# Solar and Wind Data Recognition: Fourier Regression for Robust Recovery

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## Abstract

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## 1. Introduction

## 2. Model Site Description and Data Collection

## 3. Regression-Based Fourier Model and Parameter Estimation

#### 3.1. Regression-Based Fourier Model Formulation

#### 3.2. General Model Description

## 4. Results and Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviation

${A}_{i},{B}_{i}$ | Individual data points for variables A and B, respectively. |

$\widehat{A}and\widehat{B}$ | The means of variables A and B. |

y(t) | The signal that changes over time and needs to be predicted. |

${\mathrm{T}}_{\mathrm{d}}$ | The signal’s total time duration l. |

h | The time increment between each signal sample. |

k | An index representing a specific time instant. |

${\mathrm{a}}_{0},{\mathrm{a}}_{\mathrm{i}},{\mathrm{b}}_{\mathrm{i}}$ | Unknown constant coefficients in a mathematical series used for prediction. |

${\mathsf{\omega}}_{\mathrm{N}\mathrm{y}\mathrm{q}}$ | The Nyquist frequency, half of the sampling angular frequency ${\mathsf{\omega}}_{\mathrm{s}}$. |

N | The number of data points in the signal. |

${\mathsf{\Phi}}_{\mathrm{k}}$ | A vector used in the prediction process. |

$\widehat{\mathrm{y}}$ | A vector representing the predicted signal. |

ϵ | A small positive constant. |

T | The fundamental period of the signal. |

${\mathsf{\omega}}_{0}$ | The fundamental angular frequency. |

Y | A vector containing all the signal’s sampled data points. |

$\widehat{\mathrm{y}}\left(\mathrm{k}\mathrm{h}\right)$ | The predicted or approximated signal at a specific time instant. |

M | A constant term in the mathematical series. |

${\mathsf{\omega}}_{\mathrm{s}}$ | The angular frequency at which the signal is sampled. |

W | A vector containing coefficients used for prediction. |

Φ | A matrix of vectors used in the prediction process. |

${\mathsf{\Phi}}^{\#}$ | A mathematical operation involving the pseudo-inverse matrix. |

I | The identity matrix. |

n | The number of observations in the dataset. |

${y}_{i}$ | The actual values. |

$\widehat{{y}_{i}}$ | The predicted values. |

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**Figure 1.**Case study Location, Midland, TX, USA [29].

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**MDPI and ACS Style**

Al-Aboosi, A.F.; Muñoz Vazquez, A.J.; Al-Aboosi, F.Y.; El-Halwagi, M.; Zhan, W.
Solar and Wind Data Recognition: Fourier Regression for Robust Recovery. *Big Data Cogn. Comput.* **2024**, *8*, 23.
https://doi.org/10.3390/bdcc8030023

**AMA Style**

Al-Aboosi AF, Muñoz Vazquez AJ, Al-Aboosi FY, El-Halwagi M, Zhan W.
Solar and Wind Data Recognition: Fourier Regression for Robust Recovery. *Big Data and Cognitive Computing*. 2024; 8(3):23.
https://doi.org/10.3390/bdcc8030023

**Chicago/Turabian Style**

Al-Aboosi, Abdullah F., Aldo Jonathan Muñoz Vazquez, Fadhil Y. Al-Aboosi, Mahmoud El-Halwagi, and Wei Zhan.
2024. "Solar and Wind Data Recognition: Fourier Regression for Robust Recovery" *Big Data and Cognitive Computing* 8, no. 3: 23.
https://doi.org/10.3390/bdcc8030023