## 5 Experimentation and Analysis
### Analysis of Experimental Arithmetic
#### 5.4.2 Comparison Results of the MODBO in Load Data  
In order to further validate the dung beetle algorithm for multi-strategy optimization, this study applies the MODBO to the power forecasting of real power loads, and it is compared with the fruit fly optimization algorithm, the grey wolf optimization algorithm, the sparrow optimization algorithm and the dung beetle algorithm. In order to avoid chance errors, data from four seasons are used for the experiment. The comparison results are shown in Figure 4.  
As shown in Figure 4, the MODBO algorithm converges faster than the traditional intelligent algorithms and has better adaptability for the same number of iterations. After 100 iterations, the final adaptation value of the MODBO algorithm is lower than that of the various intelligent algorithms compared. Thus, it can also be verified that the MODBO algorithm proposed in this study converges faster, has better stability, has lower final adaptation values, and has better performance compared to traditional intelligent algorithms. The effectiveness of VMD depends on the choice of parameters. Among them, the penalty factor \(\alpha\) is a balancing parameter that controls the decomposition integrity and  
Figure 4: Comparison plot of the convergence curves of different optimization algorithms. Figure 3: Comparison plot of the convergence curves for different test functions. the loss of band information. If the chosen value of a is too high, it will lead to the loss or redundancy of band information. Therefore, the optimal combination of parameters \(\left[\text{K},\,\alpha\right]\) must be found to avoid over- or under-decomposition. Currently, the center frequency observation technique is used to find the optimal value of K. However, this method can only detect the number of formats K and not the penalty factor \(\alpha\). In general, the penalty factor \(\alpha\) is in the range of 1000-3000, with a usual value of 2000.The four-season VMD obtained by the center-frequency method is shown in Figure 5.  
Table 1 shows the results of using the MODBO algorithm to determine the K-value and the center frequency method to identify the VMD. Figure 5 shows the effect of VMD. From left to right, the decomposition is performed for spring, summer, autumn, and winter for the data selected for these four seasons. The graph shows the modal number K of the decomposition calculated by applying the center frequency method, which is used to determine the IMF component for each season. The first graph for each season is the raw data for that season, respectively. For example, spring has five IMF components and summer has six IMF components. These IMFs (intrinsic mode functions) are obtained by solving a variational problem in order to make the bandwidth of each mode as small as possible. In a VMD, each IMF represents a specific frequency component of the signal, usually in the order of frequency from highest to lowest. Specifically, IMF1 is the first mode obtained from decomposition and usually contains the highest frequency component in the signal. It captures fast-changing parts of the signal, such as noise or high-frequency oscillations. IMF2 is the second mode, usually lower in frequency than IMF1. It may represent the next highest frequency component of the signal, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Season** & **K (MODBO)** & **\(\mathbf{\alpha}\) (MODBO)** & **K** & **\(\mathbf{\alpha}\)** \\ \hline Spring & 11 & 292 & 5 & 2000 \\ Summer & 10 & 100 & 6 & 2000 \\ Autumn & 8 & 223 & 5 & 2000 \\ Winter & 8 & 110 & 5 & 2000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Decomposition results of the VMD for each season. Figure 5: VMD effect diagram. capturing smoother, but still relatively fast, changes than IMF1. As the third mode, IMF3 is usually lower in frequency than both IMF1 and IMF2, and it may contain the more fundamental signal trends or cyclical components. The exact meaning and significance of each IMF depends on the characteristics of the original signal and the purpose of the analysis.