4.2. Results of the SVM, LSTM and SVM-LSTM Models
This section focuses on description of the results obtained from the simulation of the stand-alone machine learning (SVM), deep learning (LSTM) and the hybrid (SVM-LSTM) techniques for the prediction of the solar activity in terms of SSN. The three models were simulated using MATLAB 2019b software on a PC with a COREi7 processor. In the course of developing predictive machine learning model, the choice of the network structure and the learning parameters has a great influence on the prediction accuracy of the models. The training data is used to obtain the optimal models’ parameters, and the testing data is used on the trained models to test the prediction accuracy [44].
For the SVM, the key parameters include the epsilon \(\left(\epsilon \right)\), bias, mu \(\left(\mu \right)\) and the number of iterations. For this study, the values of the parameters that produced the best results are found as, epsilon \(\epsilon =7.31,\) the number of iterations is 1619, with a bias of 80.09, and \(\mu =81.80\). Similarly, For the deep learning LSTM model, selection of the network parameters, such as the number of layers, number of cells, learning rate and momentum influences the model’s performance. After several attempts, the optimal network structure is obtained with two LSTM layers with 32 cells each, one convolutional layer for feature extraction, and one output layer, with rectified linear unit (Relu) activation function. The model is trained for 400 epochs with a momentum of 0.9 and a learning rate of \({10}^{-5}\). The hybrid SVM-LSTM model is simulated based on the optimal structures of the stand-alone models.
According to Yassen et al. [45], to construct a credible prediction model, the model's performance should be evaluated using error metrics such as MAE or RMSE, as well as goodness of fit criteria such as R and R2. Therefore, the proposed techniques are evaluated using \(R\), \({R}^{2}\), RMSE and MAE to provide a sense of the models’ performances and efficiencies in terms of the error criteria and goodness of fit.
The performance of the three models is shown in Table 3. From the training and testing results it can be observed that the LSTM outperformed the linear regression SVM. This finding is corroborated by the recently published studies on the prediction of solar activity [26], [30]. Meanwhile, the results in Table III shows that the proposed hybrid SVM-LSTM model with \(R=0.995\), \({R}^{2}=0.989\), \(RMSE=7.778\), and \(MAE=4.857\) in testing step has performance superiority over the standalone SVM and LSTM. This could be attributed to the fact that the hybrid model combined the capacities of the two single models.
Table 3
Training
|
Models
|
R
|
R2
|
RMSE
|
MAE
|
SVM
|
0.937
|
0.879
|
26.284
|
19.168
|
LSTM
|
0.940
|
0.883
|
25.787
|
18.476
|
SVM-LSTM
|
0.996
|
0.991
|
6.030
|
4.579
|
Testing
|
Models
|
R
|
R2
|
RMSE
|
MAE
|
SVM
|
0.902
|
0.812
|
27.593
|
19.840
|
LSTM
|
0.906
|
0.821
|
26.989
|
18.985
|
SVM-LSTM
|
0.995
|
0.989
|
7.778
|
4.857
|
Figure 6 depict the performance of the three models based on the RMSE and MAE metrics in a bar chart. The performance superiority of the SVM-LSTM for both error metrics is indicated. For instance, the training and testing RMSEs using the SVM-LSTM is decreased by about 76.62% and 71.18% compared to the LSTM, respectively. And significantly decreased by 77.06% and 71.81% compared to SVM, for training, and testing, respectively.
Moreover, the comparison of the models’ performance in terms of goodness of fit (DC) is shown graphically using a radar chart in Fig. 7. The models with DC values closer to 1 are generally more accurate. Hence, the models can be ranked in terms of accuracy from highest to lowest as \(SVM-LSTM>LSTM>SVM\). However, since the DC of the three models are all greater than 70%, it shows that all the three developed models can provide a good forecast of the SSN [46].
Figure 8 shows the scatter plot of the predicted SSN versus the original SSN. In a scatter plot, the prediction performance is considered to be perfect when the majority of the points on the graph lies on a linear positive slope. Therefore, it can be seen from these figures that all the three models performed relatively good. However, in case of the hybrid SVM-LSTM, more points lie within the range, which indicates the performance superiority of the hybrid model over the stand-alone.
