# A Hybrid Generative Adversarial Network Model for Ultra Short-Term Wind Speed Prediction

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## Abstract

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## 1. Introduction

- (1)
- A hybrid generative adversarial network model (HGANN) is proposed for ultra-short-term wind speed prediction, which learns the distribution of wind data and predicts it through a continuous game between generators and discriminators.
- (2)
- To improve the error convergence of the model, the OBLS was developed as a generator for HGANN. The IPSO was used to optimize the hyperparameters of the OBLS. To maintain the stability of the generated samples, we used the discriminator of WGAN as the discriminator of HGANN.
- (3)
- A wind data decomposition and denoising process was carried out using CEEMDAN to reduce the randomness and instability in the original wind series.

## 2. Proposed Predictive Framework

#### 2.1. Overall Framework of HGANN

#### 2.2. CEEMDAN Model

#### 2.3. Generator OBLS for HGANN

#### 2.4. Discriminators for HGANN

#### 2.5. Prediction Steps of the Proposed HGANN Model

## 3. Case Analysis

#### 3.1. Data Description

#### 3.2. Evaluation Index

#### 3.3. Comparable Methods

#### 3.4. Experimental Results

- (1)
- Experiment I: Comparison Between Different Forecasting Methods

- (2)
- Experiment II: Multi-Step Prediction Experiment

- (3)
- Experiment III: Ablation Experiment Between Single Models and Hybrid Models.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

ANFIS | Adaptive-network-based fuzzy inference system |

BLS | Broad learning system |

BP | Back propagation |

CEEMD | Complementary ensemble empirical mode decomposition |

CEEMDAN | Complete ensemble empirical mode decomposition with adaptive noise |

CNN | Convolutional neural network |

EEMD | Ensemble empirical mode decomposition |

EMD | Empirical mode decomposition |

GA | Genetic algorithm |

GMDH | Group method of data handling neural network |

GNN | Graph neural network |

GAN | Generative adversarial network |

GPR | Gaussian process regression |

ICEEMDAN | Improved CEEMDAN |

IMF | Intrinsic mode function |

IOWA | Induced ordered weighted averaging |

LSTM | Long short-term memory |

MAE | Mean absolute error |

MAPE | Mean absolute percentage error |

MTO | Multi-tracker optimizer |

PSO | Particle swarm optimization |

OBLS | Optimized broad learning system |

RBF | Radial basis function |

RMSE | Root mean square error |

SSE | Sum of squared error |

SVR | Support vector regression |

VMD | Variational mode decomposition |

WGAN | Wasserstein generative adversarial network |

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**Figure 1.**The proposed short-term wind speed forecasting framework. In the data processing step, CEEMDAN turns the wind data into multiple modalities. The HGANN network consisting of a generator and discriminator predicts these modalities. The final wind speed prediction result can then be obtained by stacking the prediction results of all modalities.

**Figure 4.**Forecasting results of HER wind speed data sets: (

**a**) experiment results of spring wind speed sequences; (

**b**) experiment results of summer wind speed sequences; (

**c**) experiment results of autumn wind speed sequences; (

**d**) experiment results of winter wind speed sequences.

**Figure 5.**Multi-step forecasting experiments under RMSE, SSE, MAPE, and MAE indicators: (

**a**) experiment results on the RMSE indicator; (

**b**) experiment results on the SSE indicator; (

**c**) experiment results on the MAPE indicator; (

**d**) experiment results on the MAE indicator.

Season | Mean (m/s) | Median (m/s) | Max (m/s) | Min (m/s) | Standard Deviation (m/s) |
---|---|---|---|---|---|

HER data | |||||

Spring | 1.89 | 1.53 | 7.25 | 0.03 | 1.47 |

Summer | 0.82 | 0.63 | 4.27 | 0 | 0.75 |

Autumn | 1.23 | 0.83 | 6.65 | 0 | 1.19 |

Winter | 1.90 | 1.60 | 5.68 | 0.07 | 1.35 |

MHS data | |||||

Spring | 5.78 | 5.70 | 16.50 | 0.40 | 2.25 |

Summer | 5.46 | 5.45 | 12.50 | 0.40 | 2.21 |

Autumn | 5.18 | 5.20 | 16.50 | 0.40 | 2.33 |

Winter | 4.50 | 4.27 | 14.07 | 0 | 2.28 |

Model | Parameter Setting |
---|---|

PSO-ANFIS | $ite{r}_{max}$$=300,{n}_{p}$$=40,{c}_{1}$$=1.0,{c}_{2}$$=2.0,{n}_{r}$$=4,{n}_{v}$= 52 |

