# An Adaptive Hybrid Model for Wind Power Prediction Based on the IVMD-FE-Ad-Informer

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methodologies

#### 2.1. Variational Mode Decomposition

#### 2.2. Fuzzy Entropy

#### 2.3. Informer

_{MP}represents the maximum pooling layer function, f

_{Conv}denotes the convolutional layer function, and [·]

_{AB}is the attention unit.

#### 2.4. Adaptive Loss Function

## 3. Proposed Model

#### 3.1. Improved VMD

#### 3.2. IVMD-FE-Ad-Informer Model Framework

#### 3.3. Evaluation Indexes

^{2}) are used as evaluation indicators for the prediction performance of IVMD-FE-Informer and other benchmark models. The mathematical formula is as follows:

## 4. Experiment and Analysis

#### 4.1. Data Description

#### 4.2. Experiment 1: The Specific Details of Data Processing

#### 4.2.1. Data Decomposition

#### 4.2.2. New Elements Reconstruction

#### 4.2.3. Feature Selection

#### 4.3. Experiment 2: Ablation Experiment

#### 4.4. Experiment 3: Comparative Experiment

^{2}increased by about 5.64–30.78%. According to Table 6 and Figure 10, it can be inferred that the IVMD algorithm has superior data decomposition ability compared to the traditional EMD algorithm under similar data processing. This improved ability enables the IVMD algorithm to more effectively reduce non-smooth features in the original data, resulting in smoother data and improved wind power prediction accuracy. Furthermore, the prediction accuracy of Ad-Informer is much higher than that of Informer and LSTM for the same data processing method, with R

^{2}of 0.925, 0.889, and 0.808, respectively. While IVMD-FE-Ad-Informer is relatively time-consuming due to the implementation of the Ad-Informer prediction module five times after the IVMD-FE data preprocessing, it demonstrates a closer resemblance to the actual curve and produces the smallest forecasting errors. It can be indicated that the model proposed in this paper is an optimal combined model with high prediction performance.

#### 4.5. Experiment 4: The Stability of IVMD-FE-Ad-Informer Forecasting

^{2}, which are 83.01 kW, 60.43 kW, and 0.962, respectively. The results further confirm that the IVMD algorithm is a superior and effective method for wind power data decomposition.

^{2}is 0.866, whereas, on dataset B with a higher COV, R

^{2}is slightly lower at 0.858. Furthermore, the superiority of the proposed model in terms of prediction performance becomes more prominent as the original wind power sequence contains more nonlinear features. The outstanding contribution is the development of an adaptive loss function, which can accurately identify and predict violent changes in wind power, thereby effectively mitigating the impact of outliers.

## 5. Conclusions

- The IVMD-FE-Ad-Informer is a hybrid model that demonstrates high accuracy and better robustness by integrating the advantages of multiple technologies, outperforming the basic EMD- FE-Ad-Informer, Ad-Informer, LSTM, and ANN. The results of the proposed model obtained from the Spanish and Chinese datasets demonstrate a significant improvement compared to benchmark models, with a maximum reduction of 57.89% in MAE, 57.03% in RMSE, and a maximum increase of 30.78% in R
^{2}; - Compared with traditional data decomposition methods, VMD improved by MIC can better mine the nonlinear features of the original data, which effectively improves the data quality and reduces the difficulty of prediction;
- Based on a comprehensive analysis of experimental results, the adaptive loss function has a rapid response to non-Gaussian distributed wind power data, which can react quickly to outliers and predict variation trends;
- By prediction experiments on wind farm datasets with different sampling intervals, capacities, and regions, the proposed model shows the best prediction results and closest proximity to the true value. It can be demonstrated that IVMD-FE-Ad-Informer has remarkable generalization ability and broad prospects in wind power prediction.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Algorithms | Parameters | Values |
---|---|---|

IVMD | K | 17 |

FE | m r | 2 0.25std |

IVMD-FE | New mode | 4(mode1 = IMF1, IMF2, IMF17; mode2 = IMF3, IMF4, IMF15, IMF16; mode3 = IMF5, IMF12~IMF14; mode4 = IMF6~IMF11) |

EMD | K | 11 |

EMD-FE | New mode | 3(mode1 = IMF1, IMF6, IMF7; mode2 = IMF2~IMF5; mode3 = IMF8~IMF11) |

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**Figure 5.**The results of the IVMD algorithm. The IMFs curves are shown (

