# Dynamic Self-Adaptive Modeling for Real-Time Flood Control Operation of Multi-Reservoir Systems

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Generation of Flood Samples and Establishment of Operation Models

#### 2.1.1. Generation of Random Flood Samples

#### 2.1.2. Establishment of the Operation Models

- (a)
- Water balance equation:

- (b)
- Reservoir release capacity limits:

- (c)
- Reservoir water level limits:

- (d)
- End water level limits:

- (e)
- Reservoir release fluctuation limits:

#### 2.2. Establishment of the Multi-Reservoir Flood Control Hybrid Operation Cyber–Physical System

#### 2.2.1. Framework Design of the MRFCHOCPS

#### 2.2.2. Functions of Each Component of MRFCHOCPS

- (1)
- Monitoring equipment

- (2)
- Database

- (3)
- Communication network

- (4)
- Computation module

- (5)
- Control center

#### 2.3. Evaluation of the MRFCHO Model

#### 2.3.1. Evaluation of the Model Accuracy

#### 2.3.2. Evaluation of the Model Solving Efficiency

## 3. Case Study

#### 3.1. Study Area

#### 3.2. Data

## 4. Results and Discussion

#### 4.1. Accuracy of the MRFCHO Model

_{m}≥ 7000 m

^{3}/s, the equivalent qualified rate is above 90%; when 4000 m

^{3}/s ≤ QC

_{m}< 7000 m

^{3}/s, the equivalent qualified rate is between 80% and 90%; when QC

_{m}< 4000 m

^{3}/s, the equivalent qualified rate is below 80%. The MRFCHO model is put forward to mitigate the dimension disaster problem of the multi-reservoir flood control operation for the basin-wide flood. It is not necessary to carry out the joint operation of multi-reservoirs for the flood of small magnitude. In the real-time flood control operation, it is better to apply the MRFCHO model to the flood with a large magnitude.

#### 4.2. Solving Efficiency of the MRFCHO Model

#### 4.3. Adaptability of MRFCHOCPS

## 5. Conclusions

- (1)
- Among 1000 random flood samples, the equivalent qualified rate of the MRFCHO model is 84.9%. It shows that in the future real-time flood control operation, it is highly reliable to establish the MRFCHO model for flood control operation on the basis of identifying effective reservoirs.
- (2)
- The operation results of floods with different magnitudes show that the equivalent qualified rate decreases with the decrease of flood magnitude. When the peak discharge of the Lutaizi point is more than 7000 m
^{3}/s, the equivalent qualified rate is more than 90%. The MRFCHO model is more suitable for basin-wide floods. - (3)
- In random flood samples, the number of effective reservoirs is generally 4–7, and the maximum number is not more than 11. Compared with the MRFCJO model, the space and time complexity of the MRFCHO model is reduced drastically.
- (4)
- The solving efficiency of the MRFCHO model is significantly improved compared with that of the MRFCJO model under the premise of ensuring the flood control effect. The MRFCHO model provides a reliable method for the real-time operation of basin-wide floods.
- (5)
- MRFCHOCPS has better adaptability in the real-time operation of large-scale multi-reservoir systems because it can realize the intelligent identification of effective reservoirs and dynamical modeling according to the rain and flood information.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The framework of MRFCHOCPS (Labeling of the data in the database corresponds to the models in the computation module, for example, the data labeled (a) are the input to model (a)).

Serial Number | Location of Rainstorm Center | Flood Magnitude |
---|---|---|

1 | centralizing in the whole basin | medium |

2 | centralizing in the whole basin | medium |

3 | centralizing in the southeast | large |

4 | centralizing in the whole basin | large |

5 | centralizing in the southeast | large |

6 | centralizing in the southeast | medium |

7 | centralizing in the southeast | small |

8 | centralizing in the southeast | small |

9 | centralizing in the upstream of the main stream | medium |

10 | centralizing in the southeast | small |

11 | centralizing in the whole basin | medium |

12 | centralizing in the upstream of the main stream | small |

13 | centralizing in the whole basin→centralizing in the southeast | large |

Peak Discharge at the Lutaizi Point (m^{3}/s) | Number of Samples | Number of Qualified Samples | Equivalent Qualified Rate (%) | Non-Qualified Rate (%) |
---|---|---|---|---|

QC_{m} ≥ 10,000 | 50 | 50 | 100 | 0 |

9000 ≤ QC_{m} < 10,000 | 47 | 45 | 95.74 | 4.26 |

8000 ≤ QC_{m} < 9000 | 65 | 63 | 96.92 | 3.08 |

7000 ≤ QC_{m} < 8000 | 120 | 109 | 90.83 | 9.17 |

6000 ≤ QC_{m} < 7000 | 172 | 149 | 86.63 | 13.37 |

5000 ≤ QC_{m} < 6000 | 216 | 183 | 84.72 | 15.28 |

4000 ≤ QC_{m} < 5000 | 185 | 153 | 82.70 | 17.30 |

3000 ≤ QC_{m} < 4000 | 112 | 73 | 65.18 | 34.82 |

QC_{m} < 3000 | 33 | 24 | 72.73 | 27.27 |

MRFCHO Model | MRFCJO Model | ||
---|---|---|---|

POA | space complexity | O(6k^{6}) | O(14k^{14}) |

time complexity | O(6ITk^{6}) | O(14ITk^{14}) | |

GA | space complexity | O(6NT) | O(14NT) |

time complexity | O(6INT) | O(14INT) |

MRFCJO | MRFCHO | Relative Error (%) | ||
---|---|---|---|---|

S1 | (1) | 7320 | 7590 | 3.69 |

(2) | 4540 | 4610 | 1.54 | |

S2 | (1) | 12,600 | 13,000 | 3.17 |

(2) | 9260 | 9470 | 2.27 |

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**MDPI and ACS Style**

Li, J.; Zhong, P.-a.; Wang, Y.; Liu, Y.; Zheng, J.; Yang, M.; Liu, W. Dynamic Self-Adaptive Modeling for Real-Time Flood Control Operation of Multi-Reservoir Systems. *Water* **2022**, *14*, 3740.
https://doi.org/10.3390/w14223740

**AMA Style**

Li J, Zhong P-a, Wang Y, Liu Y, Zheng J, Yang M, Liu W. Dynamic Self-Adaptive Modeling for Real-Time Flood Control Operation of Multi-Reservoir Systems. *Water*. 2022; 14(22):3740.
https://doi.org/10.3390/w14223740

**Chicago/Turabian Style**

Li, Jieyu, Ping-an Zhong, Yuanjian Wang, Yanhui Liu, Jiayun Zheng, Minzhi Yang, and Weifeng Liu. 2022. "Dynamic Self-Adaptive Modeling for Real-Time Flood Control Operation of Multi-Reservoir Systems" *Water* 14, no. 22: 3740.
https://doi.org/10.3390/w14223740