# A Data-Driven Battery Degradation Estimation Method for Low-Earth-Orbit (LEO) Satellites
## 4 Experiments and Results  
To verify the convergence of the modeling performed in this study, an analysis was conducted using the satellite's on-orbit data. Figure 10 presents the results of estimating the battery voltage of the KOMPSAT-5 satellite during the on-orbit charge and discharge cycles using the transformer network developed in this study. The upper graphs are based on data from 10 June 2023, whereas the lower graphs are based on data from 10 December 2022; both compare the actual battery voltage with the values estimated by the transformer network. The development environment used for this modeling was a single Nvidia GeForce 4090 GPU and a PyTorch-based deep learning framework (Python 3.8, PyTorch 1.13.0, CUDA 11.7). The training process, which spanned approximately six months, required around four days to complete. Additionally, the voltage generation time for nine orbits (approximately 920 min) was independent of the training data and took approximately 110 s.  
In general, satellite batteries do not age abruptly, necessitating strategies for reducing the burden on a satellite's throughput. Therefore, we aimed to analyze satellite data to determine the optimal timing for updating battery aging factors. Using a DNN-based approach, the aging state of the satellite battery was assessed on the ground, and the satellite's charge-discharge state model was updated accordingly. The development environment was structured as described in order to achieve this objective. The results demonstrate that the estimated values closely match the actual values, even in the nonlinear environment with repeated charge and discharge cycles. The model accurately captured even subtle voltage variations, indicating the transformer network's high reliability in battery voltage estimation. From a temporal perspective, the transformer network consistently exhibited excellent performance in estimating battery voltage, regardless of the timeframe or environmental conditions in which the data were collected. Figure 9: Results of the analysis of the cost function based on variations in the transformer layer and embedding dimensions. Additionally, data generated after the satellite's launch were used for training in different time periods; subsequently, the prediction results were analyzed. Table 2 summarizes the predicted voltage variation profiles for mission periods based on a daily scale using the proposed model. To observe long-term trends after the launch in 2013, analyses were conducted at two-year intervals. The daily prediction period was chosen as a baseline for convergence and profile generation analysis, as it ensures a minimum ground contact time, considering the typical satellite orbit. For training, data obtained up to one week before the modeling date were utilized. Consequently, the results in Table 2 allow for an assessment of the prediction error in mission periods based on the data duration used in the modeling. The table shows that the error did not exhibit significant variation with an increase in operational time except for the very first phase after launch, indicating that the error had converged. Additionally, to compare and analyze the results of the proposed voltage variation prediction method, modeling was performed using a probability-based Autoregressive Integrated Moving Average (ARIMA) model and a Bi-directional Long Short-Term Memory (Bi-LSTM) network. Both ARIMA and Bi-LSTM networks are widely used tools for time-series modeling [24; 25]. The comparison was conducted based on key performance metrics, including mean error, maximum error, and processing time. Figure 10: Battery prediction results for the KOMPSAT-5 satellite: (**a**) on-orbit current profile (10 June 2023); (**b**) voltage prediction results (10 June 2023); (**c**) on-orbit current profile (10 December 2022); and (**d**) voltage prediction results (10 December 2022).