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Qianli Si, [Shoichi Matsuda](https://orcid.org/0000-0002-0640-3404), Yasunobu Ando, Toshiyuki Momma, [Yoshitaka Tateyama](https://orcid.org/0000-0002-5532-6134)

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[Capacity Estimation and Knee Point Prediction Using Electrochemical Impedance Spectroscopy for Lithium Metal Battery Degradation via Machine Learning](https://mdr.nims.go.jp/datasets/177c48ef-038c-47a8-8061-ef444746d444)

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Capacity Estimation and Knee Point Prediction Using Electrochemical Impedance Spectroscopy for Lithium Metal Battery Degradation via Machine LearningRESEARCH ARTICLEwww.advancedscience.comCapacity Estimation and Knee Point Prediction UsingElectrochemical Impedance Spectroscopy for Lithium MetalBattery Degradation via Machine LearningQianli Si,* Shoichi Matsuda, Yasunobu Ando, Toshiyuki Momma,and Yoshitaka Tateyama*Lithium-metal batteries (LMBs) are emerging as a promising next-generationenergy storage due to their exceptionally high energy density. However,accurately predicting their performance remains challenging because of thecomplex degradation mechanisms. In this study, a machine learning (ML)framework is proposed that combines electrochemical impedancespectroscopy (EIS) with the XGBoost algorithm to develop two predictivemodels: one for estimating capacity degradation and another for detecting theknee point (KP)—a critical inflection point in the degradation trajectory.SHapley Additive exPlanations (SHAP) analysis is employed to interpretfeature importance, revealing that low-frequency imaginary impedancecomponents—associated with diffusion-limited processes such as lithiumdepletion and accumulation—are most influential for capacity estimation.Conversely, high-frequency features related to charge transfer resistance playa dominant role in the KP detection. To reduce data complexity and improvemodel efficiency, the input by selecting specific frequency points based onSHAP values is further optimized. The optimized models exhibit comparableor improved accuracy compared to those using the whole EIS data and havereasonable performance on unseen test data. The findings highlight thatEIS-based ML models can accurately forecast heaslth of LMBs, providingdeeper insights into their aging processes and enhancing batterymanagement strategies.Q. Si, T. Momma, Y. TateyamaDepartment of Nanoscience and NanoengineeringFaculty of Science and EngineeringWaseda University3-4-1 Okubo, Shinjuku-ku 169-8555, JapanE-mail: SI.Qianli@nims.go.jp; tateyama@cls.iir.isct.ac.jpQ. Si, S.Matsuda, Y. TateyamaResearchCenter for Energy andEnvironmentalMaterials (GREEN)National Institute forMaterials Science (NIMS)1-1Namiki, Tsukuba, Ibaraki 305-0044, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/advs.202502336© 2025 The Author(s). Advanced Science published by Wiley-VCHGmbH. This is an open access article under the terms of the CreativeCommons Attribution License, which permits use, distribution andreproduction in any medium, provided the original work is properly cited.DOI: 10.1002/advs.2025023361. IntroductionLithium-ion batteries (LIBs) have becomefoundational in powering a wide range ofmodern technologies, from consumer elec-tronics to electric vehicles (EVs) and en-ergy storage systems.[1] As renewable en-ergy adoption continues to grow, there isan increasing demand for batteries withimproved performance metrics, includinghigher energy density, enhanced safety, andlonger cycle life. However, conventional LIBtechnology often faces significant difficul-ties, such as capacity degradation and in-creased impedance, particularly under highenergy-density designs or extended oper-ational cycles.[2] In critical applications,such as EVs, batteries typically need re-placement once their capacity drops be-low 80%, making accurate predictions ofbattery state of health (SoH) and remain-ing useful life (RUL) essential to preventunexpected failures and optimize batteryuse.[3] The urgency for reliable, rapid bat-tery health assessment is also driven bythe need for effective recycling and replace-ment practices. To sustain this transforma-tive energy shift, there is an urgent need toS. Matsuda, Y. TateyamaNIMS-SoftBank Advanced Technologies Development CenterNational Institute for Materials Science (NIMS)1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanY. Ando, Y. TateyamaLaboratory for Chemistry and Life ScienceInstitute of Integrated ResearchInstitute of Science Tokyo4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501, JapanAdv. Sci. 2025, 12, 2502336 2502336 (1 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbHhttp://www.advancedscience.commailto:SI.Qianli@nims.go.jpmailto:tateyama@cls.iir.isct.ac.jphttps://doi.org/10.1002/advs.202502336http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadvs.202502336&domain=pdf&date_stamp=2025-05-05www.advancedsciencenews.com www.advancedscience.comdevelop advanced battery chemistries and efficient health estima-tion technologies.One promising alternative to LIBs is the lithiummetal battery(LMB), which, with its lithiummetal anode, offers a significantlyhigher theoretical specific capacity (3860 mAh g−1 compared to372 mAh g−1 for graphite in LIBs) and a lower electrode poten-tial (−3.04 V vs standard hydrogen electrode).[4] The practical useof LMBs, however, is hindered by the limited chemical and me-chanical stability of lithiummetal. Additionally, most liquid elec-trolytes undergo decomposition on the lithium surface, resultingin an unstable solid electrolyte interphase (SEI) and the persis-tent consumption of lithium and electrolyte. These issues com-promise battery safety and reduce cycle life. These instabilitiesare influenced by a wide range of factors, including cell chem-istry, cell design parameters, and operating conditions. The com-plexity of these factors makes it challenging to efficiently exploreand optimize battery performance.[5]Traditional battery aging studies were based on modeling mi-croscopic degradation processes, such as the growth of SEI,[6]lithium plating,[7] and the loss of active material.