# Research on a Service Load Prediction Method Based on VMD-GLRT
## 2 Materials and Methods  
### Model Building  
In this paper, the result is assumed to be the output of a model component, with the load data decomposed into n components with a total of t features. The problem model is then formulated as (1) through formal description:  
\[result_{i}^{t}=\text{model}\left(y_{i}^{t}-\sum_{i=1}^{n}IMF_{i}^{t}\right)+ \sum_{i=1}^{n}p_{i}^{t} \tag{1}\]  
Service load is affected by many factors, with \(y_{i}^{t}\) representing the actual load data and \(IMF_{i}^{t}\) representing the component data, a part of the original data, after mode splitting. The component data are the result of the VMD decomposition, which represents a component of the original data, and we will refer to the VMD decomposition several times later when we discuss the VMD mode decomposition. The difference between the two is the residual sequence of the actual data. Since the components after modal decomposition cannot be entirely consistent with those before deterioration after merging, the difference between the accurate data and the sum of each component is regarded as the residual sequence of the load data and sent to the model for prediction. The prediction results of each other element are represented by \(p_{i}^{t}\), and the service load value at the next time point can be obtained by summing up the prediction results of all components, including the residual sequence.  
The model utilizes the fast convergence ability of GRU and the prediction accuracy of LSTM to accurately extract the service's load characteristics by decomposing the input signal into multiple variables using VMD. The overall structure of the model is shown in the following figure:  
The model takes \(\left[x^{1},x^{2},\dots,x^{n}\right]\) as input, where \(n\) is the number of feature vectors. Variational mode decomposition, feature extraction, and feature fusion are then applied to the input, resulting in the output of the corresponding prediction result sequence \(\left[y^{1},y^{2},\dots,y^{n}\right]\). Before the data can be input into the GRU, they need to be modally decomposed, as shown in the dashed box in Figure 1. The steps of the model processing are as follows:  
Firstly, the input data are preprocessed to form the initial input matrix \(\left[x^{1},x^{2},\dots,x^{n}\right]\), and the corresponding multivariate matrix of the data is obtained by modal decomposition for the single variable of the input data. The formal expression is shown as Equation (2), where n is the number of components and m is the dimension of the feature vector.  
Secondly, the variables after the modal decomposition of each variable are recombined according to the order of the components of the modal decomposition to form the input features. Then, the GRU is used for feature extraction, and then the residual block based on LSTM is corrected and sent to LSTM to obtain accurate prediction results.  
Finally, the correlation distance between each component is shortened through the self-attention mechanism, and the correlation relationship between each element is fully extracted. The final prediction sequence \(\left[y^{1},y^{2},\dots,y^{n}\right]\) can be obtained through feature fusion. The relevant details are presented in the following, where 2.2 is the modal decomposition process and 2.3 is the prediction process.  
\[A_{n\times m}=\left[\begin{array}{c}IMF_{1}\\ IMF_{2}\\ \dots\dots\\ IMF_{n-1}\\ IMF_{n}\end{array}\right]=\left[\begin{array}{ccc}a_{11}&\cdots&a_{1m}\\ \vdots&\ddots&\vdots\\ a_{n1}&\cdots&a_{mm}\end{array}\right] \tag{2}\]