# A modified TimeGAN-based data augmentation approach for the state of health prediction of Lithium-Ion Batteries

Soufian Echabarri, Phuc Do, Hai-Canh Vu, Pierre-Yves Liegeois

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Soufian Echabarri, Phuc Do, Hai-Canh Vu, Pierre-Yves Liegeois. A modified TimeGAN-based data augmentation approach for the state of health prediction of Lithium-Ion Batteries. Reliability Engineering and System Safety, 2025, 264 (Part A), pp.111297. 10.1016/j.ress.2025.111297. hal-05112195

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Submitted on 4 Nov 2025

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# A modified TimeGAN-based data augmentation approach for the state of health prediction of Lithium-Ion Batteries

Soufian Echabarri a,*, Phuc Do a,b, Pierre-Yves Liegeois c

## ARTICLE INFO

**Keywords:**

Lithium-ion batteries

Data augmentation

Generative adversarial network

State of health

Machine learning

## ABSTRACT

Lithium-ion batteries are critical components of zero-emission electro-hydrogen generators (GEH2), where accurate performance prediction is essential for ensuring optimal operation and enabling effective predictive maintenance. Data-driven models have become increasingly prominent for predicting the State of Health (SOH) of lithium-ion batteries due to their high accuracy and reduced development time. However, in hybrid systems like GEH2, where the battery frequently remains inactive while the fuel cell supplies most of the power, the available battery data is limited. This data scarcity presents a significant challenge for achieving accurate SOH prediction. To address this challenge, we propose a novel data augmentation approach that integrates Time-series Generative Adversarial Network with a Transformer and a Gated Recurrent Unit to enhance data availability and improve prediction accuracy. This new approach enhances the model's ability to capture long-term temporal dependencies within multivariate battery parameters while effectively addressing irregular time intervals, a common challenge in real-world batteries datasets. We evaluated the proposed approach using real-world industrial datasets from four distinct GEH2 batteries and two additional batteries from the publicly available NASA dataset. The performance of SOH prediction was assessed using a Long Short-Term Memory (LSTM) model trained on augmented data generated by various data augmentation techniques. The results consistently demonstrate that our approach outperforms all competing methods, highlighting its superior ability to enhance data for lithium-ion batteries. These findings highlight the effectiveness of our approach in enhancing predictive accuracy and robustness, making it highly suitable for real-world battery applications.

## 1. Introduction

Renewable fuels are crucial in today's energy mix and are increasingly adopted due to new energy policies aimed at significantly reducing greenhouse gas emissions. Among these technologies, fuel cells, particularly proton exchange membrane fuel cells (PEMFCs), offer an efficient and clean method for converting chemical energy into electrical energy [1,2]. In this context, Energy Observer Development (EODev) is dedicated to advancing the use of renewable fuels, especially hydrogen, as an energy carrier to promote a low-carbon society by proposing the zero-emission electro-hydrogen generator (GEH2). As a critical component of the GEH2 system, accurately estimating the battery's State of Health (SOH) is vital for maintaining optimal performance and ensuring the system's reliability.

According to recent review papers [3,4], the prediction methods for batteries' SOH can be divided into two primary categories: model-based approaches and data-driven approaches. Model-based techniques,

which include equivalent circuit models, electrochemical models, and mathematical models, aim to simulate battery performance parameters to understand degradation mechanisms and the progression of failures in lithium-ion batteries. While these methods can achieve high prediction accuracy in specific contexts, their applicability in real-world scenarios is often constrained, particularly in relation to the novel GEH2 from EODev. This limitation stems from the variations in degradation patterns experienced under dynamic conditions, as well as the complexity of the underlying degradation processes, which remain to be fully understood.

Conversely, data-driven approaches focus on exploring degradation mechanisms through a data-centric perspective, leveraging advanced algorithms such as artificial neural networks (ANN), support vector machines (SVM), relevance vector machines (RVM), and particle filters (PF) [5]. These methods are widely applied as among the most robust and effective for SOH prediction, thanks to their high accuracy and

<footnote>a Université de Lorraine, CNRS, CRAN, F-54000 Nancy, France</footnote>

<footnote>b Université de Technologie de Compiègne, Laboratoire Roberval, 60203 Compiègne, France</footnote>

<footnote>c Energy Designer and IT, EODev, 92130, Paris Region, France</footnote>

<footnote>* Corresponding author.
E-mail address: phuc.do@univ-lorraine.fr (P. Do).</footnote>
efficiency. However, they generally require large datasets for effective training. In the context of the GEH2 system, where the battery frequently remains inactive while the fuel cell provides the majority of the power, the available data for the battery is limited. This data scarcity presents a significant challenge to achieving accurate SOH predictions using conventional data-driven techniques.

To address this challenge, we propose in this work an advanced data augmentation model based on the Time-series Generative Adversarial Network (TimeGAN) [6]. The proposed approach enhances the original TimeGAN by replacing its generator with a Transformer-based architecture, which is further integrated with a Gated Recurrent Unit (GRU). This enhancement enables the model to more effectively capture long-term temporal dependencies across multivariate parameters [7]. The performance of the proposed data augmentation approach is then investigated through real-world datasets from four distinct GEH2 batteries and two additional batteries from the publicly available NASA dataset. Furthermore, the accuracy of SOH prediction using a Long Short-Term Memory (LSTM) network [8] is also examined. Indeed, the LSTM model is trained on augmented data generated through several widely-used data augmentation techniques from the literature. The results demonstrate that the proposed approach significantly improves prediction quality compared to both the original non-augmented data and conventional existing data augmentation techniques.

The remainder of this paper is organized as follows: Section 2 reviews existing literature on battery SOH prediction and data augmentation techniques, highlighting the key contributions of this study. Section 3 provides a detailed description of the dataset utilized in our research. Section 4 presents the proposed data augmentation approach, elaborating on its architecture and methodology. Section 5 describes the validation process of the proposed approach and introduces the benchmark methods used for comparison. Section 6 assesses the model's performance using data from four distinct GEH2 batteries and two NASA batteries, and benchmarks it against other data augmentation methods. Finally, Section 7 summarizes the conclusions drawn from this research.

## 2. Related work and scientific contributions

In this section, we review the existing literature on battery SOH prediction and battery data augmentation to identify research gaps and highlight the scientific contributions of this study.

### 2.1. Data-driven approaches for battery SOH prediction

The evaluation of the State of Health (SOH) and the capacity degradation of batteries is critical for ensuring the reliability and safety of battery systems, particularly in applications such as the GEH2 system. Historically, SOH assessment has relied on experimental methods and model-based approaches, which often require substantial experimentation or intricate battery models. However, the emergence of data-driven models employing machine learning (ML) and deep learning (DL) techniques has transformed SOH assessment, providing more flexible and potentially more accurate solutions without necessitating an in-depth understanding of the internal mechanisms of batteries [9]. For instance, Liu et al. [10] utilized Gaussian Process Regression (GPR) to predict the lifespan of lithium-ion batteries, successfully capturing the uncertainty within these predictions. Jia et al. [11] advanced this by integrating indirect health indicators from voltage, current, and temperature profiles with GPR, enabling robust SOH prediction without direct capacity measurements. Their method employed grey relational analysis to select features, achieving high accuracy across NASA datasets.

Further advancements are noted with [12], who explored a deep learning strategy for predicting lithium-ion battery capacity utilizing a Long Short-Term Memory (LSTM) recurrent neural network, designed to capture latent long-term dependencies in the degraded capacity.

Expanding on LSTM architectures, Jin et al. [13] developed a hybrid model pairing LSTM with XGBoost, optimized via a binary firefly algorithm for feature selection. This framework leveraged time-series forecasting of health indicators to enhance RUL prediction stability, demonstrating superior performance on NASA datasets.

Che et al. [14] presented a framework aimed at predicting critical metrics such as battery knee, lifetime, SOH degradation, aging rate variations, and overall health. This methodology employs early information to forecast knee slope and other life-related metrics through deep multi-task learning and a convolutional-long-short-term memory-Bayesian neural network. The design also supports real-time SOH and degradation rate predictions to identify accelerating aging. Complementing multi-task learning, Yang et al. [15] proposed a Grouped Board Learning System (GBLS) Booster model integrating Convolutional Neural Network (CNN) and Transformer architectures. This approach unified SOH estimation and RUL prediction through feature importance extraction and time-series learning.

The reliability and accuracy of long-term prognostic schemes for monitoring performance degradation and predicting the Remaining Useful Life (RUL) of lithium-ion batteries are further exemplified by Li et al. [16], who utilized an information fusion methodology, creating an interacting multiple model framework that integrates particle filter and support vector regression for multi-step-ahead capacity and RUL prediction. In the context of battery prognostics, Nagulapati et al. [17] investigated various data-driven approaches aimed at enhancing RUL prediction, utilizing Gaussian Process Regression (GPR) and Artificial Neural Networks (ANN) to tackle the challenges posed by the nonlinear characteristics and limited sample sizes inherent to lithium-ion batteries.

