# Metrics for Evaluating Synthetic Time-Series Data of Battery
## 1 Introduction  
Deep learning has recently been employed in various industries, and its applications include failure diagnosis in manufacturing [1], autonomous driving in the automotive industry [2], and battery state estimation in the energy industry [3]. Deep learning creates models through data-based learning; therefore, datasets are an essential element of deep learning. Notably, using a small training dataset can cause overfitting or underfitting problems. Moreover, the learning model accuracy decreases when many outliers are present in the training dataset. Therefore, building high-quality datasets is crucial to improve the performance of deep learning algorithms. The Kaggle and KITTI datasets [4] are representative open-source datasets used for training in deep learning algorithms. However, the availability of difficult-to-measure or specialized open-source datasets is limited. Datasets can be built through experiments or generated using generative adversarial networks (GANs). Representative data augmentation algorithms include deep convolutional GAN (DCGAN) [5], Wasserstein GAN (WGAN) [6], least squares GAN (LSGAN) [7], continuous recurrent neural network with GAN (C-RNN-GAN) [8], recurrent conditional GAN (RCGAN) [9], and time-series GAN (TimeGAN) [10]. In particular, NASA's battery dataset has a small amount of cell data measured under the same conditions (temperature, battery usage pattern, etc.) [11], so it is necessary to generate a synthetic battery dataset through an augmentation algorithm. Although a GAN algorithm can generate large amounts of battery data, it also generates abnormal data. In particular, when using the GAN-generated battery data for state of things (SoX) estimation algorithms, the accuracy of the algorithm is affected if the dataset contains an excessive amount of data with abnormal characteristics. Therefore, it is essential to evaluate the quality of synthetic datasets--i.e., their similarity to the original datasets--before using them in estimation algorithms. In general, qualitative and quantitative evaluation methods are used to evaluate synthetic datasets generated through GAN. A typical qualitative evaluation method involves visually evaluating data similarities. The similarity between the original and synthetic data is determined by experts from multiple perspectives [6; 7]. The image data are evaluated based on composite data. The time-series data are visually evaluated through a graph according to the time axis [12]. In addition, in the case of time-series data, data features are extracted and qualitatively evaluated using heat maps [13], which express the connection between the features, and dimension reduction algorithms such as t-distributed stochastic neighbor embedding (t-SNE) and principal component analysis (PCA) [10; 14] that represent samples as one point. This evaluation method has a limitation--the evaluation results are fluid, as there is no objective criterion, and reflect the subjectivity of the evaluator. The quality and diversity of the images generated through the Inception model are learned and evaluated by the Inception Score (IS) and Frechet Inception Distance (FID) [15]. Images are also evaluated using the CID Index, which reflects their creativity, inheritance, and diversity [16]. This evaluation method is generally suitable for evaluating image data (a field of computer vision) but not for synthetic battery data. Time-series data evaluation methods include quantitative evaluation through the learning of the loss rate of the GAN algorithm and the accuracy of the classification algorithm, which varies depending on the learning environment. Among the evaluation methods based on statistical techniques used for the time-series analysis, dynamic time warping (DTW) has been used to compare data similarity at various time axes [12]. Furthermore, data have been evaluated using the Euclidean and Wasserstein distances [13] between data points.