Identifying Failure Conditions in Li-Ion Batteries Using Distribution of Relaxation Time Method

Abstract

In this paper, the Distribution of Relaxation Times (DRT) method is introduced for analyzing aging and failure conditions in lithium-ion (Li-ion) batteries, addressing challenges associated with its implementation. While Electrochemical Impedance Spectroscopy (EIS) and Equivalent Circuit Models (ECMs) are commonly used to monitor battery performance, their interpretation is often complicated by overlapping semicircles in impedance spectra. The DRT technique resolves this issue by deconvolving relaxation times, enabling the separation of individual electrochemical processes and providing a clearer understanding of aging and failure conditions. The peaks of lower frequency components in DRT plots, specifically the charge transfer and diffusion processes, are key indicators of the battery failure point. When these two processes merge, it signals that the battery can no longer function, marking a critical failure point in Li-ion batteries. Identifying failure conditions and aging in Li-ion batteries using DRT offers a more advanced approach compared to ECM, as it delivers greater detail in the electrochemical processes that contribute to performance degradation. The analysis of two kinds of different Lithium-Ion battery cells based on the DRT reveals the specific aging and failure patterns, particularly in later battery life stages. The findings demonstrate the potential of DRT as a real-time indicator to monitor the status and the lifecycle of the battery.

1. Introduction

Lithium-ion batteries (LIBs) have become essential in modern society due to their superior energy storage capabilities [1,2]. As the LIB industry rapidly grows, both academia and industry are focusing on improving the electrochemical performance of these batteries across various applications. As electrode materials approach their performance limits, ensuring efficient and safe battery utilization has become paramount. A comprehensive understanding of the aging mechanisms and failure conditions of LIBs under different operating conditions is crucial for optimizing their performance and lifespan [3].

Since lithium-ion (Li-ion) batteries are the main part of electric vehicles (EVs), it is important to estimate and predict their lifespan [4,5,6]. Noninvasive methods should be adopted to achieve those goals as the tests need to be performed while the batteries are being used. There are many kinds of different methods proposed to achieve these goals such as the method to measure and analyze the battery performance [7], methods to evaluate the battery state [8,9], and the method to use data-driven approach [10]. These techniques provide valuable information about the battery internal condition, which is essential for the battery management system [11].

The complex structure of LIBs, consisting of components such as the cathode, anode, electrolyte, separator, and current collector, makes it challenging to identify the specific aging mechanisms during the battery use [12,13,14]. Electrochemical Impedance Spectroscopy (EIS) is a widely used tool for monitoring battery performance, providing insights into material behavior over time [15,16]. However, EIS often faces challenges in interpreting overlapping semicircles in impedance spectra, which complicate the identification of individual electrochemical processes [17]. The Equivalent Circuit Models (ECM) used in conjunction with EIS further complicates this process, often requiring assumptions that may obscure the true behavior of the battery [18,19].

In contrast, the Distribution of Relaxation Times (DRT) method offers a more advanced approach for identifying failure conditions and aging in LIBs. By deconvolving the relaxation times, DRT allows for a clearer separation of electrochemical processes, providing a detailed view of battery behavior across multiple time scales [20]. This model-free approach is particularly useful in distinguishing the overlapping relaxation processes, which are difficult to interpret with traditional ECM techniques [21]. The primary goal of this paper is to demonstrate how DRT can be used to more accurately identify failure conditions and aging in LIBs [22], offering advantages over ECM. Specifically, DRT allows for the isolation of key electrochemical processes, such as charge transfer and diffusion, which are critical for understanding battery aging and failure mechanisms. This study will show how DRT can provide insights into the aging behavior of LIBs and enhance the understanding of their performance degradation over time.

