# Deformation Prediction System of Concrete Dam Based on IVM-SCSO-RF

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}is very close to 1. The results of study provide a new method for the automatic online evaluation of dam safety performance.

## 1. Introduction

## 2. Methodology

#### 2.1. Indicator Variable Model

_{i}, the indicator variable can be expressed as

_{i}is the time of the ith interference; and V

_{i}is the indicator variable of the ith interference.

_{i}, the all-time IVM can be expressed as

_{i}is the drift caused by the ith interference.

_{j}and ${\hat{y}}_{j}$ represent the jth observation value and its estimated value, respectively, and N represents the total number of samples.

_{k}, b

_{p}, and c

_{q}are regression coefficients of water pressure component, temperature component, and time effect component, respectively.

_{i}caused by each interference can be calculated by solution (4); it is removed from the measured value in each disturbed period, and then the measured value is corrected.

#### 2.2. Sand Cat Swarm Optimization Algorithm

#### 2.2.1. Initial Population

_{i}(i = 1~d) of each dimension represents the potential solution of the optimization problem and must be located between the upper and lower boundaries. The fitness value of each cat can be obtained by substituting the variable value into the fitness function. After the best individual is evaluated according to the fitness value, other cats move towards it.

#### 2.2.2. Searching the Prey

_{M}is a parameter representing the auditory characteristics of sand cats, and its default value is 2, which can be flexibly adjusted for different optimization problems; iter

_{c}is the current iteration; iter

_{Max}is the maximum iterations.

#### 2.2.3. Attacking the Prey

#### 2.2.4. Transition between Search and Hunting Stages

#### 2.3. Random Forest Algorithm

#### 2.3.1. Decision Tree Algorithm

#### 2.3.2. Ensemble Learning

#### 2.3.3. Out-of-Bag Error

#### 2.3.4. Flow of Random Forest Algorithm

- Generate n groups of training samples randomly by bootstrap method, and construct decision trees based on the new sample sets.
- When selecting attributes for each internal node, select m attributes from all attributes randomly as the attribute set of the node. Based on CART algorithm, select the optimal attribute for splitting until the decision tree grows completely. During the growth of the decision tree, pruning is not required.
- Input the test sample set and obtain the final result on the basis of synthesizing the prediction results of all decision trees. For regression problems, the weighted average of prediction values of all decision trees is taken as the final prediction value.

#### 2.4. Construction of Deformation Prediction System of Concrete Dam Based on IVM-SCSO-RF

#### 2.4.1. Input Variables

_{0}is the water depth on the initial monitoring day; the input variables consider the influence of upstream and downstream water pressure at the same time, and the subscripts u and d represent upstream and downstream, respectively; t

_{0}is the accumulated days from the initial modeling day to the initial monitoring day; t is the accumulated days from the monitoring day to the initial monitoring day; ${\theta}_{0}$ is 0.01t

_{0}; $\theta $ is 0.01t.

#### 2.4.2. Parameters of RF

_{tree}and the number of variable choices to split on at each node m

_{try}, which are simplified as n and m, respectively. Set the OOB error of the RF algorithm as the fitness function and select n and m as the target parameters of the SCSO algorithm for optimization. Finally, the position corresponding to the minimum OOB error is the optimal combination of n and m.

#### 2.4.3. System Operation Process

- Read the original data, establish the IVM to eliminate system interference after removing the missing items in the monitoring values, and obtain the corrected sample set.
- Divide the sample set into training set and test set; the proportion of test set is generally 10%~20% of the total samples.
- Input the training set data into the SCSO-RF algorithm and obtain the optimal parameter combination of the RF algorithm by SCSO algorithm.
- Input the test set data into the RF algorithm after parameter optimization and obtain the prediction results.
- Analyze the prediction effect by comparing the predicted value with the actual value and calculating the sum of squared error SSE, the mean-square error MSE, the mean absolute error MAE, the root-mean-square error RMSE, and the coefficient of determination R
^{2}.