[8] While thesemodels provide valuable physical insights, it is impractical tocharacterize and simulate every degradation mechanism due totheir complexity. To overcome this limitation, recent studies haveshifted toward data-driven approaches. Previous research has of-ten focused on features extracted from cycle data,[9,10] yet data-driven methods face challenges in selecting physically meaning-ful inputs and developing robust statistical models. Data-drivenstudies on aging in LMBs remain limited, however, our previousstudy was able to predict the cycle life of LMBs using features de-rived from the cycle test data.[11] Additionally, Liu et al. introduceda sequential explainable learning framework (SELF) to facilitateinterpretable analysis of accelerated aging patterns in LMBs. Us-ing data from just the first 10 cycles, SELF achieved a test errorof 15.2% in predicting the knee point (KP) of the capacity degra-dation trajectory.[12]In contrast to conventional current/voltage data, electrochemi-cal impedance spectroscopy (EIS) provides rich insights into ma-terial properties, interfacial phenomena, and electrochemical re-actions by measuring the current response to a voltage pertur-bation across a wide range of frequencies (including real part,imaginary part).[13,14] EIS effectively captures changes in the cath-ode, anode, electrolyte, solid electrolyte layer, and other compo-nents of LIBs throughout the aging process.[15] Research combin-ing EIS and data-driven methods has been done in the past fewyears. For instance, Zhang et al. employed an extensive dataset ofimpedance spectra within a Gaussian process regression modelto forecast battery capacity and estimate its lifespan.[16] Similarly,T. K. Pradyumna et al. estimated the capacity of LIBs combiningconvolutional neural networks and EIS.[17] In addition, based onthe dataset of Zhang et al., Xia et al. estimated the SoH usingpartial EIS features.[18]However, the existing research primarily focuses on well-established, commercially available LIBs, where the capac-ity degradation follows relatively stable trends. In contrast,LMBs exhibit much more complex and nonlinear degrada-tion behaviors due to the instability associated with the useof lithium metal as the anode. As such, LMBs face signifi-cant challenges, including dendrite growth and rapid capacityloss,[19] particularly as the battery approaches the KP, a criti-cal point in the degradation trajectory where accelerated agingbegins.To date, most existing approaches have been limited to stable,commercial LIBs,[20–22] leaving a significant gap in the literatureregarding the application of EIS for the performance predictionof LMBs. Furthermore, while some studies have focused on pre-dicting the degradation trajectory or the remaining capacity forLIBs using EIS,[16–18,23] no work has yet been conducted to predictthe KP. To fill this gap, in this study, we integrate EIS data, theExtreme Gradient Boosting (XGBoost) machine learning (ML)algorithm,[24] and SHAP (SHapley Additive exPlanations)[25,26] topredict the discharge capacity and the KP of LMBs. TheMLmod-els are built using data from 16 LMBs, with 8 batteries used fortraining and seven out of the other eight for testing (excludingone due to its unusual degradation behavior). By carefully select-ing specific EIS features, such as the low-frequency range andthe imaginary components for the capacity estimation, and high-frequency components alongside the real impedance part for theKP prediction, we demonstrate that tailored feature selection cansignificantly enhance model accuracy, particularly when appliedto the challenging and often unstable behavior of LMBs. By de-veloping efficient and interpretable models, we aim to improvethe accuracy of predictions, providing valuable insights into bat-tery aging processes and advancing the development of predictivetools for more effective battery management and performanceoptimization.2. Experimental Section2.1. LMB Fabrication and Data ExtractionIn our project, total 16 single-layer stacked pouch-typeLMB cells (8 as training dataset, 8 as testing dataset) wereassembled, consisting of a positive electrode made ofLiNi0.8Mn0.1Co0.1O2 (40 mm × 30 mm) with mass loadingof 30 mg cm−2, a separator (46 mm × 36 mm), and a nega-tive electrode comprising a 50 μm thick layer of lithium on a10 μm thick copper (Cu) current collector (42 mm × 32 mm).The details of cell components were described in our previousreports.[25,26] All cells were assembled in a dry room with a dewpoint below −50 °C, and electrolyte injection took place in anAr-filled glovebox with a dew point below −85 °C.The fabricated cells were subjected to repeatedcharge/discharge cycle tests with different 8 kinds of condi-tions. For each condition, two cells were evaluated. The datafor one cell was used as a training machine learning model,while the other was used to test the model. The details of thecycling test condition are summarized in Table S1 (SupportingInformation). The charge/discharge cycle test of the cells wasconducted with a constant current within a voltage range of2–4.2 V, which basically underwent 100–200 cycles, and thecapacity data were recorded continuously. The EIS test wasconducted at 8 states which include 1) charge capacity 0 mAh(fully discharged state), 2) charge capacity 24 mAh, 3) chargecapacity 48 mAh, 4) charge at 4.2 V (full charge voltage), 5) dis-charge capacity 0 mAh (fully charged state), 6) discharge capacity24 mAh, 7) discharge capacity 48 mAh, and 8) discharge at 2 V(the cut-off voltage of discharge). In each state, the frequencyranges were selected between 0.009 HZ and 10 KHZ with a totalAdv. Sci. 2025, 12, 2502336 2502336 (2 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 1. Impedance spectra for Battery No. 13 and Battery No. 15. The color bar indicates different cycles.of 36 frequency points which are specified in Table S2 (Support-ing Information). The corresponding EIS data at the frequencypoints are used as features in this project. Detailed informationabout these features can be found in the supplementary Excelfile. However, during some of the states, the EIS data of some ofthe batteries were incomplete with respect to the cycles exceptfor states: charge capacity 0 mAh, charge at 4.2 V, and dischargecapacity 0 mAh. Hence, these three states are selected for furtherresearch. Here, we displayed the impedance spectra for batteriesNo. 