Introduction

In the current global context of energy transition and decarbonization of the power matrix, efficient, safe, and sustainable storage of energy has become a strategic pillar to ensure grid stability and support the widespread adoption of renewable sources.1,2 Among various energy storage technologies, lithium-ion batteries have demonstrated superior performance. Specifically, lithium iron phosphate (LFP) batteries stand out due to their high thermal stability, extended lifespan, cost-effectiveness, and improved safety compared to other lithium-ion chemistries.3,4,5

Despite these advantages, LFP batteries present significant challenges in efficient management, particularly in accurately estimating internal states: state of charge (SOC), state of health (SOH), and state of safety. These parameters cannot be directly measured using conventional sensors, and their real-time estimation is essential for optimal operation, fault detection, and system safety.6,7,8,9 Their evaluation requires advanced modeling and estimation techniques, as they are influenced by complex electrochemical processes occurring within the cell, complicating the identification of degradation mechanisms and potential performance improvements.10,11

Traditional approaches to battery state estimation are often based on modeling microscopic degradation mechanisms, such as the growth of the solid electrolyte interphase (SEI) layer on the anode.12 However, these methods typically rely on invasive measurements, limiting their practical application.13,14 Consequently, there is growing interest in non-invasive, real-time diagnostic methods integrated into battery management systems (BMS).15 Techniques such as electrochemical impedance spectroscopy (EIS)16 and the distribution of relaxation times (DRT),17 based on equivalent electrical circuit models, have gained relevance in this context.

EIS is widely used to investigate lithium-ion batteries and other electrochemical systems.18 Using a frequency response analyzer (FRA), impedance spectra are obtained by superimposing a direct current or constant voltage signal over a wide frequency range. High-frequency responses typically reflect internal ohmic resistance (electrolyte, electrodes, and contacts), mid-frequencies correspond to electrochemical processes such as SEI formation, and low frequencies are related to lithium-ion diffusion within the electrode materials.19,20

However, interpreting EIS data can be challenging due to overlapping contributions from different processes. The DRT technique addresses this limitation by deconvolving the impedance spectrum into a distribution of discrete time constants, each corresponding to a specific electrochemical mechanism. This decomposition facilitates the identification and classification of degradation modes.21,22,23,24

Several studies have confirmed that DRT enhances the interpretability of EIS by separating overlapping processes. For instance, Illig et al. demonstrated that, whereas conventional EIS often struggles to resolve phenomena occurring on similar time scales, the DRT method allows for the separation and identification of distinct processes, such as charge transfer reactions and lithium-ion diffusion. It also allows for the detection of changes in kinetic parameters over time, enabling early identification of issues like SEI growth, active material loss, and lithium plating.25

Wan et al. evaluated DRT estimation methods using different discretization techniques, including piecewise linear and radial basis functions (RBF), applied to both synthetic (ZARC, Havriliak-Negami) and experimental data. Their open-source software, DRTtools, facilitates comparative analysis and reproducibility in DRT research. RBF-based approaches demonstrated superior stability and extrapolation capability, particularly with noisy or incomplete EIS datasets.26

Goldammer et al. proposed a method for deriving the DRT from time–domain data, specifically analyzing voltage relaxation after current pulses. This alternative to frequency–domain EIS offers improved resolution of slow processes and greater potential for real-time BMS integration. The method involves solving a least-squares minimization problem to derive a gain vector that reconstructs the impedance spectrum. Experimental validation with pouch cells and aging studies confirmed the method’s suitability for in situ monitoring.27

This work proposes the development of a machine learning-based methodology for the rapid and accurate estimation of the SOH of backup batteries, using EIS data. Building on previous research that has highlighted the potential of data-driven techniques to extract meaningful health indicators from impedance spectra,28,29,30,31,32,33 this approach focuses on training a neural network to directly map EIS measurements to the DRT, thus avoiding numerically unstable inverse procedures traditionally used for DRT reconstruction. The interpretation of the resulting DRT is based on the infinite Voigt equivalent circuit model, where the overall impedance is represented as an integral of distributed RC elements. This DRT-based output will be integrated into a diagnostic framework designed to estimate SOH efficiently and non-invasively, enabling real-time monitoring of battery degradation. The proposed methodology is especially suitable for critical applications where early detection of aging is essential to ensure reliability and operational safety.

