# Metrics for Evaluating Synthetic Time-Series Data of Battery
## 4 Results and Analysis
### Application of the Proposed Evaluation Method  
After representing the original and synthetic datasets generated through TimeGAN in low dimensions using t-SNE, we calculated the Dunn index, silhouette coefficient, and rate of change in the correlation coefficient of the linear regression between the two dataset clusters. The t-SNE plot of the dimensionally reduced time-series data is shown in Figure 5. In this figure, the black and red points represent the original and synthetic data, respectively. Through t-SNE, the similarity of data based on the number of learning iterations can be partially evaluated. When the original and synthetic battery datasets are distributed close together, the similarity is evaluated as high. However, it is difficult to objectively confirm the similarity when comparing t-SNE plots in which the difference is not visually evident. Different evaluators may consider different parts to be similar, and the evaluation is likely based on individual subjectivities. \begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristic/Parameter** & **Value** \\ \hline Battery properties & 18,650 LIBs \\ Chemistry & 18,650 lithium cobalt oxide vs. graphite \\ Nominal capacity & 2.10 Ah \\ Capacity range & 0.80–2.10 Ah \\ Voltage range & 3.2–4.2 V \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data specifications for battery. Figure 4: Process of battery cycles. Furthermore, the similarity of battery data can be evaluated using learning loss as shown in Figure 6; this is the most widely used quantitative evaluation method. However, the loss varies depending on the learning environment, and it is difficult to compare loss values when the learning environments differ. Therefore, the proposed evaluation method objectified the similarity of the synthetic dataset through quantitative and qualitative evaluation, as shown in Figure 7 and Table 2. To ensure the reliability of the quantitative indicator, it was compared with the learning loss calculated in the same learning environment. In general, as shown in the Figure, as the number of learning iterations of the data augmentation algorithm increases, the learning loss decreases, and the synthetic dataset further reflects the characteristics of the original dataset. Figure 5: t-SNE plot. Figure 6: Training loss based on the number of iterations. First, the similarity between the original and composite datasets was determined using the rate of change in the correlation coefficient by comparing the linear relationship of the data using linear regression in t-SNE. Before judging the similarity, it was confirmed that the linear regression equation could sufficiently explain the data using the determination coefficient. If the determination coefficient was sufficient (0.7 or more), the similarity of the data was confirmed using the rate of change of the correlation coefficient. In Figure 7, the linear regression is indicated using a solid line for 1000 and 10,000 iterations, for the determination coefficient of 0.7 or more. The solid black line is the linear regression for the original dataset, and the solid blue line is the linear regression for the dataset comprising the composite and original datasets. When the number of iterations is 100, evaluation is difficult because linear characteristics do not appear. When the number of iterations is 1000 or more (as listed in Table 2), the rate of change in the correlation coefficient decreases as the number of iterations increases; consequently, a composite dataset close to the original dataset is generated. The rate of change of linear regression correlation coefficient is characterized by linearity in data characteristics; therefore, evaluation is possible only when the determination coefficient is greater than or equal to 0.7, and the evaluation is  
Figure 7: t-SNE according to iteration on RW9 (1 st row), RW10 (2 nd row), RW11 (3 rd row) and RW12 (4 th row).