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Qianli Si, [Shoichi Matsuda](https://orcid.org/0000-0002-0640-3404), [Youhei Yamaji](https://orcid.org/0000-0002-4055-8792), Toshiyuki Momma, [Yoshitaka Tateyama](https://orcid.org/0000-0002-5532-6134)

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[Data‐Driven Cycle Life Prediction of Lithium Metal‐Based Rechargeable Battery Based on Discharge/Charge Capacity and Relaxation Features](https://mdr.nims.go.jp/datasets/ca5f2d26-d0c5-41a8-9131-2afbf4ce84b4)

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Data&#x02010;Driven Cycle Life Prediction of Lithium Metal&#x02010;Based Rechargeable Battery Based on Discharge/Charge Capacity and Relaxation FeaturesRESEARCH ARTICLEwww.advancedscience.comData-Driven Cycle Life Prediction of Lithium Metal-BasedRechargeable Battery Based on Discharge/Charge Capacityand Relaxation FeaturesQianli Si, Shoichi Matsuda, Youhei Yamaji, Toshiyuki Momma, and Yoshitaka Tateyama*Achieving precise estimates of battery cycle life is a formidable challenge dueto the nonlinear nature of battery degradation. This study explores anapproach using machine learning (ML) methods to predict the cycle life oflithium-metal-based rechargeable batteries with high mass loadingLiNi0.8Mn0.1Co0.1O2 electrode, which exhibits more complicated andelectrochemical profile during battery operating conditions than typicallystudied LiFePO4/graphite based rechargeable batteries. Extracting diversefeatures from discharge, charge, and relaxation processes, the intricacies ofcell behavior without relying on specific degradation mechanisms arenavigated. The best-performing ML model, after feature selection, achieves anR2 of 0.89, showcasing the application of ML in accurately forecasting cyclelife. Feature importance analysis unveils the logarithm of the minimum valueof discharge capacity difference between 100 and 10 cycle(Log(|min(𝚫DQ 100–10(V))|)) as the most important feature. Despite theinherent challenges, this model demonstrates a remarkable 6.6% test error onunseen data, underscoring its robustness and potential for transformativeadvancements in battery management systems. This study contributes to thesuccessful application of ML in the realm of cycle life prediction forlithium-metal-based rechargeable batteries with practically high energydensity design.1. IntroductionLithium-ion batteries (LIBs) are extensively utilized as energystorage tools in various industries such as electric vehicles,Q. Si, T. Momma, Y. TateyamaDepartment of Nanoscience and NanoengineeringFaculty of Science and EngineeringWaseda University3-4-1 Okubo, Shinjuku-ku 169-8555, JapanE-mail: TATEYAMA.Yoshitaka@nims.go.jpThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/advs.202402608© 2024 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.202402608portable electronic devices, and gridenergy because of their remarkable prop-erties such as high energy density, lowself-discharging rate, affordability, andprolonged lifespan.[1–3] Nevertheless, likenumerous other electrochemical systems,LIBs experience unavoidable energy andpower degradation over time, leading todiminished capacity and increased in-ternal resistance.[4] Therefore, preciselypredicting the cycle life of LIBs can helpindustries optimize battery usage, replace-ment schedules, reducing unnecessaryreplacements and associated costs. In ad-dition, researchers can evaluate the qualityof batteries in advance which enables themto identify potential issues and optimizebattery design.[5,6]Due to the complex degradation mecha-nisms and non-linear degradation patternsof LIBs, predicting their lifetime is chal-lenging. In previous research, the strategiesfor battery lifetime prediction are classi-fied into three main groups: mechanismmethods,[7,8] model-based methods,[9–11]and data-driven methods.[12,13] Amongthem, data-driven methods that usestatistical data and machine learning (ML) algorithms have re-cently attracted great attention because of the big data era.In recent year, there have been several reports on predictingthe cycle life of commercial LIBs which are already quite matureQ. Si, S. Matsuda, Y. Yamaji, Y. TateyamaResearch Center for Energy and Environmental Materials (GREEN)National Institute for Materials Science (NIMS)1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanS. Matsuda, Y. TateyamaNIMS-SoftBank Advanced Technologies Development CenterNational Institute for Materials Science (NIMS)1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanY. TateyamaLaboratory for Chemistry and Life ScienceInstitute of Innovative ResearchTokyo Institute of Technology4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501, JapanAdv. Sci. 2024, 11, 2402608 2402608 (1 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbHhttp://www.advancedscience.commailto:TATEYAMA.Yoshitaka@nims.go.jphttps://doi.org/10.1002/advs.202402608http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.advancedsciencenews.com www.advancedscience.comand stable.[14,15] Wu et al. demonstrated the feasibility of onlineremaining useful life (RUL) estimation using a feed-forwardneural network. Their study achieved an error of less than5% in predicting the cycle life within the practical operation,though it’s based on the data of only two LIBs.[16] Seversonet al. conducted a study where they examined 124 rechargeablebatteries under fast charging conditions in an experiment. Thesebatteries were commercial lithium iron phosphate/graphitecells and were maintained at a forced convection temperature of30 °C throughout the tests. Various parameters of the dischargeprocess were monitored during the experiments. Through theexperimental data, combined with the ML algorithm (ElasticNet),the cycle life of the 124 batteries was predicted successfully witha 9.1% test error compared with the observed cycle life.