# DeepVELOX: INVELOX Wind Turbine Intelligent Power Forecasting Using Hybrid GWO–GBR Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Structure and Operating Framework

#### 2.1. INVELOX Wind Turbine

#### 2.2. Grey Wolf Optimization (GWO)

#### 2.3. Gradient Boosting Regressor

Algorithm 1: PSEUDOCODE of DeepVELOX |

Initialization of the grey wolf population ${\mathit{X}}_{\mathit{i}},\mathit{i}=\mathrm{1,2},\dots ,\mathit{n}$ Initialize of parameters: a, A, and CCalculate the fitness of each search agent ${\mathit{X}}_{\mathit{\alpha}}$ = the best search agent ${\mathit{X}}_{\mathit{\beta}}$ = the second search agent ${\mathit{X}}_{\mathit{\delta}}$ = the third search agent While (t < Maximum iteration number)for each search agentUpdate the current search agent position endUpdate a, A, and CCalculate the fitness of all search agents Update ${\mathit{X}}_{\mathit{\alpha}}$, ${\mathit{X}}_{\mathit{\beta}}$, and ${\mathit{X}}_{\mathit{\delta}}$ t = t + 1endreturn ${\mathit{X}}_{\mathit{\alpha}}$ Initialize the model with a constant value: ${\mathit{F}}_{0}\left(\mathit{x}\right)$ = ${\mathit{a}\mathit{r}\mathit{g}}_{\mathit{\gamma}}\mathit{m}\mathit{i}\mathit{n}\sum _{\mathit{i}=1}^{\mathit{n}}\mathit{L}\left({\mathit{y}}_{\mathit{i}},\mathit{\gamma}\right)$for m = 1 to M:Compute residuals ${\mathit{r}}_{\mathit{i}\mathit{m}}$ = −${\left. [\frac{\partial \mathit{L}({\mathit{y}}_{\mathit{i}},\mathit{F}\left({\mathit{x}}_{\mathit{i}}\right))}{\partial \mathit{F}\left({\mathit{X}}_{\mathit{i}}\right)}\right]}_{\mathit{F}\left(\mathit{x}\right)={\mathit{F}}_{\mathit{m}-1\left(\mathit{x}\right)}}$ for i = 1, …, nTrain regression tree with features x against r and create the terminal nodereasons ${\mathit{R}}_{\mathit{j}\mathit{m}}$ for j = 1, …, ${\mathit{J}}_{\mathit{m}}$compute ${\mathit{\gamma}}_{\mathit{j}\mathit{m}}$ = ${\mathit{a}\mathit{r}\mathit{g}}_{\mathit{\gamma}}\mathit{m}\mathit{i}\mathit{n}\sum _{{\mathit{x}}_{\mathit{i}\in {\mathit{R}}_{\mathit{j}\mathit{m}}}}\mathit{L}\left({\mathit{y}}_{\mathit{i}},{\mathit{F}}_{\mathit{m}-1}\left({\mathit{x}}_{\mathit{i}}\right)+\mathit{\gamma}\right)\mathit{f}\mathit{o}\mathit{r}$j = 1, …, ${\mathit{J}}_{\mathit{m}}$Update the model: ${\mathit{F}}_{\mathit{m}}\left(\mathit{x}\right)={\mathit{F}}_{\mathit{m}-1}\left(\mathit{x}\right)+\mathit{v}{\displaystyle \sum _{\mathit{j}=1}^{{\mathit{J}}_{\mathit{m}}}}{\mathit{\gamma}}_{\mathit{j}\mathit{m}}1(\mathit{x}\in {\mathit{R}}_{\mathit{j}\mathit{m}})$ |

## 3. Simulation and Results

^{2}) is a statistical measure that quantifies the fraction of variability within the dependent variable that can be elucidated by the independent variables encompassed within a regression model. Manifesting within a range from 0 to 1, R-squared attains greater magnitudes as the model’s alignment with the data augments. This index serves to gauge the appropriateness of the model’s fit to the data, rendering it a fundamental measure of goodness of fit.