13 and 15 at the fully discharged state in Figure 1, the otherbatteries’ impedance spectra are shown in Figure S1 (SupportingInformation). EIS spectra were plotted at regular intervals fromcycles 5, 10, 15, 20, …, up to the final cycle, the x-axis representsthe real part, versus the negative imaginary part in y-axis. Eachbattery shows distinct changes in impedance spectra as they age.The raw experimental EIS data are then utilized as features inthe current work.2.2. Machine Learning ProcessTotally, two ML models were constructed in this work, EIS-Capacity model and EIS-KP model. The EIS-Capacity model isa ML framework designed to estimate LMB capacity using theEIS data. The training dataset comprises EIS samples aggregatedfrom all training batteries, structured as a matrix with dimen-sions 1050 × 72. Here, each row represents a single battery cycle,and the 72 input features correspond to the impedance spectracomponents: the first 36 columns are the real parts, while theimaginary parts are listed in the remaining 36 columns. The tar-get values are the measured capacities of the training batteries,establishing a directmapping between impedance characteristicsand capacity degradation. Formodel evaluation, themeasured ca-pacities of the test battery serve as ground truth, which are com-pared with the model’s predicted capacities to assess generaliza-tion performance. This framework ensures that the model learnsthe relationship between impedance features and capacity evolu-tion across cycles, enabling robust state-of-health estimation.The EIS-KP model aims to predict the KP, a critical transi-tion in capacity degradation rate, using the EIS data. The trainingdataset consists of 572 EIS samples (572× 72matrix), where eachsample corresponds to a cycle preceding the KP detection in thetraining batteries. The target values are the remaining cycle num-bers until the KP occurs, derived from the Kneed algorithm. Thisalgorithm identifies the KP as the point ofmaximumcurvature inthe capacity degradation curve, ensuring an objective and repro-ducible reference. During testing, themodel predicts KPs for testbatteries based solely on their EIS data. The actual KPs for test-ing batteries are independently determined using the Kneed al-gorithm, serving exclusively as a validation benchmark. This ap-proach ensures that predictions are based on learned impedance-degradation relationships, while predicted KP provides an unbi-ased evaluation of model accuracy.To develop both models, XGBoost regressor was employed, awidely recognized machine learning algorithm known for its ef-ficiency, scalability, and predictive accuracy. XGBoost constructsan ensemble of decision trees sequentially, where each succes-sive tree corrects the residual errors of its predecessors, optimiz-ing the model by minimizing a specified loss function. The algo-rithm incorporates several advanced techniques, including reg-ularization, tree pruning, and parallelization, to enhance perfor-mance andmitigate overfitting. Due to its speed, robustness, andability to handle large, complex datasets, XGBoost is extensivelyused in both research and industrial applications. Moreover, XG-Boost provides valuable insights into feature importance, allow-ing for the identification of key EIS features that contribute mostsignificantly to the model’s predictions. To ensure optimal per-formance, a grid search with 5-fold cross-validation was con-ducted for hyperparameter tuning. A detailed explanation of theXGBoost algorithm and parameter optimization are provided inNotes S1 and S2 (Supporting Information) respectively in theSupporting information.To evaluate the performance of the machine learning models,the following three performance indices were implemented.1. Mean absolute error (MAE)MAE = 1nn∑i=1||yi − ŷi|| (1)2. Root mean square (RMSE)RMSE =√√√√ 1nn∑i=1(yi − ŷi)2(2)Adv. Sci. 2025, 12, 2502336 2502336 (3 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.com3. Coefficient of determination (R2)R2 = 1 −∑ni=1(yi − ŷi)2∑ni=1(yi − ȳ)2 (3)here, n represents the number of samples, yi and ŷi representsthe actual values and the predicted values. The MAE measureshow close the predictions are to the actual outcomes. In contrast,the RMSE captures the spread of errors and is more sensitive tolarger discrepancies compared to MAE. Smaller values for bothMAE andRMSE indicate bettermodel performance, while highervalues suggest poorer predictions. The coefficient of determina-tion R2 metric, expressed as a percentage, ideally reaches 100%or 1, indicating a strong correlation between the observed andpredicted values.2.3. XGBoost Feature Importance (XFI) AnalysisXFI analysis is a powerful method for identifying the key featuresin a dataset, which have the greatest influence on the model’spredictions. By understanding which features are most impor-tant, researchers can enhance model performance, reduce com-plexity, and gain valuable insights into the underlying variablesdriving the predictions. XGBoost provides severalmethods to cal-culate feature importance scores, each offering a unique perspec-tive on feature contributions. One such method is the weight ap-proach, which evaluates how often each feature is used to splitnodes across all decision trees in the model. Features that areutilized more frequently during the splitting process are consid-ered more important, as they play a more significant role in themodel’s decision-making. This method highlights the featuresthat the model relies on most heavily during training.In this project, we visualize the XGBoost Feature Importance(XFI) scores using a heatmap. These scores are intrinsic to theXGBoost model and reflect the relative contribution of each fea-ture to the model’s predictions. The heatmap is generated bycomputing saliency values, which are derived by averaging theXFI scores across all test samples. This provides a measure ofthe average importance of each feature, enabling a robust andinterpretable identification of the most influential features. Theheatmap is structured such that the x-axis represents the cyclenumber of the battery, the y-axis represents the features, and thecolor intensity corresponds to the importance of each feature.This visualization not only facilitates the interpretation of the rel-ative significance of features across different test samples but alsoreveals