An accurate vertical wind speed (WS) data estimation is required to determine the potential for wind farm installation. In general, the vertical extrapolation of WS at different heights must consider different parameters from different locations, such as wind shear coefficient, roughness length, and atmospheric conditions. The novelty presented in this article is the introduction of two steps optimization for the Recurrent Neural Networks (RNN) model to estimate WS at different heights using measurements from lower heights. The first optimization of the RNN is performed to minimize a differentiable cost function, namely, mean squared error (MSE), using the Broyden-Fletcher-Goldfarb-Shanno algorithm. Secondly, the RNN is optimized to reduce a non-differentiable cost function using simulated annealing (RNN-SA), namely mean absolute error (MAE). Estimation of WS vertically at 50 m height is done by training RNN-SA with the actual WS data a 10–40 m heights. The estimated WS at height of 50 m and the measured WS at 10–40 heights are further used to train RNN-SA to obtain WS at 60 m height. This procedure is repeated continuously until the WS is estimated at a height of 180 m. The RNN-SA performance is compared with the standard RNN, Multilayer Perceptron (MLP), Support Vector Machine (SVM), and state of the art methods like convolutional neural networks (CNN) and long short-term memory (LSTM) networks to extrapolate the WS vertically. The estimated values are also compared with real WS dataset acquired using LiDAR and tested using four error metrics namely, mean squared error (MSE), mean absolute percentage error (MAPE), mean bias error (MBE), and coefficient of determination (

Wind power plants have been used globally as a renewable energy source for household and industrial energy demand. Total deployed wind power capacity, worldwide in 2020 cumulatively, reached 743 GW [

The increase in WS with height is due to less human activities and lower surface roughness at higher heights. In addition, atmospheric conditions at a higher height have less friction and are more stable which may account for higher WS at higher heights [

Several approaches have been used to estimate WS at higher positions based on measurements at lower heights as indicated by increasing WS average and its percentage increment in

The contributions and novelties of this study are as follows:

The paper introduces two steps performance enhancement of recurrent neural networks using gradient based and simulated annealing methods to estimate WS at a higher turbine position using the measured value at lower heights.

This paper presents the comparison of the proposed method with the standard RNN, Multilayer Perceptron (MLP), Support Vector Machine (SVM), and state of the art methods like convolutional neural networks (CNN) and long short-term memory methods.

A real dataset from Dhahran, Kingdom of Saudi Arabia is used to evaluate the accuracy of the proposed method.

All methods are evaluated using error metrics such as mean squared error (MSE), mean absolute percentage error (MAPE), mean bias error (MBE), and coefficient of determination (

The remainder of this paper is structured as methodology, experimental results, and conclusion.

In this paper, we propose a hybrid method, namely recurrent neural networks with simulated annealing (RNN-SA) for vertical WS extrapolation. The RNN uses the Elman model where the hidden unit output is connected back to itself using an adjustable recurrent weight

This study uses the tangent-hyperbolic activation function defined by:

In this study, the numerical experiment is carried out by dividing the data into three parts, i.e., 70%, 10%, and 20% for training, validation, and testing, respectively. The RNN-SA is trained using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [

It can be noticed that the

Given the cost function above, the solution candidate acceptance is given by:

In this study, the multilayer perceptron (MLP) is used as a benchmark for the comparison of the performance of RNN-SA. MLP has a much simpler structure than RNN [

This study utilizes gradient descent with momentum and adaptive learning rate

The last benchmarking method used in this paper is the support vector machine (SVM) for regression [

The SVM model is trained using sequential minimal optimization (SMO), where the number of inputs determines the dimension of

Recently, state of the art methods like deep learning have been used for many tasks including wind speed prediction. For instance, convolutional neural networks (CNN) is used for WS prediction in a wind farm in Hebei Province, China with high accuracy [

This study employs four error measures based on the difference between the measured values (

This section provides the description of the experimental setup and the results. The estimation starts by training each model using WS values at heights 10, 20, 30, and 40 m, as inputs and actual WS at the height of 50 m as the target. Next, the actual WS at 10–40 m and the estimated WS at a height 50 m are used to train new model with five inputs to estimate the WS at 60 m height. This process, which uses the actual and estimated WS values at lower heights to predict the WS values at one level higher is further repeated until the estimation of the WS at a height of 180 m using the actual WS at 10–40 m, and the estimated WS at 50–170 m is obtained.