VMD-GA-BP | $k$$=11,ite{r}_{max}$$=150,{e}_{p}$$=100,{n}_{p}$$=40,{l}_{r}$$=0.1,{n}_{b1}$= 9 |

EEMD-GPR-LSTM | $k$$=11,{e}_{p}$$=200,{n}_{b1}$$=100,{n}_{b2}$$=100,{s}_{1}$$=50,\sigma $= 20 |

MWS-CE-ENN | ${e}_{p}$$=1000,{l}_{r}$$=0.1,{p}_{r}$$=0.000001,{n}_{p}$$=40,{n}_{i}$$=5,{n}_{b1}$$=6,{n}_{o}$$=1,ite{r}_{max}$$=100,{n}_{std}$= 0.2 |

EMD-ISSA-LSTM | ${e}_{p}$$=100,{l}_{r}$$=0.005,{n}_{p}$$=10,ite{r}_{max}$$=20,{v}_{e}$$=0.6,{p}_{d}$$=0.7,{p}_{e}$= 0.2 |

Proposed Model | ${n}_{std}$$=0.01,{n}_{p}$$=40,ite{r}_{max}$$=100,{c}_{1}$$=1.5,{c}_{2}$$=1.5,{e}_{p}$$=50,{l}_{r}$$=0.002,\mathsf{\lambda}$$={10}^{-30},{n}_{b1}$$=48,{n}_{b2}$$=96,{n}_{b3}$= 384 |

Season | Metrics | Proposed Model | PSO-ANFIS | VMD-GA-BP | EEMD-GPR-LSTM | MWS-CE-ENN | EMD-ISSA-LSTM |
---|---|---|---|---|---|---|---|

Spring | RMSE | 0.0065 | 0.0092 | 0.0128 | 0.0105 | 0.0093 | 0.0131 |

SSE | 0.0180 | 0.0365 | 0.0817 | 0.0471 | 0.0370 | 0.0737 | |

MAPE | 0.0300 | 0.0402 | 0.0732 | 0.0493 | 0.0632 | 0.0536 | |

MAE | 0.0048 | 0.0068 | 0.0108 | 0.0083 | 0.0071 | 0.0096 | |

Summer | RMSE | 0.0112 | 0.0172 | 0.0134 | 0.0126 | 0.0152 | 0.0117 |

SSE | 0.0537 | 0.1279 | 0.0768 | 0.0679 | 0.0989 | 0.0586 | |

MAPE | 0.0420 | 0.0641 | 0.0632 | 0.0596 | 0.0730 | 0.0500 | |

MAE | 0.0081 | 0.0123 | 0.0099 | 0.0114 | 0.0119 | 0.0093 | |

Autumn | RMSE | 0.0088 | 0.0120 | 0.0137 | 0.0126 | 0.0132 | 0.0204 |

SSE | 0.0331 | 0.0615 | 0.0806 | 0.0676 | 0.0746 | 0.1779 | |

MAPE | 0.0422 | 0.0514 | 0.0524 | 0.1177 | 0.0619 | 0.0851 | |

MAE | 0.0059 | 0.0077 | 0.0092 | 0.0089 | 0.0082 | 0.0129 | |

Winter | RMSE | 0.0063 | 0.0090 | 0.0067 | 0.0093 | 0.0104 | 0.0086 |

SSE | 0.0172 | 0.0354 | 0.0190 | 0.0370 | 0.0463 | 0.0317 | |

MAPE | 0.0575 | 0.0880 | 0.0683 | 0.0722 | 0.0923 | 0.0620 | |

MAE | 0.0043 | 0.0064 | 0.0047 | 0.0069 | 0.0073 | 0.0056 |

Season | Metrics | Proposed Model | PSO-ANFIS | VMD-GA-BP | EEMD-GPR-LSTM | MWS-CE-ENN | EMD-ISSA-LSTM |
---|---|---|---|---|---|---|---|