## 4. Comparison

## 5. Future Works

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Abbreviations | |

AI | Artificial Intelligence |

DL | Deep Learning |

NN | Neural Network |

PV | Photovoltaic |

IWT | INVELOX Wind Turbine |

ANN | Artificial Neural Network |

KNN | K-Nearest Neighborhood |

QNN | Quantum Neural Networks |

MAE | Mean Absolute Error |

LSTM | Long/Short-Term Memory |

MAPE | Mean Absolute Percentage Error |

RMSE | Root Mean Square Error |

RMSPE | Root Mean Square Percentage Error |

Parameters | |

$Vt$ [m/s] | Wind Speed |

${{\displaystyle V}}^{cut-in-INVELOX}$ [m/s] | Cut-in Wind Speed |

${{\displaystyle V}}^{Cut-Out-INVELOX}$ [m/s] | Cut-out Wind Speed |

${{\displaystyle \rho}}_{INVELOX}$ [Kg/m^{3}] | Air Density |

${{\displaystyle A}}_{INVELOX}$ [m^{2}] | Generator Blade Area |

${{\displaystyle \eta}}^{W-INVELOX}$ | Efficiency |

${{\displaystyle K}}_{P}$ | Ratio of Squares of Cross Section, and Pressure Coefficient |

${{\displaystyle S}}_{R}$ | Wind Speed Amplification Ration |

${{\displaystyle P}}_{WT-INVELOX}$ [W] | Output Power of INVELOX |

${\overrightarrow{X}}_{P}$ | The position vector of the prey |

$\overrightarrow{X}$ | The position vector of the grey wolf |

$t$ | Indicates the current iteration |

$\overrightarrow{A}$ | Coefficient vector |

$\overrightarrow{C}$ | Coefficient vector |

$\overrightarrow{a}$ | Linearly Decreasing Variable |

${\overrightarrow{r}}_{1}$ | Random vector |

${\overrightarrow{r}}_{2}$ | Random vector |

${F}_{0}$ | Initial prediction |

${r}_{1}$ | Residuals |

$\gamma $ | Denotes the prediction |

$v$ | Learning rate |

${F}_{1}$ | Combined prediction |

${r}_{2}$ | Updated residuals |

${\gamma}_{2}$ | New tree prediction |

$y$ | Target |

$L$ | Loss function |

$M$ | Denotes the number of trees |

$m$ | Index of each tree |

$i$ | Single sample |

${F}_{m-1}$ | Prediction from the previous step |

$j$ | A terminal node |

${\gamma}_{j}^{m}$ | Minimizes the loss function on each terminal node |

${X}_{i}$ | The sample |

${n}_{j}$ | The number of samples in the terminal node j |

${\varpi}_{TP}$ | Truly Positive Predicted Value |

${\varpi}_{TN}$ | Truly Negative Predicted Value |

${\varpi}_{FP}$ | Falsely Positive Predicted Value |

${\varpi}_{FN}$ | Falsely Negative Predicted Value |

$n$ | Number of Data |

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**Figure 5.**Derived forecasting of (

**a**) INVELOX power output, (

**b**) shifted for better visualization, (

**c**) model loss for $1\le {{\displaystyle S}}_{R}<4$, and $0<{{\displaystyle S}}_{R}<1$ (left to right).

**Figure 8.**Comparison of KPI results of DeepVELOX, in (

**a**) MAPE, (

**b**) RMSPE, (

**c**) Accuracy, (

**d**) F1-score, (

**e**) R

^{2}, (

**f**) Precision, (

**g**) Recall, and (

**h**) MSE with other methods.

Metric/Model | DeepVELOX | LSTM | RNN | Decision Tree | LightGBM | XGBoost | KNN |
---|---|---|---|---|---|---|---|

MAPE | 0.0002 | 0.039 | 0.1455 | 0 | 0.0023 | 0.0001 | 0 |

RMSPE | 0.0974 | 18.1168 | 66.8292 | 0.0093 | 1.2019 | 0.0316 | 0.0116 |

Accuracy | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

F1-Score | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

R2-Score | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Precision | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Recall | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

MSE | 0.0352 | 478.6547 | 4023.144 | 0.0004 | 6.2355 | 0.0052 | 0.0005 |

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## Share and Cite

**MDPI and ACS Style**

Safari, A.; Kheirandish Gharehbagh, H.; Nazari Heris, M.
DeepVELOX: INVELOX Wind Turbine Intelligent Power Forecasting Using Hybrid GWO–GBR Algorithm. *Energies* **2023**, *16*, 6889.
https://doi.org/10.3390/en16196889

**AMA Style**

Safari A, Kheirandish Gharehbagh H, Nazari Heris M.
DeepVELOX: INVELOX Wind Turbine Intelligent Power Forecasting Using Hybrid GWO–GBR Algorithm. *Energies*. 2023; 16(19):6889.
https://doi.org/10.3390/en16196889

**Chicago/Turabian Style**

Safari, Ashkan, Hamed Kheirandish Gharehbagh, and Morteza Nazari Heris.
2023. "DeepVELOX: INVELOX Wind Turbine Intelligent Power Forecasting Using Hybrid GWO–GBR Algorithm" *Energies* 16, no. 19: 6889.
https://doi.org/10.3390/en16196889