A Novel Hybrid Method for Multi-Step Short-Term 70 m Wind Speed Prediction Based on Modal Reconstruction and STL-VMD-BiLSTM
Abstract
:1. Introduction
- (1)
- The STL method decomposes the original wind speed series and obtains the trend component, seasonal component, and residual component.
- (2)
- The VMD decomposition of the wind speed is utilized to obtain the high-frequency and low-frequency intrinsic modal components; the BiLSTM model of short-term wind speed prediction is constructed based on the results of the STL-VMD dual-time-series decomposition.
- (3)
- The feasibility and superiority of the STL-VMD dual-time-series decomposition method are verified through prediction experiments using the proposed method and the STL-BiLSTM, VMD-BiLSTM and BiLSTM methods with different datasets and prediction step sizes.
- (4)
- Through comparison tests between the proposed method, support vector regression (SVR), light gradient boosting machine (LGBM) and the random forest algorithm (RF), the prediction performance and superiority of the proposed model are validated across four datasets with different time step sizes.
2. Materials and Methods
2.1. Materials
2.2. Methods
- (1)
- In Section 1 (top left), the original wind speed series observed at the height of 70 m is decomposed by STL, and the trend component, seasonal and residual component are obtained.
- (2)
- In Section 2 (middle left), the VMD method is used to decompose the actual wind speed again, and the high-frequency and low-frequency intrinsic modal components of the actual wind speed data are obtained.
- (3)
- In Section 3 (bottom left), the ECMWF grid data are interpolated to the site via a linear interpolation scheme; the temporal resolution of the site data is 15 min.
- (4)
- In Section 4 (right), the training set and validation set of the time series model are constructed. In order to verify the feasibility and superiority of the proposed method, experiments and a contrastive analysis are carried out to train and optimize the models mentioned in this paper.
2.2.1. STL
2.2.2. VMD
2.2.3. BiLSTM
2.2.4. Performance Evaluation Criteria
3. Results
3.1. Experimental Data Description
3.2. Parameter Selection
3.3. Analysis of Proposed Models
3.3.1. Decomposed Results for STL
3.3.2. Decomposed Results for VMD
3.3.3. Prediction Results with Different Time Series Decomposition Schemes
3.3.4. Prediction Results with Different Models
4. Conclusions
5. Limitations and Future Research Directions
- (1)
