Machine learning-driven time series analysis for SOH prediction of lithium-ion batteries

Machine learning-driven time series analysis for SOH prediction of lithium-ion batteries | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Machine learning-driven time series analysis for SOH prediction of lithium-ion batteries Yunlong Zhang, Xiaolei Bi, Shiqiang Wang, Bin Tao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6310092/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Apr, 2026 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Energy storage batteries are essential for stabilizing renewable energy systems and ensuring power grid efficiency. However, challenges such as capacity degradation, inadequate data quality, and the need for real-time predictions highlight the importance of accurate State of Health (SOH) models. This study explores Random Forest(RF), Long Short-Term Memory (LSTM) and Bidirectional LSTM (Bi-LSTM) for SOH prediction across single lithium-ion battery, batterywith environmental factors and battery modules. Bi-LSTM demonstrated superior performance in evaluation indicators, achieving lower MAE, MSE and R² value closest to 1, with further accuracy gains through additional features like discharge time and median voltage. The results underscore Bi-LSTM’s effectiveness in capturing long-term dependencies and its potential to enhance battery health management, contributing to reliable and sustainable energy storage systems. Physical sciences/Energy science and technology/Energy storage/Batteries Physical sciences/Energy science and technology/Energy storage Lithium-ion battery State of health Machine learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction The increasing integration of renewable energy sources, such as wind and solar power, into the global energy landscape has necessitated advanced solutions to address challenges associated with energy storage and grid stability. Energy storage batteries, especially lithium-ion batteries (LIBs) serve as critical components, mitigating power fluctuations, enhancing supply quality, and enabling peak-load shifting [ 1 , 2 ] . However, these batteries face performance degradation over time, including capacity loss and increased internal resistance, which pose risks to both efficiency and safety. Accurate and real-time State of Health (SOH) prediction models are essential for ensuring the reliability and longevity of these systems [ 3 ] . SOH prediction not only supports timely maintenance and replacement but also optimizes charge-discharge strategies, extending battery life and reducing operational costs [ 4 ] . Existing research on SOH prediction models has seen significant progress through the application of machine learning and deep learning techniques. Traditional machine learning models, such as Support Vector Machines (SVM) and Random Forest (RF), offer robust performance on small datasets but often struggle with generalizing across diverse battery types [ 5 , 6 ] . On the other hand, advanced deep learning models, including Long Short-Term Memory (LSTM) networks and their variants, effectively capture complex nonlinear relationships and temporal dependencies in time-series data [ 7 , 8 ] . Despite these advancements, several challenges remain. Limited data quality and quantity, computational inefficiencies, and the inability of models to generalize across different battery chemistries and operating conditions continue to hinder practical deployment [ 9 ] . Furthermore, achieving real-time prediction capabilities with high accuracy remains a critical bottleneck for many current methodologies. To address these challenges, this study develops and evaluates SOH prediction models using three machine learning and deep learning approaches: RF, LSTM, and Bidirectional LSTM (Bi-LSTM). The research involves extensive data preprocessing, including normalization and time-series segmentation, to prepare high-quality inputs for model training. Models are trained on datasets comprising key battery health indicators, such as voltage, current, temperature, and additional features like discharge time and median voltage. Performance evaluation is based on metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and R², providing a comprehensive comparison of the models' predictive capabilities. The findings offer valuable insights into the effectiveness of these models, particularly Bi-LSTM, in advancing SOH prediction for energy storage systems, paving the way for more reliable and efficient battery management solutions. 