Methods

Experimental Design and Initial Characterization

This study is based on the electrochemical characterization of lithium-ion LFP pouch cells through EIS, complemented by deep learning techniques for the non-invasive estimation of the SOH. Commercial pouch cells with a nominal capacity of 6.5 Ah were used, representing two different aging levels for EIS measurements: one at a pristine state (99% SOH) and another at a degraded state (empirical SOH between 83% and 86%). The empirical SOH was determined by counting the discharged ampere-hours (Ah) during cycling under standard conditions at 25 \(^{\circ }\)C and a C/5 charge–discharge rate. The analysis focuses on these two SOH levels due to the operational constraints of the battery system. Operation below approximately 80% SOH is avoided for safety reasons. and is therefore not representative of real operating conditions. Although only two levels are analyzed, the parametric generation of synthetic data allows intermediate states within the operational range to be represented, providing a reasonable approximation of battery degradation dynamics.

EIS measurements were performed at five different temperatures (0°C, 10°C, 20°C, 30°C, and 40°C) to capture the thermal evolution of the frequency response. To ensure thermal stabilization and uniformity across the cell surface, a rest period was applied between tests, and individual cell temperatures were monitored using thermocouples. Prior to each measurement, the cell was charged to 100% SOC and rested for 1 h to reach equilibrium conditions. Spectroscopy was carried out using a precision potentiostat by applying a 5-mV RMS signal over a frequency range from 1 kHz to 0.01 Hz, capturing phenomena ranging from purely ohmic responses to diffusion and double-layer charge accumulation processes.

Equivalent Circuit Model Fitting

The first stage of analysis consisted of fitting equivalent electrical circuit models to each impedance spectrum. Three main topologies were considered, all including a series ohmic resistance (\(R_\text {s}\)) and one, two, or three constant phase elements (CPE).

These models allow capturing the processes occurring at various timescales within the cell with different levels of granularity, from fast electrolyte processes to slower effects related to electrode diffusion or the formation of passivation layers. Warburg-type elements were not included at this stage, as their effect was effectively absorbed by CPEs distributed across different branches.

Each model was individually fitted to each spectrum using a nonlinear optimization procedure via the lsqnonlin function in MATLAB. The objective function minimized the sum of squared errors between the simulated and experimental complex impedance, considering both real and imaginary parts, evaluated across 30 logarithmically-spaced frequencies. The impedance reconstruction was computed according to the number of CPE branches in parallel, as shown in:

$$\begin{aligned} Z(\omega ) = R_\Omega + \sum _{k=1}^{m} \frac{1}{\frac{1}{R_{\text {s},k}} + Q_k (j\omega )^{n_k}} \end{aligned}$$
(1)

where \(R_\Omega \) is the ohmic resistance of the system, representing the resistance of the electrolyte, current collectors, and other purely resistive elements, \(R_{\text {s},k}\) is the series resistance associated with the k-th CPE, modeling phenomena such as charge transfer, m is the number of CPEs considered in the model, \(Q_k\) is the CPE coefficient related to a distributed pseudocapacitance, \(n_k\) is the CPE exponent describing the non-ideal behavior of the system, with values between 0 and 1, \(\omega \) is the angular frequency, and j is the imaginary unit.

The optimal model for each spectrum was selected as the one that presented the lowest normalized relative error. This selection ensures a suitable balance between numerical accuracy and physicochemical relevance of the extracted parameters.

Theoretical Basis for DRT Calculation

Once the equivalent circuit model was determined for each impedance spectrum, a DRT analysis was performed. This method enables decomposing the system response into characteristic timescales of the involved physicochemical processes.

The adopted approach is based on a discrete representation of the function \(G(\tau )\) using a finite-length Voigt circuit composed of a sum of N \(R_k/Q_k\) branches connected in parallel. The total impedance of the system is described by:

$$\begin{aligned} Z(\omega ) = \sum _{k=1}^{N} \frac{R_k}{1 + j \omega \tau _k} \end{aligned}$$
(2)

where \(\tau _k = (R_k Q_k)^{1/n_k}\) represents the time constant associated with the k-th branch. In this context, the function \(G(\tau )\), which characterizes the relaxation time distribution with non-ideal R/Q behavior, is given by the analytical expression in:

$$\begin{aligned} G_{R/Q}(\tau ) = \sum _{k=1}^N \frac{R}{2\pi } \cdot \frac{\sin \left( (1 - n_k) \pi \right) }{\cosh \left( n_k \ln \left( \frac{\tau _k}{\tau _{R/Q}} \right) \right) - \cos \left( (1 - n_k) \pi \right) } \end{aligned}$$
(3)

