# Application of Deep Learning Techniques for the State of Charge Prediction of Lithium-Ion Batteries
## 2 Research Model  
In this study, a preprocessing step was conducted to prepare the training data for the LSTM model. This step is crucial for enabling long-term learning, which is essential in time series data applications. The LSTM network structure for SOC estimation is illustrated in For SOC estimation using an LSTM network, the input data consists of voltage \(V_{t}\), current \(I_{t}\), and temperature \(T_{t}\) at time step \(t\). This causes the network to output \(SOC_{t}\), an estimate of SOC. This process can be expressed as a formula as follows. \[\text{Input: }(V_{t},I_{t},T_{t})\text{, Output: }SOC_{t}\text{,} \tag{1}\]  
A simple mathematical representation of how an LSTM network works is that the input (\(V_{t}\), \(I_{t}\), \(T_{t}\)) at each time step \(t\) is processed through an LSTM cell to calculate the SOC estimate \(SOC_{t}\) at that time step. LSTM cells have the ability to estimate SOC for new inputs while remembering information from previous time steps. This process can be expressed as a formula as shown in Equation (2) below. \[LSTM((V_{t},I_{t},T_{t}))\to SOC_{t}\text{,} \tag{2}\]  
This process is performed iteratively, resulting in an estimate of SOC for time series data. The detailed internal mechanisms of an LSTM network can be expressed in complex equations. Figure 2 is a schematic diagram of the inside of a forward-propagating LSTM cell, showing the main components of an LSTM cell: the input gate, forget gate, and output gate. Each gate controls the flow of information, and the cell state \(C_{t}\) is responsible for long-term memory. The input \(x_{t}\) and the previous hidden state \(h_{t-1}\) combine information through gates and determine which information to remember, delete, and output. The input of the forward propagation LSTM cell is the current data and the state of the previous time, and the state vector is obtained through each gate. The delete gate determines whether to keep or delete past information and has a value between 0 and 1, which is the range of the sigmoid function. Here, the closer it is to 1, the more past information is preserved. The input gate determines the information to be remembered for the current step, and like the delete gate, if it is 1, all information currently entered as an input is remembered. After passing through the LSTM cell, when it reaches the output layer, the estimated SOC is obtained using the state vector and bias. Here, the working principle of the LSTM cell for Figure 2 can be expressed by a formula. The main formula is as follows. The forget gate determines what information to discard from the cell state at a previous point in time. Here, ft in Equation (3) is the activation value of the forget gate at the current time \(t\), which determines which cell state information to keep and discard. \(\Sigma\) is a sigmoid activation function that converts to a value between 0 and 1 to control the amount of information that passes through the forget gate. \(W_{f}\) is the weight of the forget gate, which is adjusted during the learning process. \([h_{t-1},x_{t}]\) is a vector connecting the hidden state \(h_{t-1}\) at the previous time and the input \(x_{t}\) at the current time. \(b_{f}\) is the bias of the forget gate, which is adjusted during the learning process. \[f_{t}=\sigma(W_{f}[h_{t-1},x_{t}]+b_{f}) \tag{3}\]  
Figure 1: LSTM network structure for SOC estimation. The input gate determines whether new information will be stored in the cell state. Here, in Equation (4) it is the activation value of the input gate at current time \(t\), which determines how important the new input is to the cell state. \(W_{i}\) is the weight of the input gate. \(b_{i}\) is the bias of the input gate. \(\overset{\sim}{C}_{t}\) is the cell state candidate value at the current time \(t\), which determines how much new information is reflected in the cell state. \(W_{C}\) is the weight for generating cell state candidates. \(b_{C}\) is the bias for generating cell state candidates.