patterns in feature contributions. By analyzing these pat-terns, we gain deeper insights into the relationships between fea-tures and the target variable, enhancing our understanding of thefactors driving the model’s predictions.2.4. SHAP Feature Importance (SFI) AnalysisSHAP is a game-theory-based approach that provides a unifiedand interpretable measure of feature importance by quantifyingthe contribution of each feature to the model’s predictions. Un-like traditional feature importance methods, which typically rankfeatures based on their average impact, SHAP offers amore gran-ular and detailed explanation of how each feature influences indi-vidual predictions. This capability makes SHAP particularly valu-able for understanding complex, nonlinear relationships in MLmodels, as it not only identifies important features but also ex-plains their contribution to specific predictions.In this work, SFI analysis was applied to both the capacity es-timation model and the KP prediction model to evaluate the rela-tive contribution of each EIS feature. Specifically, SFI scores werecomputed to identify the most influential EIS features affectingcapacity degradation and KP prediction. Unlike traditional fea-ture importance methods, which only rank features based ontheir average impact, SFI offers amore detailed and interpretableexplanation of each feature’s influence on individual predictions.This method allows us to visualize the distribution of feature im-portance across different battery cycles, providing deeper insightsinto which features play the most significant role in predictingbattery behavior.Figure 2 illustrates the schematic workflows of these twomod-els. Initially, the whole EIS dataset was integrated with the XG-Boost ML algorithm to predict capacity and KP. Subsequently,SHAP analysis was employed to identify and extract key fea-tures contributing to model performance. Using these selectedfeatures, simplified machine learning models were constructed,ensuring interpretability while maintaining predictive accuracy.The workflows highlight the systematic approach taken to ad-dress the challenges of LMB degradation prediction.3. Results and Discussion3.1. LMB Capacity Estimation by EISIn this part, we conducted the capacity estimation of the LMBsusing EIS from different states. As we illustrated before, a chargecapacity 0mAh, a charge at 4.2 V, and a discharge capacity 0mAhstates are chosen to estimate the capacity separately. The EIS ofbatteries No. 1, 3, 5, 7, 9, 11, 13, and 15 in different states wereselected to train the model and the rest of the 8 batteries No. 2,4, 6, 8, 10, 12, 14, and 16 were used to test the model respec-tively. The criterion for classification of the training set from thetest set is that the charge and discharge current densities of thebatteries in both sets are identical respectively (for example, bat-tery 1 and battery 2 have the same discharge and charge densitieswhich is also shown in the supporting information). In Figure 3,it displays the prediction results for battery No. 16 using the threedifferent states.The figures indicate that predictions based on EIS data fromthe Cha_0mAh state outperform those from the other two states,exhibiting the highest R2 and the lowest MAE and RMSE val-ues. Parity plots for the predictions of the remaining seven batter-ies using Cha_0 mAh state are provided in Figure S2 (Support-ing Information). Table 1 summarizes the R2 values for differentbatteries in various states. Notably, the R2 values for cell 2 areoutside the expected range of 0–1, appearing as negative values,which reflect very poor predictive performance. Upon analysis,we observed that, despite battery 1 and battery 2 sharing the samecharge and discharge current densities, their capacity degrada-tion trajectories differ significantly, resulting in poor predictionAdv. Sci. 2025, 12, 2502336 2502336 (4 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 2. Schematic flow of a) EIS-Capacity model and b) EIS-KP model.accuracy for cell 2. Therefore, the capacity estimation of Battery 2in this work is excluded, we focus on the remaining seven cells.The R2 values for the remaining seven batteries are presented inTable 1. Overall, the Cha_0mAh state provides the best estima-tion performance. Therefore, the following research will focusspecifically on this state.The capacity estimationmodel is developed using the XGBoostML algorithm, one of the key strengths is its ability to evaluate fea-ture importance, making it especially valuable for applicationswhere understanding the contribution of each input feature tothe model’s predictions is critical. Using the XFI analysis intro-duced in Section 2.3, we assess the relative importance of EISfeatures. This approach enhances interpretability by highlight-ing the features that contribute most significantly to capacity es-timation. Figure 4a shows the XFI heat map for Battery No. 16.Evaluating this map provides a direct visualization of how themost informative frequency points are associated with capacityestimation. Four of the top five most important features (XFI-top5-features) are concentrated at low-frequency points (specifi-cally the 63rd, 64th, 51st, and 52nd), while the 28th feature standsout as being located at a relatively high-frequency point (referto the supplementary Excel file for detailed numbering), whichmay provide unexpected special correlation. Then we utilizedXFI-top5-features as the input features to estimate the capacityof the testing batteries. The estimation results of battery No.16are shown in the Figure 4b, for the other batteries, the estima-tion results are shown in Figure S3 (Supporting Information).Through the analysis of Figure 4b, we observe that the esti-mation accuracy using the XFI-top5-features shows a slight de-crease compared to the full EIS dataset. The observed reduc-Figure 3. Estimated (orange) and Measured (purple) capacity as a function of cycle number for battery No. 16 in three different states.Adv. Sci. 2025, 12, 2502336 2502336 (5 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comTable 1. Summary of the R2 of the testing batteries under 3 different states.Cell R2: Cha_0mAh R2: Cha_4.2V R2: Dis_0mAh2 −106 −110 −1174 0.971 0.974 0.9766 0.912 0.958 0.9738 0.799 0.772 0.75110 0.936 0.994 0.99212 0.900 0.784 