### 2.2. Battery data augmentation

Data-driven methodologies are increasingly utilized to estimate the SOH of lithium-ion batteries. The effectiveness of these approaches, however, is significantly influenced by the quality and quantity of the available data, with inadequate data often resulting in diminished prediction accuracy. To mitigate this issue, several studies have investigated data augmentation techniques. For instance, Fan et al. [18] introduced a method for augmenting lithium battery data through the addition of random noise, which was subsequently employed with LSTM and GRU networks for SOH prediction. In another study, Kim et al. [19] implemented the Dynamic Time Warping (DTW) approach to enhance run-to-failure data obtained from varied operational conditions. This modified dataset was then used to train a neural network model aimed at predicting the remaining service life of the system. Pyne et al. [20] combined measured operational data from battery packs to generate synthetic datasets using a combination of Markov chains and neural networks, specifically designed for estimating SOH based on real-world operational drive cycle data. Pohlmann et al. [21] utilized a linear regression model along with multilayer perceptron and convolutional neural network architectures to estimate the state of charge of a battery cell. These models were trained on varying amounts of artificially generated data to enhance predictive accuracy.

Lin et al. [22] proposed a novel method for predicting battery degradation by leveraging synthetic datasets and deep learning techniques. They employed a transferred convolutional neural network (CNN) for early-stage health prediction of lithium-ion batteries, creating a synthetic data generation strategy based on polynomial functions to reduce the need for extensive real-world data collection. Gao et al. [23] introduced an innovative data augmentation technique utilizing quantum assimilation to improve the accuracy of SOH predictions for lithium-ion batteries exhibiting unique degradation patterns. Guo et al. [24] applied a Variational Auto-Encoder for data augmentation and a temporal convolutional network to estimate the SOH.

Additionally, Hu et al. [25] presented a time series augmentation model that capitalizes on a deep convolutional generative adversarial
<table><caption>**Table 1**
Applicability of recent research works and the proposed method.</caption><thead><tr><th>References</th><th>Temporal dependencies capturing</th><th>Irregular data handling</th><th>Dynamic operating conditions</th><th>Battery in hybridization</th><th>Real dataset</th></tr></thead><tbody><tr><td>Fan et al. [18]</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Kim et al. [19]</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Pyne et al. [20]</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>Pohlmann et al. [21]</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>Lin et al. [22]</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Gao et al. [23]</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Guo et al. [24]</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Hu et al. [25]</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>Zhang et al. [26]</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Naaz et al. [28]</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Naaz et al. [27]</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td><strong>Proposed method</strong></td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></tbody></table>

network (GAN) framework. By recasting the data generation challenge into an image generation task, this approach leverages advancements in GAN-based image generation techniques to produce high-quality battery data. Zhang et al. [26] proposed a convolutional recursive GAN designed for the self-generation of multivariate time series data. This model effectively extracts significant spatial and temporal information through a two-channel fusion generator, integrating CNN and LSTM architectures.

Finally, the TimeGAN model, as demonstrated by Naaz et al. [27, 28], is employed to generate high-fidelity and diverse battery profile data, including parameters such as voltage, current, temperature, and state of charge (SOC).

## 2.3. Limits of existing models and scientific contributions

Based on the literature review above, existing approaches for predicting SOH of batteries with limited data exhibit several notable shortcomings:

* Many current methods are inadequate in capturing the complex temporal dependencies present among multivariate battery parameters. This oversight is critical for accurate SOH predictions, as time series data from batteries often display intricate temporal relationships that must be effectively modeled;

* Most data augmentation techniques assume that time series data are collected at regular intervals. However, in real-world applications, data often exhibit irregular time intervals, presenting significant challenges for time series analysis. In the context of GEH2 systems, data acquisition issues can result in gaps, leading to irregularly spaced data points. This irregularity is typical in real-world battery datasets, where measurements are not consistently recorded. Models that presuppose regular intervals, such as TimeGAN, may fail to account for important variations in the data, thereby compromising the accuracy of SOH predictions;

* While some studies focus on capturing temporal dependencies among multivariate parameters, they are often designed for specific environments and lack the flexibility to generalize across diverse operational contexts. This limitation reduces their applicability to systems like GEH2, where batteries function under highly dynamic conditions and demand models capable of handling irregular data;

* A significant number of models have been validated using experimental datasets that do not accurately reflect the complexities of real-world scenarios. This reliance diminishes the practical effectiveness of these models when applied to real-life situations, reducing their robustness and scalability.

The findings of this literature review on existing data augmentation models are reported in Table 1.

Given the limitations above, our proposed method addresses these challenges by introducing an innovative data augmentation approach

that captures long-term temporal dependencies within multivariate battery parameters and effectively handles irregular time series data, two critical issues in real-world battery monitoring. The model's effectiveness is validated using both industrial GEH2 data and publicly available NASA datasets, demonstrating its robustness and broad applicability. The main contributions of this paper are as follows:

1. We introduce a novel data augmentation model based on TimeGAN that modifies the original architecture by replacing its generator with a Transformer-based design followed by a Gated Recurrent Unit (GRU). This new approach enhances the model's ability to capture long-term temporal dependencies within multivariate battery parameters while effectively managing irregular time intervals, a common challenge in real-world datasets like those from GEH2 batteries;

2. We evaluate the proposed model using a complex industrial dataset provided by EODev, consisting of four GEH2 batteries operating under heterogeneous conditions, including hybridization with fuel cells. Additionally, we include two publicly available NASA batteries to assess the model's generalizability across different battery technologies and operational profiles. As a result, the proposed model demonstrates versatility and adaptability across different real-world operational scenarios, making it a robust solution for a wide range of applications, including GEH2 systems;

3. We conduct a comprehensive comparison between the proposed approach, the original TimeGAN, and several state-of-the-art data augmentation techniques, including advanced deep learning-based methods. The results consistently demonstrate that our approach outperforms all competing models, confirming its effectiveness and superiority in generating high-quality synthetic data for lithium-ion batteries. This highlights the strength of our method in enhancing predictive accuracy and ensuring robustness in real-world battery applications.

# 3. System description and dataset

## 3.1. Zero-emission electro-hydrogen generator (GEH2)

The GEH2, depicted in Fig. 1, is distinguished as the most compact and efficient commercially available hydrogen generator in terms of power output. This system primarily comprises PEMFCs that operate on dihydrogen, along with a 44 kWh battery. The integration of a battery is essential in the GEH2 system, as PEMFCs exhibit a relatively slow dynamic response. By combining a fuel cell with a battery during high-power demand periods, performance can be significantly enhanced [29], the service life of the PEMFC can be optimized, and customer requirements can be met. This integration not only ensures optimal performance but also extends the longevity of the system's critical components.
<figure><img src="image_4.png" /><figcaption>Fig. 1. Zero-emission electro-hydrogen generator [30].</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. Power management diagram in a battery-fuel cell GEH2 hybrid system based on power demand.</figcaption></figure>

In the GEH2 system, a fuel cell and a battery operate together in an active hybrid mode to efficiently manage power supply (see Fig. 2). This system adjusts to varying power demands by considering the battery's state of charge (SOC), as illustrated in Fig. 2. Decisions are made by comparing the power demand against predefined thresholds (Pmin and Pmax) and the battery's SOC against a threshold (BTH). Below, we explain how the hybrid system manages energy in various scenarios, as depicted in Fig. 2.

### When power demand is less than Pmin

- The fuel cell remains inactive, providing no power.

- The battery alone supplies the entire power requirement.

In this case, for low power demands below Pmin, the battery handles all the energy needs, allowing the fuel cell to stay off and conserve resources.

### When power demand is between Pmin and Pmax

- If the battery is fully charged, the fuel cell and the battery provide the required power.

- If the battery's state of charge (SOC) is below BTH, the fuel cell not only supplies the power demand but also generates additional power to charge the battery.

In this range of power demand, if the battery is fully charged, the fuel cell can supply the necessary power directly, with the battery assisting if additional power is required. When the SOC is below BTH, the fuel cell takes on the dual role of meeting the immediate power demand while also generating extra power to replenish the battery.

### When power demand exceeds Pmax

- The fuel cell operates at its maximum output capacity of Pmax.

- The battery provides the additional power needed to meet the total demand beyond what the fuel cell can supply.

In this case, for high power demands above Pmax, the fuel cell operates at its maximum capability, while the battery covers the shortfall. This setup ensures that the system can meet substantial power requirements by leveraging the strengths of both components.

