# Metrics for Evaluating Synthetic Time-Series Data of Battery
## 5 Conclusions  
In this study, we investigated methods for quantitatively evaluating the quality of synthetic time-series battery data generated using data augmentation algorithms. The existing qualitative evaluation methods (such as t-SNE based on visualization) are not suitable for battery data generated using estimation algorithms because visual evaluation methods are subjective.  
We proposed a method to quantitatively evaluate the similarity between the original dataset and the dataset generated by TimeGAN by representing the generated dataset as a two-dimensional graph using t-SNE and utilizing three evaluation metrics--the rate of change in the linear regression correlation coefficient, Dunn index for clustering, and silhouette coefficient. We also confirmed the similarity between the original and synthetic datasets through the proposed evaluation metrics.  
The rate of change in the correlation coefficient of linear regression, Dunn index, and silhouette coefficient tended to decrease as the number of iterations of the GAN algorithm increased. The rate of change in the linear regression correlation coefficient is characterized by the linearity of the data; thus, evaluation is possible even when the determination coefficient has a value of 0.7 or more. Because the Dunn index utilizes the maximum-minimum distance of the dataset, its evaluation result is accurate only when no outlier exists in the dataset distribution. The silhouette coefficient provided accurate evaluations even when some data points are distributed far apart within a cluster. Therefore, the results of the three proposed direct evaluation metrics are similar to those obtained using the existing indirect evaluation methods (training loss). Thus, the usefulness of the proposed method was confirmed. We also conclude that the silhouette coefficient is the most reliable indicator among the three proposed quantitative metrics.  
As the proposed evaluation method is based on t-SNE plot and suitable for the synthetic time-series dataset of batteries, we expect it to be utilized as a universal evaluation method for other synthetic time-series datasets.  
In the future, we will develop a comprehensive scoring system based on the correlation between the three indicators and conduct an integrated algorithm study for real-time data quality evaluation.  
Conceptualization, S.S.; methodology, S.S.; writing--original draft preparation, S.S. and J.Y.; writing--review and editing, J.L.; supervision, B.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (RS-2024-00423034, Development of 35 kW battery replaceable agricultural electrification platform technology) and Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea government (MOTIE) (RS-2024-00436689, Support for establishing reliability evaluation system for electric vehicle battery pack remanufacturing).  
Not applicable.  
The datasets generated and/or analysed during the current study are available at the NASA Open Data Portal:[[https://data.nasa.gov/Raw-Data/Randomized-Battery-Usage-1-Random-Walk/ugxu-9](https://data.nasa.gov/Raw-Data/Randomized-Battery-Usage-1-Random-Walk/ugxu-9) kjx]([https://data.nasa.gov/Raw-Data/Randomized-Battery-Usage-1-Random-Walk/ugxu-9](https://data.nasa.gov/Raw-Data/Randomized-Battery-Usage-1-Random-Walk/ugxu-9) kjx) (accessed on 6 June 2024).