# Wind Speed Prediction Model Based on Improved VMD and Sudden Change of Wind Speed

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## Abstract

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## 1. Introduction

- Physical methods require a large number of factors and data costs and are suitable for long-term forecasting.
- The construction of spatio-temporal prediction model needs to be based on a large amount of information, and the computational complexity increases. The more space-related sites are included, the lower the prediction accuracy may be.
- Statistical methods have great demand and quality for data, and the nonstationarity of data will limit the improvement of prediction level of some statistical methods.
- Common neural networks sometimes lead to prediction lag, and a single prediction model has limited ability to deal with prediction problems in different occasions, that is, the generalization performance is not strong.

- Using VMD to de-noise wind speed, a better data preprocessing effect is obtained and paves the way for subsequent forecasting.
- WSR and WRR are defined. According to WRR, the points in which wind speed changes fast are corrected, which reduces the error caused by a one-step lag of LSTM forecasting.
- A wind speed interval prediction based on the Lorenz theory is proposed. The effect of atmospheric power system on wind speed is innovatively expressed in the form of interval prediction, and its good forecasting results are verified.

## 2. Materials and Methods

#### 2.1. Variational Mode Decomposition (VMD)

Algorithm 1: Solving of VMD | |

Initialize $\left\{{\widehat{u}}_{k}^{1}\right\},\left\{{\omega}_{k}^{1}\right\},{\widehat{\lambda}}^{1},n\leftarrow 0$ Repeat $\text{}n\leftarrow n+1$ for $k=1:K$ do Update ${\widehat{u}}_{k}$$\text{}\mathrm{for}\text{}\mathrm{all}\text{}\omega \ge 0$: | |

$${\widehat{u}}_{k}^{n+1}(\omega )\leftarrow \left[\widehat{f}(\omega )-{\displaystyle \sum _{i\ne k}{\widehat{u}}_{i}(\omega )}+\frac{{\widehat{\lambda}}^{n}(\omega )}{2}\right]/\left[1+2\alpha {(\omega -{\omega}_{k}^{n})}^{2}\right]$$
| |

Update ${\omega}_{k}$:
$${\omega}_{k}^{n+1}\leftarrow {\displaystyle \underset{0}{\overset{\infty}{\int}}\omega {\left|{\widehat{u}}_{k}^{n+1}(\omega )\right|}^{2}d\omega}/{\displaystyle \underset{0}{\overset{\infty}{\int}}{\left|{\widehat{u}}_{k}^{n+1}(\omega )\right|}^{2}d\omega}$$
| |

Dual ascent for all
$\omega \ge 0$
$${\widehat{\lambda}}^{n+1}(\omega )\leftarrow {\widehat{\lambda}}^{n}(\omega )+\tau \left(\widehat{f}(\omega )-{\displaystyle \sum _{k}{\widehat{u}}_{k}^{n+1}(\omega )}\right)$$
| |

Until convergence: $\sum _{k}{\Vert {\widehat{u}}_{k}^{n+1}-{\widehat{u}}_{k}^{n}\Vert}_{2}^{2}/{\Vert {\widehat{u}}_{k}^{n}\Vert}_{2}^{2}}<\epsilon $ |

#### 2.2. Wind Speed Ramp (WSR)

- When the wind speed sequence satisfies Equation (7), that means ramp events are happening. When the positive ramp accumulates to a certain extent, Equation (8) can be satisfied. Otherwise, Equation (9) can represent the negative ramp accumulated to a certain extent.

- 2.
- In addition to the above, if the gradient does not change significantly, and $r(i)$ and $r(i-1)$ have opposite symbols, or the ramp event does not occur, the predicted wind speed value $\widehat{v}{(i+1)}_{pre}$ will not be corrected as Equation (11).

#### 2.3. Lorenz System

## 3. Proposed Wind Speed Deterministic and Interval Forecasting Models

- Phase I: Preliminary forecasting of wind speed.