**left**), and the spectral densities corresponding to the IMFs are shown (

**right**).

**Figure 8.**The prediction curve results of each sub-mode. (

**a**) Element 1 prediction curve; (

**b**) Element 2 prediction curve; (

**c**) Element 3 prediction curve; (

**d**) Element 4 prediction curve; (

**e**) Element 5 prediction curve.

**Figure 9.**The forecasting curves of the ablation experiment. The overall forecasting trends are shown at the (

**top**), and the local enlargement is shown at the (

**bottom**).

**Figure 10.**The forecasting curves of different models. The overall forecasting trends are shown at the (

**top**), and the local enlargement is shown at the (

**bottom**).

**Figure 12.**The forecasting curves of different datasets. The overall forecasting trends are shown at the (

**top**), and the local enlargement is shown at the (

**bottom**).

Dataset | Number | Max (MW) | Min (MW) | Mean (MW) | Std (MW) | COV |
---|---|---|---|---|---|---|

Dataset A | 8832 | 120.43 | 0 | 23.51 | 24.74 | 1.0523 |

Dataset B | 7920 | 2.803 | 0 | 0.8976 | 0.7885 | 0.8784 |

Reconstruction Elements | IMFs |
---|---|

Element 1 | IMF1, IMF2 |

Element 2 | IMF3, IMF4, IMF16 |

Element 3 | IMF5, IMF6, IMF7, IMF8, IMF15 |

Element 4 | IMF9, IMF10, IMF13, IMF14 |

Element 5 | IMF11, IMF12 |

Element | Input Variables |
---|---|

Element 1 | Element 1, 10 m, 30 m, 50 m, wheel height wind speed |

Element 2 | Element 2, 10 m, 50 m, wheel height wind speed |

Element 3 | Element 3, 30 m, 50 m, wheel height wind speed |

Element 4 | Element 4 |

Element 5 | Element 5 |

Parameters | Values |
---|---|

Input sequence length | 96 |

Start token length | 24–96 |

Prediction sequence length | 24–96 |

Num of encoder layers | 3 |

Num of decoder layers | 2 |

Input size of encoder | 5-1 |

Input size of decoder | 5-1 |

Decoder output | 1 |

Num of heads | 8 |

Dimension of model | 512 |

Probsparse attention factor | 5 |

Early stopping patience | 5 |

Learning rate | 0.0001 |

Dropout | 0.05 |

Epochs | 100 |

Scale factor | 1.2 |

Optimizer | Adam |

Gpu | Cuda0 |

Model | MAE (MW) | RMSE (MW) | R^{2} | Time (s) |
---|---|---|---|---|

IVMD-FE-Ad-Informer | 3.19 | 4.67 | 0.956 | 1633.21 |

Ad-Informer | 5.81 | 8.40 | 0.858 | 177.13 |

Informer | 7.91 | 10.48 | 0.779 | 165.559 |

Model | MAE (MW) | RMSE (MW) | R^{2} | Time (s) |
---|---|---|---|---|

IVMD-FE-Ad-Informer | 3.19 | 4.67 | 0.956 | 1633.21 |

EMD-FE-Ad-Informer | 4.96 | 7.31 | 0.905 | 1362.47 |

IVMD-FE-Informer | 5.81 | 8.40 | 0.889 | 1878.63 |

IVMD-FE-LSTM | 6.63 | 9.79 | 0.808 | 1732.57 |

LSTM | 7.86 | 10.95 | 0.759 | 305.11 |

ANN | 8.04 | 11.58 | 0.731 | 81.02 |

Model | MAE (kW) | RMSE (kW) | R^{2} | Time (s) |
---|---|---|---|---|

IVMD-FE-Ad-Informer | 83.01 | 60.43 | 0.962 | 1076.34 |

EMD-FE-Ad-Informer | 115.89 | 70.75 | 0.914 | 671.47 |

Ad-Informer | 144.51 | 105.46 | 0.866 | 156.91 |

LSTM | 186.63 | 131.04 | 0.762 | 228.88 |

ANN | 197.16 | 140.62 | 0.746 | 62.15 |

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## Share and Cite

**MDPI and ACS Style**

Tian, Y.; Wang, D.; Zhou, G.; Wang, J.; Zhao, S.; Ni, Y.
An Adaptive Hybrid Model for Wind Power Prediction Based on the IVMD-FE-Ad-Informer. *Entropy* **2023**, *25*, 647.
https://doi.org/10.3390/e25040647

**AMA Style**

Tian Y, Wang D, Zhou G, Wang J, Zhao S, Ni Y.
An Adaptive Hybrid Model for Wind Power Prediction Based on the IVMD-FE-Ad-Informer. *Entropy*. 2023; 25(4):647.
https://doi.org/10.3390/e25040647

**Chicago/Turabian Style**

Tian, Yuqian, Dazhi Wang, Guolin Zhou, Jiaxing Wang, Shuming Zhao, and Yongliang Ni.
2023. "An Adaptive Hybrid Model for Wind Power Prediction Based on the IVMD-FE-Ad-Informer" *Entropy* 25, no. 4: 647.
https://doi.org/10.3390/e25040647