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 Authors: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Shengyu Tao Ruifei Ma Zixi Zhao Guangyuan Ma Lin Su Heng Chang Yuou Chen Haizhou Liu Zheng Liang Tingwei Cao Haocheng Ji Zhiyuan Han Minyan Lu Huixiong Yang Zongguo Wen Jianhua Yao Rong Yu Guodan Wei Yang Li Xuan Zhang Tingyang Xu Guangmin Zhou Abstract Rapid and accurate state of health (SOH) estimation of retired batteries is a crucial pretreatment for reuse and recycling. However, data-driven methods require exhaustive data curation under random SOH and state of charge (SOC) retirement conditions. Here, we show that the generative learning-assisted SOH estimation is promising in alleviating data scarcity and heterogeneity challenges, validated through a pulse injection dataset of 2700 retired lithium-ion battery samples, covering 3 cathode material types, 3 physical formats, 4 capacity designs, and 4 historical usages with 10 SOC levels. Using generated data, a regressor realizes accurate SOH estimations, with mean absolute percentage errors below 6% under unseen SOC. We predict that assuming uniform deployment of the proposed technique, this would save 4.9 billion USD in electricity costs and 35.8 billion kg CO2 emissions by mitigating data curation costs for a 2030 worldwide battery retirement scenario. This paper highlights exploiting limited data for exploring extended data space using generative methods, given data can be time-consuming, expensive, and polluting to retrieve for many estimation and predictive tasks. Introduction Transport electrification, a critical sector in a low-carbon energy transition , has unprecedentedly reshaped the fossil fuel-based transport paradigm. Lithium-ion batteries are vital to this transition by providing affordable, durable, and safe energy supplies to electric vehicles (EVs) , . The total capacity of in-use and end-of-life EV batteries will surpass 32–62 terra-watts by 2050, considerably higher than the estimation in International Renewable Energy Agency and Storage Lab scenarios . However, retired EV batteries are strongly regulated with a huge remaining capacity value under-exploited, typically over 80% of the rated capacity , . If not handled properly, it leads to economic burdens  for manufacturers and users, as well as subsequent environmental and societal issues , including resource wastage, supply chain risks, and carbon emissions , , . 1 2 3 4 5 6 7 8 9 10 11 Promising strategies to address concerns regarding the intermittent surging of battery retirement are reuse , ,  and recycling . In reuse, retired batteries are repurposed for applications such as grid-connected energy storage systems , residential power supplies , and low-speed vehicles. However, reuse requires preliminary pretreatments, including consistency screening , capacity sorting , and regrouping ,  to meet application requirements . Despite the initiation of pilot programs , , , the absence of stringent standards for use scenarios and retirement pathways hamper the rational use of the residual capacity . Recycling alternatively uses residual values of retired batteries by materials extraction or structural repair , , suitable for irreversibly degraded retired batteries. Compared with pyrometallurgy and hydrometallurgy , , direct recycling stands out for superior profitability, lower energy consumption, and reduced carbon emissions , , . Leveraging lithium replenishment and post-processing of cathode materials, direct recycling achieves efficient material structure repair, and performance restoration . However, the state of health (SOH) determines the required chemical reagent and anticipated lithium supplementation dosages in direct recycling strategy formulations , , . Insufficient dosage can result in an incomplete repair, while excessive dosage can lead to the generation of residual alkali on the cathode surface, deteriorating the restoration performance , . Unfortunately, SOH retrieval requires invasive material characterization ,  and lengthy capacity calibration tests, the non-invasive, rapid, and sustainable SOH acquisition remains an outstanding challenge. 