[17] Thiswork is regarded as the pioneer of this research field since thedataset used in this study is the largest publicly available fornominally identical commercial LIBs that were cycled undercontrolled conditions. Inspired by this, various research groupshave attempted to employ different ML models and features topredict the cycle life of commercial LIBs.[18,19] The use of variousbattery cell systems and the application of different ML methodsdisplay the effectiveness of cycle life prediction.Lithium metal-based rechargeable battery (LMB) have at-tracted much attention for their high specific capacity (3860mAh/g) that allows for the lowest electrochemical potential(−3.04 V vs the standard hydrogen electrode) and energy density,which extends range for electric vehicles, and improved perfor-mance in various energy-intensive applications.[20,21] Actually, bycombining the high-capacity Ni-rich LiNi0.8Mn0.1Co0.1O2 (NMC)electrode, LMB with cell level energy density over 350 Wh kg−1has been reported for realizing stable charge/discharge reactionmore than 200 cycles.[22] However, compared to the conventionalgraphite-based LIBs, LMB has lower redox potential leading toeasy reductive decomposition of electrolytes, resulting in compli-cated degradation reaction of lithium metal electrodes. For exam-ple, the dendritic growth of metallic lithium is widely recognizedas a crucial problem of lithium metal electrodes, where needle-like structures form on the surface of the electrode during cyclingthat can lead to short circuits and battery failure.[20]There have been some studies to model the aging of LMB sofar. Gao et al. devised a method for real-time detection of LMBfailure modes by monitoring changes in rest voltage and Coulom-bic efficiency. The study also introduced an accelerated life-time testing method to predict the maximum lifetime of LMBsbased on a dominant ultimate failure mechanism.[23] Dessantiset al. developed a pseudo-2D aging electrochemical model for alithium metal–LiFePO4L battery, accurately representing its elec-trochemical behavior across different charge rates and predictingdischarge capacity loss for multiple cycles.[24] However, most ofthe previous works relied on mechanistic or model-based meth-ods, requiring significant computational resources for detailedanalysis and lacking sufficient validation. Furthermore, recent in-tensive investigations utilizing various analytical techniques haveunveiled the formation of isolated metallic lithium during re-peated cycling, leading to substantial volume expansion of thelithium metal electrode.[25] Besides, internal resistance signifi-cantly increases due to the electrolyte shortage,[26] and, in practi-cal cell design conditions, chemical crossover reactions betweenelectrodes must be considered. In summary, the diverse degra-dation mechanisms and unique challenges posed by safety con-cerns as well as the limited data availability of LMB highlight theneed for tailored ML-based cycle life prediction methods. The MLapproaches may offer more flexibility and mechanism-free char-acteristics compared to traditional model-based or mechanisticmethods, making them well-suited to address the complexitiesinherent in LMB aging prediction.Under such circumstances, we addressed the construction ofan ML model for high cell-level energy density LMBs. In thepresent study, 57 cells of 350 Wh/kgcell class LMB were fabricatedusing high mass loaded Ni-rich NMC electrode, 48 out of the 57cells were used to construct the ML model, the remaining ninecells were regarded as unseen data. 35 features were generatedfrom raw cell data of the first 100 cycles, which were classifiedinto three groups: charge, relaxation, and discharge-related fea-tures. Initially, the linear regression model ElasticNet[27] was ap-plied to the three feature subsets independently to predict the cy-cle life of the cells. Regrettably, the predictive performance of themodel did not meet the desired standards. Then, the correlationof the 35 features to the observed cycle life was systematicallystudied by calculating Pearson’s correlation coefficient. 12 fea-tures that exhibit strong or moderate correlations to the cycle lifewere extracted. Based on these 12 features, combining exhaus-tive feature selection, the prediction performance of non-linearregression model XGBoost[28] was analyzed. We then found thatusing XGBoost and the selected feature subset which containssix features showed the best prediction result with R2 = 0.89 anda Root mean square error (RMSE) of 8.29. Finally, we applied ourML model to eight unseen cells (Though nine cells were preparedoriginally, 1 cell was eventually excluded because of the unstablecapacity profile). The best test error of the cycle life is 6.6%.2. Computational Section2.1. LMB Fabrication and Performance TestIn our project, total 57 monolayer stacked pouch-type LMB cells(48 cells for model construction, 9 cells as unseen data) wereassembled, consisting of a positive electrode made of NMC811(40 mm x 30 mm) with mass loading of 30 mg cm−2, a separator(6 mm × 36 mm), and a negative electrode comprising a 50 μmthick layer of lithium on a 10 μm thick copper (Cu) current collec-tor (42 mm × 32 mm). The details of electrolyte solution and sep-arator used in the present study are summarized in the support-ing information (Table S1, Supporting Information). All the cellswere fabricated inside a dry room (dew point < −50 °C) and elec-trolyte injection was carried out inside a fume hood (dew point <−85 °C). The details of the charge/discharge test conditions arealso described in supporting information. Charge and dischargeof the cells were carried out with Hokuto Denko HJ1001SD8 at25 °C. All the cells were cycled at constant current in the volt-age range 2–4.2 V. Voltage, current, and capacity of the cells werecontinuously recorded during the cycling process, through thisprocess, we obtained the charge-discharge curves at all the cyclesas well as the discharge capacity retention curve. One completecycling curve of one specific cell is shown in Figure 1, which in-cludes 3 processes 1) constant-current charging, 2) relaxation af-ter charge, 3) constant-cCC discharging.Adv. Sci. 2024, 11, 2402608 2402608 (2 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 1. The cycling data for one representative cell in the first cycle.The charging phase is denoted by the yellow segment, followed by a re-laxation period indicated in blue. Subsequently, the discharging phase isrepresented by the green section.2.2. Feature ConstructionIn the present study, a total of 35 features were extracted from theraw voltage and capacity data obtained during the entire cyclingtest, encompassing charge, discharge, and voltage relaxation pro-cesses. These features were systematically categorized into threedistinct groups: discharge-related features, charge-related fea-tures, and relaxation-related features. While previous researchpredominantly focused on features generated solely from the dis-charge process, with minimal attention given to those derivedfrom voltage relaxation or charge processes, our study soughtto bridge this gap by incorporating features from all three pro-cesses concurrently to assess the model’s performance. Here, wenot only generated features from the discharge process that havebeen typically used in previous work,[17] but also calculated ca-pacity retention of different cycles. Additionally, we introducednovel features derived from both charge and relaxation processeswithin the initial 100 cycles. This strategy aimed to determine therelative importance of each process in predicting cycle life whilesimultaneously enhancing prediction performance by selectingfeatures from all three processes. Furthermore, it facilitated theselection of features from diverse processes, thereby improvingthe overall predictive capabilities of the model.2.2.1. Discharge-Related FeaturesSeventeen features were derived from the discharge process,among which six features were calculated as summary statis-tics: minimum, variance, skewness, kurtosis, mean, and the ini-tial value of the change in discharge voltage curves between dif-ferent cycles (ΔDQ (V)) extracted from the discharge capacity-voltage curves. These curves capture the electrochemical evolu-tion of individual cells during cycling, thereby encoding valuableinsights into cell degradation mechanisms. Summary statisticswere demonstrated to effectively elucidate the shape and posi-tional changes of the voltage curve, offering a succinct represen-tation of its characteristics. In the present study, we choose thesesummary statistics based on their predictive power rather thantheir direct physical significance.ΔDQ (V) serves as a pivotal metric, quantifying the disparitybetween discharge capacity-voltage curves of two cycles. Specif-ically, ΔDQ 100–10(V) is computed as the difference between thedischarge capacities at the 100th cycle and the 10th cycle, de-noted as DQ100(V) – DQ10(V), employing interpolated dischargecapacity data. This metric highlights the variation in dischargecapacity-voltage curves between the 100th and 10th cycles, provid-ing crucial insights into cell degradation dynamics. In Figure 2a,we present the original discharge profiles spanning from the 1stcycle to the 100th cycle of cell No. 32 within our dataset. To visual-ize degradation, discharge capacity-voltage curves correspondingto the 10th cycle and 100 of this cell are extracted and depicted inFigure 2b. Subsequently, in Figure 2c, the ΔDQ 100–10(V) curvesfor all 40 cells are illustrated. In an ideal scenario, the differencein the discharge capacity curves between the 100th and 10th cy-cles would typically exhibit negative values, indicating a decreasein discharge capacity over time. However, our analysis revealedinstance where one cell displayed positive segments in this curve,contrary to the expected trend. We attribute this unexpected ob-servation to phenomena such as electrode activation or capacityrecovery. Notably, as part of our data processing and visualiza-tion methodology, we uniformly scaled the voltage values by afactor of 0.8 for enhanced presentation clarity. This scaling ad-justment was uniformly applied across all voltage values in thedataset.In addition, the discharge capacity of the 2nd cycle, the 10thcycle, and the 100th cycle were extracted, which quantifies theenergy output of the cell within a cycle and how it changes overtime. Moreover, by using the discharge capacity of the 2nd, the10th and the 100th cycle, we calculated the capacity retention(CR), a fundamental metric of the discharge capacity at differentcycle, which serves as a crucial metric for accessing cell degrada-tion. Which is defined as the ratio of discharge capacity at cyclen CDch(n) to that of cycle n −1 CDch(n-1)CR =CDch(n)CDch(n−1)(1)Then we calculated features such as the slope and the interceptof the discharge curve between the 2nd cycle the 100th and thoseof the 91st cycle to the 100th cycle.2.2.2. Charge-Related FeaturesFrom the charging process, we generated 12 