A discrete approximation is adopted in this study, since the primary focus is on stationary backup batteries, where the objective is to analyze the overall variation of the DRT under different operating conditions rather than resolving each temporal contribution with high precision. Similar to the approach of Iurilli et al., who used discrete DRT representations derived from impedance spectra to construct simplified equivalent circuit models, this method facilitates interpretation and the identification of relevant trends without requiring a continuous or fully generalized model, which is consistent with our interests.34

Synthetic Dataset Generation

To train deep learning models robustly, a synthetic dataset was generated that combines the observed physical diversity with controlled simulations. For each fitted spectrum, 1000 random perturbations were applied to its physical parameters within a \(\pm 20\%\) range, while maintaining physical consistency constraints. These perturbations preserve the inherent electrochemical relationships between parameters, ensuring that each synthetic spectrum corresponds to a physically meaningful battery state.

Each variant was re-simulated and the percentage error with respect to the base spectrum was evaluated. Only those examples with an error below 5% in at least 25 of 30 points of the spectrum were retained, ensuring that variations did not introduce non-physical behavior or numerical artifacts. This threshold was selected to maintain realistic spectra while allowing the generation of a variety of synthetic examples with measurable differences in DRT features, representing distinct SOH. In this way, the data augmentation procedure provides a sufficiently diverse training set for the neural network to capture battery dynamics and learn to distinguish meaningful changes in the SOH.

The DRT was then recalculated for each synthetic spectrum, resulting in a dataset of approximately 30,000 samples including \(Z(\omega )\) spectra, circuit parameters, and \(G(\tau )\) functions. This dataset was split into training (55%) and validation (45%) sets.

Variational Autoencoder

A deep neural network based on a variational autoencoder (VAE) was implemented to automate the interpretation of EIS spectra via DRT computation. In contrast to traditional autoencoders, a VAE learns a probabilistic—rather than deterministic—representation of the data, thereby approximating the posterior distribution of latent variables through Bayesian inference. Within this framework, the model is designed not only to reconstruct the impedance spectra but also to learn a latent representation equivalent to a relaxation time distribution vector. In fact, compared to previous approaches that combine EIS with machine learning, such as CNN or ANN-based spectral reconstruction for SOH estimation,35 our VAE-DRT framework explicitly enforces a physically interpretable latent space aligned with the relaxation time distribution. While standard neural networks focus on global features or spectrum reconstruction without direct correspondence to underlying electrochemical processes, the proposed method embeds each latent variable, resolving overlapping processes and providing enhanced interpretability.36

Structurally, the architecture consists of two main components: an encoder and a decoder. The encoder maps the input impedance spectrum to a compressed latent space, whereas the decoder reconstructs the spectrum from the latent representation. Unlike conventional autoencoders, the VAE introduces a sampling layer that enables the learning of probabilistic distributions in the latent space, thus endowing the model with generative capabilities.

Specifically, the encoder receives as input a concatenated vector of the real and imaginary parts of \(Z(\omega )\) across 30 frequencies. This vector is processed through three fully connected layers with ReLU activation functions, which progressively reduce the input dimensionality and learn a latent representation with a size equal to the number of discretized times. The number of latent variables in the VAE was chosen to match the number of discretized relaxation times in the DRT representation, ensuring a one-to-one correspondence between each latent variable and a specific relaxation time. The encoder subsequently outputs two vectors: one corresponding to the mean \(\mu \) and another to the log-variance \(\log \sigma ^2\) of the latent distribution. These outputs are combined to generate the latent representation via the reparameterization in:

$$\begin{aligned} Z = \mu + \sigma \cdot \epsilon , \quad \epsilon \sim \mathcal {N}(0, I) \end{aligned}$$
(4)

where \(\sigma = \exp (0.5 \log \sigma ^2)\). As a result, the sampling process produces a continuous and differentiable latent space that effectively captures the intrinsic variability of the impedance spectra.