The optimization of DRT calculation methods will also be discussed, focusing on how to separate EIS data at overlapping time scales and resolve key electrochemical processes that are typically difficult to distinguish using ECM [23,24]. In this study, the comparison between DRT and ECM is focused on their qualitative interpretive differences rather than numerical fitting performance. DRT provides a model-free representation that separates overlapping relaxation processes more clearly than ECM, allowing aging related changes such as SEI growth, charge-transfer resistance, and diffusion limitations to be identified even when semicircles overlap. A full quantitative benchmarking of DRT and ECM fitting errors would require a dedicated framework and was beyond the scope of this work. While previous studies have explored aging aspects such as capacity fade and impedance growth [25], the low-frequency components of DRT, which are closely related to charge transfer and diffusion, have not been extensively studied. These components are essential for understanding the aging and identifying failure conditions of LIBs. This study will also provide a more complete understanding of battery aging and failure conditions, which will enhance battery management, thereby improve the performance of battery-based systems and prolonging the battery life. Therefore, this study emphasizes using DRT for precise battery aging characterization and explores its real-time monitoring applications for better lifecycle management. This study builds upon previous research on the use of DRT for battery diagnostics by addressing critical gaps in the literature. While prior works have primarily focused on general aging analysis [26], the present work identifies the convergence of charge transfer and diffusion peaks in the DRT plot as a robust indicator of battery failure. A comparative analysis involving cylindrical 18650 cells and LR2032 coin cells demonstrates the broader applicability of DRT analysis across different chemistries and form factors. Additionally, the implementation includes optimization of the Tikhonov Regularization (TR) parameter to improve feature clarity in DRT plots and supports the integration of DRT into real-time battery management systems, extending its utility beyond offline diagnostics and offering new pathways for predictive maintenance.

The remainder of this paper is organized as follows: Section 2 describes the data acquisition methods for 18650 battery aging analysis and provides the specifications of the LR2032 coin cells used in this study, obtained from an external source. Section 3 discusses the application of the DRT method, focusing on the transformation of Nyquist plots into DRT plots and emphasizing the advantages of DRT over traditional ECM for analyzing EIS data. Section 4 presents a detailed evaluation of EIS Nyquist plots and corresponding DRT plots for LIBs, tracing their performance up to the End of Life (EOL). It also highlights the use of DRT plots in diagnosing failure mechanisms and aging processes. Finally, Section 5 summarizes the key findings and outlines potential directions for future research.

2. Data Acquisition During Battery Aging

This section describes the aging test conducted on a cylindrical 18650 LIB. The cylindrical battery cell used in the measurement has the specifications provided in

Table 1. Specification of the Battery used for the Aging Test.

Property	Value
Chemistry	Nickel Manganese Cobalt
Type	18650
Maximum Capacity	2850 mAh
Nominal voltage	3.65 V

. The battery cell was subjected to aging through repeated charge and discharge cycles to prepare EIS AC impedance spectra, which were measured every 5 cycles. Changes in impedance parameters during the aging period were extracted using the measurement results and ECM followed by curve fitting. The battery aging process was carried out using HYSCLAB B.O.D Incubator equipment, maintaining a constant temperature of 25 degrees Celsius. The charge–discharge tests of the battery and EIS tests were conducted using WonATech WEIS-500. Cycle tests were performed with constant current charging at 0.5C and constant current discharging at 0.5C, as detailed in Figure 1. Additionally, a one-hour rest period was implemented after each charge–discharge cycle. EIS tests were conducted every 5 cycles, with impedance spectra measured using a 60 mV perturbation in the frequency range of 0.1–1kHz, while the State of Charge (SOC) of the battery was maintained at 100%. The charge–discharge cycle test for battery aging was conducted up to 1035 cycles, continuing until the battery reached the failure condition, when the capacity dropped below 75% of its initial value. In this work, the 75% capacity retention point was used as the practical end-of-life (EOL) threshold, as lithium-ion batteries in many applications are commonly considered to reach failure when capacity falls below approximately 70–80% of the initial value.

