# A Data-Driven Dam Deformation Forecasting and Interpretation Method Using the Measured Prototypical Temperature Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Dam Deformation Statistical Monitoring Model

#### 2.2. LGB

#### 2.3. Bayesian Optimization and Cross-Validation

- Step 1:
- The training set is randomly divided into K disjoint subsets;
- Step 2:
- The 1st and K-1th subsets are used as the training set, and the Kth subset is used as the verification set. Then, the prediction accuracy of the K group subset is calculated;
- Step 3:
- The second to Kth group subsets are used as the training set, and the first group subset is used as the verification set to obtain the prediction accuracy of the Kth group subset test;
- Step 4:
- The average prediction accuracy of the above K model is taken as the performance index of the model under K-fold cross-validation.

## 3. Case Study

#### 3.1. Project Description

^{2}, and the annual average rainfall is 650 mm. The design flood level of the dam is 481.75 m, and the dam foundation elevation is 389.5 m. The total storage capacity of the reservoir is 16.6 million m

^{3}. The dam is a concrete gravity arch dam with a fixed center and variable radius. The dam crest arc length is 154.28 m, and the dam crest central angle is 80°. The outer radius is 110.5 m, and the dam crest elevation is 490.5 m. The maximum dam height is 202 m, and the dam crest thickness is 4.5 m.

#### 3.2. Data Collection and Preprocessing

#### 3.3. Experiment Environment Setting and Parameter Tuning

^{2}), mean absolute error (MAE), and root mean squared error (RMSE) were introduced to assess the prediction performance of the proposed and the benchmark models. The formulas of these indicators can be represented as follows.