On the decoding side, the sampled \(G(\tau )\) is passed to the decoder, which reconstructs the original impedance spectrum \(Z(\omega )\) using multiple fully connected layers with ReLU activations. The reconstructed output \(\hat{Z}(\omega )\) is expressed as:

$$\begin{aligned} \hat{Z}(\omega ) = \text {Decoder}(Z) \end{aligned}$$
(5)

To guide the training process, the loss function combines two complementary components; the reconstruction loss and the latent space consistency loss. These terms jointly ensure that the model learns a meaningful latent representation while achieving accurate reconstruction of the impedance spectra.

The reconstruction loss (Eq. 6) penalizes discrepancies between the input impedance spectrum and its reconstruction, thereby ensuring that the decoded output retains the primary features of the original signal:

$$\begin{aligned} \mathcal {L}_{\text {rec}} = \frac{1}{N} \sum _{I=1}^{N} \left( Z_i - \hat{Z}_i\right) ^2 \end{aligned}$$
(6)

In addition, to reinforce the physical interpretability of the latent space, an extra term (Eq. 7) compares the estimated relaxation time distribution \(G(\tau )\) with a target distribution \(\hat{G}(\tau )\) derived from an equivalent circuit model. This constraint encourages the network to embed meaningful electrochemical information in the latent representation:

$$\begin{aligned} \mathcal {L}_{G} = \frac{1}{M} \sum _{j=1}^{M} \left( G_j - \hat{G}_j\right) ^2 \end{aligned}$$
(7)

Consequently, the total loss function (Eq. 8) is defined as a weighted sum of these two contributions:

$$\begin{aligned} \mathcal {L}{\text {total}} = \lambda _1 \cdot \mathcal {L}{\text {rec}} + \lambda _2 \cdot \mathcal {L}_{G} \end{aligned}$$
(8)

In the implementation, equal weights of \(\lambda _1 = \lambda _2 = 0.5\) were assigned to maintain a balanced training dynamic. The model was then trained using the Adam optimizer, with learning rates of \(10^{-3}\) for the encoder and \(10^{-4}\) for the decoder, over 7500 epochs and a batch size of 128. Moreover, dropout regularization was incorporated to improve generalization and mitigate overfitting.

Finally, the entire architecture was developed in MATLAB using the Deep Learning Toolbox with training and inference performed using GPU acceleration to improve computational efficiency.

Degradation Estimation from the DRT

The DRT provides valuable insights into electrochemical mechanisms and their evolution throughout the battery’s lifetime. To estimate the degradation, we focused on the changes in the position of the peaks in the DRT spectrum over time. Following the approach proposed by Jung et al., which introduced a diagnostic indicator based on the movement of peaks in the high-frequency region of the DRT, we analyzed how shifts in peak positions correlate with battery aging and degradation.37 Specifically, the degradation was estimated by tracking the shifts in peak frequencies. A drift toward lower frequencies indicates slower kinetics, reduced ionic mobility, or increased resistance in the electrodes, which points to material or electrolyte degradation. Conversely, shifts to higher frequencies suggest enhanced ionic conductivity or faster electrochemical reactions, potentially indicating improved battery performance. This method allows us to monitor the evolution of electrochemical activity without relying on integral measures, focusing solely on peak dynamics to evaluate degradation.

Results and discussion

This section presents the experimental validation of the proposed machine learning-based methodology for SOH estimation using EIS data. Building on the framework introduced earlier, we apply the trained VAE to impedance spectra measured at different temperatures and health states. The results demonstrate the model’s ability to reconstruct impedance responses accurately and to extract meaningful latent representations corresponding to the distribution of relaxation times. These latent features were then analyzed to assess their consistency with known aging effects and electrochemical behavior. Furthermore, the robustness of the approach has been evaluated across a range of operating conditions, highlighting its potential for real-time, non-invasive battery diagnostics.

Fig. 1
Fig. 1
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EIS spectra measured at different temperatures and states of health, including two specific health states: one at the beginning of life (New) and another at a more degraded state (Old).

