The wind farm site is located in Canada and has 29 months of energy data available.
The MOPSO is used to train SVM over the available 17 months of training data (at 6-hourly time resolution) using a “Round-Robin” cross-validation strategy. This gives an opportunity to train on 16 months and test the results on a ‘hold-out’ 1 month test set. By repeating the process for all the 17 months, gives a full 17 months
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of test data to compare against the observed. Since there is 29 months of data available for this site, a full 1 year of data is used in validation (completely unseen data). The results that follow are the predictions on the validation set. The results are shown on the normalized (between 1 and 1) dataset. The MOPSO-SVM results are shown with and without PCA pre-processing.
The trade-off curve for MOPSO SVM optimization for the two objectives is shown in Fig.4. The trade-off between BinRMS vs. RMSE is shown for the SVM using original input compared against SVM using Principal Components (PCs) as inputs. It can be noticed that there is little difference between the two approaches.
The PCA-SVM produced a better objective function result for BinRMS, where as simple SVM provided a better objective function result for RMSE.
Figure 5 shows the monthly mean wind power for the 12 months compared against the observed data. The results are shown for SVM prediction with and without the pre-processing using PCA. As stated above, there is a very little dif-ference between the two approaches and a good fit has been found. It can be noticed that predictions are in reasonable agreement with the observed data. The results in Fig.6show histogram of observed vs.the predicted wind power data at the 6-hourly time resolution (the prediction time step). The results are shown for SVM prediction with and without the pre-processing using PCA. It can be noticed that the distribu-tions are well-maintained using MOPSO methodology and a reasonable agreement between observed and predicted power is evident from Fig.6. A number of good-ness-of-fit measures are evaluated in Table1, which are monthly root mean square error (RMSE), monthly coefficient of determination (COD), instantaneous RMSE, instantaneous COD, and BinRMSE (histogram bin RMSE). The results in Table1 are presented for SVM prediction with and without the pre-processing using PCA.
Both monthly and instantaneous wind power are of significant interest, and thus are
0.4
Fig. 4 Trade-off curve between the two objectives BinRMS vs. RMSE for SVM and PCA-SVM 6 Multiobjective Evolutionary Optimization and Machine Learning 79
included in the current analysis. It can be noticed that not only monthly but also instantaneous power predictions are in close agreement with the observed.
5 Conclusions
Machine learning methods have gained in popularity in solving prediction problems in the area of geosciences. Due to their ability to model complex processes, the machine learning algorithms are preferred over computationally rigorous process-based
–0.7 –0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3
–0.7 –0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3
Observed
Predicted
SVM PCA-SVM
Fig. 5 Scatter plot for the mean monthly wind energy data for SVM and PCA-SVM
–1 – 0.8 – 0.6 – 0.4 – 0.2 0 0.2 0.4 0.6 0.8 1
0 50 100 150 200 250 300 350 400
Power (kw)
Observed PCA SVM SVM
Fig. 6 Histogram for SVM and PCA-SVM along with observed
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models which are usually over-parameterized and require immense amounts of data to calibrate. Support Vector Machines are well-suited for the problems exhibiting high degrees of spatial and temporal variability, issues of nonlinearity, conflicting scales, and hierarchical uncertainty.
In the current chapter, a multiobjective evolutionary computing method MOPSO is used to optimize the three parameters of SVM for wind energy predictions. The approach has been tested on data from a wind farm using NCEP’s re-analysis grid data. The prediction strategy employs SVM which is parameterized for the two objective functions. The approach is also tested by pre-processing the input data using PCA. A number of graphical and tabular results in the form of goodness-of-fit measures are presented for wind energy predictions. The results also show a trade-off curve for the two objectives employed in the MOPSO. The trade-trade-off curve is helpful in identifying the appropriate parameter set for SVM in order to achieve the desired accuracy for the two objective problem. The SVM predictions at the farm level produced excellent agreement with the observed data for the validation set. Overall, the results have been encouraging and it is recommended to use MOPSO-SVM approach for other operational projects in the area of renewable energy predictions and forecasting. While further modifications and advancements are underway, the current procedure is sound enough to be applied in operational settings.
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