This battery analysis is compared with two commercially available 45 mAh Eunicell LR2032 Li-ion coin cells. The data used in this study were acquired from experiments conducted at Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK [27], on 45 mAh Eunicell LR2032 Li-ion coin cells (LiCoO₂/graphite chemistry) cycled at a constant 25 °C. Each cell underwent continuous charge–discharge cycles, with a constant current constant voltage (CC–CV) charge up to 4.2 V and a constant current (CC) discharge down to 3 V. EIS measurements were taken at specific states of charge during each cycle, and the cells were cycled until reaching the EOL. The EIS and capacity data are available in a public repository. The 18650 cylindrical cell and LR2032 coin cells were selected to demonstrate the applicability of the DRT method across different lithium-ion battery formats and chemistries. The 18650 cell is an NMC-based system with a wound electrode structure, while the LR2032 coin cells use LiCoO₂/graphite chemistry with a compact layered design. These differences in electrode thickness, geometry, and active material lead to variations in relaxation behavior, allowing a broader comparative evaluation of DRT performance.

3. Distribution of Relaxation Time

In the world of electrochemical research, the DRT method is a valuable tool. This method effectively analyzes impedance across varying frequencies. By using special techniques, the DRT method can be used to figure out how relaxation times are spread out in electrochemical systems [28]. So, the impedance of an electrochemical system can be represented by Equation (1)

$$Z\left(\omega \right)=R_0+{\int }_0^{\infty }{\displaystyle \frac{g\left(\tau \right)}{1+j\omega \tau }}d\tau$$

(1)

where $R_0$ is the ohmic resistance and it is the impedance at very high frequencies where the capacitive effects become negligible, $g\left(\tau \right)$ is a function that describes the distribution of relaxation times within the system, ω is the angular frequency where the impedance is measured, τ = RC is the relaxation time and R and C is the effective resistance and capacitance, respectively.

The impedance of continuous representation of RC elements including inductance component L is represented by Equation (2):

$$Z\left(\omega \right)=R_0+{\int }_{-\infty }^{+\infty }{\displaystyle \frac{\gamma \left(ln\tau \right)}{1+j\omega \tau }}d\left(ln\tau \right) + jwL$$

(2)

where ${\int }_{-\infty }^{+\infty }\gamma \left(ln\tau \right)d\left(ln\tau \right)=1$.

Equation (2) illustrates the relationship between impedance data and frequency distribution. Here, R₀ represents the ohmic resistance, 1/(1 + jωτ) denotes the DRT kernel, and $\gamma \left(ln\tau \right)$ = τg(τ) ≥ 0 represents the distribution function of relaxation time. Now, since (2) includes the inductance components, excluding the inductance corresponds to EIS data without an inductive element. The modified equation will be

$$Z\left(\omega \right)=R_0+\underset{-\infty }{\overset{+\infty }{\int }}{\displaystyle \frac{\gamma \left(ln\tau \right)}{1+j\omega \tau }}d\left(ln\tau \right)$$

(3)

Now, using (3) and separating the real and imaginary parts of impedance, the following equations are obtained (4) and (5).

$$Zre\left(\omega \right)=R_0+\underset{-\infty }{\overset{+\infty }{\int }}{\displaystyle \frac{\gamma \left(ln\tau \right)}{1+{\omega }^2{\tau }^2}}d\left(ln\tau \right)$$

(4)

$$Zimg\left(\omega \right)=\underset{-\infty }{\overset{+\infty }{\int }}{\displaystyle \frac{\gamma \left(ln\tau \right)\omega \tau }{1+{\omega }^2{\tau }^2}}d\left(ln\tau \right)$$

(5)

The DRT profile $\gamma \left(ln\tau \right)$ is the unknown quantity that needs to be reconstructed from the impedance data. However, this equation represents an ill-posed problem for several reasons, including an underdetermined system, noisy data, limited frequency range, regularization issues, discretization, and numerical errors. Since (4) and (5) are in continuous form, they must be converted into a linear system in discrete form, where ${\tau }_n={\displaystyle \frac{1}{2\pi f_n}}, n=\mathrm{1,2},3\dots ,N$, and N is the total number of frequency points.