Figure 1 shows the electrochemical impedance spectroscopy spectra measured at five temperatures (0°C, 10°C, 20°C, 30°C, and 40°C)  for two SOH: a fresh (pre-aged) battery and a degraded (aged) battery. The curves correspond to the fitted impedance response obtained by optimizing the parameters of an equivalent circuit model to minimize the fitting error. The numerical values of the fitted parameters are listed in Table I. Depending on which configuration yields the lowest fitting error, the circuit includes one, two, or three CPEs. In the table, \(R_\textrm{ohm}\) and \(R_i\) (\(I=1,2,3\)) denote resistance in ohms ( \(\Omega \)), \(Q_i\) (\(I=1,2,3\)) is the CPE representing a non-ideal capacitance with units \(\mathrm {\Omega ^{-1}\,s^{n_i}}\), and \(n_i\) (\(I=1,2,3\)) is a dimensionless exponent indicating the deviation of the CPE from an ideal capacitor (\(n_i = 1\) corresponds to an ideal capacitor). These parameters quantitatively describe the impedance behavior under varying temperatures and SOH.

Table I Fitted parameters of the equivalent circuit model for each test
Full size table

The resulting Nyquist plots exhibit the characteristic semicircular shape, indicating the presence of dominant resistive and capacitive processes typically observed in electrochemical systems.

At higher temperatures (30°C, and 40°C), the diameter of the semicircle decreases, suggesting improved ion mobility and reduced internal resistance compared to measurements at lower temperatures. In contrast, the spectra corresponding to the degraded state of health show a more pronounced reduction in the semicircle, pointing to increased internal resistance. This behavior can be attributed to degradation mechanisms such as changes in electrode materials or the growth of the solid electrolyte interphase layer, which hinders charge transfer.38,39

On the other hand, the measurements at lower temperatures (0°C and 10°C) show larger semicircles, indicative of increased internal resistance. This effect is likely due to the decrease in ionic conductivity at low temperatures, which negatively impacts the overall efficiency of the battery.

Fig. 2
Fig. 2
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Relaxation time distribution derived from the EIS fitting.

Figure 2 shows the relaxation time distribution computed from the impedance spectra using the equivalent circuit model. The DRT provides insight into the charge and discharge mechanisms of the battery as a function of relaxation times. In this case, a significant change is observed in both the shape and the area under the DRT peak depending on the battery’s state of health.40

To quantify the peak shifts in the DRT spectra, the displacement of each dominant peak was calculated in seconds and expressed as logarithmic changes (\(\Delta \log \tau \)) and corresponding frequency variations. The results are summarized in Table II.

At low temperatures (0°C, 10°C, and 20°C), the dominant peaks shift toward shorter relaxation times (negative \(\Delta \log \tau \)). Comparison with the equivalent circuit parameters (Table I) shows that these negative shifts are generally associated with decreases in R1 and increases in Q1. At 30°C, a small positive shift toward longer relaxation times is observed (\(\Delta \log \tau = +0.10\)), which coincides with an increase in Q1. At 40°C, no significant peak displacement is detected, consistent with the stability of the corresponding R1.

Table II Quantified peak shifts of the DRT spectrum before and after aging
Full size table

Figure 3 shows the final architecture of the neural network implemented to analyze and reconstruct EIS data. The network is trained using impedance spectra measured at different temperatures and SOH. The encoder processes the EIS spectral features and generates a latent representation, while the decoder reconstructs the impedance spectra from this latent vector. This neural network proved effective in reconstructing the spectra and predicting relevant electrochemical parameters.

Fig. 3
Fig. 3
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Schematic of the neural network implemented for EIS data analysis and reconstruction.

Figure 4 shows the training loss curves of the neural network. It can be observed that both the reconstruction loss (Loss_Z) and the latent representation loss (Loss_G) decrease significantly as training progresses, indicating that the network is learning to accurately represent and reconstruct the input data. The total loss also decreases, reflecting convergence toward an optimal solution.

Fig. 4
Fig. 4
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Loss curves during the training of the neural network: (a) the loss associated with the latent space (distribution relaxation time in the latent space), which reaches a minimum error of \(10^{-6}\) in its best iterations; (b) the loss of the decoder output (electrochemical impedance), which reaches a minimum error of \(10^{-7}\) in its best iterations; (c) the combination of both errors, resulting in a mean squared error of \(10^{-6}\) for the total loss in the best iterations.