This hybrid approach in the GEH2 system balances the load between the fuel cell and the battery, optimizing performance and extending the operational life of both components. By dynamically adjusting the power distribution based on the current demand and battery SOC, the system ensures efficient energy management and reliable operation (see Fig. 3).
<table><caption>**Table 2**
Comparison of operational parameters and environmental conditions for the GEH2 batteries.</caption><thead><tr><th>Battery</th><th>Location</th><th>Temp Max (°C)</th><th>Temp Min (°C)</th><th>Current Max (A)</th><th>Current Min (A)</th><th>Voltage Max (V)</th><th>Voltage Min (V)</th><th>DoD (%)</th></tr></thead><tbody><tr><td>B1</td><td>Norway</td><td>32</td><td>5</td><td>3</td><td>-8</td><td>686</td><td>571</td><td>25</td></tr><tr><td>B2</td><td>France</td><td>32</td><td>8</td><td>3</td><td>-21</td><td>690</td><td>363</td><td>33</td></tr><tr><td>B3</td><td>Netherlands</td><td>32</td><td>10</td><td>6</td><td>-5</td><td>678</td><td>192</td><td>75</td></tr><tr><td>B4</td><td>France</td><td>38</td><td>8</td><td>11</td><td>-26</td><td>677</td><td>192</td><td>85</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Hybridization topology of the fuel cell-battery in the GEH2 system.</figcaption></figure>

## 3.2. Battery dataset and problem formulation

To evaluate the effectiveness of the proposed data augmentation approach, we consider two types of battery datasets: an industrial dataset from the GEH2 battery system and publicly available datasets from NASA. The following subsections describe each dataset in detail before formulating the problem addressed in this study.

### 3.2.1. GEH2 dataset

The dataset collected from various GEH2 generators, aggregated at 30-s intervals, provides vital insights into the performance and functioning of different components and sub-components, including the battery system. This information is crucial for analyzing, improving, and optimizing the overall efficiency of the GEH2 system.

Each GEH2 generator is outfitted with an internet-connected data logger that captures over 1000 signals every 30 s from sensors and control units. For the battery system, eight critical variables are monitored: the maximum allowable current for power recovery mode (IMR), battery output current (IPack), maximum battery pack temperature (TCellMax), minimum battery pack temperature (TCellMin), maximum cell voltage in the battery pack (UCellMax), minimum cell voltage in the battery pack (UCellMin), battery pack output voltage (UPack), and available capacity (CapUser). These variables provide comprehensive insights into the battery's performance and facilitate the assessment of its state of health. To gain insight into the temporal behavior of these parameters, a visualization of their normalized values over a 3-h period is shown in Fig. 4. A comparative summary of the batteries' operational characteristics and environmental conditions is presented in Table 2, while the distribution of average battery temperatures over the entire operational period is shown in Fig. 5.

### 3.2.2. NASA battery dataset

For evaluating the broad applicability of the proposed method, we apply the model to the NASA battery dataset, specifically batteries B0005 and B0006 from the NASA Prognostics Center of Excellence (PCoE), Sahaand and Goebel [31]. These lithium-ion batteries were tested at room temperature (24 °C) under three distinct operations: charge, discharge, and impedance. Each battery underwent 170 charge cycles and 168 discharge cycles, with electrochemical impedance spectroscopy performed 278 times. Initially, the batteries were charged at a constant current of 1.5 A until the terminal voltage reached 4.2 V, followed by a constant voltage charge until the current dropped to 20 mA. The discharge phase involved a constant current of 2 A, with cutoff voltages of 2.7 V for B0005 and 2.5 V for B0006. The actual life expectancy of these batteries, defined as the number of cycles before reaching 70% of their initial capacity, was recorded as 124

cycles for B0005 and 108 cycles for B0006. Although the NASA dataset is considered complete, we aggregated the data at the cycle level to simulate insufficient data scenarios, enabling us to test the robustness of our proposed model under sparse data conditions. The key measured parameters include cycle number, voltage, current, temperature, current load, and voltage load.

### 3.2.3. Problem formulation

In the GEH2 system, as battery is one of the most critical components, it is important to estimate its SOH. However, the historical battery data is limited, as the battery often remains inactive while the fuel cell supplies most of the power. This data scarcity poses a significant challenge to achieving accurate SOH predictions using conventional data-driven methods. Furthermore, the GEH2 battery data exhibits complex temporal dependencies among multiple parameters, adding another layer of difficulty.

Adding to this, data acquisition issues such as connectivity losses or data recovery system inactivity, often lead to gaps in data recordings, resulting in irregularly spaced time-series data. As illustrated in Fig. 6, although the GEH2 battery dataset is intended to be sampled every 30 s, the computed time deltas (elapsed time between consecutive observations) reveal frequent deviations from this norm. This variability is typical in real-world battery applications, where maintaining consistent sampling intervals is difficult. Consequently, there is a clear need for models that can effectively handle irregular time intervals, as conventional approaches assuming regular sampling may fail to capture the true temporal dynamics of the data.

While TimeGAN has demonstrated effectiveness in generating realistic time-series data [28], it encounters limitations when applied to the specific characteristics of GEH2 battery data. TimeGAN's original architecture is designed for regular time intervals and primarily captures short- to medium-term dependencies using its RNN-based generator. However, it struggles to address the irregular time intervals present in real-world GEH2 datasets and often fails to capture long-term dependencies across multiple variables accurately. These limitations reduce its suitability for applications where complex, multivariate dependencies and irregular time-series data are prevalent, as in GEH2 systems.

To address these challenges, we propose a modified TimeGAN-based data augmentation approach, namely TransGRU-TimeGAN. The conventional TimeGAN architecture is modified by replacing the conventional RNN-based generator by a hybrid structure combining a Transformer and a Gated Recurrent Unit (GRU). This novel architecture is specifically designed to address the two main issues in GEH2 battery data: (1)-capturing long-term dependencies across multivariate variables and (2)-handling irregular time intervals.

In the following section, we provide a detailed overview about the proposed approach.

## 4. Modified TimeGAN-based data augmentation approach

To contextualize the innovations proposed in this work and to elucidate the architecture of our method and the interconnections between its components, we provide a brief overview of the key foundational technologies that underpin our approach: TimeGAN, Transformer, and Gated Recurrent Units (GRU). Our proposed method leverages the strengths of each to overcome the limitations of traditional time-series
<figure><img src="image_7.png" /><figcaption>Fig. 4. Normalized battery parameters over a 3-h period.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. Distribution of average battery temperatures over the full operational period (%).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Distribution of elapsed time between consecutive observations for GEH2 batteries.</figcaption></figure>

data augmentation techniques, especially in capturing long-term dependencies and handling irregular time intervals.

TimeGAN, or Time-series Generative Adversarial Network [6], is an advanced deep learning model specifically designed to generate
<figure><img src="image_10.png" /><figcaption>Fig. 7. TimeGAN architecture [6].</figcaption></figure>

synthetic time-series data that closely mimics real data by capturing both the sequential and distributional characteristics of the input time-series. The architecture of TimeGAN consists of four key components: an embedding function, a recovery function, a sequence generator, and a sequence discriminator (see Fig. 7). By training the autoencoding and adversarial elements concurrently, the model learns to encode features, generate representations, and effectively model temporal sequences. The embedding network defines the latent space, while the adversarial network functions within that space, ensuring that the dynamics of real and synthetic data remain synchronized through a supervised loss.

The Transformer revolutionized sequence modeling by replacing recurrent neural networks (RNNs) with self-attention mechanisms [32]. Unlike RNNs, Transformers process sequences in parallel, capturing long-term dependencies through multi-head attention. This architecture excels at modeling contextual relationships in sequential data, making it ideal for tasks requiring global coherence.

The GRU is a type of recurrent neural network that mitigates the vanishing gradient problem prevalent in standard RNNs [7]. By utilizing update and reset gates, the GRU efficiently captures short to medium-term temporal dependencies while reducing computational complexity. Its ability to maintain and update hidden states in a controlled manner makes it well-suited for tasks where precise temporal modeling is critical.

In the following section, we present the detailed architecture of the proposed TransGRU-TimeGAN and illustrate how the integration of Transformer and GRU components enhances data augmentation.

## 4.1. Architecture of TransGRU-TimeGAN

This section presents a comprehensive overview of our proposed model, TransGRU-TimeGAN, as depicted in Fig. 8. The TransGRU-TimeGAN introduces a significant modification to the conventional TimeGAN architecture by substituting the conventional RNN-based generator with a Transformer-based design, followed by a Gated Recurrent Unit (GRU). The Transformer is particularly adept at modeling long-term dependencies due to its self-attention mechanism, making it highly effective for capturing complex temporal relationships over extended periods. In contrast, the GRU efficiently handles sequential data, allowing it to address shorter-term dependencies and the irregularities commonly found in real-world datasets, such as those from GEH2 battery systems. By integrating these two robust components, TransGRU-TimeGAN significantly enhances the generation of synthetic data that more accurately reflects long-term temporal dynamics while accommodating the inherent irregularities of such data. We elaborate on each component of the proposed model in detail in the following subsections.

### Transformer-GRU based generator

In the original TimeGAN, the generator primarily uses RNNs to model the temporal sequence, but RNNs, including LSTMs and GRUs, often struggle with capturing long-term dependencies due to the vanishing gradient problem. To address this, we introduce a Transformer followed by a GRU in the generator, forming a hybrid architecture that leverages both global attention and sequential refinement.