## 4. Results Discussion

#### 4.1. Project Description

#### 4.2. Model Generalization Capability Evaluation

#### 4.2.1. Short-Term Prediction Performance Evaluation

#### 4.2.2. Long-Term Prediction Performance Evaluation

#### 4.3. Model Interpretability Assessment

## 5. Conclusions

- The proposed BO–LGB model shows strong capability when dealing with the long-term dam monitoring data both in modeling accuracy and efficiency;
- The proposed method achieves remarkable performance in a variety of dam displacement prediction scenarios (both in short-term prediction and long-term prediction);
- The proposed method can analyze the main factors affecting dam displacement changes based on prototypical monitoring data.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Kang, F.; Li, J.; Zhao, S.; Wang, Y. Structural health monitoring of concrete dams using long-term air temperature for thermal effect simulation. Eng. Struct.
**2019**, 180, 642–653. [Google Scholar] [CrossRef] - Kang, F.; Li, J. Displacement Model for Concrete Dam Safety Monitoring via Gaussian Process Regression Considering Extreme Air Temperature. J. Struct. Eng.
**2020**, 146, 05019001. [Google Scholar] [CrossRef] - Tatin, M.; Briffaut, M.; Dufour, F.; Simon, A.; Fabre, J.-P. Thermal displacements of concrete dams: Accounting for water temperature in statistical models. Eng. Struct.
**2015**, 91, 26–39. [Google Scholar] [CrossRef] - Kang, F.; Liu, X.; Li, J. Concrete Dam Behavior Prediction Using Multivariate Adaptive Regression Splines with Meas-ured Air Temperature. Arab. J. Sci. Eng.
**2019**, 44, 8661–8673. [Google Scholar] [CrossRef] - Li, Y.; Bao, T.; Shu, X.; Chen, Z.; Gao, Z.; Zhang, K. A Hybrid Model Integrating Principal Component Analysis, Fuzzy C-Means, and Gaussian Process Regression for Dam Deformation Prediction. Arab. J. Sci. Eng.
**2020**, 46, 4293–4306. [Google Scholar] [CrossRef] - Liu, J.; Zhou, X.C.; Chen, W.; Hong, X. Breach Discharge Estimates and Surface Velocity Measurements for an Earth Dam Failure Process Due to Overtopping Based on the LS-PIV Method. Arab. J. Sci. Eng.
**2019**, 44, 329–339. [Google Scholar] [CrossRef] - Ma, C.; Gao, Z.; Yang, J.; Cheng, L.; Chen, L. Operation Performance and Seepage Flow of Impervious Body in Blast-Fill Dams Using Discrete Element Method and Measured Data. Water
**2022**, 14, 1443. [Google Scholar] [CrossRef] - Tong, F.; Yang, J.; Ma, C.; Cheng, L.; Li, G. The Prediction of Concrete Dam Displacement Using Copula-PSO-ANFIS Hybrid Model. Arab. J. Sci. Eng.
**2022**, 47, 4335–4350. [Google Scholar] [CrossRef] - Salazar, F.; Toledo, M.; Oñate, E.; Morán, R. An empirical comparison of machine learning techniques for dam behaviour modelling. Struct. Saf.
**2015**, 56, 9–17. [Google Scholar] [CrossRef] - Xi, R.; Zhou, X.; Jiang, W.; Chen, Q. Simultaneous estimation of dam displacements and reservoir level variation from GPS measurements. Measurement
**2018**, 122, 247–256. [Google Scholar] [CrossRef] - Liu, H.Z.; Wang, S.L.; Liu, J.Y. LS-SVM Prediction Model Based on Phase Space Reconstruction for Dam Deformation. Adv. Mater. Res.
**2013**, 663, 55–59. [Google Scholar] [CrossRef] - Shao, C.; Gu, C.; Yang, M.; Xu, Y.; Su, H. A novel model of dam displacement based on panel data. Struct. Control Health Monit.
**2018**, 25, e2037. [Google Scholar] [CrossRef] - Yang, L.; Su, H.; Wen, Z. Improved PLS and PSO methods-based back analysis for elastic modulus of dam. Adv. Eng. Softw.
**2019**, 131, 205–216. [Google Scholar] [CrossRef] - Li, B.; Yang, J.; Hu, D. Dam monitoring data analysis methods: A literature review. Struct. Control Health Monit.
**2020**, 27, e2501. [Google Scholar] [CrossRef] - Thangam, Y.Y.; Kalanithi, M.; Anbarasi, C.M.; Rajendran, S. Inhibition of Corrosion of Carbon Steel in a Dam Water by Sodium Molybdate–Zn2+ System. Arab. J. Sci. Eng.
**2009**, 34, 49–60. [Google Scholar] - Lin, C.; Li, T.; Chen, S.; Liu, X.; Lin, C.; Liang, S. Gaussian process regression-based forecasting model of dam deformation. Neural Comput. Appl.
**2019**, 31, 8503–8518. [Google Scholar] [CrossRef] - Qu, X.; Yang, J.; Chang, M. A Deep Learning Model for Concrete Dam Deformation Prediction Based on RS-LSTM. J. Sens.
**2019**, 2019, 4581672. [Google Scholar] [CrossRef] - Mata, J.; de Castro, A.T.; da Costa, J.S. Constructing Statistical Models for Arch Dam Deformation. Struct. Control Health Monit.
**2014**, 21, 423–437. [Google Scholar] [CrossRef] - Su, H.; Li, X.; Yang, B.; Wen, Z. Wavelet support vector machine-based prediction model of dam deformation. Mech. Syst. Signal Process.
