# Research on a Service Load Prediction Method Based on VMD-GLRT
## 2 Materials and Methods
### The Residual Structure of Long-Term Memory  
To accurately predict the future form of features under other business-aware characteristics in microservices, where the behavior of the service load is different, this paper introduces a gated neural network to extract the features of the input data, allowing the model to converge quickly. To avoid the problem of model degradation and long-term memory loss caused by depth, LSTM and the convolutional layer are combined to form the residual block. The self-attention mechanism is integrated to further improve the accuracy of prediction by enhancing the depth of the model and the correlation between the model and historical data, thus obtaining the characteristics of the load data accurately. As shown in the right-hand part of the dotted box in Figure 1.  
For each input service load data \(\left[x^{1},x^{2},\ldots,x^{n}\right]\), feature extraction is first performed through GRU, followed by residual correction through multi-layer residual blocks. The residual sequence is then learned and merged with the original sequence to obtain a more accurate result, which is then input into LSTM to receive the output result of the model. The residual connection structure diagram is shown in Figure 1 in the yellow box, while the model structure is shown in Figure 2. GRU is composed of an update gate and reset gate, and LSTM is composed of an input gate, output gate, and forget gate. This paper combines multiple GRU units to achieve preliminary model feature extraction. For any set of service load data \(\left[x^{1},x^{2},\ldots,x^{n}\right]\), it is directly input into the gating unit. Then, with the last unit output logic operation, it aims to ensure the memory of important information. Its forgetting process (Equation (10)) and memory process (Equation (11)) is expressed as follows. \[R_{t} =\sigma(X_{t}W_{xx}+H_{t-1}W_{hr}+b_{r}) \tag{10}\] \[Z_{t} =\sigma(X_{t}W_{xz}+H_{t-1}W_{hz}+b_{z}) \tag{11}\]  
where \(X\) is the service load data, \(H\) is the output of the gating unit at the last time, \(W\) is the weight value that should be questioned or remembered at the corresponding time, and \(b\) is the bias value. The memory and forgetting capabilities of the gated unit can be provided by calculation, and the results of the two will directly affect the feature extraction of the next unit. Therefore, the final processing result can be obtained by fusing the output with the hidden state. The calculation is as follows, as shown in (12):  
\[H_{t}=Z_{t}\odot H_{t-1}(1-Z_{t})+\tan\mathrm{h}\odot(X_{t}W_{xh}+(R_{t}\odot H _{t-1})W_{hh}+b_{h}) \tag{12}\]  
\(\odot\) symbol according to the elements multiplication. To improve the accuracy of the model, the results of the above calculations are fed into the residual block of the LSTM. Let the output of the upper layer network be \(\left\{y_{n}^{\prime}\right\}\) and \(H(x)\) be the desired output of the residual network, while this paper builds the following mathematical model based on the current assumptions, as shown in (13):  
\[H(x)=\left\{y_{n}^{\prime}\right\}+f(x)+x \tag{13}\]  
Figure 2: Structure diagram of GRU (**left**) and LSTM (**right**) network units. where \(f(x)\) is the residual sequence fit and \(x\) is the feature sequence of the LSTM. In the model, the characteristics of the key information should not be forgotten, so that the forgetting process can be constructed, as shown in (14). \[f_{t}=\sigma\Big{(}W_{f}\cdot[h_{t-1},x_{t}]+b_{f}\Big{)} \tag{14}\]  
Since the update gate is similar in structure to the forget gate, the only differences between the two are the weights and biases, so \(i_{t}\) can be expressed as shown in (15). Similarly, the output gate \(o_{t}\) is the same, differing only in weight and bias. While the forgotten gate is processed, the original signal is concatenated and scaled to obtain \(\widetilde{C}_{t}\), as shown in (16).