- In this study, the historical period of the wind speed data used to build the model is only one year, and the optimization algorithms are not applied to adjust the parameters and enhance the accuracy of the short-term wind speed forecasting results. In the future, an optimization strategy and longer training and testing sets should be used for prediction and verification.
- (2)
- This study does not predict the wind speed at a forecast horizon longer than 2 h. In the future, the longer-sequence time series forecasting of the wind speed should be conducted to achieve prediction at longer forecast horizons.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Case | Maximum (m/s) | Std (m/s) | Mean (m/s) | K | Loc | Scale |
---|---|---|---|---|---|---|
Spring | 24.80 | 4.383 | 7.116 | 1.731 | −0.012 | 8.033 |
Summer | 20.99 | 3.579 | 6.921 | 2.055 | −0.008 | 7.844 |
Fall | 19.67 | 3.299 | 5.688 | 1.830 | −0.028 | 6.452 |
Winter | 20.280 | 2.84 | 4.529 | 1.732 | −0.140 | 5.245 |
Model Parameter | Test Parameters | Optimal Parameter |
---|---|---|
Window_size L | (8,12,16,20,24,28) | 20 |
Batch_size | (64,128,256,512) | 256 |
Epoch | (10,15,20) | 15 |
Neurons of fully connected layer | 8 | |
Rate | 0.2 | |
Activation function | ReLu | |
Objective function | MAE | |
Optimizer | Adam |
Model | Parameter | |
---|---|---|
SVR | kernel | rbf |
epsilon | 0.2 | |
shrink | True | |
tol | 0.001 | |
LGBM | boosting_type | gbdt |
num_leaves | 31 | |
learning_rate | 0.02 | |
feature_fraction | 0.9 | |
RF | bagging_fraction | 0.8 |
bagging_freq | 5 | |
estimators | 10 | |
max_depth | 5 | |
random_state | 0 |
Type | Model | Optimal Features () | Label () |
---|---|---|---|
1 | RF SVR LGBM BiLSTM | WS10m(t − k), …, WS10m(t) WS100m(t − k), …, WS100m(t) WS70m(t − k), …, WS70m(t) | WS70m(t + k), …, WS70m(t + N) |
2 | STL-RF STL-SVR STL-LGBM STL-BiLSTM | WS10m(t − k), …, WS10m(t) WS100m(t − k), …, WS100m(t) WS70m(t − k), …, WS70m(t) STL-Trend(t − k), …, STL-Trend(t) | STL-Trend(t + k), …, STL-Trend(t + N) |
WS10m(t − k), …, WS10m(t) WS100m(t − k), …, WS100m(t) WS70m(t − k), …, WS70m(t) STL-Seasonal(t − k), …, STL-Seasonal(t) | STL-Seasonal(t + k), …, STL-Seasonal(t + N) | ||
3 | VMD-RF VMD-SVR VMD-LGBM VMD-BiLSTM | WS10m(t − k), …, WS10m(t) WS100m(t − k), …, WS100m(t) WS70m(t − k), …, WS70m(t) VMD-IMF(t − k), …, VMD-IMF(t) | VMD-IMF(t + k), …, VMD-IMF(t) |
4 | STL-VMD-RF STL-VMD-SVR STL-VMD-LGBM STL-VMD-BiLSTM | WS10m(t − k), …, WS10m(t) WS100m(t − k), …, WS100m(t) WS70m(t − k), …, WS70m(t) STL-Trend(t − k), …, STL-Trend(t) STL-Seasonal(t − k), …, STL-Seasonal(t) VMD-IMF(t − k), …, VMD-IMF(t) | VMD-IMF(t + k), …, VMD-IMF(t + N) |
Case | STL-Trend (m/s) | STL-Seasonal (m/s) | STL-Remainder (m/s) | FT | FS | ||||
---|---|---|---|---|---|---|---|---|---|
Max | Min | Mean | Max | Min | Max | Min | |||
