## 5 Conclusions  
The short-term prediction accuracy of the nonlinear PV power time series in this work proposes a multi-frequency combined prediction model based on VMD mode decomposition. Specifically, the following was observed:  
(1) For the first time, this paper introduces the VMD method into PV power plant output forecasting, decomposes the unstable PV output sequence, and conducts in-depth research on the characteristics of VMD. When traditional decomposition methods deal with sequences that contain both trend and wave terms, accurately extracting the shortcomings of the trend items is impossible. A combination method based on VMD-ARMA-DBN is proposed, which not only reflects \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Evaluation Index** & **\(\mathbf{e_{\text{NMAE}}}\)** & **\(\mathbf{e_{\text{NRMSE}}}\)** & **TIC** \\ \hline ARMA & 3.74146 & 7.17435 & 0.11359 \\ DBN & 3.19754 & 6.43502 & 0.10139 \\ RNN & 3.21145 & 6.548871 & 0.10328 \\ GBDT & 3.27612 & 6.434691 & 0.10812 \\ EMD-ARMA-DBN & 2.11062 & 3.49985 & 0.05456 \\ EEMD-ARMA-DBN & 1.35409 & 2.67181 & 0.04171 \\ DWT-RNN-LSTM & 1.48241 & 2.74976 & 0.04265 \\ VMD-ARMA-DBN & 1.03374 & 2.05776 & 0.03201 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Forecast results for each model. the development trend of the size of PV output, but also decomposes the fluctuation series into a set of less complex and some strong periodical parameters, which greatly reduced the difficulty of prediction. (2) If the VMD cannot restore the original sequence completely, and cannot determine the number of decomposition layers automatically, we propose a method to determine the number of VMD decomposition layers via a spectrum analysis, which can restore the original sequence to a large extent and ensure the stability of the component. First, according to the spectrum diagram of the sample data, we determined the number of modal components. If the overlapping phenomenon occurred in the center frequency iteration curve, the number of decompositions was selected and divided into high- and low-frequency components according to the characteristics of the different components. ARMA and DBN were used to simulate and predict high-frequency and low-frequency components. Then, the predictive value of each component was determined using DBN. Each one had a strong nonlinear mapping ability, and high self-learning ability and self-adaptive capability. The sample data of each component was taken as input, and the actual PV sample value was used as an output to train the model. Then, the predicted value of each component was used as input for the prediction. Finally, the PV output predicted value was obtained. (3) To test the prediction effect of the VMD combinatorial model, the normalized absolute mean error, normalized root-mean-square error, and the Hill inequality coefficient were used to compare the single prediction models with the combined prediction models. The simulation results show that the different decomposition methods have been improved to varying degrees in terms of forecast accuracy. Thus, the VMD-ARMA-DBN model proposed in this work offers better accuracy and stability than the single prediction methods and the combined prediction models. In the prediction process, we found that although the VMD improved the phenomenon of modal aliasing and false components, it was not eliminated. In addition, the DBN's component-RBM needs to be further improved. The weight and offset of each layer of RBM are initialized during training. Therefore, even if the number of hidden layer nodes is compared and selected, the optimal model cannot be obtained, and the final prediction result will show diversification; that is, the same model yields different results, and to obtain optimal results, it is necessary to train the model multiple times, which makes the workload cumbersome. The above deficiencies inevitably increase the errors in the prediction process of each component and affect the final prediction results.