2. Model selection and construction Deep learning methodologies, particularly neural network-based models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and their variants, including LSTM networks, have demonstrated remarkable efficacy in processing nonlinear and high-dimensional data [ 10 , 11 ] . These models excel in capturing intricate patterns within time-series datasets. For instance, LSTM networks address the gradient vanishing or exploding issues inherent in traditional RNNs by incorporating gating mechanisms, thereby enabling the model to account for a broader temporal range of historical information when predicting battery SOH [ 12 ] . Moreover, deep learning models possess the capacity to autonomously extract meaningful features from raw data, significantly enhancing their generalization capability and robustness. Leveraging these advancements, researchers have developed a variety of SOH prediction frameworks by integrating diverse and heterogeneous datasets, including voltage, current, and temperature data derived from battery charge-discharge processes. These models not only provide precise predictions of Remaining Useful Life (RUL) but also identify critical factors contributing to battery performance degradation, offering a scientific basis for effective battery maintenance and fault diagnosis [ 13 , 14 ] . Conversely, traditional machine learning algorithms, such as SVM, RF, and Gradient Boosting Trees (GBT), have also played a pivotal role in predicting battery health [ 15 , 16 ] . These approaches typically require manually engineered features but exhibit strong adaptability and interpretability when applied to small datasets, making them well-suited for scenarios with limited data availability or constrained computational resources. Studies have shown that ensemble learning techniques, which integrate multiple machine learning algorithms, can further enhance predictive accuracy and stability [ 17 ] . For instance, stacked generalization, a method where primary models (e.g., SVM, RF) conduct preliminary analysis on battery data, followed by a secondary model (e.g., a neural network) synthesizing the outputs has been shown to yield more precise SOH predictions [ 18 , 19 ] . Additionally, to address challenges like data imbalance commonly encountered in real-world applications, strategies such as oversampling, under sampling, and cost-sensitive learning have been explored to ensure reliable predictions across varying SOH levels [ 20 – 22 ] . This study adopts RF, LSTM, and Bi-LSTM networks to construct SOH prediction models for energy storage batteries, systematically comparing their accuracy to identify the most effective approach. 2.1 Random Forest Model The RF regression algorithm, a powerful ensemble learning method, enhances predictive accuracy and model generalization by combining multiple decision trees constructed through bootstrap sampling, as illustrated in Fig. 1 [ 23 ] . In time-series forecasting, RF improve model performance by capturing nonlinear relationships and interaction effects, making them particularly effective for time-series data with complex patterns. By incorporating lagged features, such as past observations or seasonal indicators, RF can leverage this information to boost predictive power [ 24 ] . Furthermore, RF exhibit strong robustness to outliers and noise, which makes them highly effective in handling real-world data that often contains uncertainty and irregularities. However, the application of RF regression in time-series forecasting also presents certain challenges [ 25 ] . Firstly, RF lack explicit modeling of the inherent temporal order and dependencies in time-series data, which can result in the model's inability to fully exploit temporal information, thereby compromising the accuracy of long-term predictions [ 26 ] . Secondly, compared to traditional time-series models, such as ARIMA or state-space models, RF offer limited interpretability and struggle to provide clear causal explanations. This represents a significant limitation in fields where understanding the dynamic relationships between variables is crucial [ 27 ] . Furthermore, when handling long sequences or high-frequency data, RF can become computationally demanding, particularly in real-time prediction scenarios, where the speed of model training and prediction may become a bottleneck [ 28 ] . 