Now expanding these equations up to n angular frequency ${\omega }_n, n = \mathrm{1,2},3\dots ,n,$ points and the impedance of series nth RC elements can be expressed by the set in (6) and (7).

$$Zre\left(\omega \right)=R_0+{\sum }_{n=1}^N{\displaystyle \frac{\gamma \left(\mathit{ln}\left(\tau \right)\right)\Delta \mathit{ln}\left(\tau \right)}{1+{\omega }^2{\tau }_n^2}}$$

(6)

$$Zimg\left(\omega \right)=\sum _{n=1}^N{\displaystyle \frac{\gamma \left(\mathit{ln}\left(\tau \right)\right)\Delta \mathit{ln}\left(\tau \right)\omega \tau }{1+{\omega }^2{\tau }_n^2}}$$

(7)

Equations (6) and (7) represent an inverse problem that is mathematically ill-posed, meaning small variations or noise in the measured impedance can lead to large fluctuations in the calculated distribution. For this reason, these equations cannot be solved through direct inversion. To obtain a stable and physically meaningful DRT solution, TR is applied, which introduces a smoothness constraint to suppress numerical noise and stabilize the inversion process. DRT represents the impedance as an infinite series of small RC elements [29]. Equations (6) and (7) from Tikhonov cannot be solved directly. To ensure the solution is stable, TR is applied [30]. This regularization extends the cost function by incorporating a term that considers the smoothness of the solution. The regularization level is determined by a parameter, and its value significantly influences the appearance of features in the distribution function. High values may blur features, while low values may introduce incorrect oscillations unrelated to the physicochemical processes of the system. The detailed mathematical formulation and implementation of the DRT method, including regularization, are provided in [31]. In this study, the regularization parameter was carefully selected to generate meaningful distribution functions from the impedance data. A value of 1E-5 was found to be a suitable compromise between indicating features and minimizing residuals. The regularization parameter of 1E-5 was selected through iterative residual analysis to ensure numerical stability while preserving the resolution of the relaxation peaks. Lower values introduced oscillations, whereas higher values caused excessive smoothing. The inductive component was neglected because the EIS measurements were performed within a frequency range of 0.1 Hz to 1 kHz, where the influence of test-lead and current-collector inductance is negligible compared with the electrochemical impedance. Additionally, the DRT curve can be segmented into four peaks (R_Ohm, R_SEI, R_ct and R_D), as depicted in Figure 2b. The identification of specific electrochemical processes within distinct time constant regions in the DRT spectrum is supported by established electrochemical theory and literature. Each peak in the DRT corresponds to a process with a unique characteristic relaxation time (τ = RC), determined by the combination of resistance and capacitance within that region. Specifically, the high-frequency region is associated with ohmic resistance, primarily due to the electrolyte and electrode materials, and typically appears as a sharp peak with a minimal time constant. In the intermediate frequency range, the first broad peak is attributed to the SEI layer, while the second corresponds to the charge transfer resistance at the electrode–electrolyte interface. These processes involve resistive and capacitive elements, resulting in mid-range time constants. The low-frequency region reflects lithium-ion diffusion within the electrode material, modeled by the Warburg element, and produces the largest time constants due to slow ion transport kinetics. This division aligns with prior studies on EIS interpretation using DRT [32,33], which reinforces the physical and electrochemical basis for assigning relaxation time to specific degradation phenomena.

These impedance parameters can be derived by integrating the time constants within each interval of the DRT curve, serving as the basis for regrouping criteria. For each interval, the polarization resistance (Rp) can be calculated using the following formula:

$$R_p= {\int }_{{\tau }_L}^{{\tau }_U}\gamma \left(\tau \right)d\tau$$

(8)

where ${\tau }_U$ and ${\tau }_L$ is the upper and lower limit of time constant, respectively.

