | 0.907 | 0.989 | 0.873 | 0.665 |

LD3-2 | 0.995 | 0.926 | 0.991 | 0.951 |

LD3-3 | 0.991 | 0.93 | 0.905 | 0.937 |

LD3-4 | 0.919 | 0.541 | 0.829 | 0.745 |

LD3-5 | 0.799 | 0.991 | 0.753 | 0.409 |

LD4-2 | 0.995 | 0.983 | 0.994 | 0.962 |

LD4-3 | 0.994 | 0.991 | 0.99 | 0.96 |

LD5-2 | 0.995 | 0.985 | 0.987 | 0.961 |

LD5-3 | 0.993 | 0.95 | 0.761 | 0.946 |

LD5-4 | 0.974 | 0.781 | 0.947 | 0.87 |

LD5-5 | 0.88 | 0.99 | 0.867 | 0.635 |

LD6-2 | 0.993 | 0.974 | 0.988 | 0.941 |

LD6-3 | 0.981 | 0.779 | 0.917 | 0.865 |

LD6-4 | 0.87 | 0.754 | 0.793 | 0.579 |

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**MDPI and ACS Style**

Hu, Y.; Gu, C.; Meng, Z.; Shao, C.; Min, Z.
Prediction for the Settlement of Concrete Face Rockfill Dams Using Optimized LSTM Model via Correlated Monitoring Data. *Water* **2022**, *14*, 2157.
https://doi.org/10.3390/w14142157

**AMA Style**

Hu Y, Gu C, Meng Z, Shao C, Min Z.
Prediction for the Settlement of Concrete Face Rockfill Dams Using Optimized LSTM Model via Correlated Monitoring Data. *Water*. 2022; 14(14):2157.
https://doi.org/10.3390/w14142157

**Chicago/Turabian Style**

Hu, Yating, Chongshi Gu, Zhenzhu Meng, Chenfei Shao, and Zhongze Min.
2022. "Prediction for the Settlement of Concrete Face Rockfill Dams Using Optimized LSTM Model via Correlated Monitoring Data" *Water* 14, no. 14: 2157.
https://doi.org/10.3390/w14142157