2.2 Long Short-Term Memory Model In RNNs, when the time-series data becomes excessively long, the network encounters issues such as gradient vanishing or explosion during training, which impedes the effective updating of the network parameters [ 29 ] . To address these challenges, significant research has been conducted, culminating in the development of Long Short-Term Memory (LSTM) networks by Hochreiter and Schmidhuber in 1997. LSTM networks are a variant of RNNs, specifically designed to overcome the limitations of traditional RNNs by incorporating memory cells and gating mechanisms. These innovations allow LSTM networks to learn long-term dependencies within time-series data while mitigating the problems of gradient vanishing and explosion [ 30 , 31 ] . The architecture of an LSTM network unit is depicted in Fig. 2 . An LSTM neural network comprises a series of identical LSTM unit structures [ 32 ] . Each unit is composed of three gating mechanisms: the forget gate ( \(\:{\text{f}}_{\text{t}}\) ), the input gate ( \(\:{\text{i}}_{\text{t}}\) ), and the output gate ( \(\:{\text{O}}_{\text{t}}\) ). The specific functions and effects of the three gating mechanisms are elaborated in the supporting literature. These gates dynamically regulate the learning, forgetting, and retention of historical sequence information. LSTM networks effectively address the issues of gradient explosion and vanishing that commonly hinder traditional RNNs, thereby enabling the modeling of long-term dependencies in sequential data [ 33 ] . 2.3 Bidirectional Long Short-Term Memory Model Bi-LSTM networks represent an advanced extension of RNN architectures, designed to enhance representational capacity by simultaneously processing forward and backward information in a time sequence [ 34 ] . As illustrated in Fig. 3 , the core of Bi-LSTM lies in its bidirectional structure, which integrates a forward LSTM layer that processes data in the natural sequence and a backward LSTM layer that handles the same sequence in reverse [ 35 ] . This bidirectional mechanism enables Bi-LSTM to access both preceding and succeeding contextual information at any given time step 𝑡t, facilitating a more comprehensive understanding of the dependencies within the sequence. Leveraging memory cells and gating mechanisms, including the input gate, forget gate, and output gate, Bi-LSTM effectively controls the storage and flow of information, ensuring robust modeling of complex sequential data [ 36 ] . The choice of Bi-LSTM for SOH prediction models in LIBs stems from its unique advantages. First, the health status of LIBs in energy storage system is influenced by multiple factors, including charge-discharge history, environmental temperature, and usage frequency. These factors are not only tied to the current state but can also be impacted by future operational patterns. For instance, frequent high-current discharges over a short period can negatively affect battery health. Bi-LSTM’s ability to simultaneously consider historical and future data features enhances its accuracy in predicting battery health [ 37 ] . Secondly, battery performance degradation is a gradual process involving complex dynamic changes over extended time scales. Traditional machine learning methods or unidirectional LSTM networks may struggle to capture such long-term dependencies. Bi-LSTM, leveraging its memory cells, effectively retains long-range information, making it particularly well-suited for modeling the battery aging process [ 38 ] . Moreover, as battery operations generate substantial amounts of time-series data, Bi-LSTM efficiently processes these sequences, extracting features critical for health status evaluation. Finally, compared to other deep learning models, such as CNNs, Bi-LSTM is more adept at handling one-dimensional time-series data. While CNNs excel in two-dimensional data tasks like image recognition, they require additional architectural adjustments to preserve temporal information when applied to time-series data. Bi-LSTM’s inherent design eliminates this need, making it a more natural fit for SOH prediction [ 39 , 40 ] . 3. Results and discussion The SOH prediction of LIBs, based on the RF, LSTM and Bi-LSTM algorithm, aims to accurately assess the current state of the battery by analyzing its historical operational data. This process begins with the collection of extensive historical data, including, but not limited to, charge/discharge current, voltage, and temperature, typically derived from prior foundational research. Data preprocessing is a crucial step, encompassing tasks such as outlier removal, imputation of missing values, and data normalization to ensure the quality and reliability of model training. The construction of the LIBs health status prediction model involves three key frameworks: a single-cell time-series SOH prediction model, a single-cell time-series SOH prediction model incorporating environmental factors, and a battery module time-series SOH prediction model. Data preprocessing begins with visualizing the SOH variation curve of single-cell battery cycling data, specifically over 1000 cycles, to support time-series prediction as shown in Figure S1 . To effectively predict the SOH of batteries, the raw SOH data was first subjected to min-max normalization. Specifically, the MinMaxScaler method was