# A Bayesian Optimization-Based LSTM Model for Wind Power Forecasting in the Adama District, Ethiopia

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## Abstract

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## 1. Introduction

- Bayesian optimization (BO) was employed to identify optimal hyperparameters, such as the number of neurons and activation function, for the purpose of enhancing wind power forecasting.
- The BO-LSTM model proposed in this paper was evaluated using real wind power data and found to outperform baseline methods in terms of statistical error metrics.
- The paper presents a robust BO-LSTM model for day-ahead wind power forecasting, utilizing actual wind power data.
- A wind power dataset was created for the first time in the Adama district of Ethiopia, following a comprehensive and arduous data collection process.

## 2. Related Works

- Physics-based methods: This approach predicts desired variables using real-time atmospheric variables, such as temperature, pressure, surface roughness, and obstacles. However, it is computationally intensive and may not be suitable for short-term forecasting tasks due to the high computation time and computing resources required [29,30].
- Traditional statistical methods: Autoregressive (AR), autoregressive moving average (ARMA), and autoregressive integrated moving average (ARIMA) models are conventional statistical methods for time series forecasting, and they are effective in capturing linear mathematical relationships in time series data. However, their prediction accuracy decreases for longer forecast horizons, and they struggle to model complex seasonal patterns and exogenous variables [31,32,33]. Nevertheless, the combination of ARIMA and LSTM techniques has resulted in successful approaches in recent years [34].
- Machine learning methods: Machine learning is a data-driven approach that maps between dependent and independent variables and is widely used for classification and prediction tasks [29]. This category includes feed-forward neural networks, support vector regression (SVR), k-nearest neighbor, fuzzy neural networks, extreme learning machines, and others. For example, Ahmed et al. [35] proposed using gradient boosting machines (GBMs) and support vector machines (SVMs) to predict wind power over medium to long-term time frames and found that the SVM model performed better with some computational run-time concerns. Another study proposed a wind turbine power generation prediction model using linear regression, k-nearest neighbor regression, and decision tree regression algorithms to predict one-minute time resolution data [36]. Shabbir et al. [37] used an SVM-based algorithm to predict wind energy production one day ahead, and they found that the proposed algorithms had better forecasting results with the lowest root mean square error (RMSE) values. However, conventional machine learning algorithms may struggle to capture temporal information effectively and produce more accurate forecasts for complex and nonlinear wind power data [38]. In [39], a method was proposed to predict power generation by exploiting wind speed data from different heights in the same area and achieved a 3.1% improvement in accuracy compared to the traditional support vector machine method. Gao proposed an approach based on grey models and machine learning for monthly wind power forecasting using data from China [40]. A hybrid model based on Laguerre polynomials and the multi-objective Runge-Kutta algorithm was proposed in [41] for wind power forecasting, and the effectiveness of the method was demonstrated using wind power data from a Chinese wind farm.

## 3. Materials and Methods

#### 3.1. Deep Learning Architectures

#### 3.1.1. Long-Short Term Memory Network

- Handling long-term dependencies: One of the main challenges in wind energy forecasting is capturing long-term dependencies in the data. LSTMs are particularly well suited for this task because they are designed to handle long-term dependencies by selectively forgetting or retaining information from previous time steps.
- Handling non-linear relationships: Wind energy is affected by many non-linear factors, such as temperature, humidity, and pressure. LSTMs are capable of capturing non-linear relationships in the data, making them a good choice for wind energy forecasting.
- Handling multivariate time series: LSTMs can handle multiple inputs, making them well suited for multivariate time series data, such as wind energy data, which often includes multiple sources of information.
- Good performance: LSTMs have shown good performance in wind energy forecasting tasks, outperforming traditional time series forecasting methods, such as ARIMA and SARIMA.
- Robustness to noise: LSTMs are less sensitive to noise in the data compared to traditional time series methods, making them a good choice for wind energy forecasting where data quality can be a challenge.