features, includ-ing six summary statistics: minimum, variance, skewness, kur-tosis, mean, and the initial value of the change in charge volt-age curves between different cycles (ΔCQ(V)) extracted from thecharge capacity-voltage curves. These features exhibit crucial in-formation regarding the charging behavior of the cells and offervaluable insights into their performance characteristics.In Figure 3a, we present the original charge profile spanningfrom the 1st cycle to the 100th cycle of cell No. 41 within ourdataset. To provide further insight into the charging behavior,charge capacity–voltage curves corresponding to the 10th cycle tothe 100th cycle of this cell are extracted and depicted in Figure 3b.Adv. Sci. 2024, 11, 2402608 2402608 (3 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 2. a) Discharge profile from 1st cycle to 100th cycle of cell No. 32 in our dataset. The color changed from dark to light as the cycle number increased.b) Discharge capacity -Voltage curves for 10th and 100th cycles for cell No. 32. The abbreviation “DC” denotes discharge capacity. c) Discharge capacitydifference (ΔDQ 100–10) as a function of voltage between the 10th and 100th cycles for 40 cells.Additionally, Figure 3c illustrates the ΔCQ 100–10(V) curves forall 40 cells in our dataset, offering a comprehensive view of thecharging dynamics across the sampled cells. Similar to the dis-charge process, three cells’ ΔCQ 100–10(V) curves showed positivesegments in the curve.Charge capacity of the 2nd, the 10th, and the 100th cycle werealso included. Coulombic efficiencies (CEs) of those cycles cal-culated from charge capacity of the 2nd, the 10th, and the 100thcycle, respectively, were also selected as features to predict the cellcycle life. The CE of cycle n is defined as the ratio of measureddischarge capacity of cycle n CDch(n) and measured the chargecapacity of cycle n CCh(n)CE =CDch(n)CCh(n)(2)Typically, for an idealized cell where side-reactions are absent,Coulombic Efficiency (CE) reaches unity due to the absence oflosses in both lithium transfer and electron transfer processes.Figure 3. a) Charge profile from the 1st cycle to the 100th cycle of cell No. 41 in our dataset. The color gradient shifts from dark to light as the cyclenumber increases. b) Charge capacity-voltage curves for the 10th and 100th cycles of cell No. 41. The abbreviation “CC” denotes charge capacity c)ΔCQ 100–10(V) as a function of voltage between the 10th and 100th cycles for 40 cells. d) Discharge capacity, charge capacity, and coulombic efficiencyas a function of the cycle number of cell No. 41.Adv. Sci. 2024, 11, 2402608 2402608 (4 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 4. Relaxation voltage as a function of the relax time of cell No. 13from the first cycle to the last cycle (200 cycles). The color of the line isdifferentiated by the voltage at 600s.The Coulombic Efficiency of the cells used in our project were allrecorded, which is displayed in Figure 3d. By tracking these fea-tures across multiple cycles, we gain insights into how the cell’sperformance changes over time and how it evolves through re-peated charge-discharge cycles. In addition, these features rep-resent different stages of cell operation, including initial condi-tioning, mid-term performance, and long-term degradation. Byincluding them, we capture a comprehensive view of the cell’sbehavior across its operational lifespan, which may enhance thepredictive capabilities of the model.2.2.3. Relaxation Related FeaturesIt has been demonstrated that the relaxation process, encompass-ing the voltage value during a particular time interval and thevoltage curve within a designated timeframe, exhibits a correla-tion with the State of Health (SoH) of the cell.[29–31] Six featureswere generated during the relaxation process, including mini-mum, maximum, variance, skewness, kurtosis, and mean of theterminal voltage from the 1st cycle to the 100th cycle from therelaxation voltage-time curves, which provide valuable informa-tion about the voltage distribution and dynamics during relax-ation periods. These metrics can help in detecting abnormalitiesor irregularities in the cell’s behavior, which may indicate poten-tial degradation mechanisms or performance issues. The voltageof cell No. 13 between the 1st cycle to the 100th cycle during thecell relaxation is shown in Figure 4.We summarized the total 35 features in Table 1.2.3. Machine Learning ProcessThe entire dataset was utilized as the training dataset, employinga four-fold cross-validation strategy for model evaluation. Thismethodology involved partitioning the dataset into four mutuallyexclusive subsets. Iteratively, the model was trained and evaluatedfour times, with each subset serving as the test set once while theremaining three subsets collectively constituted the training set.By adopting this four-fold cross-validation approach, we ensureda thorough and reliable assessment of the model’s performance,enhancing our understanding of its generalization capabilities.In the present study, we employed two machine learning meth-ods: ElasticNet, a linear regression model combining Lasso (L1)and Ridge (L2) regularization techniques, and XGBoost, a non-linear regression model. ElasticNet was chosen for its ability tohandle high-dimensional datasets with potentially correlated fea-tures. By incorporating both L1 and L2 penalties, ElasticNet al-lows for feature selection and regularization, which can mitigateoverfitting and improve generalization performance. XGBoost,on the other hand, is a powerful gradient-boosting algorithmknown for its scalability, efficiency, and ability to handle complexnonlinear relationships in the data. It can capture intricate pat-terns and interactions in the dataset, leading to enhanced predic-tive accuracy. Additionally, XGBoost provides insights into fea-ture importance, aiding in the identification of the most relevantvariables for prediction. The adoption of XGBoost was motivatedby its superior performance in achieving accurate and reliablepredictions when ElasticNet failed to produce satisfactory results.Both ElasticNet and XGBoost algorithms are further illustrated inthe supporting information.The performance of the ML models was evaluated by the fol-lowing three statistical metrics:Table 1. 