0.83514 0.971 0.920 0.96516 0.969 0.884 0.392Average 0.923 0.898 0.841tion in R2 when utilizing only the top features reflects a well-known trade-off between model complexity and generalizability.While the model trained with the complete feature set achievesa higher R2, suggesting superior performance on the currentdataset, it may also be more prone to overfitting due to its de-pendence on a larger number of features. In contrast, the modelusing the XFI-top5-features exhibits a modest reduction in per-formance but may demonstrate better generalization by concen-trating on the most impactful features. Interestingly, the predic-tive accuracy improved when using the reduced feature set forcertain test batteries, such as Battery No. 4 and Battery No. 6.This underscores the complexity and variability of XFI analysisacross different samples, suggesting that the optimal feature setcan vary depending on the specific characteristics of the testingbatteries.Furthermore, for all other test batteries, the XFI-top5-featureswere consistent with those of Battery No. 16. This consistencyhighlights a limitation of the XFI analysis, which provides aglobal ranking of feature importance but lacks the ability to of-fer detailed, sample-specific insights into how individual fea-tures influence predictions. Despite these limitations, our find-ings demonstrate that capacity estimationmay be achieved usinga subset of carefully selected frequency points from the EIS data.This insight suggests that focusing on specific frequency regions,rather than the entire EIS spectrum, could be an effective strategyfor improving prediction efficiency while maintaining accuracy.Hence, finding a sample-specific explanation of how each featureinfluences the model’s prediction for individual test samples isimportant.In this study, the SHAPmethod was employed to evaluate andrank the contributions of 72 impedance features to capacity esti-mation for various test batteries. Figure 5a illustrates the contri-bution of each impedance feature to the first-cycle capacity esti-mation. The estimated capacity value, f(x)= 1.162, is displayed inthe top-right corner, while the gray numbers on the left indicatethe SHAP values of the features, ranked from highest to lowest.Notably, the top five ranked features account for a significantlylarger contribution compared to the cumulative contributions ofthe remaining 67 features.Figure 5b presents the mean absolute SHAP values of SFI-selected top five ranked features (SFI-top5-features) for BatteryNo. 16 across all cycles of capacity estimation. Based on thisanalysis, the impedance features 63, 64, 62, 52, and 36 areidentified as the most influential for Battery No. 16. For othertest batteries, SFI-top5-features differ, as shown in Table S3(Supporting Information). This variability reflects the battery-specific nature of feature importance as determined by SFI. Theidentified SFI-top5-features for each battery were subsequentlyused as inputs to the ML model for re-evaluation of capacityestimation.Figure 5c compares the capacity estimation results for BatteryNo. 16 using the SFI-top5-features versus using the whole EISfeatures. The results indicate that for Battery No. 16, capacity es-timation using whole EIS features outperformed the SFI-top5-features. The parity plots of other batteries are shown in FigureS4 (Supporting Information). A summary of the capacity estima-tion for all test batteries, including comparisons between the SFI-top5-features, XFI-top5-features, and whole EIS features is pro-vided in Table 2.From the results in Table 2, it can be observed that the capacityestimation for Battery No. 6 and Battery No. 8 shows improve-ment when using SFI-top5-features compared to both the wholeEIS features and XFI-top5-features. For Battery No. 10, No. 12,and No. 14, the estimation results with SFI-top5-features es areslightly improved or comparable but remain less accurate thanthose obtained using the whole EIS features. Overall, the SFI-top5-features demonstrate superior performance compared tothe XFI-top5-features. Further analysis reveals that although theFigure 4. a). In the XFI heat map of Battery No. 16, the x-axis indicates the cycle numbers of the battery, the y-axis represents the impedance data at 36frequency points ranging from 0.0093 HZ to 10 KHZ (bottom to top). b). Comparison of the estimation results of battery 16 using the whole EIS dataand the top five most important EIS features.Adv. Sci. 2025, 12, 2502336 2502336 (6 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 5. a). Waterfall plot illustrating the contribution of each impedance feature, ranked by SHAP value, to the first-cycle capacity estimation of batteryNo. 16. b). Ranking of impedance features based on their importance across the battery’s entire life cycle by the order of SHAP values. c). Comparisonof the estimation results for battery 16 using the whole EIS features versus SFI-top5-features identified by SHAP values.SFI-top5-features differ across the test batteries, they are consis-tently located within the low-frequency region of the impedancespectrum. Additionally, all these features are derived from theimaginary component of the impedance data. An exception isBattery No. 10, where one of the SFI-top5-features (the 28th fea-ture) is extracted from the real component of the impedancedata.Finally, to simplify the model while simultaneously enhanc-ing its generalizability, we aggregate the SFI-top5-features iden-tified for each test battery. By summing the SHAP values of theSFI-top5-features across all testing batteries, we identify the top5 features with the highest “overall” SHAP values (O-SFI-top5-features), representing those with the greatest impact across theentire dataset, which is detailed in the Table S4 (Supporting Infor-mation). The O-SFI-top5-features are 63, 64, 52, 51, and 53 sub-sequently, which are all extracted from the low-frequency regionand imaginary part of the EIS data, the corresponding frequencypoints are 0.2352, 0.1583, 18.08, 8.121, and 12.18 Hz respectively.These O-SFI-top5-features are utilized to build the LMB capac-ity estimation model. Figure 6, displays the estimation results ofusing the O-SFI-top5-features of three testing batteries, for theother 4 batteries, the results are shown in Figure S5 (SupportingInformation).Through the analysis, it was observed that the EIS-Capacitymodel employing the O-SFI-top5-features generally yielded su-perior or comparable performance compared to the model utiliz-ing the SFI-top5-features. However, slight decreases in predictiveaccuracy were observed for Battery No. 10, No. 14, and No. 16For these three batteries, the discrepancy can be attributed toseveral factors. In the case of Battery No. 10, which was subjectedto a high charging rate of 3.0 mA cm−2 and a low dischargingrate of 0.6 mA cm−2, this charge/discharge protocol has beendemonstrated to accelerate battery degradation significantly inprevious research. As illustrated in Figure S4b, its measured ca-pacity degradation trajectory exhibits significant fluctuations be-tween cycles 50 and 100—an anomaly not observed in the degra-dation patterns of other test batteries. This suggests that BatteryNo. 