As illustrated in Fig. 8, the process begins with an input random noise sequence Z. This input is first processed by the Transformer module which leverages multi-head self-attention to compute relationships between all time steps simultaneously, thereby capturing long-term dependencies across the sequence. The self-attention mechanism can be described as:

$$ \text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right) V, \quad (1) $$

where, Q (query), K (key), and V (value) are linear transformations of the input sequence, and $d_k$ is the dimension of the key vectors. The softmax operation ensures that the attention scores, which determine how much focus is placed on different elements of the sequence, sum to 1. The output of the Transformer, denoted by $x_i^{trans}$, encapsulates the global contextual information from the input.

This transformed sequence $x_i^{trans}$ then serves as the input for the GRU layer. GRU is designed to effectively model temporal dependencies while addressing the vanishing gradient problem common in traditional Recurrent Neural Networks (RNNs). The GRU's gating mechanism controls the flow of information, determining what information from previous time steps to retain and how much new information to incorporate, which is critical for handling both regular and irregular time-series data.

At each time step t, the GRU updates its hidden state $c_t$ based on two key gates: the update gate $u_t$ and the reset gate $r_t$. The gates control how much past information is carried forward and how much is updated by new inputs. This process can be described as follows:

$$ u_t = \sigma(W_u \cdot [c_{t-1}, x_i^{trans}]) \quad (\text{Update gate}) \quad (2) $$

$$ r_t = \sigma(W_r \cdot [c_{t-1}, x_i^{trans}]) \quad (\text{Reset gate}) \quad (3) $$

$$ \tilde{c}_t = \tanh(W \cdot [r_t * c_{t-1}, x_i^{trans}]) \quad (\text{Candidate hidden state}) \quad (4) $$

$$ c_t = (1 - u_t) * c_{t-1} + u_t * \tilde{c}_t \quad (\text{Final hidden state update}) \quad (5) $$

where $c_t$ is the hidden state, updated from the previous state $c_{t-1}$. * denotes element-wise multiplication. The update gate $u_t$ controls how much of $c_{t-1}$ is retained, while the reset gate $r_t$ determines how much of $c_{t-1}$ is reset before calculating the candidate hidden state $\tilde{c}_t$. The weight matrices $W_u$, $W_r$, and $W$ transform the inputs and hidden states. Sigmoid $\sigma(\cdot)$ and hyperbolic tangent $\tanh(\cdot)$ functions regulate the update and candidate hidden states, ensuring effective control of information flow across time steps.

By combining the Transformer's ability to capture long-term dependencies with the GRU's efficiency in modeling temporal sequences, the proposed TransGRU-TimeGAN model is capable of handling irregular time intervals and complex dependencies in multivariate time-series data. Indeed, the GRU component in TransGRU-TimeGAN model processes sequential data considering time intervals between observations. The model explicitly integrates time deltas (elapsed time between consecutive observation) as an additional input feature. This allows the GRU to learn temporal patterns that account for irregular sampling rates. For example, if two measurements are separated by a large time interval, the GRU's hidden state update is modulated by this interval, ensuring the model adapts to sparse or unevenly spaced data. Furthermore, the Transformer's self-attention mechanism complements the GRU by capturing long-range dependencies across irregular intervals. The Transformer dynamically weights historical observations based on
<figure><img src="image_11.png" /><figcaption>Fig. 8. The high-level architecture of TransGRU-TimeGAN. The blue dotted lines represent the optimization process.</figcaption></figure>

their relevance, regardless of their temporal distance, while the GRU refines local sequential coherence. Further details on how the model can manage long-term dependencies and handle irregular time intervals will be discussed in Section 6.4.

### Embedding, recovery, and discriminator networks

The recovery network, similar to that in the original TimeGAN, is responsible for reconstructing the generated time-series data from the latent representations learned by the generator. It takes the latent codes produced by the embedding and transformer layers and maps them back to the original data space. This component is crucial for ensuring that the generated data maintains the statistical properties of the real data.

The discriminator and embedding networks in TransGRU-TimeGAN remain similar to those in the original TimeGAN architecture. The discriminator aims to distinguish between real and synthetic time-series sequences, while the embedding network reduces the dimensionality of the time-series data, mapping it into a latent space that is easier to work with.

### Optimization

As shown in Fig. 8, the TransGRU-TimeGAN optimizes the following three key loss functions:

**Reconstruction Loss:** Encourages the generator to produce realistic reconstructions of the input data from its latent representation.

$$ \mathcal{L}_R = \mathbb{E}_{s,x_1:T \sim p} \left[ \|s - \tilde{s}\|^2 + \sum_t \|x_t - \tilde{x}_t\|^2 \right], \quad (6) $$

where $s$ represents the static features, $x_t$ denotes the temporal features at time step $t$, and $\tilde{s}$ and $\tilde{x}_t$ are their respective reconstructions, and $\| \cdot \|$ represents the Euclidean norm.

**Unsupervised Loss:** Ensures that the discriminator can effectively distinguish between real and synthetic data, improving the generator's ability to create realistic time-series sequences.

$$ \mathcal{L}_U = \mathbb{E}_{s,x_1:T \sim p} \left[ \log y_s + \sum_t \log y_t \right] \\ + \mathbb{E}_{\tilde{s},\tilde{x}_1:T \sim \hat{p}} \left[ \log(1 - \hat{y}_s) + \sum_t \log(1 - \hat{y}_t) \right], \quad (7) $$

where $y_s$ and $y_t$ are the discriminator's outputs for the static and temporal features, respectively, and $\hat{y}_s$ and $\hat{y}_t$ are the outputs for the generated samples.

**Supervised Loss:** Helps the generator learn the conditional transitions between the latent representations of the time-series data.

$$ \mathcal{L}_S = \mathbb{E}_{s,x_1:T \sim p} \left[ \sum_t \|h_t - g_X(h_S, h_{t-1}, z_t)\|^2 \right]. \quad (8) $$

Where $g_X$ represents the function that generates the synthetic sample based on the static features $h_S$, the previous hidden state $h_{t-1}$, and the random noise $z_t$,

In the following section, we will present the implementation process for the TransGRU-TimeGAN model, along with a detailed outline of the parameters chosen for this endeavor.

## 4.2. Implementation and parameters setting

In this section, the implementation of the proposed model and outline of the process are illustrated. The parameters of the TransGRU-TimeGAN model, along with their respective values, are summarized in Table 3.

The implementation of TransGRU-TimeGAN begins with the initialization of the model using essential parameters, such as sequence length, feature dimensions, the number of hidden units for GRU layers, and the number of attention heads for the Transformer. These parameters configure the various layers of each model component. The architecture consists of four key modules: the generator, discriminator, encoder, and decoder, as illustrated in Fig. 8. In the generator, a Transformer layer equipped with multi-head attention is followed by a GRU layer, enabling the capture of long-term dependencies prior to the output layer, which generates the feature sequence. The discriminator, structured as a GRU followed by a dense layer, processes the sequence to classify it as either real or synthetic. The encoder and decoder map input sequences to a latent space and back, assisting the generator during training through reconstruction loss.

Once constructed, each component is compiled with its respective loss functions. The training process consists of two primary phases: first, the encoder and decoder are pre-trained as an autoencoder to minimize reconstruction error, thus creating a meaningful latent space
<table><caption>**Table 3**
TransGRU-TimeGAN parameters.</caption><thead><tr><th>Parameter</th><th>Description</th><th>GEH2 data</th><th>NASA data</th></tr></thead><tbody><tr><td>Feature dimension</td><td>Dimensionality of each input feature vector at each time step</td><td>7</td><td>6</td></tr><tr><td>Hidden dimension</td><td>Number of hidden units in the GRU layers for each model component (encoder, decoder, generator, discriminator)</td><td>128</td><td>128</td></tr><tr><td>Number of heads</td><td>Number of attention heads in the Transformer layer in the generator</td><td>16</td><td>4</td></tr><tr><td>Epochs</td><td>Number of training epochs for each training phase</td><td>200</td><td>150</td></tr><tr><td>Batch size</td><td>Number of samples per training batch</td><td>32</td><td>32</td></tr><tr><td>Sequence length</td><td>Number of time steps in each sample in the dataset</td><td>20</td><td>10</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Flowchart for the evaluation process.</figcaption></figure>

before moving on to adversarial training. In the second phase, the generator and discriminator participate in adversarial training, where the discriminator learns to differentiate between real sequences and generated ones, while the generator strives to produce realistic data. Ultimately, after the training is complete, the generator utilizes random noise to create synthetic data, which is then combined with the original dataset to form an expanded and augmented dataset that enhances the effectiveness of downstream model training.

We assess the effectiveness of TransGRU-TimeGAN using real-world datasets from four distinct GEH2 batteries and two NASA batteries. In the subsequent section, we will outline the evaluation process and provide an overview of the most commonly used battery data augmentation methods found in the literature.

