# Comparison of Multiple Linear Regression, Artificial Neural Network, Extreme Learning Machine, and Support Vector Machine in Deriving Operation Rule of Hydropower Reservoir

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Deterministic Hydropower Reservoir Operation to Produce Dataset

#### 2.1. Objective Function

#### 2.2. Operation Constraints

#### 2.3. Optimization Methods

## 3. Brief Introductions of the Adopted Methods

#### 3.1. Multiple Linear Regression (MLR)

#### 3.2. Artificial Neural Network (ANN)

#### 3.3. Extreme Learning Machine (ELM)

- Step 1:
- Define the amount of hidden neurons and the activation function of each neuron.
- Step 2:
- Produce the input-hidden weights as well as the hidden biases.
- Step 3:
- Use all the data samples to obtain the output matrix of the hidden layer.
- Step 4:
- Choose the suitable method to calculate the hidden-output weights.
- Step 5:
- Use the optimized ELM network to produce the simulated output for new samples.

#### 3.4. Support Vector Machine (SVM)

## 4. Experimental Results

#### 4.1. Study Area and Dataset

^{2}and an average annual runoff of 4.89 billion m

^{3}. The dead water level is 1076 m and the dead storage is 1.14 billion m

^{3}; the normal water level is 1140 m and the corresponding storage volume is 4.5 billion m

^{3}. In Hongjiadu, the flood control level is 1138 m from 1 June to 1 September, while its regulation storage is about 3.4 billion m

^{3}. Obviously, the active-storage volume of the Hongjiadu reservoir is rather large in comparison with its annual inflow volume, meaning it plays a large role in determining the efficiencies to be achieved by any operation rules. Besides, the Hongjiadu reservoir has three mixed-flow turbine generating units with 200 MW per unit and its total installed capacity is 600 MW. Under normal circumstances, almost all of the flow of Hongjiadu is through the hydropower turbines. As a leading carry-over storage reservoir on the trunk stream of Wu River, the Hongjiadu reservoir begins to provide comprehensive benefits to promote the healthy and orderly development of Guizhou Province since being put into operation, like power generation, ecological protection, water supply, flood control, and environment governance. In practice, various scheduling purposes can be well addressed in the derived operating rule by setting the necessary constraints on some variables, like water levels, power outputs, or discharge rates [43,44,45,46].

#### 4.2. Performance Criterion

#### 4.3. Model Development

#### 4.3.1. MLR Model Development

#### 4.3.2. ANN Model Development

#### 4.3.3. ELM Model Development

#### 4.3.4. SVM Model Development

#### 4.4. Comparison and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Deterministic optimization results by dynamic programing for Hongjiadu reservoir in different periods (month).

**Figure 4.**Sensitivity of the number of hidden nodes in the ANN method for Hongjiadu reservoir. RMSE—root-mean-square error.

**Figure 5.**Simulation results of the extreme learning machine (ELM) model for Hongjiadu reservoir in 10 runs. GGR—generation guarantee rate; APG—average power generation.

**Figure 6.**Comparison of different methods for Hongjiadu reservoir. DP—dynamic programming; MLR—multiple linear regression; SGM—scheduling graph method.

**Figure 9.**Graphic models (outflow–inflow–water level) for Hongjiadu reservoir in August: (

**a**) DP; (

**b**) SVM; (

**c**) ELM; (

**d**) ANN.

Coefficient | Month | |||||
---|---|---|---|---|---|---|

1 | 3 | 5 | 7 | 9 | 11 | |

a | 740.9 | 966.6 | −205.9 | −7001.2 | 2698.6 | 6297.8 |

b | −0.54 | −0.73 | 0.30 | 6.30 | −2.34 | −5.49 |

c | −0.04 | 0.02 | 0.58 | 0.50 | 0.73 | 0.84 |

**Table 2.**Comparison of different methods in Hongjiadu reservoir. DP—dynamic programming; MLR—multiple linear regression; ANN—artificial neural network; ELM—extreme learning machine; SVM—support vector machine; SGM—scheduling graph method; GGR—generation guarantee rate; APG—average power generation.

Method | DP | SGM | MLR | ANN | ELM | SVM |
---|---|---|---|---|---|---|

APG (10^{8} kWh) | 23.38 | 21.03 | 21.36 | 22.41 | 23.11 | 22.71 |

Gap (%) | - | −10.05 | −8.64 | −4.15 | −1.15 | −2.87 |

GGR (%) | 98.18 | 89.84 | 92.97 | 95.83 | 97.66 | 97.40 |

Gap (%) | - | −8.49 | −5.31 | −2.39 | −0.53 | −0.79 |

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## Share and Cite

**MDPI and ACS Style**

Niu, W.-J.; Feng, Z.-K.; Feng, B.-F.; Min, Y.-W.; Cheng, C.-T.; Zhou, J.-Z.
Comparison of Multiple Linear Regression, Artificial Neural Network, Extreme Learning Machine, and Support Vector Machine in Deriving Operation Rule of Hydropower Reservoir. *Water* **2019**, *11*, 88.
https://doi.org/10.3390/w11010088

**AMA Style**

Niu W-J, Feng Z-K, Feng B-F, Min Y-W, Cheng C-T, Zhou J-Z.
Comparison of Multiple Linear Regression, Artificial Neural Network, Extreme Learning Machine, and Support Vector Machine in Deriving Operation Rule of Hydropower Reservoir. *Water*. 2019; 11(1):88.
https://doi.org/10.3390/w11010088

**Chicago/Turabian Style**

Niu, Wen-Jing, Zhong-Kai Feng, Bao-Fei Feng, Yao-Wu Min, Chun-Tian Cheng, and Jian-Zhong Zhou.
2019. "Comparison of Multiple Linear Regression, Artificial Neural Network, Extreme Learning Machine, and Support Vector Machine in Deriving Operation Rule of Hydropower Reservoir" *Water* 11, no. 1: 88.
https://doi.org/10.3390/w11010088