10 follows a distinct degradation behavior. Additionally, sincethe O-SFI-top5-features were selected based on the overall batterypopulation, they may not fully capture the unique degradationcharacteristics of individual batteries. Conversely, the SFI-top5features include specific variables (e.g., Feature 28 for Battery No.Table 2. Summary of the R2 of the testing batteries using whole EIS fea-tures, XFI-top5-features, and SFI-top5-features.Cell R2: Whole EIS R2: XFI-top5-features R2: SFI-top5-features4 0.971 0.978 0.9606 0.912 0.921 0.9428 0.799 0.695 0.74310 0.936 0.896 0.92612 0.900 0.902 0.86914 0.971 0.924 0.96216 0.969 0.932 0.960Average 0.914 0.893 0.90810) that are particularly relevant for capturing the irregular pat-tern, thereby enhancing predictive accuracy. Feature 28, in par-ticular, likely plays a crucial role in representing the fluctuationsobserved in BatteryNo. 10′s degradation trajectory. In addition, inthe previous research,[27] the high charge current density, and lowdischarge current density will make the battery degrade severelyas proved by experiment.Similarly, for Battery No. 14 and Battery No. 16, features 51 and53 are not among their respective SFI-top5-features, which mayexplain the reduced prediction performance when using the O-SFI-top5 -features. Despite this, the overall performance remainsreasonable. The primary objective of this study is to reduce thenumber of input features while maintaining reliable predictiveaccuracy. The results indicate that, although there are some ex-ceptions, the O-SFI-top5 features still provide satisfactory perfor-mance across most cases, demonstrating the feasibility of featurereduction without significantly compromising predictive capabil-ity.This finding supports the hypothesis that focusing on specificsegments of the EIS data, particularly the low-frequency regionand the imaginary component, is sufficient to achieve high ca-pacity estimation accuracy. This approach not only simplifies themodel by reducing the number of input features but also en-hances its generalizability, providing a more efficient and inter-pretable framework for capacity estimation in LMBs.Adv. Sci. 2025, 12, 2502336 2502336 (7 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 6. Comparison of the estimation results using SFI-top5-features and O-SFI-top5-features on three different Batteries a) Battery No. 4, b) BatteryNo. 8, and c) Battery No. 12.3.2. LMB Knee Point Estimation by EISLMBs examined in this study demonstrate distinct nonlinear ca-pacity degradation, presenting unique challenges for accuratelifetime prediction and effective battery management, unlike thecommercialized lithium-ion counterparts. This nonlinear degra-dation is characterized by an initial phase of gradual capacity de-cline, followed by a critical transition into a region of rapid ca-pacity loss. The transition point, commonly referred to as KP, iscrucial as it marks the onset of accelerated aging and reducedperformance. While notable advancements have been made inpredicting the KP for lithium-ion batteries, this task is particu-larly complex for LMBs due to their less mature state of researchand more intricate degradation behaviors.In this study, we developed a ML model to predict the KP forLMBs using the EIS data, the KP prediction model follows thesame framework as the capacity estimation model, utilizing EISdata recorded at the charge capacity 0 mAh. Given the substan-tial fluctuations observed in the degradation curves of our bat-teries, we employed the Locally Weighted Scatterplot Smoothing(LOWESS) algorithm to enhance the clarity of the capacity degra-dation trends which has been used in the previous work. [28] Thissmoothing technique was applied to normalize the measured ca-pacity data and estimated capacity across the cycle range, using asmoothing parameter set to 0.2. This parameter determines theproportion of data points included in each localized regression,striking a balance between preserving local variations and gener-ating a general trend. The smoothed capacity data was then uti-lized for further analysis and visualization, effectively reducingnoise and highlighting the underlying degradation patterns.Figure 7a illustrates the smoothed measured capacity degra-dation trajectories and their corresponding KPs for the trainingbatteries. Figure 7b presents the prediction results of battery No.14 obtained solely from the EIS data, excluding capacity variationconsiderations. Here, the x-axis represents the actual KP, plottedin reverse to reflect a countdown from the traditional perspective,with the y-axis following the same reversed orientation. The datapoints in this figure indicate the remaining cycles until the KP oc-curs. However, we primarily focus on the prediction result for thefirst cycle, as this represents the mathematically precise point atwhich the KP occurs in the degradation trajectory, which is high-lighted in red. Figure 7c illustrates the comparison between theactual and predicted KP for all testing batteries. The mean abso-lute error (MAE) is 12.75%, demonstrating improved accuracy tothe prior work by Liu et al.,[12] which predicted LMB KP usingdischarge voltage curves.Here, we utilized SFI analysis to analyze the impact of featureselection on model performance for KP prediction. SFI analysisrevealed that, across different testing batteries, SFI-top5-featuresremained consistent, specifically features 