From Lidar Measurement to Rotor Effective Wind Speed Prediction: Empirical Mode Decomposition and Gated Recurrent Unit Solution
Abstract
:1. Introduction
- The novel data-driven prediction framework based on lidar measurement information is put forward to predict the REWS, enabling advanced predictive controls of wind turbines.
- Three prediction models based on the proposed EMD–GRU prediction framework are designed and compared based on professional BLADED software V4.8.
- The frequency classification and intelligent aggregation are presented to optimize the EMD–GRU models so as to reduce the prediction error and simplify the modeling complexity.
2. Lidar Measuring and REWS Calculation
3. EMD–GRU Prediction Schemes
3.1. Data Processing Based on EMD
3.1.1. Determination of Input Data
3.1.2. Empirical Mode Decomposition
3.1.3. Delay Processing
3.2. Prediction Modeling Based on GRU Neural Network
3.2.1. Frequency Classification Preparation
3.2.2. GRU Neural Network
3.2.3. EO Algorithm
3.2.4. GRU Prediction Based on EO
3.3. Aggregation Computing Based on EO
3.3.1. Aggregation Computing
3.3.2. Aggregation Weight Optimization with EO
4. Results and Discussions
4.1. Statistical Characteristics of Six Wind Speed Datasets
4.2. Parameter Setting of the Model
4.3. Evaluation Criteria
4.4. Results of GRU Prediction
4.4.1. Results of Aggregation Optimization
4.4.2. Prediction Results of EMD–GRU Schemes
- From the aspect of modeling accuracy, the average MAE of Scheme 3 is 0.2781, which represents the highest modeling accuracy, while that of Scheme 1 is 0.6629, representing the lowest modeling accuracy among the three schemes. The MAEs of Scheme 2 under H1–H6 are 0.2401, 0.3302, 0.3621, 0.4136, 0.3881, and 0.3271, respectively. Among these six datasets, the prediction accuracy of Scheme 2 performs best at an average wind speed of 10 m/s.
- From the aspect of modeling stability, when the lidar information is combined with the mechanism modeling, the prediction stability is obviously improved. The RMSE of Scheme 1 is approximately from 0.72 to 0.95 at six different average wind speeds. However, the RMSEs of Scheme 2 and Scheme 3 are both distributed within 0.51. When the modeling stability is improved, the prediction result will be less sensible to the change in wind speed.
- From the aspect of modeling effectiveness, Scheme 3 has a better fitting effect compared to Scheme 2, and that of Scheme 1 is the worst. The average value of MAPE in Scheme 3 is 0.0198 in the six datasets, followed by 0.0242 in Scheme 2. The average value of MAPE in Scheme 1 is about twice that in Scheme 3.
4.4.3. Comparations with Other Models
- Compared to the traditional mechanism modeling, the proposed EMD–GRU model has significantly improved the prediction performance. For example, when the average wind speed is 12 m/s, the RMSE and MAE of the mechanism model are 0.6663 and 0.5432, respectively, while the RMSE and MAE of the EMD–GRU model are 0.3058 and 0.2525, respectively.
- Compared to the original GRU data-driven model, the predicted value of the EMD–GRU model is more consistent with the actual value of the REWS. From the average wind speed of 10 m/s to 20 m/s, the improvement rates of MAPE corresponding to the EMD–GRU model are 7.14%, 19.46%, 5.49%, 15.38%, 0.93%, and 8.81%, respectively.
- The EMD–GRU model has higher predictive stability than the other two models. For example, under the average wind speed of 10 m/s, compared to those of the other two models, the RMSE of the EMD–GRU model is decreased by 0.2629 and 0.0131, respectively.
5. Conclusions
- ➢
- Among three EMD–GRU schemes with different input, the prediction accuracy, stability, and effectiveness of Scheme 3 exhibit obvious superiority compared to those of the other two schemes.
- ➢
- The EO and PSO algorithms could effectively optimize the prediction performance of EMD–GRU model, and the optimization effect of EO algorithm is better than that of PSO. The RMSE of the EMD–GRU model after EO optimization is reduced by 0.0592, which is about 0.03 lower than that of PSO.
