# Machine Intelligent Hybrid Methods Based on Kalman Filter and Wavelet Transform for Short-Term Wind Speed Prediction

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## Abstract

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## 1. Introduction

## 2. Background Theories

#### 2.1. ARIMA Model

#### 2.2. Wavelet Transform (WT)

#### 2.3. Kalman Filter (KF)

- the prediction step
- the correction step

## 3. Hybrid Models Framework

#### 3.1. ARIMA-WT-ML

#### 3.2. KF-WT-ML

## 4. Data Description and Evaluation Metrics

#### 4.1. Data Description

#### 4.2. Evaluation Metrics

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Wind Farm (Dataset) | Data Points | Time Interval (Min.) | Terrain (on/off Shore) | Mean (m/s) | Std Dev |
---|---|---|---|---|---|

TN | 4460 | 10 | on-land | 5.03 | 1.48 |

EDP T01 | 57,428 | 10 | on-land | 5.79 | 2.48 |

Jaisalmer | 52,000 | 30 | on-land | 3.73 | 2.09 |

EDP T01 | 8808 | 60 | on-land | 4.50 | 1.81 |

Az HT1 | 8808 | 10 | hilly | 4.44 | 2.31 |

Cal HT2 | 4000 | 10 | hilly | 3.60 | 1.78 |

NREL | 20,000 | 10 | Offshore | 10.16 | 4.62 |

Orsted | 11,362 | 10 | Offshore | 9.45 | 4.72 |

Metrics | ML SVR | RF | ARIMA-WT-ML SVR | RF | KF-WT-ML SVR | RF |
---|---|---|---|---|---|---|

R2 | 0.81842 | 0.84237 | 0.99594 | 0.99996 | 0.99812 | 0.99998 |

RMSE | 0.63806 | 0.59450 | 0.06932 | 0.00648 | 0.06323 | 0.00627 |

MAE | 0.40712 | 0.35344 | 0.06229 | 0.00394 | 0.05214 | 0.00003 |

Metrics | ML SVR | RF | ARIMA-WT-ML SVR | RF | KF-WT-ML SVR | RF |
---|---|---|---|---|---|---|

R2 | 0.93240 | 0.96738 | 0.99809 | 0.99770 | 0.99888 | 0.99813 |

RMSE | 0.82982 | 0.57640 | 0.11358 | 0.12458 | 0.09861 | 0.12715 |

MAE | 0.68861 | 0.33224 | 0.09760 | 0.01552 | 0.08626 | 0.01616 |

Metrics | ML SVR | RF | ARIMA-WT-ML SVR | RF | KF-WT-ML SVR | RF |
---|---|---|---|---|---|---|

R2 | 0.48459 | 0.64206 | 0.99679 | 0.99978 | 0.99711 | 0.99997 |

RMSE | 1.48526 | 1.23775 | 0.09436 | 0.02374 | 0.11117 | 0.01023 |

MAE | 2.20600 | 1.53203 | 0.08258 | 0.00056 | 0.10023 | 0.00010 |

Metrics | ML SVR | RF | ARIMA-WT-ML SVR | RF | KF-WT-ML SVR | RF |
---|---|---|---|---|---|---|

R2 | 0.53552 | 0.66426 | 0.99694 | 0.99498 | 0.99840 | 0.99970 |

RMSE | 1.23116 | 0.9540 | 0.07311 | 0.07435 | 0.07010 | 0.03109 |

MAE | 1.51577 | 0.91011 | 0.06366 | 0.00552 | 0.05576 | 0.00096 |

Dataset | On Land TN | EDP T01 | Off-Shore Portland | Orsted | Hilly Regions Az HR1 | Cal HR2 |
---|---|---|---|---|---|---|

R2 | 0.99812 | 0.99888 | 0.99810 | 0.99703 | 0.99747 | 0.99742 |

RMSE | 0.06323 | 0.09861 | 0.20321 | 0.27273 | 0.11514 | 0.07940 |

MAE | 0.05214 | 0.08626 | 0.16784 | 0.22727 | 0.10199 | 0.00096 |

Dataset | On Land TN | EDP T01 | Off-Shore Portland | Orsted | Hilly Regions Az HR1 | Cal HR2 |
---|---|---|---|---|---|---|

R2 | 0.99998 | 0.99813 | 0.999826 | 0.99859 | 0.999961 | 0.99997 |

RMSE | 0.00627 | 0.12715 | 0.06140 | 0.18788 | 0.01428 | 0.00813 |

MAE | 0.00003 | 0.01616 | 0.003770 | 0.03530 | 0.000203 | 0.00006 |

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**MDPI and ACS Style**

Patel, Y.; Deb, D.
Machine Intelligent Hybrid Methods Based on Kalman Filter and Wavelet Transform for Short-Term Wind Speed Prediction. *Wind* **2022**, *2*, 37-50.
https://doi.org/10.3390/wind2010003

**AMA Style**

Patel Y, Deb D.
Machine Intelligent Hybrid Methods Based on Kalman Filter and Wavelet Transform for Short-Term Wind Speed Prediction. *Wind*. 2022; 2(1):37-50.
https://doi.org/10.3390/wind2010003

**Chicago/Turabian Style**

Patel, Yug, and Dipankar Deb.
2022. "Machine Intelligent Hybrid Methods Based on Kalman Filter and Wavelet Transform for Short-Term Wind Speed Prediction" *Wind* 2, no. 1: 37-50.
https://doi.org/10.3390/wind2010003