Figure 5 presents a visualization of the latent space for a random subset of data reserved for testing. This suggests that the network has successfully learned to identify key features associated with the electrochemical behavior of the batteries as a function of their health status. Furthermore, the figure shows a comparison between real EIS spectra and those reconstructed by the decoder from a randomly selected test sample. The close similarity between the real and reconstructed spectra with an average mean squared error of the impedance equal to 0.0008, confirms the ability of the VAE to accurately capture the underlying impedance response. In addition to the mean squared error, the VAE-DRT framework achieved an average mean absolute error of 0.000117 for the impedance magnitude, indicating that deviations remain small across all frequencies. Moreover, the coefficient of determination \(\textrm{R}^2\) reached a value of 0.999936, reflecting an agreement between predicted and true spectra.

Fig. 5
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(a) Latent space of the neural network (DRT reconstruction), where Gtrue denotes the DRT theoretically calculated from the test data and Gpred represents the neural network output; (b) Reconstruction of the EIS for a random test sample, where Ztrue corresponds to the original impedance data and Zpred to the decoder output of the neural network.

Specifically, the validation on the test dataset, which comprises 12,600 spectra, indicates an average computation time of 0.00478 s per spectrum for the VAE-DRT framework. The network contains 14,830 parameters. By comparison, conventional Tikhonov-based DRT inversion methods typically require 1–5 s per spectrum on modern CPUs,41 yielding a speed-up of approximately a factor of 209 for our approach. This substantial improvement in computational efficiency highlights the potential of the VAE-DRT framework for rapid EIS analysis and real-time battery diagnostics.

To further assess the usefulness of the neural network, we analyzed the initial measurements after computing the DRT with the encoder of our model and verified its reconstruction through the decoder. Figure 6 presents both the DRT and the reconstructed EIS, in this case shown only for the temperatures 0°C, 10°C, and 20°C in order to avoid redundancy in the results. This new approach enables us to clearly identify the shifts in the DRT peaks.

Fig. 6
Fig. 6
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Distribution of relaxation times and reconstructed impedance spectra of the experimental samples at 0°C, 10°C, and 20°C.

This phenomenon is typically associated with reduced ionic mobility, often attributed to the thickening of the solid electrolyte interphase layer or the formation of less conductive phases within the electrodes. Such changes hinder the efficiency of charge transfer processes, leading to increased internal resistance and a decline in overall battery performance. The rate and extent of these peak shifts are strongly influenced by temperature.42 At elevated temperatures, higher kinetic energy accelerates degradation processes, resulting in more pronounced shifts in the DRT peaks. Conversely, at lower temperatures, although degradation progresses more slowly, the overall performance of the battery is nevertheless limited due to reduced ionic mobility.43,44

Finally, although the proposed VAE-DRT framework was developed and validated using EIS data from LFP cells, the architecture itself is general and can be applied to other battery chemistries. However, the latent representation learned during training reflects the electrochemical features characteristic of LFP systems and therefore cannot be assumed to generalize reliably to chemistries with different kinetic behavior or time–constant distributions, such as NMC or LTO. For this reason, transferring the framework to a different chemistry would require retraining or fine-tuning the model using impedance spectra representative of the target chemistry.

Conclusion

This work presented a machine learning-based methodology for the non-invasive estimation of the degradation of lithium iron phosphate batteries using electrochemical impedance spectroscopy data. By combining equivalent circuit modeling, synthetic dataset generation, and a variational autoencoder, the proposed approach overcomes the limitations of traditional DRT reconstruction methods, which are often numerically unstable and computationally intensive.

The experimental results confirmed that the VAE architecture is capable of accurately reconstructing impedance spectra across different temperatures and degradation levels, while simultaneously learning a latent representation that captures the distribution of relaxation times. The extracted DRT features not only align with the evolution of electrochemical parameters but also provide a foundation for degradation estimation through their direct implementation in a BMS equipped with a cell-level impedance sensor. By enabling real-time DRT computation with a trained neural network and subsequent interrogation of a three-dimensional lookup table, which links peak characteristics with temperature, this approach could serve as a low-cost and computationally efficient pathway for advanced state-of-health diagnostics.

The methodology provides three key advantages: (1) robustness to variations in battery states achieved through training on physically consistent synthetic EIS spectra generated by perturbing equivalent circuit model parameters, (2) real-time applicability enabled by bypassing iterative inversion procedures, and (3) enhanced interpretability of degradation mechanisms could be expected through DRT-informed latent features, as the shifts and evolution of DRT peaks may correspond to specific degradation pathways. Together, these strengths make the approach well-suited for integration into battery management systems, especially in critical applications requiring early detection of performance decline and safety risks.