- ➢
- Compared to the traditional mechanism model and the single GRU model, the prediction performance of the proposed EMD–GRU model is significantly improved. Relative to the mechanism model, the EMD–GRU model demonstrates MAE improvements of 49.18%, 53.43%, 52.10%, 65.95%, 48.18%, and 60.33% across the six datasets.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Acronyms | |
REWS | Rotor effective wind speed |
EMD | Empirical mode decomposition |
GRU | Gated recurrent unit |
IMF | Intrinsic mode function |
EO | Equilibrium optimizer |
IMF | Intrinsic mode function |
LSTM | Long short-term memory |
MAE | Mean absolute error |
RMSE | Root mean squared error |
MAPE | Mean absolute percentage error |
PSO | Particle swarm optimization |
H1–H6 | Dataset 1–Dataset 6 |
Symbols | |
Vi | Line-of-sight wind speed for each laser beam i (m/s) |
Va | Projection of V1 on horizontal plane (m/s) |
Vb | Projection of V2 on horizontal plane (m/s) |
θ | Angle between laser beam and horizontal plane (rad) |
ui | Horizontal wind speed at height of Vi (m/s) |
α | Angle between Va and u1 (rad) |
S | Sector area (m2) |
R | Radius of the rotor (m) |
h | Height of the sector area (m) |
Ai | Sector i of the rotor |
SAi | Area of Ai (m2) |
ueq | Value of REWS (m/s) |
X(t) | Original wind speed series |
Ci(t) | Decomposed IMF |
Rn(t) | Residual of EMD |
T | Time delay (s) |
x | Distance between lidar measurement spot and lidar (m) |
Average wind speed (m/s) | |
zt | Update gate |
rt | Reset gate |
ht−1 | State information of the previous moment |
xt | Input vector |
ht | Output vector |
Candidate activation vector | |
W | Parameter matrices |
b | Parameter vectors |
Initial concentration | |
Cmin | Lower limit of variables |
Cmax | Upper limit of variables |
randi | Random vector between [0,1] |
n | Population number |
Ceq,pool | Equilibrium pool |
Ceq,i | Optimal solutions in the current iteration |
Ceq,ave | Average value of optimal solutions |
F | Exponential term |
λ | Random number between 0 and 1 |
t0 | Initial time |
t | Function of iteration |
G | Generation rate |
G0 | Initial value |
k | Decay constant |
V | Control volume |
fHF | High-frequency group |
fMF | Medium-frequency group |
fLF | Low-frequency group |
fRes | Residual |
wi | Weights of fHF, fMF, fLF and fRes, respectively |
fi | Real value at time i (m/s) |
Predicted value at time i (m/s) |
References
- Jiao, X.; Yang, Q.; Zhu, C.; Fu, L.; Chen, Q. Effective wind speed estimation and prediction based feedforward feedback pitch control for wind turbines. In Proceedings of the 12th Asian Control Conference (ASCC), Kitakyushu, Japan, 9–12 June 2019. [Google Scholar]
- Song, D.; Yang, J.; Cai, Z.; Dong, M.; Su, M.; Wang, Y. Wind estimation with a non-standard extended Kalman filter and its application on maximum power extraction for variable speed wind turbines. Appl. Energy 2017, 190, 670–685. [Google Scholar] [CrossRef]
- Ning, J.; Tang, Y.; Gao, B. A time-varying potential-based demand response method for mitigating the impacts of wind power forecasting errors. Appl. Sci. 2017, 7, 1132. [Google Scholar] [CrossRef]
- Bakhtiari, F.; Nazarzadeh, J. Optimal estimation and tracking control for variable-speed wind turbine with PMSG. J. Mod. Power Syst. Clean Energy 2019, 8, 159–167. [Google Scholar] [CrossRef]