## 5. Validation and benchmark methods

The validation process is illustrated in Fig. 9. We assess the effectiveness of the proposed model, TransGRU-TimeGAN, using real-world industrial datasets from four distinct GEH2 batteries, as well as two NASA batteries. The data for each battery is divided into two subsets: 60% for training and 40% for validation, ensuring a balanced evaluation of the predictive capabilities of the augmented data. For every battery, we implement data augmentation using the proposed TransGRU-TimeGAN model, the original TimeGAN, and the benchmark methods outlined in Section 5.1.

To validate the augmented data, it is crucial to evaluate its influence on predictive performance, particularly in estimating the SOH of GEH2 and NASA batteries. Given that the primary aim of data augmentation is to enhance the training dataset and improve the accuracy of predictive models, we employ an LSTM neural network to assess the effectiveness of the augmented data in this scenario. Therefore, the LSTM model is trained on both the original data (without augmentation) and on the augmented datasets generated by the TransGRU-TimeGAN and benchmark methods, as previously mentioned. This approach enables us to evaluate how effectively the proposed method enhances SOH prediction accuracy and to compare its performance against other data augmentation techniques.

To evaluate the predictive performance of the LSTM, we utilize two metrics: Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). These metrics are computed as follows:

$$RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2} \qquad (9)$$

$$MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i|, \qquad (10)$$

where *n* is the number of observations, *y*ᵢ is the true value, and ŷᵢ is the predicted value.

In the following section, we detail the benchmark augmentation methods and provide an overview of the LSTM model architecture used for this evaluation.

### 5.1. Background of benchmark methods

#### Variational Autoencoders (VAE)

VAEs are generative models that learn a continuous latent representation of the input data [33]. The VAE structure consists of an encoder network that maps the input time series into a probabilistic latent space, and a decoder network that reconstructs the data from latent representations. The model is trained to minimize both the reconstruction error and the divergence between the learned latent distribution and a prior distribution, ensuring that generated synthetic sequences reflect the underlying data distribution.

#### C-RNN-GAN

Continuous Recurrent Neural Network GAN (C-RNN-GAN) is designed to generate continuous sequential data using recurrent neural networks [34]. Its architecture features a generator and a discriminator, both built with recurrent layers, typically LSTM. The generator learns to produce realistic sequences from random noise, while the discriminator evaluates the authenticity of these sequences against real data.

#### TCGAN

TCGAN leverages the strengths of Temporal Convolutional Networks (TCN) to model long-range dependencies in time series data [35].
The architecture is fully convolutional, using dilated causal convolutions to capture temporal patterns over varying time scales. The generator employs a stack of dilated convolutional layers with gated activation units and residual connections, which collectively synthesize realistic sequences. Meanwhile, the discriminator is constructed using convolutional layers that extract hierarchical features from the input data, ultimately classifying sequences as real or synthetic.

## Jittering

Jittering consists of adding noise to the time series to perform data augmentation [36]. It assumes that the data are inherently noisy, which is often true for sensor data. By simulating this noise, jittering generates new samples. Typically, Gaussian noise is added to each time step, and the magnitude and shape of the noise deformation are defined by its mean and standard deviation. The jittering process can be defined as follows:

$$x'(t) = x(t) + \epsilon_t, \quad \epsilon_t \sim \mathcal{N}(0, \sigma^2), \qquad (11)$$

where $x(t)$ is the original time series, and $\epsilon_t$ represents the noise added at each step with variance $\sigma^2$.

## Scaling

Scaling adjusts the magnitude of the time series by multiplying it by a random scaling factor [37]. This technique assumes that variations in amplitude do not alter the underlying structure of the time series. The scaling factor is typically sampled from a uniform distribution:

$$x'(t) = \alpha \cdot x(t), \quad \alpha \sim \mathcal{U}(a, b), \qquad (12)$$

where $\alpha$ is the scaling factor, and $\mathcal{U}(a, b)$ represents a uniform distribution over the range $[a, b]$.

## Slicing

Slicing involves extracting random sub-segments from the time series to create new samples [38]. This method assumes that smaller portions of the data retain useful patterns. Slicing can be defined as:

$$x'(t) = x(t + k), \quad k \in [0, T - \tau], \qquad (13)$$

where $\tau$ is the length of the sliced segment, and $k$ is the starting point of the slice.

## Time warping

Time warping modifies the time axis by stretching or compressing certain parts of the signal [39]. It assumes that slight misalignments in time do not significantly affect the signal's underlying patterns. The warping process is described as:

$$x'(t) = x(\phi(t)), \quad \phi(t) = t + \gamma(t), \qquad (14)$$

where $\phi(t)$ is a warping function that distorts the time axis, and $\gamma(t)$ is the random time shift.

## Permutation

Permutation involves randomly shuffle the order of time steps within the series, thus creating a new synthetic sample [40]. This method assumes that the exact order of the time points is not crucial. The permutation process is expressed as:

$$x'(t) = x(\pi(t)), \qquad (15)$$

where $\pi(t)$ is a random permutation of the time indices.

## 5.2. Validation using LSTM model

The Long Short-Term Memory (LSTM) model was selected for SOH prediction due to its exceptional capability to handle the GEH2 battery data utilized in this study [41]. As detailed in Section 3, our dataset exhibits long-term dependencies among various battery parameters and features irregular time intervals. The LSTM architecture, characterized by its memory cells and gating mechanisms, is adept at capturing these complex dependencies over time, allowing it to retain significant historical patterns while effectively minimizing the impact of short-term fluctuations. This dual capability to model both short-and long-term interactions within intricate, multi-variable data positions the LSTM as an ideal choice for SOH prediction [42]. Moreover, LSTMs are proficient at addressing the vanishing gradient problem, enabling them to identify subtle, evolving patterns within sequences in a more stable manner. In comparison to the Gated Recurrent Unit (GRU), the LSTM's more intricate architecture offers the potential to learn more complex patterns and relationships within the data. This complexity enhances their suitability for tasks that necessitate capturing long-term dependencies. Additionally, LSTMs thrive in contexts involving irregular time intervals and prolonged temporal relationships, which is pertinent to the GEH2 data. These attributes render LSTMs a robust option for estimating battery SOH.

The LSTM architecture comprises three layers with 128, 64, and 24 units, respectively, all employing ReLU activation to introduce non-linearity. The stacked LSTM layers improve the model's capacity to handle long-range dependencies and time-series data with varying time steps. The final layer is a fully connected Dense layer that produces the predicted SOH. For the NASA dataset, the model begins with an LSTM layer of 50 units, followed by a Dropout layer (rate 0.2) to mitigate overfitting. A second LSTM layer with 8 units further processes the sequence, accompanied by another Dropout layer (rate 0.02), and a final Dense layer outputs the predicted capacity. The two models are optimized using the Adam optimizer, which is particularly effective in managing noisy and sparse gradient data.

SOH prediction relies on various battery parameters that serve as input features for the predictive model. The inputs of the LSTM model include the maximum allowable current for power recovery mode (IMR), battery output current (IPack), maximum and minimum battery pack temperatures (TCellMax and TCellMin), maximum cell voltage in the battery pack (UCellMax), battery pack output voltage (UPack), and the number of cycles from the GEH2 dataset. For the NASA battery dataset, the input features include cycle number, voltage measured, current measured, temperature measured, current load, and voltage load. These parameters capture the battery's electrochemical behavior during charge-discharge cycles, providing valuable insights for SOH prediction. The output of the models is the SOH, represented by capacity retention for the GEH2 dataset and capacity (Ah) for the NASA dataset, which reflects the battery's ability to store and deliver energy over time. To enhance the robustness and generalization capability of the predictive model, data augmentation is applied exclusively to the input features of the training data, ensuring a more diverse and representative training dataset while preserving the integrity of the target variable.

The results of the comparison, alongside the model's performance on different augmented datasets, will be presented and analyzed in the following section.

# 6. Results and discussions

## 6.1. Performances and model optimization

To assess the performance of the TransGRU-TimeGAN model and its ability to effectively learn from the data, we monitor the progression of three vital loss metrics: reconstruction loss, supervised loss, and unsupervised loss, as defined in Eqs. (6), (8), and (7), respectively.
<figure><img src="image_13.png" /><figcaption>Fig. 10. Evolution of reconstruction, supervised, and unsupervised losses during TransGRU-TimeGAN training.</figcaption></figure>

The model was trained for 200 epochs, with the progression of these loss metrics illustrated in Fig. 10. This provides valuable insights into the model's optimization and generalization capabilities throughout the training process.

The figure illustrates that the reconstruction loss decreases from 0.30 to below 0.05, indicating the model's impressive ability to capture and reconstruct the original data from its latent representations. The rapid decrease in this loss within the first 50 epochs suggests that the encoder-decoder architecture is highly effective at compressing and recovering information from the latent space. The low final reconstruction loss highlights the model's capability to represent the input data with minimal error, which is crucial for ensuring that the generated sequences retain the core characteristics of the real data.