#### 3.1.2. Gated Recurrent Unit Neural Network

#### 3.2. Bayesian Optimization

- Surrogate (probabilistic) model: BO is guided by Bayes’ theorem, and in each iteration, it uses a surrogate model to approximate the objective function, which can be sampled efficiently. A Gaussian process is the most effective surrogate model for selecting the promising set of hyperparameters to be evaluated in the true objective function [74]. The surrogate model estimates the objective function, which is used to guide future sampling.
- Acquisition function: BO uses an acquisition function [75] to determine which points in the search space should be evaluated and to provide information on the optimal value of f. The purpose of the acquisition function is to use posterior information to find the best sample point in each iteration and to propose a new sampling point to identify the most promising set of hyperparameters to be evaluated next. The acquisition function balances exploitation and exploration. Exploitation involves focusing on the search space with a higher likelihood of improving the current solution based on the current surrogate model, while exploration is the strategy of moving towards less explored regions of the search space.

- Efficient hyperparameter tuning: BO provides a more efficient and effective way of tuning the hyperparameters of an LSTM model than traditional grid search or random search methods. It does this by intelligently selecting the next set of hyperparameters to evaluate based on the results of previous evaluations, leading to faster convergence and better results.
- Improved model performance: By tuning the hyperparameters of an LSTM model using BO, the model can be improved to better fit the wind energy data and achieve higher accuracy in its predictions.
- Better understanding of the model: BO can provide insights into the impact of different hyperparameters on the performance of the LSTM model, allowing for better understanding of the model and its behavior.
- Robustness to hyperparameter selection: By using BO to select the hyperparameters, the model can be made more robust to the choice of hyperparameters, reducing the risk of poor performance due to poor hyperparameter selection.

#### 3.3. Data Description

#### 3.4. Data Pre-Processing

#### 3.5. Problem Formulation

#### 3.6. Performance Evaluation

## 4. Results Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Acronym

ANN | artificial neural network |

ARIMA | autoregressive integrative moving average |

BO-LSTM | Bayesian optimized long short-term memory |

GRU | gated recurrent unit |

KNN | K-nearest neighbor |

LSTM | Long-short term memory |

MAE | mean absolute error |

MAPE | mean absolute percentage error |

RNN | recurrent neural network |

RMSE | root mean square error |

SCADA | supervisory control and data acquisition |

SVM | support vector machine |

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**Figure 8.**Training vs. validation loss based on BO-LSTM. (

**a**) Training vs. validation loss for Site I. (

**b**) Training vs. validation loss for Site II.

**Figure 9.**Training vs. validation loss without LSTM Model tuning. (

**a**) Training vs. validation loss for Site I. (

**b**) Training vs. validation loss for Site II.

Hyperparameters | Range Values | Optimal Parameters Selected by Bayesian Optimization |
---|---|---|

Learning rate | $\left(\right)$ | 0.01 |

Epochs | $\left(\right)$ | 80 |

Batch size | $\left(\right)$ | 32 |

Dropout | $\left(\right)$ | 0.2 |

Activation function | $\left(\right)$ | tanh |

Optimizer | $\left(\right)$ | RMSprop |

Neurons | $\left(\right),\left(\right)open="["\; close="]">20,40,60,80,100$ | $\left(\right)$ |