While this study does not reconstruct the impedance spectrum from the DRT distribution g(τ), it focuses on analyzing experimental EIS data to reveal overlapping electrochemical processes that are challenging to interpret using conventional Nyquist plots. The DRT method enables the identification of distinct peaks corresponding to SEI resistance, charge transfer, and diffusion, even when these are superimposed in the frequency domain. The trends observed in the DRT plots are consistent with known aging phenomena in lithium-ion batteries, such as increased SEI resistance and the merging of charge transfer and diffusion processes near EOL, thereby the interpretive accuracy of the method is validated.

EIS Nyquist plots are graphical representations used in electrochemical analysis, where the real part of impedance (Z′) is plotted on the x-axis and the imaginary part (Z″) on the y-axis. These plots provide valuable insights into the electrical properties of the system, including resistance, capacitance, charge transfer kinetics, and diffusion processes.

In the ultra-high frequency region, the Nyquist plot primarily reflects the ohmic resistance. The first semicircle, observed in the high-frequency region, corresponds to the Solid Electrolyte Interface (SEI). The second semicircle, located in the intermediate frequency region, is associated with the charge transfer process. The impedances in the lower frequency region, found on the right side of the Nyquist plot and forming an angle of about 45 degrees with the second semicircle, can be represented by Warburg impedance (Zw), as illustrated in Figure 2 [31].

The Nyquist plot is typically analyzed using curve-fitting software to develop an ECM that accurately represents the electrical behavior of a system. However, DRT analysis provides a more advanced alternative to traditional ECM fitting. Unlike the analysis with an ECM, which involves matching impedance data to a predefined circuit model, the DRT analysis directly examines impedance spectra without relying on an explicit model. DRT identifies and quantifies individual relaxation processes with each peak in the DRT spectrum corresponding to a specific process within the system. This approach delivers clear and detailed insights into electrochemical phenomena, making it easier to interpret system behavior. Figure 2 illustrates the transformation between EIS Nyquist plots and DRT plots, highlighting how DRT provides a more comprehensive representation of system parameters and key processes.

4. Results and Analysis

4.1. Evolution of Nyquist Plots over the Battery Life

The Nyquist plots for three types of cells in Figure 3 were obtained from EIS measurements. Impedance spectra were collected every 5 charge–discharge cycle until the cells reached the end of their lifespans. Each spectrum can be divided into four frequency ranges, ultra-high, high, intermediate, and low frequency. The intermediate frequency range is associated with the charge transfer reaction, while the low-frequency range pertains to the diffusion process. Figure 3 shows that the impedances in those frequency ranges are significantly impacted by aging, as can also be found in [34,35]. In contrast, the ultra-high and high-frequency regions correspond to ohmic resistance and the SEI which are less influenced by cycling.

In the ultra-high frequency region, inductive reactance appears below the zero axis, transitioning to ohmic resistance as the frequency decreases. The high and intermediate frequency regions show capacitive reactance, where SEI and charge transfer processes occur. In the low-frequency region, diffusion impedance, represented by a Warburg element, is observed.

The EIS plots reveal that ohmic resistance slightly increases as the batteries approach EOL. The high-frequency region shows a distorted semicircle related to charge transfer and SEI processes. Overlapping semicircles make it challenging to distinguish individual electrochemical processes, though an increase in the height and width of the semicircle is noted with cycling. However, due to the similarity in reaction time constants, these semicircles are superimposed in the impedance spectrum, complicating the derivation of each relaxation time and amplitude.