In contrast, the supervised loss, which measures the generator's ability to create data that can fool the discriminator, decreases and stabilizes at around 0.44. This gradual decline indicates that the generator progressively learns to produce more realistic data. Although the drop is not as steep as that of the reconstruction loss, it reflects a consistent improvement, meaning that the generated data increasingly resembles real sequences as training progresses. The unsupervised loss, which assesses the generator's ability to distinguish between real and synthetic data, follows a similar trend, decreasing to around 0.44. It is important to note that this unsupervised loss should not approach zero, as a value too close to zero would suggest that the discriminator is overly dominant and easily distinguishing between real and synthetic data. In adversarial training, maintaining a non-zero unsupervised loss is essential for ensuring that the generator continues to improve. The final value of around 0.44 indicates that the model has achieved a healthy balance between the generator and discriminator, where the generator has learned to produce convincing data while the discriminator remains adequately challenged.

In conclusion, the TransGRU-TimeGAN model demonstrates solid convergence across all three loss metrics, reflecting its ability to learn both the temporal structure of the sequences and generate realistic synthetic data.

## 6.2. Statistical visualizations

To statistically assess the quality of the synthetic data generated by the TransGRU-TimeGAN model and highlight its similarity to real data, we present various statistical measures for the GEH2 Battery 1 and NASA Battery B0005 datasets. A visualization of real and generated time-series samples is provided in Fig. 11, offering an initial statistical evaluation of their resemblance.

Table 4 summarizes a range of statistical measures, including the mean, standard deviation, minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3), computed for each key feature in both the real and generated data. These metrics indicate that the overall distributional characteristics of the generated data closely mirror those of the original measurements.

To further highlight the similarities between the real data and generated data, Fig. 12 displays two-dimensional projections of the data using three distinct dimensionality reduction techniques: Principal Component Analysis (PCA), Multidimensional Scaling (MDS), and Spectral Embedding. Each method offers a different perspective: PCA highlights directions of maximum variance, potentially exaggerating differences if variance profiles differ; MDS preserves pairwise distances and provides a view of the global structure; while Spectral Embedding, through neighborhood graph decomposition, robustly captures local non-linear structures. The high degree of overlap observed in all three projections confirms that the synthetic data generated by TransGRU-TimeGAN retains the intrinsic structure of the real data across both GEH2 and NASA datasets.

In the following section, we assess how effectively the proposed method enhances the quality of SOH predictions.

## 6.3. Analysis and comparison of prediction results

To assess the effectiveness of the proposed TransGRU-TimeGAN model, we compared its performance against the original TimeGAN and several widely used data augmentation techniques from the literature. The primary objective of this evaluation is to determine how
<figure><img src="image_14.png" /><figcaption>Fig. 11. Visualization of real and generated time-series samples.</figcaption></figure>

<caption>**Table 4**</caption>

Descriptive statistics of real and generated data for GEH2 Battery 1 (normalized) and NASA Battery B0005.

<table><thead><tr><th rowspan="2">Variable</th><th colspan="6">Real data</th><th colspan="6">Synthetic data</th></tr><tr><th>Mean</th><th>Std</th><th>Min</th><th>Q1</th><th>Q2</th><th>Q3</th><th>Max</th><th>Mean</th><th>Std</th><th>Min</th><th>Q1</th><th>Q2</th><th>Q3</th><th>Max</th></tr></thead><tbody><tr><td colspan="14" style="text-align: left; font-weight: bold;">GEH2 Battery 1</td></tr><tr><td>IMR</td><td>0.39090</td><td>0.01856</td><td>0.33578</td><td>0.37727</td><td>0.39202</td><td>0.40504</td><td>0.43673</td><td>0.37859</td><td>0.03522</td><td>0.29167</td><td>0.36111</td><td>0.38021</td><td>0.40278</td><td>0.45833</td></tr><tr><td>IPack</td><td>0.72455</td><td>0.03039</td><td>0.63631</td><td>0.70154</td><td>0.72509</td><td>0.74776</td><td>0.80419</td><td>0.74301</td><td>0.04597</td><td>0.57419</td><td>0.71724</td><td>0.74299</td><td>0.76392</td><td>0.91257</td></tr><tr><td>TCellMax</td><td>0.83749</td><td>0.17252</td><td>0.36613</td><td>0.70816</td><td>0.83656</td><td>0.96585</td><td>1.00000</td><td>0.76533</td><td>0.15910</td><td>0.21429</td><td>0.67857</td><td>0.78571</td><td>0.89286</td><td>1.00000</td></tr><tr><td>TCellMin</td><td>0.66768</td><td>0.08918</td><td>0.41254</td><td>0.60218</td><td>0.66772</td><td>0.73324</td><td>0.90124</td><td>0.64348</td><td>0.08575</td><td>0.31034</td><td>0.58621</td><td>0.65517</td><td>0.68966</td><td>0.82759</td></tr><tr><td>UCellMax</td><td>0.25663</td><td>0.02348</td><td>0.19511</td><td>0.23934</td><td>0.25574</td><td>0.27356</td><td>0.32490</td><td>0.28691</td><td>0.10313</td><td>0.19672</td><td>0.24590</td><td>0.25683</td><td>0.26594</td><td>0.65027</td></tr><tr><td>UPack</td><td>0.34361</td><td>0.01047</td><td>0.31054</td><td>0.33600</td><td>0.34314</td><td>0.35091</td><td>0.37792</td><td>0.35314</td><td>0.06122</td><td>0.26099</td><td>0.32503</td><td>0.33701</td><td>0.35012</td><td>0.70585</td></tr><tr><td colspan="14" style="text-align: left; font-weight: bold;">NASA Battery B0005</td></tr><tr><td>voltageMeasured</td><td>3.5162</td><td>0.0383</td><td>3.4325</td><td>3.4836</td><td>3.5173</td><td>3.5483</td><td>3.5962</td><td>3.5171</td><td>0.0326</td><td>3.4640</td><td>3.4873</td><td>3.5146</td><td>3.5512</td><td>3.5641</td></tr><tr><td>currentMeasured</td><td>-1.8417</td><td>0.0504</td><td>-1.9619</td><td>-1.8807</td><td>-1.8416</td><td>-1.8027</td><td>-1.7269</td><td>-1.8084</td><td>0.0844</td><td>-1.9389</td><td>-1.8847</td><td>-1.8168</td><td>-1.7315</td><td>-1.6674</td></tr><tr><td>temperatureMeasured</td><td>32.9514</td><td>0.7312</td><td>31.3244</td><td>32.3723</td><td>32.9430</td><td>33.5526</td><td>34.4789</td><td>32.7827</td><td>0.7133</td><td>31.3300</td><td>32.2755</td><td>32.8569</td><td>33.3516</td><td>34.3109</td></tr><tr><td>currentLoad</td><td>1.2783</td><td>0.7380</td><td>-1.5105</td><td>0.7210</td><td>1.2340</td><td>1.8429</td><td>3.0966</td><td>1.1369</td><td>1.3930</td><td>-1.9005</td><td>1.6718</td><td>1.7386</td><td>1.8313</td><td>2.7253</td></tr><tr><td>voltageLoad</td><td>2.2885</td><td>0.1750</td><td>1.9378</td><td>2.1421</td><td>2.2941</td><td>2.4353</td><td>2.6449</td><td>2.3159</td><td>0.1504</td><td>2.0627</td><td>2.1822</td><td>2.3107</td><td>2.4731</td><td>2.5296</td></tr></tbody></table>

well the proposed model improves predictive accuracy, particularly in estimating the batteries State of Health (SOH) of GEH2 batteries.

Real-world data from four distinct GEH2 battery systems were utilized, and to assess broader applicability, the proposed method was also applied to the NASA battery dataset, specifically batteries

B0005 and B0006. An LSTM model (as detailed in Section 5.2) was trained on multiple datasets: the original unaugmented data, data augmented using TransGRU-TimeGAN, and data augmented using the benchmark methods described in Section 5.1. The numerical results for each battery are summarized in Table 5, and Fig. 13 provides a visual
<figure><img src="image_15.png" /><figcaption>Fig. 12. MDS, PCA, and Spectral Embedding projections of real and synthetic data for GEH2 Battery 1 and NASA Battery B0005.</figcaption></figure>