## 3. Case Study

#### 3.1. Project Overview

^{®}(R2020a) software was employed to implement all algorithms and models in this study. Furthermore, the statistics and machine learning toolbox and deep learning toolbox in the software were used to apply all the machine learning algorithms.

#### 3.2. Performance Verification of IVM

#### 3.3. Application of Deformation Prediction System of Concrete Dam Based on IVM-SCSO-RF

#### 3.3.1. Correction of Measured Value by IVM

#### 3.3.2. Parameter Optimization of RF Algorithm

- The trial-and-error method

^{−3}.

- 2.
- Particle swarm optimization algorithm

^{−3}, and the corresponding optimal parameter combination was n = 712, m = 8.

- 3.
- Sand cat swarm optimization algorithm

^{−3}, and the corresponding optimal parameter combination was n = 437, m = 12.

#### 3.3.3. Training and Prediction of Model

^{2}and 0.217 mm, respectively. It lost a lot of characteristic information of the monitoring data because this method selected parameters of RF relying on subjective experience, and thus the stability of the model is poor, with its MSE and RMSE of 0.097 mm

^{2}and 0.312 mm, respectively, and R

^{2}of 0.731. The prediction accuracy and stability of RF optimized by PSO algorithm have been improved. Compared with TAE-RF, the SSE, MSE, MAE, and RMSE of PSO-RF are reduced by 47%, 46%, 17% and 27%, respectively, and R

^{2}is 0.856. However, due to falling into the local extreme value in parameter optimization, the RF optimized by the PSO algorithm does not give full play to its best performance. The common LSTM and SVM are similar in this case, and the prediction accuracy and stability of LSTM are slightly better than those of SVM. Compared with PSO-RF, the SSE, MSE, MAE, and RMSE of LSTM are reduced by 29%, 29%, 17%, and 16% respectively, and its R

^{2}is close to 0.9, but the prediction accuracy is still not satisfactory. With powerful capability of global optimization, the SCSO algorithm has improved the prediction performance of RF greatly. The SSE, MSE, MAE, and RMSE of SCSO-RF have all reached the minimum of all models. The four evaluation criteria have decreased by 91%, 92%, 76%, and 71% respectively, compared with the LSTM with better prediction accuracy, and by 97%, 97%, 83%, and 82%, respectively, compared with the TAE-RF with the worst prediction accuracy. Moreover, the R

^{2}of SCSO-RF is very close to 1. The results further verify the reliability and prediction performance of the deformation prediction system proposed in this paper.

^{2}is still very close to 1, which indicates that the model can mine the effective information in the input variables fully and make more accurate prediction for large changes in displacement caused by variations of environmental factors. Furthermore, the performance of LSTM at these points is significantly worse than that of the global prediction, indicating that the model ignores part of the effective information in the input variables.

## 4. Discussion

## 5. Conclusions

^{2}of SCSO-RF is very close to 1. At the same time, SCSO-RF has more obvious advantages in the prediction of designated points with large changes of displacement. The above results fully verify that the RF algorithm optimized by the SCSO algorithm has excellent abilities of nonlinear data mining and prediction, which can be widely used in practical projects. In addition, the deformation prediction system proposed in this paper has strong applicability and can be applied to other types of concrete dams with a little modification.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Process diagram of measured values, measured values with drift, and corrected values of PL23-1.

Change Point | Actual Drift Value (mm) | Calculated Drift Value (mm) | Absolute Error (mm) | Error Rate (%) |
---|---|---|---|---|

140 | 3.00 | 3.078 | 0.078 | 2.6% |

270 | −6.00 | −6.037 | 0.037 | 0.6% |

450 | 5.00 | 4.926 | 0.074 | 1.5% |

Evaluation Criterion | TAE-RF | PSO-RF | SCSO-RF | LSTM | SVM |
---|---|---|---|---|---|