4.2. Evolution of DRT Plots over the Battery Life

Combining frequency-domain and time-domain analysis with EIS is essential for understanding battery characteristics and diagnosing issues. EIS interpretation can be challenging due to overlapping semicircles in Nyquist plots, making it difficult to discern individual electrochemical processes. DRT analysis, however, allows for a clearer breakdown of these processes. This study compared the behavior of a Li-ion 18650 battery with two LR2032 coin cells throughout their lifespan. DRT plots derived from EIS Nyquist plots revealed differences in frequency ranges, with the 18650-battery showing four peaks and the coin cells showing five or six. This mainly results from the difference in EIS frequency range the 18650 cell was measured from 0.1 Hz to 1 kHz, while the coin cells were measured over a wider range of 0.01 Hz to 20 kHz, allowing additional relaxation processes to be captured. Furthermore, cell geometry contributes to this difference. The 18650 cell has thicker wound electrodes with smoother current distribution, leading to fewer separable processes, whereas the LR2032 coin cells have thinner electrodes and a larger surface-area-to-volume ratio, resulting in additional interfacial and diffusion-related features in the DRT spectra. The lower time constants τ values for the 18650 battery and the higher range for the coin cells were attributed to these variations. The DRT curves provided a clear visualization of overlapping semicircles, enabling separate quantification of each process and offering a deeper understanding regarding the behavior of the battery over time. A significant observation in the DRT plots is the steady increase in the diffusion process peak at the far-right end of the graph with the number of cycles. This trend is consistent across all batteries, indicating ongoing changes in the diffusion process as the batteries age [22]. The peaks associated with the SEI and charge transfer also increased with cycling. As the batteries approached the end of their life cycle, the charge transfer and diffusion peaks begin to converge, ultimately merging into a single peak after a specific number of cycles: 600 cycles for the 18650 battery and 200 cycles for two-coin cells, as shown in Figure 4, Figure 5 and Figure 6. This merging indicates accelerated diffusion kinetics. More specifically, it signifies a dominance of diffusion-related impedance, reflecting hindered lithium-ion transport as the battery ages. As structural degradation, SEI layer growth, and Loss of Active Material (LAM) progress, diffusion resistance increases significantly and begins to overlap with charge transfer resistance. This overlap causes the two processes to lose separation in their characteristic time constants, resulting in merged peaks in the DRT plot. The convergence of these peaks marks a shift in the electrochemical behavior toward slower, transport-limited kinetics and serves as a clear indicator of EOL conditions. This phenomenon aligns with findings from recent studies that link peak merging in DRT spectra to aging-induced diffusion constraints and structural changes within the electrodes. The leftmost peak in the DRT represents the contact or ohmic resistance between the active materials and the collectors. There was a slight increase in this resistance towards EOL, which may be influenced by initial variations introduced during production. These variations can affect the aging behavior over time, contributing to resistance increases during prolonged cycling. The second peak, associated with the SEI layer, initially increased before stabilizing as the battery approached EOL, highlighting the dynamic evolution of the SEI layer. An increase.

Ohmic resistance indicated reduced electrical conductivity, usually resulting from the consumption and decomposition of the electrolyte. Additionally, the rise in SEI resistance suggested degradation, leading to a loss of lithium ions, which in turn decreased both capacity and performance.

Charge transfer resistance, associated with electron movement through the electrode materials and the electrolyte interface, increases as internal resistance rises, thereby hindering the movement of electrons. Similarly, diffusion resistance, which affects the movement of lithium ions between the anode and cathode increases with higher resistance, reducing ion transport efficiency. The growth of the SEI layer and the subsequent loss of cyclable lithium ions further elevate the overall internal resistance [36,37]. LAM is due to mechanical stress from repeated charge–discharge cycles, which can cause fractures in the graphite anode and compromise the structural integrity required for lithium-ion storage. The DRT method can be implemented in real-time battery management systems usingplatforms such as LabVIEW. Real-time impedance data acquisition is performed by interfacing measurement hardware with LabVIEW, followed by preprocessing and numerical inversion using TR. DRT plots are computed and visualized dynamically through LabVIEW dashboards, enabling continuous monitoring of battery health. This implementation supports real-time identification of aging and failure conditions, demonstrating the practical applicability of the DRT approach in embedded systems.