**2018**, 110, 412–427. [Google Scholar] [CrossRef] - Beaujoint, N.J. Discussion of “Dead Load Stress in Model Dams by Method of Integration”. J. Struct. Div.
**1962**, 88, 317–318. [Google Scholar] [CrossRef] - Belmokre, A.; Mihoubi, M.K.; Santillán, D. Analysis of Dam Behavior by Statistical Models: Application of the Random Forest Approach. KSCE J. Civ. Eng.
**2019**, 23, 4800–4811. [Google Scholar] [CrossRef] - Salazar, F.; Morán, R.; Toledo, M.; Oñate, E. Data-Based Models for the Prediction of Dam Behaviour: A Review and Some Methodological Considerations. Arch. Comput. Methods Eng.
**2017**, 24, 1–21. [Google Scholar] [CrossRef] - Hu, J.; Wu, S. Statistical modeling for deformation analysis of concrete arch dams with influential horizontal cracks. Struct. Health Monit.
**2019**, 18, 546–562. [Google Scholar] [CrossRef] - Wieland, M.; Kirchen, G.F. Long-term dam safety monitoring of Punt dal Gall arch dam in Switzerland. Front. Struct. Civ. Eng.
**2012**, 6, 76–83. [Google Scholar] [CrossRef] - Li, M.; Shen, Y.; Ren, Q.; Li, H. A new distributed time series evolution prediction model for dam deformation based on constituent elements. Adv. Eng. Inform.
**2019**, 39, 41–52. [Google Scholar] [CrossRef] - Ren, Q.; Li, M.; Song, L.; Liu, H. An optimized combination prediction model for concrete dam deformation considering quantitative evaluation and hysteresis correction. Adv. Eng. Inform.
**2020**, 46, 101154. [Google Scholar] [CrossRef] - Li, Y.; Bao, T.; Gong, J.; Shu, X.; Zhang, K. The Prediction of Dam Displacement Time Series Using STL, Extra-Trees, and Stacked LSTM Neural Network. IEEE Access
**2020**, 8, 94440–94452. [Google Scholar] [CrossRef] - Bui, K.-T.T.; Tien Bui, D.; Zou, J.; Van Doan, C.; Revhaug, I. A novel hybrid artificial intelligent approach based on neural fuzzy inference model and particle swarm optimization for horizontal displacement modeling of hydropower dam. Neural Comput. Appl.
**2018**, 29, 1495–1506. [Google Scholar] [CrossRef] - Li, X.; Wen, Z.; Su, H. An approach using random forest intelligent algorithm to construct a monitoring model for dam safety. Eng. Comput.
**2021**, 37, 39–56. [Google Scholar] [CrossRef] - Milillo, P.; Perissin, D.; Salzer, J.T.; Lundgren, P.; Lacava, G.; Milillo, G.; Serio, C. Monitoring dam structural health from space: Insights from novel InSAR techniques and multi-parametric modeling applied to the Pertusillo dam Basilicata, Italy. Int. J. Appl. Earth Obs. Geoinf.
**2016**, 52, 221–229. [Google Scholar] [CrossRef] - Ribeiro, L.S.; Wilhelm, V.E.; Faria, F.; Correa, J.M.; dos Santos, A.C.P. A comparative analysis of long-term concrete deformation models of a buttress dam. Eng. Struct.
**2019**, 193, 301–307. [Google Scholar] [CrossRef] - Gui, G.; Pan, H.; Lin, Z.; Li, Y.; Yuan, Z. Data-driven support vector machine with optimization techniques for structural health monitoring and damage detection. KSCE J. Civ. Eng.
**2017**, 21, 523–534. [Google Scholar] [CrossRef] - Ma, J.; Cheng, J.C.; Jiang, F.; Chen, W.; Wang, M.; Zhai, C. A bi-directional missing data imputation scheme based on LSTM and transfer learning for building energy data. Energy Build.
**2020**, 216, 109941. [Google Scholar] [CrossRef] - Malekloo, A.; Ozer, E.; AlHamaydeh, M.; Girolami, M. Machine Learning and Structural Health Monitoring Overview with Emerging Technology and High-Dimensional Data Source Highlights. Struct. Health Monit.
**2022**, 21, 1906–1955. [Google Scholar] [CrossRef] - Chen, S.; Gu, C.; Lin, C.; Zhao, E.; Song, J. Safety Monitoring Model of a Super-High Concrete Dam by Using RBF Neural Network Coupled with Kernel Principal Component Analysis. Math. Probl. Eng.
**2018**, 2018, 1712653. [Google Scholar] [CrossRef] - Su, Y.; Weng, K.; Lin, C.; Zheng, Z. An Improved Random Forest Model for the Prediction of Dam Displacement. IEEE Access
**2021**, 9, 9142–9153. [Google Scholar] [CrossRef] - Ren, Q.; Li, M.; Li, H.; Song, L.; Si, W.; Liu, H. A robust prediction model for displacement of concrete dams subjected to irregular water-level fluctuations. Comput. -Aided Civ. Infrastruct. Eng.
**2021**, 36, 577–601. [Google Scholar] [CrossRef] - Li, M.; Li, M.; Ren, Q.; Li, H.; Song, L. DRLSTM: A dual-stage deep learning approach driven by raw monitoring data for dam dis-placement prediction. Adv. Eng. Inform.
**2022**, 51, 101510. [Google Scholar] [CrossRef] - Ren, Q.; Li, M.; Kong, T.; Ma, J. Multi-sensor real-time monitoring of dam behavior using self-adaptive online sequential learning. Autom. Constr.
**2022**, 140, 104365. [Google Scholar] [CrossRef]