<table><caption>**Table 5**
Comparison of TransGRU-TimeGAN to benchmark data augmentation methods for GEH2 dataset (Battery 1–4) and NASA dataset (B0005, B0006).</caption><thead><tr><th rowspan="2"></th><th colspan="2">Battery 1</th><th colspan="2">Battery 2</th><th colspan="2">Battery 3</th><th colspan="2">Battery 4</th><th colspan="2">B0005</th><th colspan="2">B0006</th></tr><tr><th>RMSE</th><th>MAE</th><th>RMSE</th><th>MAE</th><th>RMSE</th><th>MAE</th><th>RMSE</th><th>MAE</th><th>RMSE</th><th>MAE</th><th>RMSE</th><th>MAE</th></tr></thead><tbody><tr><td>No augmentation</td><td>0.0031</td><td>0.0020</td><td>0.0221</td><td>0.0194</td><td>0.0036</td><td>0.0029</td><td>0.0215</td><td>0.0169</td><td>0.0465</td><td>0.0364</td><td>0.0681</td><td>0.0592</td></tr><tr><td>Jittering</td><td>0.0020</td><td>0.0016</td><td>0.0229</td><td>0.0157</td><td>0.0546</td><td>0.0546</td><td>0.0094</td><td>0.0069</td><td>0.0595</td><td>0.0520</td><td>0.1172</td><td>0.1078</td></tr><tr><td>Scaling</td><td>0.0078</td><td>0.0077</td><td>0.0135</td><td>0.0128</td><td>0.0279</td><td>0.0278</td><td>0.0290</td><td>0.0251</td><td>0.0310</td><td>0.0255</td><td>0.0766</td><td>0.0621</td></tr><tr><td>Slicing</td><td>0.0108</td><td>0.0078</td><td>0.0232</td><td>0.0167</td><td>0.0233</td><td>0.0232</td><td>0.0253</td><td>0.0192</td><td>0.0285</td><td>0.0253</td><td>0.1050</td><td>0.0889</td></tr><tr><td>Time Warping</td><td>0.0070</td><td>0.0067</td><td>0.0138</td><td>0.0135</td><td>0.0070</td><td>0.0065</td><td>0.0107</td><td>0.0099</td><td>0.0706</td><td>0.0622</td><td>0.1330</td><td>0.1102</td></tr><tr><td>Permutation</td><td>0.0036</td><td>0.0024</td><td>0.0170</td><td>0.0147</td><td>0.0178</td><td>0.0175</td><td>0.0313</td><td>0.0245</td><td>0.0908</td><td>0.0773</td><td>0.0617</td><td>0.0513</td></tr><tr><td>VAE</td><td>0.0031</td><td>0.0026</td><td>0.0188</td><td>0.0182</td><td>0.0210</td><td>0.0207</td><td>0.0166</td><td>0.0158</td><td>0.0601</td><td>0.0553</td><td>0.0864</td><td>0.0736</td></tr><tr><td>C-RNN-GAN</td><td>0.0500</td><td>0.0460</td><td>0.0094</td><td>0.0088</td><td>0.0161</td><td>0.0158</td><td>0.0095</td><td>0.0087</td><td>0.0917</td><td>0.0801</td><td>0.1531</td><td>0.1351</td></tr><tr><td>TCGAN</td><td>0.0030</td><td>0.0027</td><td>0.0196</td><td>0.0186</td><td>0.0105</td><td>0.0104</td><td>0.0219</td><td>0.0218</td><td>0.0413</td><td>0.0389</td><td>0.0431</td><td>0.0377</td></tr><tr><td>TimeGAN</td><td>0.0094</td><td>0.0092</td><td>0.0405</td><td>0.0336</td><td>0.0105</td><td>0.0102</td><td>0.0342</td><td>0.0259</td><td>0.0937</td><td>0.0893</td><td>0.0593</td><td>0.0456</td></tr><tr><td>Proposed method</td><td><strong>0.0020</strong></td><td><strong>0.0014</strong></td><td><strong>0.0086</strong></td><td><strong>0.0071</strong></td><td><strong>0.0019</strong></td><td><strong>0.0014</strong></td><td><strong>0.0092</strong></td><td><strong>0.0077</strong></td><td><strong>0.0254</strong></td><td><strong>0.0233</strong></td><td><strong>0.0248</strong></td><td><strong>0.0204</strong></td></tr></tbody></table>

comparison with error bars for each method and battery, with gold stars marking the best-performing method for each case.

The results show a clear advantage of the proposed TransGRU-TimeGAN model over the benchmark methods. Across nearly all batteries, the model consistently achieved lower Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), with an impressive RMSE of 0.0019 for Battery 3 and a MAE of 0.0014 Battery 3. Fig. 13 further highlights this performance, showing that most augmentation methods, such as Jittering, Time Warping, and C-RNN-GAN often degrade prediction accuracy, particularly for battery B0006. In contrast, the TransGRU-TimeGAN consistently achieved smaller RMSE and MAE values compared to the unaugmented data. Jittering, for instance, showed improvement over no augmentation for Battery 1 in terms of RMSE and for Battery 4 in terms of MAE. However, it failed to maintain this improvement for other batteries, especially NASA batteries, indicating its limitations in handling complex battery dynamics.

A comparative analysis of the deep learning-based augmentation methods reveals that while the VAE and TCGAN models can be competitive for certain batteries (notably Battery 1), their performance is inconsistent across different datasets. This variability suggests that these models struggle to capture the complex, non-linear battery behavior, long-term dependencies, and to handle irregular time intervals

effectively. Conversely, the C-RNN-GAN approach exhibits notably poor performance, especially for Battery 1 and NASA Battery B0006, where it registers the highest error values among the evaluated methods. These findings indicate that, although some deep learning methods may capture certain aspects of battery behavior under specific conditions, they generally lack the robustness and generalizability required for reliable SOH prediction across diverse operating environments.

A direct comparison between the TransGRU-TimeGAN and the original TimeGAN highlights the superiority of the proposed modifications. For all battery types, the RMSE and MAE values for TimeGAN are consistently higher than those of TransGRU-TimeGAN, demonstrating the effectiveness of incorporating transformer mechanisms and GRU networks into the architecture. While Jittering yields better results than TimeGAN in certain cases, it still does not match the performance of TransGRU-TimeGAN, which consistently surpasses all other methods. This significant improvement suggests that the transformer-based architecture is more adept at capturing long-term dependencies and managing irregular time series data, both of which are crucial for accurate State of Health (SOH) predictions. To visualize the SOH predictions obtained with TimeGAN and the proposed method, Fig. 14 presents the SOH prediction curves for NASA batteries B0005 and
<figure><img src="image_16.png" /><figcaption>Fig. 13. Comparison of RMSE and MAE metrics between the proposed TransGRU-TimeGAN model and benchmark data augmentation methods for both GEH2 and NASA datasets.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 14. SOH prediction curves for NASA batteries B0005 (left) and B0006 (right), comparing predictions based on original unaugmented data, TimeGAN, and the proposed method.</figcaption></figure>

B0006, comparing predictions based on original unaugmented data, TimeGAN, and the TransGRU-TimeGAN model.

To enable a comprehensive evaluation of each augmentation method's general performance, Fig. 13 presents the average RMSE and MAE values aggregated across all batteries. This summary visualization reinforces the consistency and effectiveness of the proposed TransGRU-TimeGAN model, which outperforms all benchmark techniques by achieving the lowest average errors. Unlike alternative methods whose performance fluctuates depending on the battery type, TransGRU-TimeGAN demonstrates a robust capability to generalize across different operating conditions. These results highlight the model's strong potential for practical deployment in real-world battery health monitoring systems, where both accuracy and reliability are critical.

The superior performance of the TransGRU-TimeGAN model can be attributed to its innovative architecture, which effectively captures the intricate temporal dynamics within the data. This design allows for more precise modeling of batteries with diverse characteristics and aging patterns, making it particularly well-suited for varied datasets. The model's adaptability and generalization capabilities are evident in its consistent performance across all battery types, as it maintains lower RMSE and MAE values, even when compared to the best-performing benchmark methods.

Overall, the results indicate that the proposed TransGRU-TimeGAN model represents a significant advancement in data augmentation techniques for battery health monitoring. It not only enhances SOH prediction accuracy but also demonstrates robustness and versatility, making it a valuable tool for predictive maintenance strategies in real-world battery systems.

To further investigate the contribution of each individual component within the proposed TransGRU-TimeGAN architecture, the following section presents a detailed ablation study. This analysis aims to quantify the impact of each architectural element on the model's overall performance and to better understand the design choices underlying the proposed method.

### 6.4. Ablation studies: Evaluating the contribution of model components

To better understand the influence of individual architectural components on the overall performance of the proposed approach, we conducted several ablation studies using the GEH2 battery dataset. We evaluated four configurations: the baseline TimeGAN, TimeGAN with its generator replaced by a Transformer-based architecture (TransTimeGAN), TimeGAN with its generator replaced by a GRU-based architecture (GRU-TimeGAN), and the proposed hybrid approach combining both Transformer and GRU components (TransGRU-TimeGAN). Table 6 summarizes the RMSE and MAE results for each configuration across the four batteries. To better understand the influence of each
<table><caption>**Table 6**
RMSE and MAE results for ablation studies.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Battery 1</th><th colspan="2">Battery 2</th><th colspan="2">Battery 3</th><th colspan="2">Battery 4</th></tr><tr><th>RMSE</th><th>MAE</th><th>RMSE</th><th>MAE</th><th>RMSE</th><th>MAE</th><th>RMSE</th><th>MAE</th></tr></thead><tbody><tr><td>TimeGAN</td><td>0.0094</td><td>0.0092</td><td>0.0405</td><td>0.0336</td><td>0.0105</td><td>0.0102</td><td>0.0342</td><td>0.0259</td></tr><tr><td>Tans-TimeGAN</td><td>0.0082</td><td>0.0080</td><td>0.0188</td><td>0.0181</td><td>0.0190</td><td>0.0189</td><td>0.0217</td><td>0.0216</td></tr><tr><td>GRU-TimeGAN</td><td>0.0040</td><td>0.0037</td><td>0.0186</td><td>0.0164</td><td>0.0101</td><td>0.0099</td><td>0.0243</td><td>0.0242</td></tr><tr><td>Proposed method</td><td><strong>0.0020</strong></td><td><strong>0.0014</strong></td><td><strong>0.0086</strong></td><td><strong>0.0071</strong></td><td><strong>0.0019</strong></td><td><strong>0.0014</strong></td><td><strong>0.0092</strong></td><td><strong>0.0077</strong></td></tr></tbody></table>

<figure><img src="image_18.png" /><figcaption>**Fig. 15.** Percentage improvement over baseline TimeGAN.</figcaption></figure>

individual component on TimeGAN, Fig. 15 presents the RMSE and MAE improvements over the baseline TimeGAN.