In the context of this study, battery failure is defined as the point at which the cell experiences a critical loss in performance and capacity, marked by a significant increase in internal resistance, the convergence of distinct electrochemical processes, and the onset of irreversible degradation mechanisms. One such mechanism is lithium plating, which occurs when lithium-ion diffusion becomes severely hindered, leading to metallic lithium deposition on the anode surface. This behavior is reflected in the DRT analysis through a pronounced rise in diffusion resistance and the merging of charge transfer and diffusion peaks. These trends align with prior studies that link lithium plating to increased impedance and altered electrochemical kinetics during the EOL phase of lithium-ion batteries [38,39]. In this study, the merging of the charge-transfer and diffusion peaks was used to indicate the onset of transport-limited behavior, which is commonly associated with lithium plating. As the 18650 cell approached EOL, the DRT spectra showed a progressive convergence of these peaks along with a clear increase in internal resistance and a shift toward longer relaxation times. These electrochemical signatures are consistent with the behavior typically observed when lithium-ion transport becomes restricted and plating begins to occur. Although post-mortem examination was not performed, the strong correlation between peak merging, rising impedance, and diffusion limitation provides reliable indirect evidence of this failure mechanism.

When the charge transfer and diffusion peaks merge, the battery exhibits significantly increased internal resistance and transport limitations, which are associated with the onset of lithium plating on the anode. In this process, lithium ions combine with free electrons to form metallic lithium, increasing internal resistance and impeding voltage production and electrochemical reactions. Although direct observation is beyond the scope of this study, previous investigations have demonstrated that lithium plating commonly occurs under such conditions, where charge transfer resistance and diffusion limitations dominate the impedance response [40,41]. This phenomenon reduces ionic conductivity and contributes to EOL failure. The merging of charge transfer and diffusion process peaks into a single peak indicates a uniform rise in internal resistance, ultimately preventing efficient electrochemical activity and signaling the EOL of the battery. The movement and merging of peaks in the DRT plots are critical indicators of battery failure. The DRT analysis provides a powerful tool for identifying battery failure conditions by resolving overlapping electrochemical processes. As shown in Figure 4, Figure 5 and Figure 6, the peaks corresponding to charge transfer and diffusion resistance evolve throughout the battery life cycle, increasing in amplitude and shifting in time constant due to aging mechanisms such as SEI layer growth, lithium plating, and structural degradation of electrode materials. A critical observation is the eventual merging of these peaks into a single broad peak, which signifies a uniform rise in internal resistance and marks the transition to EOL stage of the battery. This convergence serves as a reliable diagnostic indicator of failure conditions and offers strong potential for integration into real-time monitoring systems for predictive maintenance applications. When the charge transfer and diffusion impedance peaks converge, it signals the beginning of battery failure. This highlights the necessity for timely battery replacement to ensure the continued functionality of the system.

5. Conclusions

This paper addresses the limitations of traditional EIS and ECM in analyzing LIB aging and failure conditions. EIS-ECM approaches often encounter challenges with overlapping impedance responses, which makes it difficult to separate individual electrochemical processes and prevents accurate assessments of battery health. To overcome these issues, the DRT method is employed, providing a more advanced approach to analyzing complex battery behaviors. By isolating relaxation times without reliance on specific models, DRT effectively differentiates overlapping processes, such as charge transfer and diffusion, and enables a more detailed examination of battery aging. In this study, DRT analysis of LIBs reveals that, as batteries age, peaks associated with charge transfer and diffusion processes begin to merge, signaling a critical failure condition that indicates the EOL stage of a battery. This insight highlights the value of DRT in accurately identifying failure conditions, offering significant improvements over ECM in real-time monitoring applications. Key quantitative findings from DRT analysis include the stabilization of SEI resistance after initial growth, a steady increase in charge transfer resistance due to electrode degradation, and a significant rise in diffusion resistance near the EOL. The convergence of charge transfer and diffusion peaks serves as a diagnostic marker of failure. Additionally, the shift of charge transfers process toward higher relaxation time and diffusion process toward lower relaxation time indicates evolving aging mechanisms. The ratio of these relaxation times provides a strong quantitative indicator for tracking battery degradation and estimating State of Health (SOH), offering practical value for advanced battery management systems. Integration of DRT into battery management systems promises enhanced capabilities for fault detection and thermal management, thereby contributing to safer and more reliable battery usage in electric vehicles and other demanding applications.