employed to map the SOH data to a range of [-1, 1], ensuring numerical stability during model training and improving convergence speed. This normalization process eliminates the influence of differing data scales, enhancing the comparability of data features and facilitating the accelerated learning of subsequent neural network models. The normalized SOH data was subsequently used to construct input-output sequences for the time-series prediction model. A fixed-length time window (set to 10-time steps in this study) was defined, and a sliding window technique was applied to extract continuous data segments as input sequences, with the data point following each segment serving as the corresponding output label. This process not only preserves the temporal dependencies within the data but also provides the model with the opportunity to learn long-term dependencies, which is critical for accurately predicting SOH. Furthermore, to evaluate model performance and mitigate the risk of overfitting, the constructed sequence dataset was divided into training and testing sets, with 80% of the data used for model training and the remaining 20% reserved for assessing the model's generalization capability. The battery SOH time-series prediction experiment employed evaluation metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and R² to assess the performance of the models. The specific calculation formulas of MAE, MSE and R 2 are described in detail in the supporting information. Figure 4 illustrates the results of predicting the SOH status of a single LIB using the RF model, LSTM model and Bi-LSTM model. The evaluation results of all models are summarized in Table 1 . The evaluation results show that the RF model achieves MAE, MSE, and R² values of 0.0523, 0.0159, and 0.8960, respectively. In comparison, the LSTM model demonstrates slightly improved performance, with MAE and MSE values slightly reduced and R² increased to 0.9057, indicating better predictive accuracy than the Random Forest model. The Bi-LSTM model delivers the best prediction results, with MAE as low as 0.0073, MSE at 0.0045, and R² reaching 0.9231. These results highlight that Bi-LSTM has a distinct advantage in capturing long-term dependencies within time-series data and utilizing contextual information, making it particularly well-suited for tackling complex SOH prediction problems. Table 1 Prediction results of various models for SOH of LIBs Model MAE MSE R 2 Single LIB RF 0.0523 0.0159 0.8960 LSTM 0.0238 0.0089 0.9057 Bi-LSTM 0.0073 0.0045 0.9231 Single LIB with Parameters RF 0.0515 0.0153 0.9020 LSTM 0.0225 0.0085 0.9136 Bi-LSTM 0.0068 0.0042 0.9253 LIB Module RF 0.0535 0.0165 0.8760 LSTM 0.0225 0.0092 0.8852 Bi-LSTM 0.0078 0.0053 0.9023 To enhance the model's predictive capabilities, this study incorporates two critical parameters into the model inputs: charge-discharge rate and plateau voltage. The charge-discharge rate is crucial for understanding the degradation of lithium-ion battery health. Under high-rate charge-discharge conditions, the accelerated internal electrochemical reactions lead to rapid declines in battery capacity and SOH. The inclusion of plateau voltage further aids in uncovering trends in the battery's internal chemical reactions, such as electrolyte decomposition and active material detachment. By integrating these additional parameters, the predictive model achieves a more comprehensive understanding of battery aging mechanisms, significantly improving its accuracy and reliability. Figure 5 illustrates the prediction results of the models after incorporating critical influencing parameters. The evaluation metrics summarized in Table 1 , which include charge-discharge rate and plateau voltage as additional input features, demonstrate a significant improvement in the predictive accuracy of all three models. This indicates that by integrating these additional features, the models can more accurately capture the dynamic changes occurring during the battery aging process, thereby markedly enhancing the precision and reliability of SOH predictions. In addition to investigating the time-series SOH prediction for single LIB with integrated influencing factors, this study further explores the application of models in predicting the SOH of battery modules to evaluate their generalizability and adaptability. A battery module, comprising multiple single cells, has its overall performance influenced by the states of individual cells. Consequently, SOH prediction for battery modules presents greater challenges, requiring a comprehensive consideration of the interactions and variances among individual cells. This study applies RF, LSTM and Bi-LSTM models to battery module SOH prediction to assess their robustness and