Deep FS: A Deep Learning Approach for Surface Solar Radiation

2.1. Research Gaps

2.2. Rsearch Contributions

3.1. Data Acquisition

3.2. Data Analysis and Preprocessing

3.3. Feature Extraction

3.4. Feature Selection and Visualization

3.5. Model Design and Prediction

• The solar data is acquired from both datasets. Let X represent the data points in the dataset.

  $$X=\{x_1,x_2,\dots ,x_n\}$$

  (4)
• Data are then normalized for a specific range using the mean and standard deviation.

  $$X^{\prime }={\displaystyle \frac{X-\mu }{\sigma }}$$

  (5)
• Relevant features are extracted from the features mentioned in Table 3 using the feature extraction process:
  • The data points are normalized.
  • Convolution is applied to extract the local features.
  • The RelU Activation function, along with pooling and flattening, is applied for capturing essential features.
• CNN-LSTM and CNN-GRU models are designed.
  LSTM:

  $$\begin{array}{cc}\hfill Z_1& =Conv(X^{\prime };W_1,b_1)\hfill \end{array}$$

  (6)

  $$\begin{array}{cc}\hfill A_1& =Activation\left(Z_1\right)\hfill \end{array}$$

  (7)

  $$\begin{array}{cc}\hfill P_1& =MaxPool\left(A_1\right)\hfill \end{array}$$

  (8)

  $$\begin{array}{cc}\hfill L& =LSTM(P_1;{\theta }_{LSTM})\hfill \end{array}$$

  (9)

  $$\begin{array}{cc}\hfill E_{CNN-LSTM}& =Output(L;W_O,b_O)\hfill \end{array}$$

  (10)
  GRU:

  $$\begin{array}{cc}\hfill Z_2& =Conv(X^{\prime };W_2,b_2)\hfill \end{array}$$

  (11)

  $$\begin{array}{cc}\hfill A_2& =Activation\left(Z_2\right)\hfill \end{array}$$

  (12)

  $$\begin{array}{cc}\hfill P_2& =MaxPool\left(A_2\right)\hfill \end{array}$$

  (13)

  $$\begin{array}{cc}\hfill G& =GRU(P_2;{\theta }_{GRU})\hfill \end{array}$$

  (14)

  $$\begin{array}{cc}\hfill E_{CNN-GRU}& =Output(G;W_O,b_O)\hfill \end{array}$$

  (15)

  where
  • W: Filter;
  • b: bias;
  • $Z_1$: ReLU Activation.
  The LSTM Cell Process is defined as

  $$\begin{array}{cc}\hfill f_t& =\sigma (W_f·[h_{t-1},x_t]+b_f)\hfill \end{array}$$

  (16)

  $$\begin{array}{cc}\hfill i_t& =\sigma (W_i·[h_{t-1},x_t]+b_i)\hfill \end{array}$$

  (17)

  $$\begin{array}{cc}\hfill C_t^{\prime }& =tanh(W_C·[h_{t-1},x_t]+b_C)\hfill \end{array}$$

  (18)

  $$\begin{array}{cc}\hfill C_t& =f_t\ast C_{t-1}+i_t\ast C_t^{\prime }\hfill \end{array}$$

  (19)

  $$\begin{array}{cc}\hfill o_t& =\sigma (W_o·[h_{t-1},x_t]+b_o)\hfill \end{array}$$

  (20)

  $$\begin{array}{cc}\hfill h_t& =o_t\ast tanh\left(C_t\right)\hfill \end{array}$$

  (21)

  where
  • $f_t$: Forget Gate;
  • $i_t$: Input Gate;
  • h: Hidden State;
  • $C_t$: Candidate Cell State;
  • W: Weight.
• Train the model and optimize the loss function.

  $$\mathcal{L}(\theta ,X,y)={\displaystyle \frac{1}{n}}\sum _{i=1}^n{(y_i-f(X_i;\theta ))}^2$$

  (22)
• Evaluate the performance with different performance metrics RMSE, RRMSE, MAE, and R² as follows.

  $$\begin{array}{cc}\hfill RMSE& =\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}\hfill \end{array}$$

  (23)

  $$\begin{array}{cc}\hfill RRMSE& ={\displaystyle \frac{RMSE}{\overline{Y}}}={\displaystyle \frac{\sqrt{\frac{1}{n}{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}{\overline{y}}}\hfill \end{array}$$

  (24)

  $$\begin{array}{cc}\hfill R^2& =1-{\displaystyle \frac{{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}{{\sum }_{i=1}^n{(y_i-{\overline{y}}_i)}^2}}\hfill \end{array}$$

  (25)

  $$\begin{array}{cc}\hfill MAE& ={\displaystyle \frac{1}{n}}\sum _{i=1}^n|y_i-{\widehat{y}}_i|\hfill \end{array}$$

  (26)
• Perform a comparative analysis with traditional approaches for the validation of the proposed method.

3.6. Elaboration on Model Selection

3.7. Advantages over Specific Algorithms