6 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 26 27 30 31 32 33 34 27 35 36 37 To secure consistent SOH information, EV batteries are monitored, and operational data are recorded by cloud platforms  and battery passports . European Parliament adopted the Batteries Directive on June 14, 2023, to ensure that retired batteries could be reused, reconditioned, or recycled at the end of service life . However, the required monitoring and recording procedure is merely accessible in the EV service phase, retired batteries are no longer connected to the in-vehicle monitoring unit. Thus, it is challenging to retrieve field-available SOH data. The lifetime data integrity remains a major challenge, calling for the SOH estimation only using field data, opposite to historical data or under controllable conditions , , . One solution is to perform a capacity calibration test at the retired battery collection field, i.e., state of charge (SOC) conditioning, which is straightforward, however, it requires unaffordable test time and extra electricity costs. The hybrid pulse power characterization test is an alternative for SOH estimation by dynamic pulse injection, but the complete test sequence takes over 12 hours. Tao et al. utilized short pulses for SOH estimation of retired batteries, assuming that a SOC conditioning to 5% SOC was performed, which was barely compatible with random retirement SOC conditions . Recent advances in sensory-based measurements include X-ray imaging , electrochemical impedance , , optical fiber sensing , , acoustics sensing , , partial charging , , and pulse injection , . Sensing-based techniques are in the laboratory stage due to invasion, while pulse injection features untangling the battery degradation without physical damage, simultaneously faster than partial charging and electrochemical impedance-based methods , , , , , . However, pulse injection is a data-centric method that is only feasible under the ideal assumption that physically measured data encompasses retirement conditions of the model deployment phase, known as the common challenge of domain shift in the machine learning community. Despite advances in transfer learning and domain adaption methods , , , challenges persist since the target domain to align still requires prior information upon deployment, and existing learning methods can hardly be updated for random retirement conditions . An alternative is spanning data testing scale under unexplored retirement conditions to mitigate data scarcity and heterogeneity while it can lead to increased costs. Wang et al. proposed a temperature excavation method to interpolate reaction kinetic preferences at different intermediate states during a thermochemical process, allowing for the construction of extensive training databases at minimal thermochemistry experimental scale and cost as a data augmentation for machine learning model training . Besides, generative learning also demonstrates the possibilities of estimating SOH with augmented data from partially cycled profiles, saving required physically tested data , . However, the data scarcity and heterogeneity in battery reuse and recycling context are even more complex due to a mixture of cathode material types, physical formats, capacity designs, and historical usages, restricting the potential integration of condition-specific knowledge of degradations into machine learning models. Thus, it is reasonable to consider the dependency relationship between retirement conditions and pulse voltage responses for data generation, inflicting no lengthy time series capacity calibration and extra physical experiments simultaneously, to boost SOH estimation performance. 38 24 39 30 40 41 41 42 43 44 45 46 47 48 49 50 17 41 17 51 52 53 54 55 56 57 58 59 60 61 62 In this study, we perform retired battery pretreatment, i.e., SOH estimation, using the pulse voltage response data generated by an attentional variational autoencoder at a saved physical measurement time and cost. The high-level process of general pretreatment steps, generative model training, and practical model deployment steps are illustrated in Fig.  . The research idea is to use generative learning to exploit already measured data for the pulse voltage responses exploration in continuous retirement conditions, i.e., SOC distribution in retired battery collection stage. Downstream SOH estimation is implemented without physically measured pulse response data, saving pretreatment electricity costs and carbon emissions otherwise required from conditioning SOC to the anticipated level. Compared with the ampere-hour integral method and the machine-learning pulse injection, generative learning underscores a faster generation speed and accurate estimation. With generated data, a simple regressor successfully estimates the SOH with low error under unseen or inaccessible SOC retirement conditions in the database, a challenging out-of-distribution (OOD) issue. The OOD issue is resolved by learning the inherited physical pattern between the SOC condition and voltage response induced by the rapid pulse. We demonstrate the generalizability of our method by verifying through 2700 physically measured samples, spanning 3 cathode material types, 3 physical formats, 4 capacity designs, and 4 historical usages (1 laboratory accelerated aging, 1 pure battery EV driving, and 2 hybrid EV driving). Generative learning suits interpolation and extrapolation by integrating prior knowledge of retirement conditions into latent space scaling of the model parameters, saving measurement time, electricity costs, and consequent carbon emissions while not compromising SOH estimation accuracy. A conservative global case study of battery retirement in 2030 highlights the significance of rapid and sustainable SOH estimation in pyrometallurgical, hydrometallurgical, and direct recycling circumstances. Through technical-economic analysis, generative learning-assisted SOH estimation could save $4.9 billion electricity costs and 35.8 billion kg CO2 emissions by 2030 worldwide. We discuss the model interpretability, recycling pretreatment implications, and broader aspects of future smart recycling pretreatment directions integrated with machine learning. 