35 features extracted from discharge, charge, and voltage relaxation process.Feature types Feature descriptionDischarge-relatedfeaturesLog(|min(ΔDQ 100–10(V))|),Log(|mean(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|),Log(|ΔDQ 100–10(V) [0]|),Log(|skew(ΔDQ 100–10(V))|), Log(|Kur(ΔDQ 100–10(V))|);Slope and Intercept of the linear fit to the capacity fade curve, cycles 2 to 100, 91 to 100 (Slope_DQ, Intercept_DQ);Discharge capacity of 2, 10, and 100 (DQ_n);Max difference of discharge capacity of 100 and 2;Capacity_retention_1:100, 2:1, 99:100 (CR_n).Charge-related features Log(|min(ΔCQ 100–10(V))|),Log(|mean(ΔCQ 100–10(V))|), Log(|var(ΔCQ 100–10(V))|),Log(|ΔCQ 100–10(V) [0]|),Log(|skew(ΔCQ 100–10(V))|), Log(|Kur(ΔCQ 100–10(V))|);Charge capacity of 2, 10, and 100 (CQ_n);Coulombic efficiency of 2, 10, and 100 (CEn).Relaxation-relatedfeaturesMax, Min, Var, Mean, Skew and Kurtosis for the terminal voltage between 1 and 100 cycles.Adv. Sci. 2024, 11, 2402608 2402608 (5 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 5. a) The discharge capacity degradation curves of the 48 examined cells. The color of each line is distinguished by the discharge capacity ofthe last cycle. b) Discharge capacity degradation curve of cell No. 40. c) Discharge capacity degradation curve of cell No. 39. d) Discharge capacitydegradation curve of cell No. 9 which exhibits fluctuations.Mean absolute error (MAE):MAE = 1nn∑i = 1|yi − ŷi| (3)Root mean square error (RMSE):RMSE =√√√√ 1nn∑i=1(yi − ŷi)2 (4)R2:R2 = 1 −∑nk = 1(yi − ŷi)2∑nk = 1(yi − ȳ)2(5)Here, n represents the number of cells, yi and ŷi represents theobserved cycle life and the predicted cycle life for sample i. TheMean Absolute Error (MAE) gauges the proximity of predictionsto the respective outcomes. On the other hand, the Root MeanSquare Error (RMSE), which captures the dispersion of errors, ex-hibits higher sensitivity toward substantial deviations comparedto the MAE. For these two values, small values represent goodperformance of the models. The R2 is a metric expressed in per-centages, and in an optimal scenario, R2 approaches 100% or1, indicating a strong alignment between the observed and pre-dicted values.Furthermore, in our project, we used Pearson’s correlation co-efficient to depict the relationship between the features and cellcycle life. The coefficient is defined are calculated by[32]:r =∑pi=1(xi − x̄)(yi − ȳ)√((xi − x̄)2√((yi − ȳ)2(6)The correlation coefficient is bounded within the range of −1to 1, which signifies the strength and direction of the correlationbetween two variables, x and y. A positive correlation yields val-ues between 0 and 1, indicating that as one variable increases,the other tends to increase. Conversely, a negative correlation re-sults in values between −1 and 0, implying that as one variableincreases, the other tends to decrease. Interpretation of the co-efficient involves magnitude: a value exceeding |0.8| points to astrong correlation, while a value lower than |0.5| signifies a weakcorrelation. Within the range of |0.5| and |0.8|, a correlation ofmoderate strength is observed.3. Results and DiscussionIn the present study, we prepared the cells with different techno-logical parameters (kinds of electrolyte and separator). Besides,we also change the evaluation condition parameters, such as cur-rent density, separator thickness, and confining pressure whichrefers to the pressure exerted on the battery cell components dur-ing the cycling test. The detailed technological parameters of thecells investigated were summarized in Table S1 (Supporting In-formation). Such differences result in the change of life spanamong the cells. In Figure 5a, the cells’ degradation trajectoriesAdv. Sci. 2024, 11, 2402608 2402608 (6 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 6. Parity plots for observed and predicted cycle lives for different feature sets using the ElasticNet model. a) discharge-related feature subset. b)charge-related feature subset. c) relaxation-related feature subset.of all investigated 48 cells as a function of cycle life was shown. Inaddition, the distribution of the lifespan of the cells is also shownin Figure S1 (Supporting Information). The end-of-life capacity isdefined as when the discharge capacity falls to 80% of the nomi-nal capacity (available maximum capacity).Figure 5b shows the representative discharge profile of onecell (cell No. 40). The cell exhibited the 1st discharge capacity of0.86 mAh with average discharge voltage of 3.7 V. With progressof cycle, the cell exhibited a capacity higher than 0.68 mAh upto the 138th cycle. After that the discharge capacity gradually de-creased and reached to 0.21 mAh at 200th cycle. In Figure 5c,the profile of the different LMB cell with the same technolog-ical parameters (cell No. 39) was also shown. As the two pro-files showed almost identical degradation trajectories, suggestingthe high reproducibility of the cells investigated in the presentstudy. Although most of