- Zhang, G.; Xu, B.; Liu, H.; Hou, J.; Zhang, J. Wind power prediction based on variational mode decomposition and feature selection. J. Mod. Power Syst. Clean Energy 2020, 9, 1520–1529. [Google Scholar] [CrossRef]
- Arbaoui, M.; Essadki, A.; Kharchouf, I.; Nasser, T. A new robust control by active disturbance rejection control applied on wind turbine system based on doubly fed induction generator DFIG. In Proceedings of the International Renewable and Sustainable Energy Conference (IRSEC), Tangier, Morocco, 4–7 December 2017. [Google Scholar]
- Dong, Y.; Ma, S.; Zhang, H.; Yang, G. Wind Power Prediction Based on Multi-class Autoregressive Moving Average Model with Logistic Function. J. Mod. Power Syst. Clean Energy 2022, 10, 1184–1193. [Google Scholar] [CrossRef]
- Xu, Y.; Yin, W. A globally convergent algorithm for nonconvex optimization based on block coordinate update. J. Sci. Comput. 2017, 72, 700–734. [Google Scholar] [CrossRef]
- Song, D.; Tu, Y.; Wang, L.; Jin, F.; Li, Z.; Huang, C.; Xia, E.; Rizk-Allah, R.M.; Yang, J.; Su, M.; et al. Coordinated optimization on energy capture and torque fluctuation of wind turbines via variable weight NMPC with fuzzy regulator. Appl. Energy 2022, 312, 118821. [Google Scholar] [CrossRef]
- Chen, B.; Wu, Q.H.; Li, M.; Xiahou, K. Detection of false data injection attacks on power systems using graph edge-conditioned convolutional networks. Prot. Control Mod. Power Syst. 2023, 8, 265–276. [Google Scholar] [CrossRef]
- Song, D.; Yan, J.; Zeng, H.; Deng, X.; Yang, J.; Qu, X.; Rizk-Allah, R.M.; Snášel, V.; Joo, Y.H. Topological optimization of an offshore-wind-farm power collection system based on a hybrid optimization methodology. J. Mar. Sci. Eng. 2023, 11, 279. [Google Scholar] [CrossRef]
- Gao, X.; Chen, Y.; Xu, S.; Gao, W.; Zhu, X.; Sun, H.; Yang, H.; Han, Z.; Wang, Y.; Lu, H. Comparative experimental investigation into wake characteristics of turbines in three wind farms areas with varying terrain complexity from LiDAR measurements. Appl. Energy 2022, 307, 118182. [Google Scholar] [CrossRef]
- García-Gutiérrez, A.; Domínguez, D.; López, D.; Gonzalo, J. Atmospheric boundary layer wind profile estimation using neural networks applied to lidar measurements. Sensors 2021, 21, 3659. [Google Scholar] [CrossRef] [PubMed]
- Bao, J.; Yue, H.; Leithead, W.E.; Wang, J.-Q. Feedforward control for wind turbine load reduction with pseudo-LIDAR measurement. Int. J. Autom. Comput. 2018, 15, 142–155. [Google Scholar] [CrossRef]
- Simley, E.; Pao, L.; Kelley, N.; Jonkman, B.; Frehlich, R. Lidar wind speed measurements of evolving wind fields. In Proceedings of the 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Nashville, TN, USA, 9–12 January 2012. [Google Scholar]
- Jiao, X.; Zhang, D.; Wang, X.; Tian, Y.; Liu, W.; Xin, L. Wind Speed Prediction Based on Error Compensation. Sensors 2023, 23, 4905. [Google Scholar] [CrossRef]
- Liu, J.; Yang, X.; Zhang, D.; Xu, P.; Li, Z.; Hu, F. Adaptive Graph-Learning Convolutional Network for Multi-Node Offshore Wind Speed Forecasting. J. Mar. Sci. Eng. 2023, 11, 879. [Google Scholar] [CrossRef]
- Song, D.; Tan, X.; Deng, X.; Yang, J.; Dong, M.; Elkholy, M.H.; Talaat, M.; Joo, Y.H. Rotor equivalent wind speed prediction based on mechanism analysis and residual correction using Lidar measurements. Energy Convers. Manag. 2023, 292, 117385. [Google Scholar] [CrossRef]