1, 0, 4, 37, and 56. Thiscontrasts with the capacity estimation model, where the top fea-tures varied among batteries. Hence, we utilized the SFI-top5Figure 7. a) Smoothed measured capacity degradation trajectories and corresponding KP (black dots) for the training batteries. b) Actual versus pre-dicted remaining cycles to KP for Battery No. 14. c) Actual versus predicted KPs for all testing batteries.Adv. Sci. 2025, 12, 2502336 2502336 (8 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 8. Comparison of prediction results using different input featuresets. The blue dots represent the results obtained using the whole EISfeature set, while the red dots indicate the outcomes based on the SFI-top5-features.features from 10 kHz, 6.74 kHz, 2.063 kHz, 3.728 Hz to recon-struct the model. The comparison results, illustrated in Figure 8,show that the MAE for the model using the SFI-top5-featuresis 12.43%, which is slightly lower than that of the model uti-lizing the entire EIS dataset and prior work. Given the inherentcomplexity of lithium-metal battery degradation, our findings in-dicate that concentrating on specific EIS data regions, particu-larly high-frequency components (except feature 56), is possibleto achieve a relatively high level of accuracy in KP prediction.Here, we notice for these two ML models, the contrasting fea-ture selections for KP prediction and capacity estimation can beattributed to the distinct degradation processes influencing eachtask. KP prediction is primarily driven by high-frequency com-ponents of the impedance (Feature 0, 1, 4, and 37), which cap-ture rapid, early-stage degradation mechanisms associated withthe onset of accelerated capacity loss. In contrast, capacity esti-mation relies more on low-frequency components and the imag-inary part, which reflects long-term degradation trends and over-all battery health. These differences highlight the importance ofselecting appropriate features based on the degradation phase be-ing studied, with high-frequency features beingmore relevant forpredicting KP and low-frequency features for estimating capac-ity. By focusing on the most relevant EIS segments for each task,both models achieve high accuracy while improving efficiencyand generalizability.3.3. Machine Learning Model Generalizability ValidationAfter we build the ML model using the partial EIS features, weneed to validate their generalizability. Here, we implemented ourEIS-Capacity and EIS-KP models on 4 unseen batteries. Theseunseen batteries have different cycling test conditions comparedto the previously used batteries in our ML models. The cyclingtest condition are shown in Table S1. In Figure 9, it displays theprediction results of the unseen batteries using the EIS-Capacitymodel.The EIS-Capacity model demonstrates strong predictive per-formance for Batteries B and C, mainly because their capacitydegradation is gradual and similar to the patterns in the trainingdata. They exhibit a relatively steady decline in capacity withoutabrupt drops or recoveries, resembling the degradation trajecto-ries that the model has learned. In contrast, Batteries A and Dshow irregular degradation with sharp fluctuations—Battery Abetween cycles 90–125 and Battery D between 50 and 80. Theseanomalies are absent from the training dataset, which makes itdifficult to accurately capture such unpredictable behaviors, re-sulting in lower prediction accuracy. The unusual degradationpatterns are likely influenced by different discharge/charge rate(C-rate) conditions, which differ considerably from those of thetraining batteries. Interestingly, Battery No. 10 also has strongfluctuations but is predicted more accurately because the train-ing data includes Battery No. 9, which has a similar pattern. Thishighlights the value of including a wide variety of degradationbehaviors in the training data.The EIS-KP model shows varied prediction accuracy acrossdifferent test batteries, depending on their degradation patternsand similarity to the training data. For Batteries A and B, themodel predicts KPs reasonably well, with small errors (e.g., Bat-tery A: predicted 79 versus actual 84; Battery B: predicted 86 ver-sus actual 95), resulting in an average MAE of 7.71%. AlthoughBattery A’s degradation pattern differs from those in the train-ing dataset, its fluctuations are relatively regular, enabling theLOWESS smoothing method to retain critical inflection pointsand allowing the model to capture its actual KP with reasonableaccuracy. In contrast, Battery D’s KP is overpredicted (predicted:80 versus actual: 50), likely due to artifacts introduced by theLOWESS smoothing method. Unlike Battery A’s regular fluctua-tions, Battery D’s degradation trajectory exhibits severe and irreg-ular fluctuations. While smoothing mitigates noise in degrada-tion trajectories, aggressive application to highly fluctuating datacan obscure critical inflection points, particularly in batteries withrapid early degradation followed by stabilization. Battery C’s KPis severely underestimated (predicted: 81 versus actual: 146), pri-marily because the training dataset lacks examples of batterieswith KPs exceeding 100 cycles. Machine learning models inher-ently struggle to extrapolate beyond the scope of their trainingdata, particularly for nonlinear degradation behaviors, leading tosystematic underestimation in such cases.These findings highlight themodel’s sensitivity to degradationpatterns and the importance of comprehensive training data cov-erage. To enhance robustness, future research should prioritizeexpanding the diversity of the training dataset, incorporating bat-teries exhibiting a wider spectrum of degradation behaviors, cy-cle life ranges, and a wider range of C-rate conditions, refiningsmoothing techniques to better capture key degradation features,and integrating physics-informed constraints to improve extrapo-lation capability. Additionally, from a data quality perspective, thepresence of batteries with severe and irregular fluctuations, suchas Battery A and Battery D, is undesirable for both model train-ing and evaluation, as these cases introduce inconsistencies thathinder the model’s ability to learn meaningful degradation pat-terns. While Battery A’s fluctuations are relatively regular and donot significantly impact prediction accuracy, Battery