## 4 Result and Discussion
### Evaluation Metrics of the Model  
To validate the predictive performance of the CEEMDAN-MIC-FCBF-BiLSTM model, this paper selects Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Square Error (MSE), Coefficient of Determination (R\({}^{2}\)), and Residual Prediction Deviation (RPD) as the primary evaluation metrics for assessing the model's predictive accuracy.  
MAPE measures the average absolute percentage error between predicted and actual values, which is suitable for assessing prediction accuracy but sensitive to outliers. RMSE calculates the root mean square of prediction errors, emphasizing larger errors, and is commonly used for overall prediction accuracy assessment. MAE computes the mean absolute value of prediction errors, insensitive to outliers, reflecting the overall average error level. MSE measures the mean square of prediction errors, emphasizing larger errors, and is commonly used in mathematical computations. R\({}^{2}\) gauges the model's ability to explain variance in the target variable, with values ranging from 0 to 1, where closer to 1 indicates better explanatory power. Residual Prediction Deviation evaluates the model's predictive performance relative to the standard deviation and is utilized to assess the model's relative performance in a specific context. The calculation equation is shown in (20)-(25):  
\[MAPE=\frac{1}{n}\underset{i=1}{\overset{n}{\underset{i=1}{\sum}}}\left|\frac{ \hat{y}_{i}-y_{i}}{y_{i}}\right|\times 100\% \tag{20}\]  
\[RMSE=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\underset{i=1}{\sum}}}(\hat{y }_{i}-y_{i})^{2}} \tag{21}\]  
\[MAE=\frac{1}{n}\underset{i=1}{\overset{n}{\underset{i=1}{\sum}}}\left|y_{i}- \hat{y}_{i}\right| \tag{22}\]  
\[MSE=\frac{1}{n}\underset{i=1}{\overset{n}{\underset{i=1}{\sum}}}\left(y_{i}- \hat{y}_{i}\right)^{2} \tag{23}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature** & **Abbreviation** & **Type** & **Unit** \\ \hline Date & Day & Independent & 1, 2, 3,..., 31 \\ Time & Time & Independent & 1, 2, 3,..., 24 \\ Type of weekday & WT & Independent & Weekday and \\ Day of the week & DT & Independent & Weekend \\ Air temperature & AT & Continuous & Sunday, Monday, \\ Air humidity & AH & Continuous & Saturday \\ Barometric pressure & BP & Continuous & hPa \\ Wind speed & WS & Continuous & m/s \\ Cloud cover & CC & Continuous & 0–10 percent \\ Total solar irradiance at & RP & Continuous & W/m\({}^{2}\) \\ the previous moment & & TR & Continuous & W/m\({}^{2}\) \\ Total solar irradiance & & & Continuous & W/m\({}^{2}\) \\ Energy consumption at & & & & \\ the previous moment & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Energy consumption prediction input feature list.  
\[R^{2}=1-\frac{\sum\limits_{i=1}^{n}{(y_{i}-\hat{y}_{i})^{2}}}{\sum\limits_{i=1}^{n }{(y_{i}-\overline{y})^{2}}} \tag{24}\]  
\[RPD=\frac{2|y_{i}-\hat{y}_{i}|}{(y_{i}+\hat{y}_{i})}\times 100\% \tag{25}\]  
\(\hat{y}_{i}\) is the predicted value of the ith sample of the test set, \(y_{i}\) is the true value of the ith sample in the test set, n is the total number of samples, \(\overline{y}\) is the average of the predicted actual values, and \(\sigma(y)\) is the standard deviation of the actual value.