- Yin, X.; Lei, M. Jointly improving energy efficiency and smoothing power oscillations of integrated offshore wind and photovoltaic power: A deep reinforcement learning approach. Prot. Control Mod. Power Syst. 2023, 8, 420–430. [Google Scholar] [CrossRef]
- Martinez, J.; Aguiar, B.; Estrada-Manzo, V.; Bernal, M. Actuator fault detection for discrete-time descriptor systems via a convex unknown input observer with unknown scheduling variables. Math. Probl. Eng. 2021, 2021, 8825609. [Google Scholar] [CrossRef]
- Neeraj; Mathew, J.; Behera, R.K. EMD-Att-LSTM: A data-driven strategy combined with deep learning for short-term load forecasting. J. Mod. Power Syst. Clean Energy 2021, 10, 1229–1240. [Google Scholar]
- Jin, X.-B.; Yang, N.-X.; Wang, X.-Y.; Bai, Y.-T.; Su, T.-L.; Kong, J.-L. Hybrid deep learning predictor for smart agriculture sensing based on empirical mode decomposition and gated recurrent unit group model. Sensors 2020, 20, 1334. [Google Scholar] [CrossRef]
- Jung, S.; Moon, J.; Park, S.; Hwang, E. An attention-based multilayer GRU model for multistep-ahead short-term load forecasting. Sensors 2021, 21, 1639. [Google Scholar] [CrossRef]
- Higgins, C.W.; Froidevaux, M.; Simeonov, V.; Vercauteren, N.; Barry, C.; Parlange, M.B. The effect of scale on the applicability of Taylor’s frozen turbulence hypothesis in the atmospheric boundary layer. Bound.-Layer Meteorol. 2012, 143, 379–391. [Google Scholar] [CrossRef]
- Yentes, J.M.; Hunt, N.; Schmid, K.K.; Kaipust, J.P.; McGrath, D.; Stergiou, N. The appropriate use of approximate entropy and sample entropy with short data sets. Ann. Biomed. Eng. 2013, 41, 349–365. [Google Scholar] [CrossRef] [PubMed]
- Faramarzi, A.; Heidarinejad, M.; Stephens, B.; Mirjalili, S. Equilibrium optimizer: A novel optimization algorithm. Knowl.-Based Syst. 2020, 191, 105190. [Google Scholar] [CrossRef]
- Zhou, Y.; Sun, Y.; Wang, S.; Mahfoud, R.J.; Alhelou, H.H.; Hatziargyriou, N.; Siano, P. Performance Improvement of Very Short-term Prediction Intervals for Regional Wind Power Based on Composite Conditional Nonlinear Quantile Regression. J. Mod. Power Syst. Clean Energy 2022, 10, 60–70. [Google Scholar] [CrossRef]
Datasets | Wind Speed | Samples | Mean | Max | Median | Min | Std. |
---|---|---|---|---|---|---|---|
H1 | 10 | All | 9.6115 | 12.9672 | 9.4057 | 7.8553 | 1.0714 |
Training Set | 9.4598 | 11.0997 | 9.3919 | 7.8626 | 0.7962 | ||
Testing Set | 10.0667 | 12.9672 | 9.5563 | 7.8553 | 1.5535 | ||
H2 | 12 | All | 12.0045 | 14.0607 | 11.9957 | 9.8206 | 0.8960 |
Training Set | 11.9482 | 14.0607 | 11.9000 | 9.8206 | 0.9044 | ||
Testing Set | 12.1734 | 13.6158 | 12.4482 | 10.3123 | 0.8483 | ||
H3 | 14 | All | 13.3294 | 17.3582 | 13.2469 | 9.9518 | 1.2814 |
Training Set | 13.7240 | 17.3582 | 13.5764 | 11.4107 | 1.1030 | ||
Testing Set | 12.1455 | 14.4256 | 12.1977 | 9.9518 | 1.0241 | ||
H4 | 16 | All | 15.8433 | 19.0663 | 15.8330 | 12.2807 | 1.5796 |
Training Set | 15.9308 | 19.0299 | 16.1401 | 12.2807 | 1.6052 | ||
Testing Set | 15.5808 | 19.0663 | 15.2350 | 13.1170 | 1.4693 | ||
H5 | 18 | All | 17.6392 | 23.5735 | 17.5249 | 13.9425 | 1.9126 |
Training Set | 17.8968 | 23.5735 | 18.1743 | 13.9425 | 2.0529 | ||
