Abstract
In this research, monthly wind speed time series of the Kirsehir was investigated using the stand-alone, hybrid and ensemble models. The artificial neural networks, Gaussian process regression, support vector machines and multivariate adaptive regression splines were employed as stand-alone machine learning models, while the discrete wavelet transform was utilized as a pre-processing technique to create hybrid models. Moreover, for the first time in wind speed predictions, we generated a multi-stage ensemble model by using the M5 Model Tree (M5) algorithm to increase the model accuracies. Two major tasks considered to be necessary, in which the first is to obtain the lag times by using autocorrelation functions, and the latter is to determine the optimum mother wavelet as well as the decomposition level to reduce the uncertainties in wavelet modeling. The results revealed that the hybrid wavelet models outperformed the stand-alone models, while a significant improvement was also observed in M5 ensemble models as the highest Nash–Sutcliffe efficiency coefficient values were obtained in M5 hybrid wavelet multi-stage ensemble models for each lead time prediction. The findings of the study were assessed with respect to the various performance indicators and Kruskal–Wallis test to indicate whether the results are statically significant. The proposed multi-stage ensemble framework also benchmarked with the classical tree-based ensembles, such as Random forest, AdaBoost and XGBoost.
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Abbreviations
- ACF:
-
Autocorrelation Function
- AI:
-
Artificial Intelligence
- ANFIS:
-
Adaptive Neuro-Fuzzy Inference Systems
- ANN:
-
Artificial Neural Networks
- BFGS:
-
Broyden-Fletcher-Goldfarb-Shanno
- BPNN:
-
Back-Propagation Neural Networks
- CCO:
-
Crisscross Optimization
- DBN:
-
Deep Belief Network
- DWT:
-
Discrete Wavelet Transform
- EEMD:
-
Ensemble Empirical Mode Decomposition
- ELM:
-
Extreme Learning Machines
- EMD:
-
Empirical Mode Decomposition
- FEEMD:
-
Fast Ensemble Empirical Mode Decomposition
- FFBP:
-
Feed-Forward Back-Propagation
- GCV:
-
Generalized Cross-Validation
- GPD:
-
Gaussian Probability Distribution
- GPR:
-
Gaussian Process Regression
- LSSVM:
-
Least Square Support Vector Machine
- M5:
-
M5 Model Tree
- M5-ST:
-
M5 Model Tree Stand-Alone Ensemble Models
- M5-W:
-
M5 Model Tree Hybrid Wavelet Ensemble Models
- MAE:
-
Mean Absolute Error
- MARS:
-
Multivariate Adaptive Regression Splines
- MGM:
-
Turkish State Meteorological Service
- ML:
-
Machine Learning
- MLP:
-
Multilayer Perceptron
- MOCS:
-
Multi-Objective Cuckoo Search
- NSE:
-
Nash–Sutcliffe Efficiency Coefficient
- PACF:
-
Partial Autocorrelation Function
- PI:
-
Performance Index
- RBF:
-
Radial Basis Function
- RELM:
-
Regularized Extreme Learning Machine
- RMSE:
-
Root-Mean-Square Error
- SA-ST:
-
Simple Average Stand-Alone Ensemble Models
- SA-W:
-
Simple Average Hybrid Wavelet Ensemble Models
- SDR:
-
Standard Deviation Reduction
- SVM:
-
Support Vector Machines
- W-ANN:
-
Hybrid Wavelet Artificial Neural Networks
- WA-ST:
-
Weighted Average Stand-Alone Ensemble Models
- WA-W:
-
Weighted Average Hybrid Wavelet Ensemble Models
- W-GPR:
-
Hybrid Wavelet Gaussian Process Regression
- WI:
-
Wilmott’s Refined Index
- W-MARS:
-
Hybrid Wavelet Multivariate Adaptive Regression Splines
- WPT:
-
Wavelet Packet Transform
- W-SVM:
-
Hybrid Wavelet Support Vector Machines
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Başakın, E.E., Ekmekcioğlu, Ö., Çıtakoğlu, H. et al. A new insight to the wind speed forecasting: robust multi-stage ensemble soft computing approach based on pre-processing uncertainty assessment. Neural Comput & Applic 34, 783–812 (2022). https://doi.org/10.1007/s00521-021-06424-6
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DOI: https://doi.org/10.1007/s00521-021-06424-6