Due to lack of resources in some countries, WS is typically measured up to a height of 40 m and its extrapolation to higher levels require sophisticated methods. Therefore, the WS at the higher heights is obtained using models, given the WS measured at lower heights. As shown in

Heights (m) | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MSE | 0.024 | 0.098 | 0.162 | 0.263 | 0.371 | 0.516 | 0.628 | 0.780 | 0.931 | 1.051 | 1.193 | 1.359 | 1.457 | 1.649 |

MBE | 0.012 | 0.037 | 0.048 | 0.068 | 0.081 | 0.093 | 0.061 | 0.024 | 0.000 | 0.056 | 0.054 | 0.053 | 0.049 | 0.144 |

MAPE (%) | 2.06 | 3.79 | 4.57 | 5.57 | 6.31 | 7.22 | 7.63 | 8.10 | 8.49 | 8.85 | 9.15 | 9.37 | 9.54 | 10.16 |

99.03 | 96.56 | 94.72 | 92.24 | 89.78 | 86.96 | 84.75 | 82.32 | 80.35 | 78.74 | 77.07 | 75.10 | 73.94 | 72.53 |

Heights (m) | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RNN-SA | 0.027 | 0.105 | 0.182 | 0.313 | 0.463 | 0.674 | 0.834 | 1.054 | 1.259 | 1.416 | 1.601 | 1.817 | 1.929 | 2.089 |

RNN | 0.028 | 0.113 | 0.185 | 0.314 | 0.475 | 0.681 | 0.855 | 1.064 | 1.262 | 1.426 | 1.614 | 1.831 | 1.950 | 2.123 |

MLP | 0.049 | 0.120 | 0.209 | 0.351 | 0.510 | 0.739 | 0.931 | 1.165 | 1.321 | 1.552 | 1.735 | 2.005 | 2.168 | 2.367 |

SVM | 0.032 | 0.145 | 0.239 | 0.401 | 0.581 | 0.834 | 1.042 | 1.364 | 1.516 | 1.852 | 2.017 | 2.323 | 2.365 | 2.632 |

CNN | 0.125 | 0.265 | 0.539 | 0.392 | 1.059 | 1.402 | 1.092 | 1.411 | 2.241 | 1.833 | 2.437 | 1.940 | 3.265 | 2.378 |

LSTM | 0.054 | 0.140 | 0.221 | 0.458 | 0.570 | 0.726 | 1.469 | 1.160 | 1.440 | 2.396 | 1.750 | 1.982 | 2.676 | 3.497 |

Heights | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RNN-SA | −0.02 | −0.03 | −0.05 | −0.07 | −0.09 | −0.11 | −0.15 | −0.20 | −0.22 | −0.18 | −0.20 | −0.20 | −0.20 | −0.13 |

RNN | −0.02 | −0.03 | −0.04 | −0.06 | −0.08 | −0.14 | −0.15 | −0.13 | −0.18 | −0.19 | −0.18 | −0.18 | −0.20 | −0.14 |

MLP | −0.01 | −0.04 | −0.06 | −0.07 | −0.11 | −0.15 | −0.17 | −0.18 | −0.20 | −0.21 | −0.20 | −0.20 | −0.21 | −0.20 |

SVM | −0.02 | −0.07 | −0.09 | −0.12 | −0.15 | −0.18 | −0.20 | −0.24 | −0.24 | −0.26 | −0.25 | −0.28 | −0.26 | −0.26 |

CNN | −0.16 | −0.31 | −0.39 | 0.03 | −0.56 | −0.84 | −0.45 | −0.58 | −0.98 | −0.58 | −0.82 | −0.31 | −1.14 | −0.18 |

LSTM | 0.983 | 0.959 | 0.940 | 0.908 | 0.870 | 0.838 | 0.810 | 0.776 | 0.758 | 0.724 | 0.710 | 0.685 | 0.675 | 0.656 |

The scatter plots between the estimated RNN-SA with actual WS values at 60, 100, 140, and180 m are shown in

The estimated WS profiles along with the actual ones up to 180 m, are compared in

Finally, the training duration statistics is shown in

This paper introduced a novel optimization method for the RNN using simulated annealing for accurate vertical WS extrapolation tasks. Each model is trained using the actual WS at lower heights (10–40 m) to estimate the WS up to 180 m. The novel method outperformed the standard RNN as well as other methods and state of the art models for all error measures on a real WS dataset. The novel method achieved the highest coefficient of determination (

Artificial intelligence

Artificial neural networks

Broyden-Fletcher-Goldfarb-Shanno

Convolution neural networks

Greenhouse gases

Gigawatt

Gigawatt hour

Kilowatt

Kilowatt hour

Long short-term memory

Meter

Mean absolute error

Mean absolute percentage error

Mean bias error

Multilayer perceptron

Mean square error

Megawatt

Megawatt hour

Recurrent neural networks

Recurrent neural networks with simulation annealing

Simulation annealing

Sequential minimal optimization

Support vector machine

^{2}

Coefficient of determination

Wind speed (m/s)

This research was funded by

The program is written using Matlab and is available at (

The authors declare that they have no conflicts of interest to report regarding the present study.