1    The retired battery pretreatment steps include SOC conditioning, physical measurements, machine learning for SOH diagnosis, and the second-life decision-making process before reuse or recycling. SOC conditioning refers to adjusting the SOC values of the retired batteries to desired levels using the traditional constant current constant voltage (CCCV) method.   The schematic of attentional variational autoencoder for pulse voltage response data generation.   The practical usage of the data generation model for SOH estimation requires no extra SOC conditioning. The trained machine learning model is supervised by the generated data and receives immediate pulse voltage responses when in the deployment phase.   The economic and environmental benefits and rapid generation speed of our generative learning methodology by saving SOC conditioning costs in the 2030 battery retirement scenario globally. a b c d Results Dataset acquisition Data scarcity and heterogeneity are major challenges in data-driven battery diagnosis and prognosis, especially for retired batteries. We collected 2700 samples from 270 physically retired batteries across wide SOC levels, i.e., from 5% to 50% with a 5% grain. In Fig.  , the dataset covers 3 prevailing cathode material types, including 119 physically collected NMC (nickel manganese cobalt oxide), 56 LFP (lithium iron phosphate), and 95 LMO (lithium manganese oxide) retired batteries, spanning 3 physical formats (cylindric, pouch, prismatic) and 4 historical usage patterns (1 laboratory accelerated test, 3 EV usages, including 1 purely electrified power-train mode and 2 hybrid power-train modes). We stress that the inclusion of highly heterogeneous testing samples makes our dataset the largest rapid pulse-based dataset for SOH estimation of retired batteries up to date, facilitating the model generalizability beyond the physically measured datasets. 2a    The Sankey plot for retired batteries distribution, comprises cathode material types, physical formats, capacity designs, and historical usages.   Pulse current and the subsequent voltage response of the retired batteries, where the features are extracted from the turning points, i.e., the points with zero second-order derivative of the voltage response curve. The 21 feature points, from U1 to U21, are extracted. The recording frequency for the raw data is 100 Hz. The rest time is 25 seconds between each pulse in C-rate. Note that the term C stands for charge (discharge) rate when a 1 h of charge (discharge) is performed. The ambient temperature is controlled at 25 .   The state of health (SOH) distribution (Gaussian fit) of the 2.1 Ah and 21 Ah retired batteries for illustration, respectively. For SOH distribution of other battery types, one can refer to Supplementary Fig.  .   The relationship between measured pulse voltage response and calibrated SOH from capacity calibration test, with varying state of charge (SOC) conditions. The first feature dimension, U1, is illustrated.   The interpolation and extrapolation data generation case illustration under different battery retirement SOC distributions. Detailed testing settings are in   and  , noting that the C-rate setting is identical across cathode material types. Source data are provided as a Source Data file. a b c 1 d e Supplementary Notes1 2 In contrast to regular constant current constant voltage (CCCV) testing, the pulse test inflicts no lengthy test time and extra damage to the retired batteries. Therefore, we use the CCCV results as the SOH benchmarking capacity values. Pulse test data are used as training data for the generative learning model. Even though the battery cathode material type varies, we perform a standardized and accessible feature engineering, ensuring compatibility in practical use. Figure   demonstrates the feature extraction after pulse current injection. The CCCV and pulse injection experimental settings can be found in Supplementary Note  . For the first five injected pulses, the turning points, i.e., the points with zero second-order derivative of the voltage responses, are recorded as features, resulting in 21-dimensional features. Despite pulse time at a 5 s level, we also perform sensitivity measurement on pulse width with dual aims to verify pulse robustness and further shorten test time, ranging from 30 ms to 5 s. 2b 1 We consider accelerated aging in laboratory tests (Supplementary Note  ) and real EV driving aging, though agnostic to the explicit driving profiles due to data privacy restrictions. In Fig.  , the SOH distribution of accelerated aging batteries (NMC, 2.1 Ah) and pure battery EV driving aging batteries (NMC, 21 Ah) are illustrated. Noting that SOH values are complementary in a wide SOH region, from 0.6 to 1, the collected data is representative of battery retirement scenarios, also with extreme early retirement cases. SOH distributions of other collected batteries (LMO, 10 Ah, and LFP 35 Ah) cover a wide SOH distribution, see Supplementary Fig.  . The pulse tests are repeated in different SOC levels, ranging from 5% to 50%, to simulate the randomness of retirement batteries collection. The tested SOC region is under the assumption that retired batteries either exhibit low SOC or are subject to compulsory discharging for safe stationary warehouse storage requirements, thus the SOC upper limit is set at 50%. In Fig.  , the first dimension of the extracted features from accelerated aging batteries (NMC, 2.1 Ah) and EV driving aging batteries (NMC, 21 Ah) are illustrated. Despite differences in capacity designs and historical usages, the pulse voltage responses exhibit a consistent degradation pattern, and so do other retired batteries for other feature dimensions, see Supplementary Figs.  – . However, the SOC distribution of retired batteries is continuous, and thus it cannot be exhausted by physical measurements. Rather than spanning the data test scale, we use already-tested pulse voltage response data to generate more diversified data across SOC conditions. In Fig.  , two-generation scenarios, i.e., the interpolation and extrapolation, are illustrated, with unit conditioning savings, electricity savings, CO2 emissions reductions, and their calculation methods presented in Supplementary Tables.  – , respectively. 2 2c 1 2d 2 5 2e 1 3 Pulse voltage response data generation We first consider using the already-measured pulse voltage response data to reconstruct themselves, rather than directly generating new data samples. The reconstruction means that the measured data are first compressed into a latent variable space while maintaining a learned structure from original statistical distributions (Supplementary Fig.  ) and then decompressed to the original dimensions. In this study, the reconstruction is equivalent to supervising the encoder neural network model and decoder neural network model training phase, as illustrated in Fig.  . The core idea is to balance the exploitation of limited measured data and the exploration of extended data space using latent dependencies between retirement conditions and pulse voltage response data with cross-attention mechanisms, see “Methods”. Then measured data fused with conditional information are fed into the encoder neural network, obtaining latent variables containing retirement conditions. Compressed latent variables are decompressed by training a decoder neural network model and reconstructing the input data samples, also guided by the feed-forward retirement conditions. Another input of the decoder neural network is only random noise, subject to Gaussian assumption (Supplementary Fig.  ), inflicting no physical experimental measurement otherwise involved with additional test time, energy consumption, and even safety hazards. 6 1b 7 Figure   shows the data reconstruction results of the first feature dimension U1 at selected SOC values (35% and 50%), with a mean absolute percentage error (MAPE) lower than 1%, indicating that the model learned the dependencies between pulse voltage response data and SOC conditions. Such dependencies are of generality in a wide SOH range, from 0.6 to 0.95. Regarding other feature dimensions, the data reconstruction results are still satisfactory, with a MAPE lower than 1%, see Fig.  . The reconstruction results for other types of retired batteries (NMC, 21 Ah, LMO, 10 Ah and LFP, 35 Ah) are presented in Supplementary Figs.  – , demonstrating the model generality and flexibility. It is noted that lower SOC regions exhibit comparatively higher reconstruction MAPE, though still lower than 1%, which can be rationalized by the sensitivity of the polarization response at low SOC regions. It is, therefore, recommended to perform pulse injections at a middle SOC region for reliable representation of battery degradation. However, as we highlight the random retirement conditions with different SOCs, pulse injection at fixed SOC needs extensive conditioning time and energy consumption, exacerbating a dilemma between pulse injection regions and unaffordable conditioning time and cost, see Supplementary Fig.  . 3a 3b 8 10 11

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