cells investigated in the present studyshowed a similar capacity profile with that of cell No. 40, the un-stable capacity profile was also observed among the cells. Forexample, in case of cell No. 9, there can be seen the fluctua-tion of capacity value after the 100th cycle (Figure 5d). Such un-stable profile originated in the non-uniform reaction character-istics of lithium metal electrode, such as, micro-short or elec-trolyte shortage. Actually, after the 100th cycle, the over-chargingoccurs, which is a typical deterioration mechanism of LMB.Cells of this type pose challenges in understanding their capac-ity degradation mechanism, which is both elusive and distinctfrom real-world conditions. Consequently, we opted to eliminatecertain cells from our dataset. Following our analysis, we haveexcluded eight cells from our project, leaving us with a total of 40cells.Next, we applied discharge-related features, charge-related fea-tures, and relaxation-related features independently to predict thecycle life using ElasticNet. We try to determine which feature sub-set could provide better prediction results. In Figure 6, from leftto right it displays the prediction results for different feature sub-sets.The X and Y axes in Figure 6 indicate the experimentally ob-served cycle life and mean value of ML predicted cycle life af-ter the four-fold cross-validation respectively. Figure 6a showsthe prediction result of using discharge-related features, thetesting MAE equals to 9.81, RMSE equals to 13.54 and theR2 is 0.67, which is the best prediction performance amongthe three machine-learning methods. For charge-related features(Figure 6b) and relaxation-related features (Figure 6c), the parityplots become more and more scattered, their MAE and RMSEbecome larger, meanwhile, the R2 becomes smaller, meaningthat the prediction results become worse than the first situation.However, despite their superiority, the prediction performanceachieved using discharge-related features alone, with an R2 valueof 0.67, did not meet our anticipated standards. Hence, to im-prove the prediction accuracy, we sought to optimize both thefeature selection process and the machine learning methodologyemployed.For the feature part, we mapped the Pearson’s correlation coef-ficient heatmap matrix among variables in our data set includingfeature to feature and feature to target value which is shown inFigure 7a.It is a square matrix where rows and columns represent fea-tures and observed cycle life, and each cell contains the corre-lation coefficient between corresponding variables. The correla-tion coefficient between two features measures the magnitudeand direction of the linear connection between those features,offering insights into how changes in one feature correspond tovariations in another feature. The most important correlation inour research should focus on the relationship between the fea-tures and the observed cycle life which is the rightmost columnin the correlation matrix. From the coefficient value we can at-tain a distinct comprehension of the correlation existing betweenthem. Features with highe coefficient are regarded as importantpredictors to the cycle life.From Figure 7b, the coefficients of discharge-related featuresare relatively higher than those of charge-related features andrelaxation-related features. Some of the features show strong cor-relation with the observed cycle life, for example, the most cor-related feature is the logarithm of the minimum value of theΔDQ 100–10(V), which has a negative Pearson’s correlation coef-ficient (r = −0.9) with the observed cycle life, next is the loga-rithm of the variance value of the ΔDQ 100–10(V). However, thereare several features that show a very weak correlation to the ob-served cycle life such as the discharge capacity of the 100th cycle,coulombic efficiency at the 100th cycle, and variance of the relax-ation terminal voltage.Adv. Sci. 2024, 11, 2402608 2402608 (7 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 7. a) The relationship heatmap matrix of the variables in our dataset. b) Pearson’s correlation coefficient of the features to the target valueobserved cycle lives of the 40 cells.Here, we choose several features of the cells in our dataset andplot the observed cycle life of the cells as a function of these fea-tures in Figure 8.In Figure 8a, thefeature “log(|min(ΔDQ 100–10(V))|)” exhibits astrong correlation as evidenced by their Pearson’s correlation co-efficient absolute value surpassing |0.8|. The cycle life of the cellshas an obvious linear relationship with the feature. It’s importantto highlight that our calculations did not merely entail extract-ing the summary statistics of ΔDQ 100–10(V); rather, we calculatedthe logarithm to the base 10 of these values. In our investiga-tion, when addressing the logarithmic function, a ΔDQ 100–10(V)approaching zero signifies a reduced disparity between the dis-charge capacity-voltage curves, leading to more negative logarith-mic values. According to the visual representation, the greater thenegativity of the logarithmic value, the longer the observed cyclelife of the cell—implying less noticeable capacity degradation.Figure 8b illustrates the correlation between the slope of dis-charge capacity from the 2nd cycle to the 100th and cycle life, re-vealing a moderate correlation (r = 0.53). This plot demonstratesa gradual but not noticeable upward trend. For cells with shorterAdv. Sci. 2024, 11, 2402608 2402608 (8 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 8. The cycle life of the cells plotted as a function for different features. a) cycle life as a function of the