Spring | 23.674 | 0.570 | 7.116 | 1.790 | −1.841 | 7.004 | −5.474 | 0.971 | 0.292 |
Summer | 20.164 | −1.841 | 6.921 | 2.264 | −2.199 | 6.281 | −3.709 | 0.956 | 0.308 |
Fall | 18.387 | 0.912 | 5.688 | 1.943 | −1.952 | 3.554 | −3.566 | 0.966 | 0.324 |
Winter | 19.198 | −0.022 | 4.529 | 1.251 | −1.429 | 3.276 | −2.830 | 0.968 | 0.337 |
Groups | Modal Number K | ||||||||
---|---|---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | 6 | 7 | 8 | 10 | 20 | |
1–3 | 4.546 | 2.490 | 1.614 | 1.136 | 0.784 | 0.688 | 0.461 | 0.292 | 0.144 |
2–4 | 4.844 | 2.594 | 1.793 | 1.177 | 0.867 | 0.67 | 0.457 | 0.300 | 0.079 |
3–5 | 4.575 | 2.409 | 1.716 | 1.203 | 0.757 | 0.612 | 0.442 | 0.292 | 0.134 |
4–6 | 4.260 | 2.285 | 1.593 | 1.145 | 0.914 | 0.574 | 0.420 | 0.276 | 0.137 |
5–7 | 4.162 | 2.305 | 1.552 | 1.107 | 0.722 | 0.606 | 0.412 | 0.282 | 0.095 |
6–7 | 4.156 | 2.317 | 1.489 | 1.164 | 0.699 | 0.588 | 0.407 | 0.283 | 0.074 |
7–9 | 4.339 | 2.369 | 1.683 | 1.262 | 0.744 | 0.625 | 0.411 | 0.300 | 0.145 |
8–10 | 4.195 | 2.079 | 1.659 | 1.148 | 0.717 | 0.598 | 0.392 | 0.269 | 0.136 |
9–11 | 4.534 | 2.395 | 1.429 | 1.170 | 0.889 | 0.572 | 0.413 | 0.280 | 0.076 |
10–12 | 4.658 | 2.672 | 1.846 | 1.241 | 0.880 | 0.796 | 0.421 | 0.278 | 0.154 |
Case | Model | t + 15 | t + 60 | t + 120 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | R2 | RMSE | MAE | R2 | RMSE | MAE | R2 | ||
(a) Spring | STL-VMD-BiLSTM | 0.668 | 0.483 | 0.958 | 0.754 | 0.550 | 0.946 | 0.920 | 0.696 | 0.918 |
VMD-BiLSTM | 0.735 | 0.544 | 0.954 | 0.830 | 0.623 | 0.943 | 1.048 | 0.800 | 0.906 | |
STL-BiLSTM | 0.915 | 0.668 | 0.919 | 1.184 | 0.861 | 0.868 | 2.108 | 1.516 | 0.548 | |
BiLSTM | 1.320 | 0.982 | 0.865 | 2.073 | 1.521 | 0.643 | 2.725 | 2.008 | 0.290 | |
(b) Summer | STL-VMD-BiLSTM | 0.665 | 0.504 | 0.946 | 0.749 | 0.567 | 0.929 | 0.835 | 0.631 | 0.910 |
VMD-BiLSTM | 0.742 | 0.543 | 0.931 | 0.837 | 0.623 | 0.909 | 0.991 | 0.751 | 0.860 | |
STL-BiLSTM | 1.058 | 0.785 | 0.845 | 1.136 | 0.850 | 0.814 | 1.899 | 0.423 | 0.392 | |
BiLSTM | 1.401 | 1.070 | 0.758 | 2.017 | 1.519 | 0.399 | 2.271 | 1.740 | 0.118 | |
(c) Fall | STL-VMD-BiLSTM | 0.561 | 0.439 | 0.961 | 0.627 | 0.481 | 0.951 | 0.715 | 0.558 | 0.939 |
VMD-BiLSTM | 0.568 | 0.428 | 0.964 | 0.656 | 0.499 | 0.952 | 0.803 | 0.661 | 0.914 | |
STL-BiLSTM | 0.783 | 0.587 | 0.932 | 0.881 | 0.679 | 0.909 | 1.362 | 1.166 | 0.669 | |
BiLSTM | 1.026 | 0.786 | 0.878 | 1.542 | 1.138 | 0.667 | 1.919 | 1.555 | 0.236 | |
(d) Winter | STL-VMD-BiLSTM | 0.435 | 0.321 | 0.937 | 0.470 | 0.347 | 0.922 | 0.542 | 0.405 | 0.893 |
VMD-BiLSTM | 0.439 | 0.323 | 0.934 | 0.508 | 0.380 | 0.909 | 0.610 | 0.460 | 0.859 | |