Spring | RMSE | 0.0237 | 0.0344 | 0.0264 | 0.0276 | 0.0339 | 0.0291 |

SSE | 0.2404 | 0.5054 | 0.2977 | 0.3250 | 0.4918 | 0.3624 | |

MAPE | 0.0724 | 0.0830 | 0.1007 | 0.1055 | 0.0990 | 0.0866 | |

MAE | 0.0146 | 0.0244 | 0.0187 | 0.0198 | 0.0229 | 0.0203 | |

Summer | RMSE | 0.0156 | 0.0267 | 0.0179 | 0.0205 | 0.0189 | 0.0236 |

SSE | 0.0104 | 0.3045 | 0.1375 | 0.1799 | 0.1529 | 0.2384 | |

MAPE | 0.0433 | 0.0857 | 0.0588 | 0.0697 | 0.0680 | 0.0765 | |

MAE | 0.0110 | 0.0200 | 0.0136 | 0.0171 | 0.0149 | 0.0192 | |

Autumn | RMSE | 0.0166 | 0.0245 | 0.0190 | 0.0183 | 0.0214 | 0.0262 |

SSE | 0.1179 | 0.2570 | 0.1543 | 0.1433 | 0.1960 | 0.2937 | |

MAPE | 0.0410 | 0.0641 | 0.0505 | 0.0439 | 0.0762 | 0.0658 | |

MAE | 0.0131 | 0.0185 | 0.0149 | 0.0137 | 0.0170 | 0.0211 | |

Winter | RMSE | 0.0266 | 0.0394 | 0.0309 | 0.0325 | 0.0286 | 0.0312 |

SSE | 0.3034 | 0.6645 | 0.4075 | 0.4521 | 0.3501 | 0.4166 | |

MAPE | 0.0828 | 0.1698 | 0.1540 | 0.1215 | 0.0937 | 0.1200 | |

MAE | 0.0190 | 0.0284 | 0.0228 | 0.0276 | 0.0193 | 0.0257 |

Model | RMSE | SSE | MAPE | MAE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1-Step | 2-Step | 3-Step | 1-Step | 2-Step | 3-Step | 1-Step | 2-Step | 3-Step | 1-Step | 2-Step | 3-Step | |

Proposed | 0.0091 | 0.0136 | 0.0178 | 0.0356 | 0.0679 | 0.1361 | 0.0463 | 0.0712 | 0.1087 | 0.0061 | 0.0098 | 0.0134 |

PSO-ANFIS | 0.0120 | 0.0174 | 0.0238 | 0.0615 | 0.1299 | 0.2428 | 0.0514 | 0.0885 | 0.1270 | 0.0077 | 0.0119 | 0.0161 |

VMD-GA-BP | 0.0137 | 0.0151 | 0.0203 | 0.0806 | 0.0976 | 0.1764 | 0.0524 | 0.0721 | 0.1123 | 0.0092 | 0.0101 | 0.0213 |

EEMD-GPR-LSTM | 0.0126 | 0.0164 | 0.0192 | 0.0676 | 0.1151 | 0.1578 | 0.1177 | 0.1353 | 0.1536 | 0.0089 | 0.0129 | 0.0157 |

MWS-CE-ENN | 0.0132 | 0.0176 | 0.0213 | 0.0746 | 0.1326 | 0.1942 | 0.0619 | 0.0826 | 0.1121 | 0.0082 | 0.0172 | 0.0224 |

EMD-ISSA-LSTM | 0.0109 | 0.0139 | 0.0183 | 0.0508 | 0.0827 | 0.1433 | 0.0503 | 0.0919 | 0.1325 | 0.0086 | 0.0134 | 0.0192 |

Indicators | Proposed Model | WGAN-OBLS | OBLS | WGAN | CNN | BLS |
---|---|---|---|---|---|---|

RMSE | 0.0088 | 0.0119 | 0.0122 | 0.0138 | 0.0221 | 0.0308 |

SSE | 0.0331 | 0.0603 | 0.0642 | 0.0819 | 0.2090 | 0.4058 |

MAPE | 0.0422 | 0.0506 | 0.0546 | 0.0571 | 0.0601 | 0.0648 |

MAE | 0.0059 | 0.0076 | 0.0080 | 0.0086 | 0.0161 | 0.0164 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Q.; Huang, L.; Huang, J.; Liu, Q.; Chen, L.; Liang, Y.; Liu, P.X.; Li, C.
A Hybrid Generative Adversarial Network Model for Ultra Short-Term Wind Speed Prediction. *Sustainability* **2022**, *14*, 9021.
https://doi.org/10.3390/su14159021

**AMA Style**

Wang Q, Huang L, Huang J, Liu Q, Chen L, Liang Y, Liu PX, Li C.
A Hybrid Generative Adversarial Network Model for Ultra Short-Term Wind Speed Prediction. *Sustainability*. 2022; 14(15):9021.
https://doi.org/10.3390/su14159021

**Chicago/Turabian Style**

Wang, Qingyuan, Longnv Huang, Jiehui Huang, Qiaoan Liu, Limin Chen, Yin Liang, Peter X. Liu, and Chunquan Li.
2022. "A Hybrid Generative Adversarial Network Model for Ultra Short-Term Wind Speed Prediction" *Sustainability* 14, no. 15: 9021.
https://doi.org/10.3390/su14159021