- 2.
- Phase II: Reducing one-step lag of preliminary forecasting results.

- 3.
- Phase III: Interval forecasting based on LDS.

## 4. Experimental Results and Discussions

#### 4.1. Dataset

#### 4.2. Metrics

#### 4.3. Deterministic Forecasting Results and Discussions

#### 4.4. Interval Forecasting Results and Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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MSE | MAE | RMSE | MAPE | |
---|---|---|---|---|

ARMA | 0.2853 | 0.4195 | 0.5341 | 6.6086 |

SVM | 0.6042 | 0.5953 | 0.7773 | 9.1708 |

GBDT | 0.8502 | 0.7321 | 0.9221 | 13.2483 |

XGBoost | 0.4409 | 0.5352 | 0.6640 | 8.2239 |

BP | 0.2867 | 0.3958 | 0.5355 | 6.2363 |

LSTM | 0.2565 | 0.3896 | 0.5064 | 6.1140 |

MSE | MAE | RMSE | MAPE | |
---|---|---|---|---|

ARMA | 0.2361 | 0.3754 | 0.4859 | 12.8248 |

SVM | 1.3405 | 0.9185 | 1.1578 | 37.4274 |

GBDT | 1.2722 | 0.8859 | 1.1279 | 27.4912 |

XGBoost | 0.5611 | 0.5565 | 0.7490 | 19.2091 |

BP | 0.2943 | 0.4130 | 0.5425 | 14.7883 |

LSTM | 0.2061 | 0.3574 | 0.4540 | 12.1753 |

Error | MSE | MAE | RMSE | MAPE | |||||
---|---|---|---|---|---|---|---|---|---|

Model | Before PSOR | After PSOR | Before PSOR | After PSOR | Before PSOR | After PSOR | Before PSOR | After PSOR | |

WD-LSTM (lev = 2) | 0.1880 | 0.1384 | 0.3183 | 0.2779 | 0.4336 | 0.3720 | 5.1055 | 4.2841 | |

WD-LSTM (lev = 3) | 0.2103 | 0.1709 | 0.3621 | 0.3300 | 0.4586 | 0.4134 | 5.7926 | 5.1563 | |

WD-LSTM (lev = 4) | 0.2588 | 0.2071 | 0.4062 | 0.3639 | 0.5087 | 0.4550 | 6.4514 | 5.7514 | |

WD-LSTM (lev = 5) | 0.2621 | 0.2077 | 0.4091 | 0.3733 | 0.5119 | 0.4557 | 6.4973 | 5.8561 | |

VMD-LSTM (IMF = 4) | 0.1796 | 0.1502 | 0.3459 | 0.3157 | 0.4238 | 0.3876 | 5.5162 | 4.8386 | |

VMD-LSTM (IMF = 5) | 0.1526 | 0.1263 | 0.2965 | 0.2682 | 0.3906 | 0.3554 | 4.6730 | 4.0650 | |

VMD-LSTM (IMF = 6) | 0.1465 | 0.1248 | 0.2899 | 0.2655 | 0.3828 | 0.3532 | 4.5463 | 4.0041 | |

VMD-LSTM (IMF = 7) | 0.1462 | 0.1280 | 0.2872 | 0.2696 | 0.3824 | 0.3578 | 4.5058 | 4.0653 | |

VMD-LSTM (IMF = 8) | 0.1519 | 0.1408 | 0.2947 | 0.2795 | 0.3897 | 0.3753 | 4.6511 | 4.2372 |

Error | MSE | MAE | RMSE | MAPE | |||||
---|---|---|---|---|---|---|---|---|---|

Model | Before PSOR | After PSOR | Before PSOR | After PSOR | Before PSOR | After PSOR | Before PSOR | After PSOR | |

WD-LSTM (lev = 2) | 0.1659 | 0.1271 | 0.3227 | 0.2815 | 0.4073 | 0.3565 | 11.3157 | 9.0404 | |