As the results indicate, the Trans-TimeGAN variant outperforms the baseline TimeGAN for Battery 2 and Battery 4. This highlights the Transformer's strength in capturing long-term dependencies via its self-attention mechanism, which enables the modeling of relationships between distant time points irrespective of their sequential order. However, a critical limitation emerges: for Battery 3, Trans-TimeGAN significantly degrades performance, with an 80% increase in RMSE and an 85% increase in MAE compared to the baseline TimeGAN. This substantial performance deterioration indicates that the Transformer architecture alone struggles with the irregular time intervals present in the battery. The Transformer's position encoding mechanism, while effective for uniform sequences, appears inadequate for handling the irregular time intervals present in the data. This pattern confirms that while Transformers excel at modeling long-term dependencies, they require additional components to effectively handle irregular temporal patterns.

The GRU-TimeGAN variant demonstrates impressive performance improvements for Battery 1 and Battery 2, showcasing the GRU's natural ability to process sequential data. The recurrent structure of GRUs allows them to maintain state information across time steps, making them well-suited for handling the irregular time intervals in these batteries. But the improvements is moderate for other batteries, especially, for Battery 3, suggesting GRUs alone have difficulty capturing distant dependencies across extended time horizons in the presence of irregular time intervals. This highlights that while GRUs can adapt to irregular sampling intervals through their gating mechanisms, they have inherent limitations in capturing dependencies across very long sequences due to the vanishing gradient problem and their sequential information processing nature.

The proposed TransGRU-TimeGAN architecture demonstrates remarkable improvements across all batteries, with RMSE reductions ranging from 73% to 81% and MAE reductions from 70% to 86%. Most notably, it achieves an 81% RMSE improvement for Battery 3, where Trans-TimeGAN alone failed dramatically. This consistent performance across all batteries demonstrates the powerful effect of combining Transformer and GRU in the TimeGAN generator. By combining the Transformer's ability to capture long-term dependencies with the GRU's

efficiency in modeling temporal sequences, the proposed TransGRU-TimeGAN model is capable of handling irregular time intervals and complex dependencies in multivariate time-series data. The GRU component processes sequential data considering time intervals between observations. The model integrates time deltas (elapsed time between consecutive observation) as an additional input feature. This allows the GRU to learn temporal patterns that account for irregular sampling rates. Furthermore, the Transformer's self-attention mechanism complements the GRU by capturing long-term dependencies across irregular intervals. The Transformer dynamically weights historical observations based on their relevance, regardless of their temporal distance, while the GRU refines local sequential coherence.

To gain deeper insight into the performance dynamics of TransGRU-TimeGAN, it is crucial to examine how various parameters – particularly those related to the generator – influence the model’s overall effectiveness. As the core component of the architecture, the generator significantly shapes the quality of the generated data and, by extension, the system’s predictive performance. In the following section, we present a detailed analysis of key parameter settings, with a focus on the hidden dimension size and the number of attention heads, and evaluate their impact on the model’s predictive capabilities.

## 6.5. Influence of generator parameters on the performance of TransGRU-TimeGAN

In this section, we will investigate how key hyperparameters affect the performance of the proposed TransGRU-TimeGAN model, with a particular focus on the generator component. Specifically, we will analyze two crucial parameters: the hidden dimension size and the number of attention heads. These parameters directly influence the architecture of the generator, which is essential for generating high-quality augmented data and ultimately improving the model’s predictive accuracy. The results are illustrated in Fig. 16.

As illustrated in Fig. 16, the heatmaps of RMSE and MAE provide a clear visualization of how the parameters of hidden dimension and number of heads impact the performance of the TransGRU-TimeGAN model. The results indicate that smaller hidden dimensions (e.g., 64)
<figure><img src="image_19.png" /><figcaption>Fig. 16. Impact of hidden dimension and number of heads on TransGRU-TimeGAN Performance.</figcaption></figure>

combined with fewer heads (e.g., 2) generally yield optimal perfor-
mance, as evidenced by the lowest RMSE of 0.0037 and a corre-
sponding MAE of 0.0024. However, increasing the number of heads
while maintaining the same hidden dimension typically leads to a
significant decline in performance. Notably, with 64 hidden dimensions
and 8 heads, the RMSE escalates to 0.0205, signaling inferior model
generalization.

For larger hidden dimensions (128, 256, 300), the model displays a
more nuanced behavior. In these cases, moderate values for the number
of heads (e.g., 8 or 16) result in enhanced performance. For example,
at 128 hidden dimensions and 16 heads, the RMSE decreases to 0.0033
and the MAE to 0.0027, marking the best overall results. This sug-
gests that the model reaps benefits from the increased representational
capacity of higher hidden dimensions, but only when paired with an
appropriate number of attention heads. An excessive number of heads
(e.g., 16), however, can still lead to diminishing returns or instability
in certain instances.

In conclusion, the results indicate that both hidden dimension and
the number of heads are vital parameters in modulating the genera-
tor's capacity to model temporal dependencies, as these elements are
key components of the transformer architecture. Moderate configura-
tions often achieve the best balance between model complexity and
generalization, ultimately optimizing performance.

7. Conclusion

In this paper, we propose TransGRU-TimeGAN, a novel generative adversarial network model designed for data augmentation, building on the foundation of TimeGAN. Our approach introduces an innovative enhancement by replacing the conventional generator with a Transformer-based architecture, followed by a Gated Recurrent Unit (GRU). This design addresses key limitations of existing battery data augmentation methods, particularly in capturing long-term dependencies across multivariate battery parameters and effectively handling irregular time series data. We evaluated our model using a complex industrial dataset from EODev, encompassing four distinct batteries operating under diverse conditions, including hybridization with fuel cells. Additionally, to further validate the broad applicability of the proposed method, we applied it to the NASA battery dataset, specifically batteries B0005 and B0006. The results highlight that the proposed TransGRU-TimeGAN demonstrates excellent versatility and adaptability across a variety of real-world operational scenarios, showing its robustness in industrial applications such as GEH2 systems.

Furthermore, We conducted a comprehensive comparison of the
proposed TransGRU-TimeGAN model with the original TimeGAN and
other state-of-the-art battery data augmentation techniques. The results
consistently show that TransGRU-TimeGAN outperforms all competing
methods, demonstrating its superior effectiveness in augmenting data
for lithium-ion batteries. These findings underscore the strengths of
our approach in improving predictive accuracy and robustness for
real-world battery applications.

Ultimately, the TransGRU-TimeGAN model represents a significant advancement in data augmentation techniques for battery health monitoring. By enhancing the accuracy of State of Health (SOH) prediction and improving robustness and versatility, it serves as a valuable asset for predictive maintenance strategies real-world battery systems.

In future studies, it would be interesting to explore the applicability
of the proposed TransGRU-TimeGAN model in domains beyond battery
health monitoring, potentially extending its use to various time-series
forecasting tasks across different industries. Furthermore, investigating
how the incorporation of external factors, such as temperature, humid-
ity, or usage patterns, affects battery performance and the effectiveness
of the TransGRU-TimeGAN model would be essential. By integrating
these external variables, we aim to enhance the model's robustness and
adaptability under varying environmental conditions, ultimately im-
proving its predictive capabilities and practical applicability in diverse
scenarios.

CRediT authorship contribution statement

**Soufian Echabarri**: Writing – original draft, Visualization, Investigation, Conceptualization. **Phuc Do**: Writing – review & editing, Visualization, Validation, Supervision, Methodology, Funding acquisition, Formal analysis. **Hai-Canh Vu**: Writing – review & editing, Visualization, Supervision, Methodology, Funding acquisition, Conceptualization. **Pierre-Yves Liegeois**: Writing – review & editing, Supervision, Project administration, Funding acquisition, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.

Acknowledgment

This work was financed in part by the ANRT (Association nationale de la recherche et de la technologie) with a CIFRE n° 2023/0482.

Data availability

The data that has been used is confidential.
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