## 2 Methodology  
In this paper, by applying VMD, mRMR and DBN, a photovoltaic output prediction method based on \"decomposition-feature selection-prediction\" is formed. 1. The VMD proposed by [PERSON] in 2014 is the new kind of non-stationary signal adaptive decomposition estimation method [31], which aims to decompose the original complex non-stationary photovoltaic sequence into sub-sequences with different characteristics. Compared with wavelet decomposition, EMD decomposition and EEMD decomposition, VMD decomposition can suppress modal aliasing more effectively. 2. The mRMR was proposed by [PERSON], [PERSON]. et al. in 2005, and is a feature selection method that uses mutual information and correlation distance to calculate correlation [32]. It has the feature of maximizing the correlation between features and categorical variables, and minimizing the correlation between features and features, mainly used to solve the redundancy of feature variables. 3. DBN is a deep network efficient learning algorithm proposed by [PERSON] et al., with adaptive and self-learning capabilities, mainly used to deal with high-dimensional, large-scale data problems [33]. A DBN network consists of several layers of unsupervised restricted Boltzmann machine (RBM) and a supervised back-propagation (BP). RBM is a probability graph model consisting of visible layers and hidden layers, two layers of neurons are connected by weights. In general, visible layer units are used to describe the characteristics of data, while hidden layer units can be regarded as feature extraction layers. The structure of the RBM is shown in Figure 1.  
The BP network model classifies the features extracted by RBM, and returns the wrong information to the RBM network model, fine-tunes the parameters of the RBM network, and optimizes the DBN model. A network model of a two-tier DBN is shown in Figure 2.  
Figure 1: The restricted Boltzmann machine(RBM) model. As shown in Figure 2, a two-tier DBN network model figure, that is, after the data is input into the network, they first pass the two RBM layers, and after the output of the RBM layer, they pass through the BP layer, and the result is output after being filtered by the BP layer. On this basis, according to different needs, the RBM layer can continue to join the more layers to construct multi-layer DBN network. The VMD, mRMR and DBN have been widely applied once they are proposed, so the theory of these methods will not be repeated here. The prediction process of this paper is shown in Figure 3.  
It can be clearly seen from Figure 3 that the photovoltaic output will obtain IMFs with different fluctuation characteristics after being decomposed by VMD, and then mRMR will be used to select the component feature set \(J_{n}\) corresponding to each modal component from the feature set \(F\) consisting of meteorological factors and photovoltaic output historical values. After obtaining these component feature sets, the component feature sets and their corresponding components are simultaneously input into the DBN for prediction. Finally, the prediction values of each components are integrated using DBN to obtain the final photovoltaic output prediction value. Figure 2: A network model of a two-tier deep belief network (DBN). In this paper, after obtaining the final photovoltaic output prediction value, the average absolute error (MAE), root mean square error (RMSE) and Theil inequality coefficient (TIC) will be used as the three performance evaluation indicators of the prediction model. The calculation formula is as follows:  
\[MAE=\frac{1}{N}{\sum\limits_{n=1}^{N}{\left|{{Y_{n}}-{F_{n}}}\right|}} \tag{1}\]  
\[RMSE=\sqrt{\frac{1}{N}{\sum\limits_{n=1}^{N}{\left({{Y_{n}}-{F_{n}}}\right)^{ 2}}}} \tag{2}\]  
Figure 3: Theprediction flow figure.