Testing Set | 16.8665 | 19.0372 | 16.7214 | 14.7905 | 1.0917 | ||
H6 | 20 | All | 19.5343 | 24.3731 | 19.4811 | 15.2719 | 1.7119 |
Training Set | 19.9127 | 24.3731 | 19.8991 | 15.2719 | 1.7167 | ||
Testing Set | 18.3988 | 20.6271 | 18.3912 | 16.1519 | 1.0780 |
Model | Parameter Name | Parameter Value |
---|---|---|
GRU | Hidden Units | 230 |
Learning Rate Drop Period | 4 | |
Epoch | 60 | |
EO1 | n | 20 |
0.001 | ||
0.01 | ||
Max_iter | 100 | |
EO2 | n | 20 |
0 | ||
5 | ||
Max_iter | 50 |
DATA | Not Optimized | EO | PSO |
---|---|---|---|
H1 | 0.2804 | 0.2803 | 0.2804 |
H2 | 0.3889 | 0.3058 | 0.3875 |
H3 | 0.3547 | 0.3443 | 0.3501 |
H4 | 0.3139 | 0.2866 | 0.3078 |
H5 | 0.4865 | 0.4273 | 0.4837 |
H6 | 0.4319 | 0.4032 | 0.4276 |
Data | Model | RMSE | MAE | MAPE |
---|---|---|---|---|
H1 | Scheme 1 | 0.7356 | 0.6605 | 0.0586 |
Scheme 2 | 0.2855 | 0.2401 | 0.0233 | |
Scheme 3 | 0.2803 | 0.2212 | 0.0208 | |
H2 | Scheme 1 | 0.7855 | 0.6720 | 0.0540 |
Scheme 2 | 0.3898 | 0.3302 | 0.0266 | |
Scheme 3 | 0.3058 | 0.2525 | 0.0207 | |
H3 | Scheme 1 | 0.7371 | 0.6065 | 0.0513 |
Scheme 2 | 0.3981 | 0.3621 | 0.0272 | |
Scheme 3 | 0.3443 | 0.2898 | 0.0241 | |
H4 | Scheme 1 | 0.7828 | 0.6555 | 0.0420 |
Scheme 2 | 0.5026 | 0.4136 | 0.0270 | |
Scheme 3 | 0.2866 | 0.2236 | 0.0143 | |
H5 | Scheme 1 | 0.7258 | 0.5942 | 0.0354 |
Scheme 2 | 0.4726 | 0.3881 | 0.0229 | |
Scheme 3 | 0.4273 | 0.3606 | 0.0214 | |
H6 | Scheme 1 | 0.9448 | 0.7887 | 0.0434 |
Scheme 2 | 0.4037 | 0.3271 | 0.0179 | |
Scheme 3 | 0.4032 | 0.3211 | 0.0176 |
Data | Model | RMSE | MAE | MAPE |
---|---|---|---|---|
H1 | Mechanism | 0.5432 | 0.4353 | 0.0452 |
GRU | 0.2934 | 0.2265 | 0.0224 | |
EMD–GRU | 0.2803 | 0.2212 | 0.0208 | |
H2 | Mechanism | 0.6663 | 0.5423 | 0.0454 |
GRU | 0.3891 | 0.3229 | 0.0257 | |
EMD–GRU | 0.3058 | 0.2525 | 0.0207 | |
H3 | Mechanism | 0.7570 | 0.6051 | 0.0461 |
GRU | 0.3686 | 0.3027 | 0.0255 | |
EMD–GRU | 0.3443 | 0.2898 | 0.0241 | |
H4 | Mechanism | 0.8315 | 0.6567 | 0.0417 |
GRU | 0.3317 | 0.2609 | 0.0169 | |
EMD–GRU | 0.2866 | 0.2236 | 0.0143 | |
H5 | Mechanism | 0.8741 | 0.6959 | 0.0394 |
GRU | 0.4871 | 0.3895 | 0.0216 | |
EMD–GRU | 0.4273 | 0.3606 | 0.0214 | |
H6 | Mechanism | 0.9972 | 0.8095 | 0.0419 |
GRU | 0.4393 | 0.3359 | 0.0193 | |
EMD–GRU | 0.4032 | 0.3211 | 0.0176 |
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Shi, S.; Liu, Z.; Deng, X.; Chen, S.; Song, D. From Lidar Measurement to Rotor Effective Wind Speed Prediction: Empirical Mode Decomposition and Gated Recurrent Unit Solution. Sensors 2023, 23, 9379. https://doi.org/10.3390/s23239379
Shi S, Liu Z, Deng X, Chen S, Song D. From Lidar Measurement to Rotor Effective Wind Speed Prediction: Empirical Mode Decomposition and Gated Recurrent Unit Solution. Sensors. 2023; 23(23):9379. https://doi.org/10.3390/s23239379
Chicago/Turabian StyleShi, Shuqi, Zongze Liu, Xiaofei Deng, Sifan Chen, and Dongran Song. 2023. "From Lidar Measurement to Rotor Effective Wind Speed Prediction: Empirical Mode Decomposition and Gated Recurrent Unit Solution" Sensors 23, no. 23: 9379. https://doi.org/10.3390/s23239379
APA StyleShi, S., Liu, Z., Deng, X., Chen, S., & Song, D. (2023). From Lidar Measurement to Rotor Effective Wind Speed Prediction: Empirical Mode Decomposition and Gated Recurrent Unit Solution. Sensors, 23(23), 9379. https://doi.org/10.3390/s23239379