STL-BiLSTM | 0.621 | 0.444 | 0.859 | 0.696 | 0.522 | 0.809 | 1.189 | 0.941 | 0.298 | |
BiLSTM | 0.836 | 0.589 | 0.750 | 1.223 | 0.953 | 0.317 | 1.458 | 1.180 | −0.339 |
Case | Model | t + 15 | t + 60 | t + 120 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | R2 | RMSE | MAE | R2 | RMSE | MAE | R2 | ||
(a) Spring | STL-VMD-SVR | 0.678 | 0.516 | 0.960 | 0.860 | 0.658 | 0.931 | 1.221 | 0.943 | 0.840 |
VMD-SVR | 0.688 | 0.523 | 0.959 | 0.858 | 0.653 | 0.932 | 1.177 | 0.908 | 0.855 | |
STL-SVR | 0.942 | 0.681 | 0.919 | 1.727 | 1.252 | 0.700 | 2.576 | 1.893 | 0.235 | |
SVR | 1.228 | 0.894 | 0.862 | 2.070 | 1.510 | 0.547 | 2.738 | 2.030 | 0.119 | |
STL-VMD-LGBM | 0.909 | 0.654 | 0.902 | 1.080 | 0.784 | 0.853 | 1.382 | 1.036 | 0.749 | |
VMD-LGBM | 0.924 | 0.662 | 0.897 | 1.083 | 0.788 | 0.852 | 1.368 | 1.028 | 0.753 | |
STL-LGBM | 1.019 | 0.741 | 0.873 | 1.389 | 0.988 | 0.754 | 2.211 | 1.585 | 0.270 | |
LGBM | 1.151 | 0.853 | 0.850 | 1.979 | 1.446 | 0.497 | 2.658 | 1.974 | 0.042 | |
STL-VMD-RF | 0.743 | 0.544 | 0.950 | 1.013 | 0.748 | 0.900 | 1.428 | 1.089 | 0.797 | |
VMD-RF | 0.737 | 0.537 | 0.950 | 1.021 | 0.756 | 0.899 | 1.381 | 1.052 | 0.802 | |
STL-RF | 0.877 | 0.633 | 0.927 | 1.358 | 0.979 | 0.820 | 2.258 | 1.616 | 0.448 | |
RF | 1.071 | 0.786 | 0.900 | 1.999 | 1.465 | 0.613 | 2.716 | 2.006 | 0.255 | |
(b) Summer | STL-VMD-SVR | 0.758 | 0.561 | 0.927 | 0.903 | 0.682 | 0.889 | 1.168 | 0.890 | 0.796 |
VMD-SVR | 0.803 | 0.593 | 0.916 | 0.950 | 0.711 | 0.874 | 1.144 | 0.869 | 0.804 | |
STL-SVR | 0.983 | 0.733 | 0.869 | 1.597 | 1.207 | 0.611 | 2.058 | 1.575 | 0.217 | |
SVR | 1.300 | 0.963 | 0.776 | 1.925 | 1.453 | 0.409 | 2.188 | 1.678 | 0.095 | |
STL-VMD-LGBM | 0.915 | 0.705 | 0.859 | 1.005 | 0.777 | 0.820 | 1.175 | 0.913 | 0.735 | |
VMD-LGBM | 0.916 | 0.707 | 0.859 | 1.014 | 0.785 | 0.815 | 1.189 | 0.928 | 0.722 | |
STL-LGBM | 1.049 | 0.800 | 0.800 | 1.222 | 0.937 | 0.713 | 1.839 | 1.445 | 0.242 | |
LGBM | 1.265 | 0.957 | 0.736 | 1.974 | 1.514 | 0.225 | 2.352 | 1.855 | −0.300 | |
STL-VMD-RF | 0.826 | 0.614 | 0.911 | 0.964 | 0.732 | 0.869 | 1.181 | 0.890 | 0.787 | |
VMD-RF | 0.828 | 0.615 | 0.911 | 0.965 | 0.732 | 0.868 | 1.180 | 0.889 | 0.784 | |
STL-RF | 0.963 | 0.707 | 0.874 | 1.217 | 0.910 | 0.777 | 1.860 | 1.437 | 0.387 | |
RF | 1.212 | 0.889 | 0.817 | 1.973 | 1.461 | 0.416 | 2.281 | 1.750 | 0.061 |
Case | Model | t + 15 | t + 60 | t + 120 | ||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | R2 | RMSE | MAE | R2 | RMSE | MAE | R2 | ||
(a) Fall | STL-VMD-SVR | 0.585 | 0.446 | 0.962 | 0.719 | 0.551 | 0.940 | 0.983 | 0.763 | 0.877 |
VMD-SVR | 0.615 | 0.466 | 0.958 | 0.747 | 0.570 | 0.935 | 0.963 | 0.746 | 0.883 | |
