Open AccessOpen Access


Improving Performance of Recurrent Neural Networks Using Simulated Annealing for Vertical Wind Speed Estimation

Shafiqur Rehman1,*, Hilal H. Nuha2, Ali Al Shaikhi3, Satria Akbar2, Mohamed Mohandes1,3

1 Interdisciplinary Research Center for Renewable Energy and Power Systems (IRC-REPS), KFUPM, Dhahran, 31261, Saudi Arabia
2 HUMIC Engineering, School of Computing, Telkom University, Bandung, 40257, Indonesia
3 Electrical Engineering Department, King Fahd University of Petroleum & Minerals (KFUPM), Dhahran, 31261, Saudi Arabia

* Corresponding Author: Shafiqur Rehman. Email:

Energy Engineering 2023, 120(4), 775-789.


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 (). The numerical experimental results show that the MSE values between the estimated and actual WS at 180 m height for the RNN-SA, RNN, MLP, and SVM methods are found to be 2.09, 2.12, 2.37, and 2.63, respectively.


Cite This Article

Rehman, S., Nuha, H. H., Shaikhi, A. A., Akbar, S., Mohandes, M. (2023). Improving Performance of Recurrent Neural Networks Using Simulated Annealing for Vertical Wind Speed Estimation. Energy Engineering, 120(4), 775–789.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 402


  • 168


  • 1


Share Link