Figure 9 illustrates the comparison of the predicted SSN against the original SSN using time series plots. Time series plot is used to further indicate the performance of the models in predicting the time series SSN. As shown in Fig. 9, the data has seasonality, with some peaks higher than others, and a bit of noise. It is clear from Fig. 9 that although the stand-alone models can capture the dynamics of the SSN, there are some errors especially in predicting the peak values. Nonetheless, the SVM-LSTM predicted SSN are more consistent with the original data including during the peaks.
The box plot, displayed in Fig. 10, provides additional visualization of the models' performance. The various whiskers and quartiles can be used to quantify the cumulative distribution of values in the predicted SSN using the three models and the original SSN. As shown in Fig. 10, the distribution of the data predicted by the hybrid SVM-LSTM is closer to the real data, making it the best of the three models. Furthermore, the SVM and LSTM are unable to match the original data's median and whiskers, indicating their inability to capture the maximum SSN values.
The performance accuracy of the proposed SVM-LSTM model for the prediction of the solar activity is further revealed through a quantitative comparison with the existing models in the literature. Pala and Atici [[26] employed two stand-alone deep learning methods; the LSTM and NNAR for prediction of the solar activity. Although the LSTM with \(RMSE=35.9\) outperformed the NNAR in their study, the performance of the LSTM developed in our study is better with \(RMSE=26.989\) in the validation stage. Moreover, the proposed hybrid SVM-LSTM proved best with validation \(RMSE=7.778\). A hybrid of three models comprising of Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing with Error, Trend and Seasonality (ETS), and SVM is proposed in [27]. The model with validation \(RMSE=22.726, MAE=16.549 and {R}^{2}=0.97\) is less accurate in comparison to our proposed hybrid model with \(RMSE=7.778, MAE=4.857 and {R}^{2}=0.99\), both in terms of goodness of fit and error criteria. Notably, Zhu et al.[25] employed optimized LSTM to predict solar activity in terms of monthly sunspot area (SSA). Their proposed method is not like our study which relies on the SSN directly without the need of first predicting the SSA. Benson et al. [30], combines two deep learning methods; LSTM and WaveNet to predict the solar activity. The hybrid of WaveNet-LSTM attracted more computational cost and complexity. Moreover, their proposed LSTM has 132 cells compared to our proposed LSTM with 32 cells. Nghiem et al.[47] applied Bayesian inference in hybrid LSTM with Convolutional Neural Network (CNN), to predict the SSN. Their proposed hybrid model attained an accuracy with \(RMSE=26.10 and MAE=18.74\). Comparatively, a proposed hybrid deep neural network with LSTM (DNN-LTSM) in[48] achieved a validation \(RMSE=20.34 and MAE=13.75\). In both scenarios our proposed hybrid model shows higher performance with validation \(RMSE=7.778 and MAE=4.857\).
4.3. Future scenarios in energy microgrid systems
Solar activity will affect space, weather, and technology like communication and navigation systems. These disruptions can interfere with satellite communication, for example used in remote sensing and data communication in decentralized systems. Decentralization refers to the shift from a centralized energy system, where power is generated in large-scale power plants and distributed across long distances, to a more localized and distributed system. Complex patterns in the data create uncertainties. There is a growing need of adoption and implementation of microgrid energy systems with decentralized systems, for example for rural development. Increasingly all data makes are necessary to have more accurate predictions while being less computationally expensive so that local users can afford to actually use the data. Such systems would offer numerous benefits, including resilience, renewable energy integration, energy efficiency, local empowerment, and grid flexibility, contributing to a more sustainable and reliable energy future.
The future will also include shared data to create new business models. For example, the energy surplus at one component in the energy system can be sold to neighbor in the local energy community either at the time it occurs, or to be predicted in the future to occur. With more players in the system, the complexity is increased by including the present and future energy production and use. Prediction of behaviors will affect the new business or predicted business. More reliable data, computations and simulation with digital learning models are necessary to predict the scenarios. At the end, this will align with local aims, such as CO2 neutrality, net zero carbon, etc of local place-based network municipalities and regions to be aligned with climate needs.