STL-SVR | 0.738 | 0.558 | 0.936 | 1.304 | 0.968 | 0.775 | 1.963 | 1.497 | 0.364 | |
SVR | 1.005 | 0.746 | 0.880 | 1.612 | 1.198 | 0.629 | 2.118 | 1.632 | 0.196 | |
STL-VMD-LGBM | 0.781 | 0.604 | 0.910 | 0.874 | 0.676 | 0.883 | 1.078 | 0.831 | 0.811 | |
VMD-LGBM | 0.781 | 0.604 | 0.910 | 0.877 | 0.678 | 0.882 | 1.087 | 0.838 | 0.804 | |
STL-LGBM | 0.863 | 0.661 | 0.885 | 1.060 | 0.812 | 0.817 | 1.712 | 1.319 | 0.429 | |
LGBM | 1.066 | 0.813 | 0.826 | 1.648 | 1.254 | 0.492 | 2.160 | 1.684 | −0.148 | |
STL-VMD-RF | 0.649 | 0.488 | 0.952 | 0.826 | 0.634 | 0.916 | 1.058 | 0.821 | 0.853 | |
VMD-RF | 0.650 | 0.488 | 0.952 | 0.823 | 0.632 | 0.917 | 1.067 | 0.830 | 0.847 | |
STL-RF | 0.722 | 0.542 | 0.940 | 1.036 | 0.772 | 0.865 | 1.767 | 1.315 | 0.528 | |
RF | 0.972 | 0.719 | 0.891 | 1.587 | 1.183 | 0.644 | 2.086 | 1.598 | 0.175 | |
(b) Winter | STL-VMD-SVR | 0.446 | 0.327 | 0.927 | 0.557 | 0.424 | 0.872 | 0.751 | 0.589 | 0.711 |
VMD-SVR | 0.466 | 0.341 | 0.919 | 0.577 | 0.438 | 0.863 | 0.739 | 0.577 | 0.742 | |
STL-SVR | 0.598 | 0.453 | 0.860 | 0.986 | 0.781 | 0.552 | 1.340 | 1.089 | −0.074 | |
SVR | 0.797 | 0.591 | 0.757 | 1.206 | 0.959 | 0.302 | 1.433 | 1.162 | −0.303 | |
STL-VMD-LGBM | 0.604 | 0.493 | 0.828 | 0.674 | 0.548 | 0.769 | 0.806 | 0.648 | 0.625 | |
VMD-LGBM | 0.604 | 0.493 | 0.828 | 0.683 | 0.556 | 0.762 | 0.828 | 0.664 | 0.601 | |
STL-LGBM | 0.692 | 0.553 | 0.761 | 0.841 | 0.682 | 0.614 | 1.253 | 1.028 | −0.166 | |
LGBM | 0.851 | 0.660 | 0.657 | 1.289 | 1.051 | −0.078 | 1.545 | 1.283 | −1.155 | |
STL-VMD-RF | 0.471 | 0.349 | 0.921 | 0.594 | 0.454 | 0.861 | 0.758 | 0.589 | 0.741 | |
VMD-RF | 0.471 | 0.350 | 0.921 | 0.594 | 0.454 | 0.861 | 0.763 | 0.597 | 0.731 | |
STL-RF | 0.583 | 0.436 | 0.872 | 0.758 | 0.591 | 0.767 | 1.186 | 0.950 | 0.225 | |
RF | 0.756 | 0.537 | 0.794 | 1.221 | 0.962 | 0.286 | 1.474 | 1.201 | −0.422 |
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Da, X.; Ye, D.; Shen, Y.; Cheng, P.; Yao, J.; Wang, D. A Novel Hybrid Method for Multi-Step Short-Term 70 m Wind Speed Prediction Based on Modal Reconstruction and STL-VMD-BiLSTM. Atmosphere 2024, 15, 1014. https://doi.org/10.3390/atmos15081014
Da X, Ye D, Shen Y, Cheng P, Yao J, Wang D. A Novel Hybrid Method for Multi-Step Short-Term 70 m Wind Speed Prediction Based on Modal Reconstruction and STL-VMD-BiLSTM. Atmosphere. 2024; 15(8):1014. https://doi.org/10.3390/atmos15081014
Chicago/Turabian StyleDa, Xuanfang, Dong Ye, Yanbo Shen, Peng Cheng, Jinfeng Yao, and Dan Wang. 2024. "A Novel Hybrid Method for Multi-Step Short-Term 70 m Wind Speed Prediction Based on Modal Reconstruction and STL-VMD-BiLSTM" Atmosphere 15, no. 8: 1014. https://doi.org/10.3390/atmos15081014