SSE/mm^{2} | 0.742 | 0.552 | 1.209 | 3.728 | 2.136 |

MSE/mm^{2} | 0.001 | 0.001 | 0.002 | 0.007 | 0.004 |

MAE/mm | 0.027 | 0.024 | 0.036 | 0.066 | 0.046 |

RMSE/mm | 0.037 | 0.032 | 0.048 | 0.084 | 0.064 |

R^{2} | 0.998 | 0.998 | 0.997 | 0.990 | 0.994 |

Evaluation Criterion | TAE-RF | PSO-RF | SCSO-RF | LSTM | SVM |
---|---|---|---|---|---|

SSE/mm^{2} | 12.810 | 6.851 | 0.418 | 4.857 | 5.016 |

MSE/mm^{2} | 0.097 | 0.052 | 0.003 | 0.037 | 0.038 |

MAE/mm | 0.217 | 0.181 | 0.036 | 0.150 | 0.170 |

RMSE/mm | 0.312 | 0.228 | 0.056 | 0.192 | 0.195 |

R^{2} | 0.731 | 0.856 | 0.991 | 0.898 | 0.895 |

Time | Measured Value/mm | Predicted Value/mm | ||||
---|---|---|---|---|---|---|

TAE-RF | PSO-RF | SCSO-RF | LSTM | SVM | ||

9 September 2017 | 0.51 | 0.48 | 0.62 | 0.60 | 0.63 | 0.48 |

6 October 2017 | 0.50 | 0.51 | 0.56 | 0.50 | 0.49 | 0.16 |

16 October 2017 | 0.23 | 0.35 | 0.35 | 0.18 | 0.39 | −0.01 |

20 November 2017 | −0.28 | 0.05 | −0.04 | −0.24 | −0.01 | −0.39 |

21 November 2017 | −0.32 | 0.03 | −0.08 | −0.26 | −0.02 | −0.38 |

25 November 2017 | −0.46 | −0.04 | −0.14 | −0.36 | −0.10 | −0.43 |

26 November 2017 | −0.57 | −0.09 | −0.21 | −0.46 | −0.12 | −0.41 |

27 November 2017 | −0.59 | −0.11 | −0.22 | −0.49 | −0.15 | −0.45 |

28 November 2017 | −0.58 | −0.13 | −0.26 | −0.54 | −0.18 | −0.51 |

29 November 2017 | −0.66 | −0.14 | −0.27 | −0.57 | −0.21 | −0.56 |

16 December 2017 | −0.75 | −0.33 | −0.35 | −0.69 | −0.66 | −0.89 |

23 December 2017 | −1.31 | −0.50 | −0.78 | −1.32 | −0.80 | −1.01 |

Evaluation Criterion | TAE-RF | PSO-RF | SCSO-RF | LSTM | SVM |
---|---|---|---|---|---|

SSE/mm^{2} | 2.189 | 1.204 | 0.060 | 1.359 | 0.365 |

MSE/mm^{2} | 0.182 | 0.100 | 0.005 | 0.113 | 0.030 |

MAE/mm | 0.369 | 0.287 | 0.062 | 0.297 | 0.144 |

RMSE/mm | 0.427 | 0.317 | 0.071 | 0.337 | 0.174 |

R^{2} | 0.307 | 0.619 | 0.981 | 0.570 | 0.884 |

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**MDPI and ACS Style**

Zhang, S.; Zheng, D.; Liu, Y.
Deformation Prediction System of Concrete Dam Based on IVM-SCSO-RF. *Water* **2022**, *14*, 3739.
https://doi.org/10.3390/w14223739

**AMA Style**

Zhang S, Zheng D, Liu Y.
Deformation Prediction System of Concrete Dam Based on IVM-SCSO-RF. *Water*. 2022; 14(22):3739.
https://doi.org/10.3390/w14223739

**Chicago/Turabian Style**

Zhang, Shi, Dongjian Zheng, and Yongtao Liu.
2022. "Deformation Prediction System of Concrete Dam Based on IVM-SCSO-RF" *Water* 14, no. 22: 3739.
https://doi.org/10.3390/w14223739