minimum value of the ΔDQ100 − 10(V).b) cycle life as a function of the slope of discharge capacity between the 2nd cycle and the 100th cycle. c. cycle life as function of the variance of therelaxation voltage between the 1st cycle to the 100t cycle.lifespans, the degradation tends to decline relatively faster, indi-cating a steeper slope, as the graph corroborates. In the case ofcells with longer cycle life, their slopes are less negative, and thedegradation trajectory exhibits a milder decline. However, by an-alyzing our dataset, we identified some uncertainties regardingcells with longer cycle life, which can be explained by the moder-ate correlation of this feature with cycle life.In Figure 8c, the data points are scattered much more than theprevious two features which signifies a weak correlation betweenobserved cycle life and the variance of relaxation voltage from the1st cycle to the 100th cycle. Therefore, this particular feature isconsidered as a poor predictor for cell cycle life. Based on ourexamination, we have identified nine discharge-related featuresand three relaxation-related features exhibiting strong or moder-ate correlation with cell cycle life. Nevertheless, all charge-relatedfeatures exhibit a weak correlation to cell cycle life. These 12 fea-tures are selected to use in the following research.Next, for the ML method part, to leverage the predictive per-formance, we implemented the ElasticNet and XGBoost ML al-gorithms to the 12 selected features separately. The predictionresults based on XGBoost and ElasticNet using the 12 selectedfeatures are shown in the Figure 9.From the parity plots, it’s obvious the plot of ElasticNet is morescattered than that of XGBoost. In addition, based on the pre-diction results, it can be observed that XGBoost shows a slightdecrease in RMSE and MAE, with values of 9.49 and 7.8, respec-tively, when compared to ElasticNet, where the RMSE and MAEare 12.06 and 8.8. Meanwhile, the R2 of these two models are 0.86and 0.72, which demonstrates non-linear ML model XGBoost hasa better prediction performance on the cell cycle life than Elastic-Net. Hence, we decided to build our ML model based on XG-Boost.To eliminate the potential feature overfitting, we conductedexhaustive feature selection (EFS) on the 12 features. EFS is anTable 2. The best R2 score and the feature subsets when using exhaustive feature selection as a function of the feature numbers.n Best R2 Feature combination1 0.722 Log(|min(ΔDQ 100–10(V))|)2 0.854 Log(|min(ΔDQ 100–10(V))|), slope_DQ2:1003 0.871 Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|)4 0.874 Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|), Slope_DQ91:1005 0.884 Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|), Slope_DQ2:100, Mean6 0.890 CR_10:100, Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|), Slope_DQ2:100, Mean7 0.877 CR_10:100, Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|), Slope_DQ2:100, Slope_DQ91:100, Mean8 0.885 CR_10:100, Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|), Log(|mean(ΔDQ 100–10(V))|), Slope_DQ2:100, Mean,Slope_DQ91:1009 0.871 CR_10:100, DQ_2, Intercept_DQ2:100, Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|), Log(|mean(ΔDQ 100–10(V))|),Slope_DQ91:100, Mean10 0.870 CR_10:100, DQ_2, Intercept_DQ2:100, Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|), Log(|mean(ΔDQ 100–10(V))|),Slope_DQ91:100, Mean, Max11 0.857 CR_10:100, DQ_2, Intercept_DQ91:100, Log(|min(ΔDQ 100–10(V))|), Log(|var(ΔDQ 100–10(V))|), Log(|mean(ΔDQ 100–10(V))|), Slope_DQ2:100,Slope_DQ91:100, Mean, Max, Skew12 0.859 All featuresAdv. Sci. 2024, 11, 2402608 2402608 (9 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 9. a). Parity plots of using ElasticNet and XGBoost on the 12 fea-tures. b). Prediction result histogram. The blue bar represents the resultsof ElasticNet and the Orange bar indicates XGBoost.approach that impartially evaluates the optimal feature subsetusing a specified evaluation metric. This method guarantees theassessment of all possible combinations, ensuring a compre-hensive analysis without undue computational cost. ThroughEFS, a total of 4095 feature combinations were generated fromthe 12 features, each of the combinations was assessed byXGBoost with four-fold cross-validation, the optimal predictiveperformance for various feature numbers (n) was identified, andthe outcomes are presented in Table 2.Table 2 reveals that there is minimal variation in the scoreswithin the range of n = 3 to n = 10. However, relatively large de-viations are observed for values outside this range, both for n < 3and n > 10. We find that the model provides the most accurateFigure 10. a) Parity plot of the best prediction using XGBoost with six fea-tures. b) Relative feature importance ranking for the six features in lifetimeprediction.predictions with n = 6, resulting in an R2 value of 0.89. The val-ues of the six features of each cells are shown in the Table S2(Supporting Information). The parity plot illustrating the use ofthis specific set of features is depicted in Figure 10a in which theRMSE = 8.29 and MAE = 6.45.According to this 6-feature subset, we analyzed the feature im-portance. In Figure 10b, the feature importance of the six featuresis plotted, different feature has different relative importance tothe model. In this feature subset, the discharge-voltage-relatedfeatures such as the logarithm of the minimum value and thevariance value of ΔDQ 100–10(V) play crucial roles in the modelperformance, and the logarithm of the minimum value ofΔDQ 100–10(V) (former) is the most important feature in this case.The slope of linear fit of the discharge capacity between the 2ndcycle and the 100th cycle, and the Mean value of the relaxationvoltage have the same contribution to the model but their relativeimportance is lowest, the feature importance of capacity retentionfrom 10 to 100 is higher than both of them, however, according tothe Pearson’s correlation coefficient, it has a weaker correlationAdv. Sci. 2024, 11, 2402608 2402608 (10 of 12) © 2024 The Author(s). Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode=www.advancedsciencenews.com www.advancedscience.comFigure 11. Prediction results of the eight new NMC811/Li metal cells, thered points indicate the training data, and the blue points represent thetesting data.to the observed cycle life compared with these two features,which indicates it has a higher ability to reduce the error of theprediction result, but it has less linear relationship with the cyclelife. Through exhaustive feature selection method and use of ad-vanced ML method XGBoost, we realized a satisfying ML modelfor LMB cycle life, which we name as “XGB-LMBCLpredictor”.Finally, we applied our model “XGB-LMBCLpredictor” witheight new NMC811/Li metal cells as unseen data to test whetherour model can predict the cycle life accurately. The details of thecells are shown in Supporting Information. Here, one cell is dis-carded because of its unstable capacity profile. The prediction re-sult is shown in Figure 11, the MAE and RMSE of the testing dataare relatively small and the test error (Mean Absolute PercentageError: MAPE) equals to 6.6%. The achieved RMSE and MAE val-ues suggest that the model provides predictions with reasonableaccuracy. The relatively low MAPE reinforces the model’s accu-racy, especially considering the percentage-wise deviation. As in-dicated by these metrics, the model’s performance is well-suitedfor accurate cycle life predictions.4. ConclusionUtilizing machine learning modeling holds great potential forthe diagnosis and prediction of batteries. It provides possibili-ties in various aspects, including their development, manufac-turing, and optimization. In the present study, we focus on usingthe ML method to model the complex degradation mechanismsand predict the cycle life of NMC811/Li metal batteries via dif-ferent features generated from different cycle processes. 48 ofNMC811/Li metal batteries’ degradation data are recorded andfeatures generated from the data are classified into three groupsincluding discharge-related features, charge-related features, andrelaxation-related features. Linear regression model ElasticNetwas first used in different feature groups, however the predic-tion performance was unsatisfactory, then by Pearson’s correla-tion coefficient analysis, we selected 12 features out of the 35 fea-tures which have a strong or moderate correlation with the cyclelife and applied non-linear regression model XGBoost to predictthe cycle life of the cells. Compared with the result of ElasticNet,XGBoost is much superior for cell cycle life prediction with anRMSE of around 9.49 and MAE 7.8. Exhaustive feature selectionresults show that six features out of the 12 features can give thebest prediction result which decreases the RMSE to 8.29, MAE to6.45, and increase R2 to 0.89, where Log(|min(ΔDQ 100–10(V))|) isfound the most important feature, contributing more than 44%for lifetime prediction. Finally, by testing the unseen data, ourbest model achieves a 6.6% test error, which indicates our ma-chine learning model “XGB-LMBCLpredictor” is suitable for thecycle life prediction of LMB.Through our investigation, utilizing the capabilities of ma-chine learning algorithms, our goal is to attain heightened pre-cision and dependability in predicting the cycle life of LMB. Byexpanding the horizons of predictive precision, our study has thepotential to give clues of LMB advancement and implementa-tion. This could lead to transformative outcomes in the realm ofenergy storage, ensuring enhanced safety, greater efficiency, andextended longevity for energy storage solutions.Supporting 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 for Shuntaro Miyakawa, and Takaya Saito forvaluable discussions. This work was also partially supported by MEXT as“Program for Promoting Research on the Supercomputer Fugaku” grantnumber JPMXP1020230325, Data Creation and Utilization Type MaterialResearch and Development Project grant JPMXP1122712807. The calcula-tions were performed on the supercomputers at NIMS (Numerical Mate-rials 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.Keywordsbattery, cycle life, features, Li metal anode, machine learning modelReceived: March 12, 2024Revised: June 2, 2024Published online: June 27, 2024Adv. Sci. 2024, 11, 2402608 2402608 (11 of 12) © 2024 The Author(s). 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Advanced Science published by Wiley-VCH GmbH 21983844, 2024, 33, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202402608 by National Institute For, Wiley Online Library on [22/10/2024]. 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://onlinelibrary.wiley.com/action/rightsLink?doi=10.1002%2Fadvs.202402608&mode= Data-Driven Cycle Life Prediction of Lithium Metal-Based Rechargeable Battery Based on Discharge/Charge Capacity and Relaxation Features 1. Introduction 2. Computational Section 2.1. LMB Fabrication and Performance Test 2.2. Feature Construction 2.2.1. Discharge-Related Features 2.2.2. Charge-Related Features 2.2.3. Relaxation Related Features 2.3. Machine Learning Process 3. Results and Discussion 4. Conclusion Supporting Information Acknowledgements Conflict of Interest Data Availability Statement Keywords