WD-LSTM (lev = 3) | 0.1827 | 0.1305 | 0.3444 | 0.2865 | 0.4275 | 0.3612 | 10.6325 | 9.2621 | |

WD-LSTM (lev = 4) | 0.1778 | 0.1383 | 0.3338 | 0.2932 | 0.4216 | 0.3718 | 10.6544 | 9.5665 | |

WD-LSTM (lev = 5) | 0.1951 | 0.1427 | 0.3527 | 0.2943 | 0.4417 | 0.3777 | 11.2441 | 9.7730 | |

VMD-LSTM (IMF = 3) | 0.1680 | 0.1238 | 0.3223 | 0.2663 | 0.4098 | 0.3518 | 11.4498 | 8.6970 | |

VMD-LSTM (IMF = 4) | 0.1420 | 0.1039 | 0.2828 | 0.2401 | 0.3769 | 0.3223 | 9.7019 | 7.6814 | |

VMD-LSTM (IMF = 5) | 0.1334 | 0.1200 | 0.2855 | 0.2701 | 0.3652 | 0.3464 | 9.5620 | 8.1130 | |

VMD-LSTM (IMF = 6) | 0.1374 | 0.1201 | 0.2921 | 0.2727 | 0.3707 | 0.3466 | 9.7768 | 8.2673 | |

VMD-LSTM (IMF = 7) | 0.1427 | 0.1333 | 0.3778 | 0.2923 | 0.3824 | 0.3651 | 10.4884 | 8.8785 |

Parameter | Confidence Interval | ${\mathit{R}}_{\mathit{c}\mathit{o}\mathit{v}\mathit{e}\mathit{r}}$ | ${\mathit{d}}_{\mathit{a}\mathit{v}\mathit{e}\mathit{r}\mathit{a}\mathit{g}\mathit{e}}\text{}(\mathbf{m}/\mathbf{s})$ | Uncovered Points | |
---|---|---|---|---|---|

Fitting Method | |||||

KDE Fitting LDS (on dataset 1) | 90% | 93% | 1.5009 | 2, 17, 23, 39, 71, 74, 84 | |

98% | 91% | 1.718 | 2, 17, 19, 23, 39, 71, 74, 81, 95 | ||

B-spline interpolation fitting LDS (on dataset 1) | 90% | 95% | 1.5075 | 17, 23, 39, 71, 84 | |

98% | 94% | 1.6923 | 2, 17, 23, 39, 71, 74 | ||

KDE Fitting LDS (on dataset 2) | 90% | 92% | 1.5009 | 6, 11, 25, 59, 69, 90, 96, 98 | |

98% | 88% | 1.718 | 6, 11, 18, 25, 26, 49, 69, 70, 80, 90, 96, 98 | ||

B-spline interpolation fitting LDS (on dataset 2) | 90% | 94% | 1.5075 | 6, 11, 59, 69, 90, 96 | |

98% | 92% | 1.6923 | 6, 11, 25, 69, 70, 90, 96, 98 |

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## Share and Cite

**MDPI and ACS Style**

Wang, S.; Liu, C.; Liang, K.; Cheng, Z.; Kong, X.; Gao, S.
Wind Speed Prediction Model Based on Improved VMD and Sudden Change of Wind Speed. *Sustainability* **2022**, *14*, 8705.
https://doi.org/10.3390/su14148705

**AMA Style**

Wang S, Liu C, Liang K, Cheng Z, Kong X, Gao S.
Wind Speed Prediction Model Based on Improved VMD and Sudden Change of Wind Speed. *Sustainability*. 2022; 14(14):8705.
https://doi.org/10.3390/su14148705

**Chicago/Turabian Style**

Wang, Shijun, Chun Liu, Kui Liang, Ziyun Cheng, Xue Kong, and Shuang Gao.
2022. "Wind Speed Prediction Model Based on Improved VMD and Sudden Change of Wind Speed" *Sustainability* 14, no. 14: 8705.
https://doi.org/10.3390/su14148705