Models | Parameters | Values/Type |
---|---|---|

ANN | Epoch | 4 |

Learning rate | 0.001 | |

Batch size | 32 | |

Neuron at hidden layer | 20 | |

Optimizer | Adam | |

Activation function | ReLu | |

XGBoost | n_estimators | 116 |

Learning rate | 0.3 | |

max_depth | 3 | |

gamma | 5 | |

min_child_weight | 6 | |

colsample_bytree | 0.6 | |

ARIMA | P | 4 |

d | 0 | |

q | 1 | |

GRU | Learning _rate | 0.0001 |

Batch size | 32 | |

Epoch | 80 | |

Neuron at hidden layers | 100, 20 | |

Dropout_rate | 0.1 | |

Activation function | ReLu | |

Optimizer | Adam | |

LSTM | Learning_rate | 0.001 |

Batch size | 32 | |

Neuron at hidden layer | 20 | |

Activation function | ReLu | |

Optimizer | Adam |

Data | Models | MAE | RMSE | MAPE (%) |
---|---|---|---|---|

Site I | ANN | 0.1009 | 0.1310 | 0.916 |

XGBoost | 0.1312 | 0.1664 | 1.3737 | |

ARIMA | 0.1939 | 0.2277 | 1.8680 | |

LSTM | 0.1070 | 0.1264 | 2.0642 | |

BO-GRU | 0.0651 | 0.0826 | 1.1470 | |

BO-LSTM | 0.0621 | 0.0793 | 1.1353 | |

Site II | ANN | 0.1024 | 0.1307 | 2.4062 |

XGBoost | 0.1489 | 0.1926 | 1.7796 | |

ARIMA | 0.1844 | 0.2214 | 2.2057 | |

LSTM | 0.1137 | 0.1399 | 1.1725 | |

BO-GRU | 0.0707 | 0.0910 | 1.1621 | |

BO-LSTM | 0.0708 | 0.0893 | 1.2275 | |

Site III | ANN | 0.1440 | 0.1791 | 1.9741 |

XGBoost | 0.1452 | 0.1878 | 1.6768 | |

ARIMA | 0.1748 | 0.2106 | 2.1963 | |

LSTM | 0.1137 | 0.1401 | 1.1903 | |

BO-GRU | 0.0972 | 0.1247 | 1.0896 | |

BO-LSTM | 0.0948 | 0.1220 | 1.0674 |

Dataset | Models | Training | Testing | ||
---|---|---|---|---|---|

MAE | RMSE | MAE | RMSE | ||

Site I | LSTM | 0.0909 | 0.1167 | 0.1118 | 0.1371 |

GRU | 0.0825 | 0.1046 | 0.1004 | 0.1205 | |

BO-GRU | 0.0611 | 0.0807 | 0.0693 | 0.0881 | |

BO-LSTM | 0.0590 | 0.0782 | 0.0627 | 0.0800 | |

Site II | LSTM | 0.0848 | 0.1104 | 0.0950 | 0.1146 |

GRU | 0.0875 | 0.1142 | 0.0970 | 0.1163 | |

BO-GRU | 0.0714 | 0.0967 | 0.0775 | 0.0989 | |

BO-LSTM | 0.0689 | 0.0956 | 0.0741 | 0.0930 | |

Site III | LSTM | 0.1167 | 0.1461 | 0.1095 | 0.1386 |

GRU | 0.1219 | 0.1505 | 0.1088 | 0.1363 | |

BO-GRU | 0.1063 | 0.1377 | 0.0993 | 0.1274 | |

BO-LSTM | 0.1032 | 0.1352 | 0.0986 | 0.1258 |

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## Share and Cite

**MDPI and ACS Style**

Habtemariam, E.T.; Kekeba, K.; Martínez-Ballesteros, M.; Martínez-Álvarez, F.
A Bayesian Optimization-Based LSTM Model for Wind Power Forecasting in the Adama District, Ethiopia. *Energies* **2023**, *16*, 2317.
https://doi.org/10.3390/en16052317

**AMA Style**

Habtemariam ET, Kekeba K, Martínez-Ballesteros M, Martínez-Álvarez F.
A Bayesian Optimization-Based LSTM Model for Wind Power Forecasting in the Adama District, Ethiopia. *Energies*. 2023; 16(5):2317.
https://doi.org/10.3390/en16052317

**Chicago/Turabian Style**

Habtemariam, Ejigu Tefera, Kula Kekeba, María Martínez-Ballesteros, and Francisco Martínez-Álvarez.
2023. "A Bayesian Optimization-Based LSTM Model for Wind Power Forecasting in the Adama District, Ethiopia" *Energies* 16, no. 5: 2317.
https://doi.org/10.3390/en16052317