**Figure 6.**Intuitive display of environmental variable process: (

**a**) reservoir level process, (

**b**) thermometer data.

**Figure 9.**Intuitive comparison of the prediction results of the proposed and the benchmark methods at the typical three monitoring points. (

**a**) PL01, (

**b**) PL02, and (

**c**) IP01.

**Figure 10.**Intuitive comparison of the prediction results of the proposed and benchmark methods at the typical three monitoring points. (

**a**) PL01, (

**b**) PL02, and (

**c**) IP01.

**Figure 11.**Factor importance assessment results of three typical monitoring sites: (

**a**–

**c**) denotes monitoring points PL1, PL2, and IP01.

Parameters | Parameter Optimization Range |
---|---|

$n\_estimator$ | $[10,500]$ |

$num\_leaves$ | $[10,100]$ |

$\mathrm{min}\_child\_samples$ | $[1,20]$ |

$\mathrm{max}\_depth$ | $[1,100]$ |

$feature\_fraction\_rate$ | $[0.5,0.9999]$ |

$bagging\_fraction$ | $[0.5,0.9999]$ |

n_Estimators | num_Leaves | min_Child_Samples | Max_Depth | Feature_Fraction | Bagging_Fraction | |
---|---|---|---|---|---|---|

PL01 | 474 | 19 | 9 | 50 | 0.96 | 0.67 |

PL02 | 500 | 10 | 20 | 73 | 0.5 | 0.5 |

IP01 | 424 | 48 | 17 | 2 | 0.73 | 0.89 |

**Table 3.**The comparison of short-term dam displacement prediction performance of the proposed and benchmark methods.

Proposed | RD_LGB | HST | ANN | SVM | RF | GP | ||
---|---|---|---|---|---|---|---|---|

PL01 | R^{2} | 0.9600 | 0.9238 | 0.9490 | 0.9103 | 0.8739 | 0.9243 | 0.9323 |

MSE | 0.1920 | 0.2689 | 0.1950 | 0.2532 | 0.3171 | 0.2666 | 0.2440 | |

MAE | 0.1622 | 0.2226 | 0.1378 | 0.2057 | 0.2598 | 0.2106 | 0.1882 | |

PL02 | R^{2} | 0.9703 | 0.9638 | 0.9621 | 0.9607 | 0.3334 | 0.9289 | 0.9608 |

MSE | 0.1751 | 0.1928 | 0.2072 | 0.1981 | 0.7291 | 0.2806 | 0.2104 | |

MAE | 0.1327 | 0.1641 | 0.1591 | 0.1423 | 0.6231 | 0.2474 | 0.1589 | |

IP01 | R^{2} | 0.9855 | 0.9836 | 0.8879 | 0.8796 | 0.5692 | 0.8499 | 0.9354 |

MSE | 0.0269 | 0.0284 | 0.0688 | 0.0678 | 0.1198 | 0.0764 | 0.0528 | |

MAE | 0.0217 | 0.0227 | 0.0633 | 0.0573 | 0.1120 | 0.0663 | 0.0480 |

**Table 4.**Performance comparison of the proposed and comparative methods in long-term dam displacement prediction.

Proposed | RD_LGB | HST | ANN | SVM | RF | GP | ||
---|---|---|---|---|---|---|---|---|

PL01 | R^{2} | 0.9067 | 0.8703 | 0.8669 | 0.8833 | 0.8656 | 0.8746 | 0.8703 |

MSE | 0.3044 | 0.3708 | 0.3354 | 0.3354 | 0.3306 | 0.3440 | 0.3708 | |

MAE | 0.2472 | 0.3158 | 0.2801 | 0.2758 | 0.2578 | 0.2793 | 0.3158 | |

PL02 | R^{2} | 0.9724 | 0.8505 | 0.8390 | 0.8737 | 0.9454 | 0.9454 | 0.8737 |

MSE | 0.1804 | 0.4542 | 0.4753 | 0.4179 | 0.2559 | 0.2559 | 0.4179 | |

MAE | 0.1490 | 0.4151 | 0.4348 | 0.3723 | 0.1942 | 0.1942 | 0.3723 | |

IP01 | R^{2} | 0.7792 | 0.7734 | 0.2823 | 0.3622 | 0.6911 | 0.6186 | 0.3518 |

MSE | 0.1064 | 0.0932 | 0.2139 | 0.1853 | 0.0968 | 0.1114 | 0.1976 | |

MAE | 0.0825 | 0.0770 | 0.2028 | 0.1736 | 0.0793 | 0.0925 | 0.1884 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

He, P.; Li, Y.
A Data-Driven Dam Deformation Forecasting and Interpretation Method Using the Measured Prototypical Temperature Data. *Water* **2022**, *14*, 2538.
https://doi.org/10.3390/w14162538

**AMA Style**

He P, Li Y.
A Data-Driven Dam Deformation Forecasting and Interpretation Method Using the Measured Prototypical Temperature Data. *Water*. 2022; 14(16):2538.
https://doi.org/10.3390/w14162538

**Chicago/Turabian Style**

He, Peng, and Yueyang Li.
2022. "A Data-Driven Dam Deformation Forecasting and Interpretation Method Using the Measured Prototypical Temperature Data" *Water* 14, no. 16: 2538.
https://doi.org/10.3390/w14162538