## 2 SSA-SVR Prediction Model
### Principle of SSA-SVR Prediction Model  
The principle of the support vector regression algorithm for the optimization of the Sparrow Search Algorithm (SSA-SVR) is to set the fitness value of the Sparrow Search Algorithm (SSA) to the Mean Square Error (MSE) of the support vector regression algorithm and then to search for the combination of C and \(\gamma\), which makes the fitness value optimal through a number of iterations. Moreover, the use of the found optimal values of C and \(\gamma\) train the Support Vector Regression (SVR) algorithm to make the support vector regression algorithm perform better [23; 24]. Therefore, the dimension of the sparrow population in the sparrow search algorithm is two. When the model training is completed, the performance of the model can be evaluated by the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the coefficient of determination (R\({}^{2}\)), and the formula is calculated as follows:  
\[RMSE=\sqrt{\frac{1}{m}{\sum\limits_{i=1}^{m}{{{(y_{i}-\hat{y_{i}})}^{2}}}}} \tag{12}\]  
\[MAE=\frac{1}{m}{\sum\limits_{i=1}^{m}{{{\left|{y_{i}-\hat{y_{i}}}\right|}}}} \tag{13}\]  
\[R^{2}=1-\frac{{\sum\limits_{i=1}^{m}{{{(y_{i}-\hat{y_{i}})}^{2}}}}}{{\sum \limits_{i=1}^{m}{{{(y_{i}-\overline{y})}^{2}}}}} \tag{14}\]  
The Root Mean Square Error (RMSE) is a square root operation based on the average of the sum of the squares of the errors between the true and predicted values, i.e., the Mean Square Error (MSE), which is easier to interpret and understand than the mean square error because the unit of the RMSE is the same as the unit of the sample data. As a result of the squared term, the root mean square error is more sensitive to large errors and better captures the model's performance around extreme values, with a tendency to amplify larger errors; however, it is also, therefore, more susceptible to disturbances from very small anomalies in the data. The Mean Absolute Error (MAE) is the average of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Sign** & **Meaning** \\ \hline \(X_{ij}^{t}\) & The position of the \(i\)-th sparrow in the \(j\)-th dimension in the \(t\)-th iteration \\ \(\alpha\) & Random numbers in [0,1] \\ \(ST\) & Safe value, constant within (0.5,1] \\ \(L\) & unit matrix \\ \(X_{p}\) & Current optimal finder position \\ \(A^{+}\) & \(A^{+}=A^{T}(AA^{T})^{-1}\) \\ \(\beta\) & Random numbers that follow a normal distribution with mean 0 variance 1 \\ \(f_{i}\) & Current individual fitness value \\ \(f_{m}\) & Current global worst fitness value \\ \(iter_{\max}\) & Maximum number of iterations \\ \(R_{2}\) & Early warning value, random number within [0,1] \\ \(Q\) & Random numbers, normally distributed. \\ \(X_{\text{norm}}^{t}\) & Global worst position in the tht iteration \\ \(A\) & Matrices(1 \(\times\)\(d\)), element is a randomly assigned 1 \(\pm\) 1 \\ \(X_{\text{best}}^{t}\) & Global optimal position in tht iteration \\ \(K\) & [\(-\)1,1] Random numbers to control the sparrow’s movement in steps and direction. \\ \(f_{g}\) & Current global best fit value \\ \(\varepsilon\) & Minimum constant to avoid 0 in the denominator \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of sparrow search algorithm parameters. absolute values of the prediction errors, which is simple to calculate and less susceptible to interference from anomalous data but does not provide a better representation of the prediction effect of the data near extreme values. Therefore, the results of both are usually combined to evaluate the merits of the model training. The coefficient of determination (R\({}^{2}\)) is an indicator used to measure the goodness of fit of a regression model. Its value ranges between 0 and 1, where a value closer to 1 indicates a better fit of the model to the data, and a value closer to 0 indicates a poorer fit.