# Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction

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## Abstract

**:**

## 1. Introduction

## 2. Maximum Prediction Steps Based on Lyapunov Exponent

## 3. Fractional Levy Stable Motion

#### 3.1. Parameter Meaning of Levy Stable Motion

#### 3.2. Long-Range Dependence and Self-Similarity Fractional Levy Stable Motion

## 4. Iterative Forecasting Model Based on Fractional Levy Stable Motion

#### 4.1. Iterative Forecasting Model

#### 4.2. Parameter Estimation with the Characteristic Function

## 5. Wind Speed Forecasting

## 6. Relationship between Wind Speed and Wind Power

_{i}is the cut-in wind speed, ${v}_{c}$ is the cut-out wind speed also known as the cut-off wind speed, v

_{r}is the rated wind speed, and ${f}_{p}\left(v\right)$ is the output characteristic of the wind speed between ${v}_{i}$ and v

_{r}. Its characteristics can be linear functions, quadratic functions, or cubic functions.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Influence of different characteristic index values on the probability distribution function.

Parameter Name | Parameter Value |
---|---|

Average period | 12 |

Embedding Dim | 5 |

Time delay | 2 |

Lyapunov exponent | 0.0238 |

Max. prediction steps | 43 |

Name | Unweighted | 5 Weighted | 10 Weighted |
---|---|---|---|

Max error percentage | 3.7319 | 0.4425 | 0.1419 |

H | 0.7595 | 0.7595 | 0.7595 |

α | 1.7959 | 1.8280 | 1.6305 |

var | 173.7598 | 4344 | 17376 |

Years | Name | GA-BP Network | FLSM Forecasting |
---|---|---|---|

2011 | Max error percentage | 0.2706 | 0.1419 |

2011 | Mean error percentage | 0.0350 | 0.0304 |

2012 | Max error percentage | 0.2676 | 0.1022 |

2012 | Mean error percentage | 0.0378 | 0.0282 |

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**MDPI and ACS Style**

Duan, S.; Song, W.; Cattani, C.; Yasen, Y.; Liu, H.
Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction. *Symmetry* **2020**, *12*, 605.
https://doi.org/10.3390/sym12040605

**AMA Style**

Duan S, Song W, Cattani C, Yasen Y, Liu H.
Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction. *Symmetry*. 2020; 12(4):605.
https://doi.org/10.3390/sym12040605

**Chicago/Turabian Style**

Duan, Shouwu, Wanqing Song, Carlo Cattani, Yakufu Yasen, and He Liu.
2020. "Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction" *Symmetry* 12, no. 4: 605.
https://doi.org/10.3390/sym12040605