D’s abruptvariations create substantial challenges in KP estimation. Suchbatteries with extreme fluctuations should ideally be excludedfrom both the training dataset and unseen test data to ensurea more reliable and generalizable model. Future studies shouldAdv. Sci. 2025, 12, 2502336 2502336 (9 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 9. Comparison of the estimation results using O-SFI-top5-features and Measured capacity on four unseen Batteries a) Battery A, b) Battery B, c)Battery C, and d) Battery D.establish strict criteria for identifying and filtering out these out-liers, focusing on training the model with batteries exhibitingphysically meaningful degradation behaviors and incorporatingdiverse cathode materials in LMB to enhance the generalizabil-ity and robustness of the findings. This approach would allowthe model to generalize effectively while maintaining robustnessacross real-world applications.4. ConclusionIn conclusion, this study presents a comprehensive investigationof the degradation behaviors of LMBs through ML models im-plementing EIS data. By addressing capacity estimation and KPprediction, we provide new insights into the electrochemical andphysical processes governing LMB degradation.For capacity estimation, the results demonstrate that low-frequency impedance features, particularly those associated withthe imaginary component, are critical for capturing the long-termdegradation behavior of LMBs. The dominance of low-frequencyfeatures highlights their sensitivity to interfacial resistance andcharge transfer processes, which are directly influenced by thelithium depletion/dendrite growth and electrolyte decomposi-tion. These processes collectively dictate the gradual capacity de-cline observed during cycling. By identifying and focusing onthese specific impedance regions, our model simplifies the fea-ture set while maintaining high accuracy, underscoring the im-portance of the low-frequency regime in reflecting the battery’shealth state.In contrast, the prediction of KP—a crucial transition wherecapacity degradation accelerates—relies predominantly on high-frequency features and the real component of the impedance.These features indicate the system’s resistance and electronicconductivity changes, which are often linked to the early stagesof SEI instability, pore-clogging, and the onset of lithium plat-ing. The observed shift in key features for KP prediction empha-sizes the distinction between the early detection of rapid degra-dation mechanisms and the comprehensive assessment of long-term capacity loss. Our findings demonstrate that high-frequencyimpedance features are particularly effective in capturing thesubtle structural and kinetic changes preceding KP, providing avaluable tool for proactive battery management.A key finding of this study is the ability to minimize the re-quired frequency range of the impedance spectra for LMB capac-ity and KP estimation, thereby significantly reducing measure-ment time. Unlike conventional approaches that rely on extract-ing features from the entire impedance spectrum, ourmethod fo-cuses on directly selecting the most relevant frequency range formeasurement. As a result, while traditional techniques requirecapturing the full impedance spectrum, our approach stream-lines the process by concentrating only on the essential frequencycomponents. This enables the identification of themost informa-tive impedance frequency points for battery health assessment,enhancing both the efficiency and accuracy of predictions. Ourmethod offers significant potential for optimizing the use of EISin real-world LMB health monitoring.In conclusion, this study enhances the understanding of LMBdegradation by establishing connections between critical EIS fea-Adv. Sci. 2025, 12, 2502336 2502336 (10 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comtures and specific physical and chemical degradation mecha-nisms.While there is room for further improvement inmodel ro-bustness, these findings contribute to the improvements in mea-surement efficiency and prediction accuracy, paving the way forpractical applications in advanced LMB prognostics andmanage-mentSupporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThis work was in part supported by the SoftBank-NIMS Advanced Tech-nologies Development Center as a joint research between NIMS and Soft-Bank Corp. The authors thank Shuntaro Miyakawa, and Takaya Saito fortheir valuable discussions. This work was also partially supported byMEXTas “Program for Promoting Research on the Supercomputer Fugaku” grantnumbers JPMXP1020230325 and JPMXP1020230327, Data Creation andUtilization Type Material Research and Development Project grant JP-MXP1122712807. The calculations were performed on the supercomput-ers at NIMS (Numerical Materials Simulator).Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from the cor-responding author upon reasonable request.Keywordsdegradation, electrochemical impedance spectroscopy, knee points,lithium-metal batteries, machine learning modelsReceived: February 7, 2025Revised: April 4, 2025Published online: May 5, 2025[1] J. B. Goodenough, K. S. Park, J. Am. Chem. Soc. 2013, 135,1167.[2] R. Schmuch, R. Wagner, G. Hörpel, T. Placke, M. Winter, Nat. Energy2018, 3, 267.[3] M. Elmahallawy, T. Elfouly, A. Alouani, A. M. 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Sci. 2025, 12, 2502336 2502336 (11 of 11) © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2025, 27, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202502336 by National Institute For, Wiley Online Library on [08/09/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comhttps://doi.org/10.2139/ssrn.4778973 Capacity Estimation and Knee Point Prediction Using Electrochemical Impedance Spectroscopy for Lithium Metal Battery Degradation via Machine Learning 1. Introduction 2. Experimental Section 2.1. LMB Fabrication and Data Extraction 2.2. Machine Learning Process 2.3. XGBoost Feature Importance (XFI) Analysis 2.4. SHAP Feature Importance (SFI) Analysis 3. Results and Discussion 3.1. LMB Capacity Estimation by EIS 3.2. LMB Knee Point Estimation by EIS 3.3. Machine Learning Model Generalizability Validation 4. Conclusion Supporting Information Acknowledgements Conflict of Interest Data Availability Statement Keywords