generalization capabilities in handling complex battery systems. The comprehensive SOH time-series variation for the battery module is illustrated in Fig. 6 . As shown in Table 1 , compared to the prediction metrics for single-cell batteries, all models exhibit slightly higher MAE and MSE values and a decrease in R² when predicting the SOH of battery modules. This indicates that the models perform less effectively for battery modules than for single cells. The reduced performance is primarily due to the increased complexity of battery modules, which are influenced by a broader range of factors. For instance, variations in the series-parallel configurations of individual cells and initialization differences among cells can significantly impact the SOH of the module. Despite this slight decline in predictive performance for battery modules, all models still demonstrate robust predictive capabilities. Future research could improve the accuracy of SOH predictions for battery modules and even entire battery packs by adopting strategies such as performance balancing and incorporating critical influencing parameters. 4. Conclusion This study presents a comprehensive exploration of SOH prediction for LIBs across various contexts, leveraging RF, LSTM, and Bi-LSTM models. The research introduces innovative contributions, such as incorporating critical parameters (charge-discharge rate and plateau voltage), to enhance prediction accuracy by capturing dynamic battery aging processes. Bi-LSTM consistently demonstrated superior performance across single cells, single cells with additional parameters, and battery modules, achieving the highest predictive accuracy. The findings underline Bi-LSTM’s ability to effectively model long-term dependencies and handle complex systems like battery modules, where performance is influenced by intercell interactions and configuration variations. Despite the reduced accuracy in battery module predictions due to increased complexity, all models showcased robust capabilities. 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Supplementary Files SupportingInformation.docx Cite Share Download PDF Status: Published Journal Publication published 14 Apr, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 26 May, 2025 Reviews received at journal 20 May, 2025 Reviews received at journal 15 May, 2025 Reviewers agreed at journal 09 May, 2025 Reviewers agreed at journal 30 Apr, 2025 Reviewers invited by journal 27 Mar, 2025 Editor assigned by journal 27 Mar, 2025 Editor invited by journal 27 Mar, 2025 Submission checks completed at journal 27 Mar, 2025 First submitted to journal 26 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6310092","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":440867797,"identity":"9ce5e003-10c1-4899-89ea-52c4f6d8e107","order_by":0,"name":"Yunlong Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYBACNvb+hw8+GPyrn8/f2PggoaKGsBY+njPMhjMqDjBunHH4sMGDM8cIa5GTyGET5jlzgLHhQFqa5MMWZiIcxnP2GANv2x1mxoYzZhWJDWwM/O3dCQT80pf2QLLtGRs7c4/ZjcQdMgwSZ85uIGDLAXMDwzZmHpAtNxLPsDEYSOQS0CKRYCaR2MYswXAgx6wAyCBGS46ZxIEzhw0YgN5nIE4Lz7Fkw4aKtARDYCBLJJw5xkPQL/LtzQcf/zGwSZAHRuXHHxU1cvztvfi1YAAe0pSPglEwCkbBKMAKAJuuT97bghVwAAAAAElFTkSuQmCC","orcid":"","institution":"SINOPEC Research Institute of Safety Engineering Co., Ltd. Qingdao","correspondingAuthor":true,"prefix":"","firstName":"Yunlong","middleName":"","lastName":"Zhang","suffix":""},{"id":440867798,"identity":"72db7ee0-8d06-43e4-9f69-69c61bc1db6e","order_by":1,"name":"Xiaolei Bi","email":"","orcid":"","institution":"SINOPEC Research Institute of Safety Engineering Co., Ltd. Qingdao","correspondingAuthor":false,"prefix":"","firstName":"Xiaolei","middleName":"","lastName":"Bi","suffix":""},{"id":440867799,"identity":"b43a1f1f-50c9-4bfc-adb0-015bec1aad47","order_by":2,"name":"Shiqiang Wang","email":"","orcid":"","institution":"SINOPEC Research Institute of Safety Engineering Co., Ltd. Qingdao","correspondingAuthor":false,"prefix":"","firstName":"Shiqiang","middleName":"","lastName":"Wang","suffix":""},{"id":440867800,"identity":"1012e608-93ae-416f-9cd5-8b1fd793d7be","order_by":3,"name":"Bin Tao","email":"","orcid":"","institution":"SINOPEC Research Institute of Safety Engineering Co., Ltd. Qingdao","correspondingAuthor":false,"prefix":"","firstName":"Bin","middleName":"","lastName":"Tao","suffix":""}],"badges":[],"createdAt":"2025-03-26 08:08:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6310092/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6310092/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-33725-w","type":"published","date":"2026-04-14T15:57:45+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":80629956,"identity":"fc99fdc7-7e9c-453c-81da-ef1995d1ef82","added_by":"auto","created_at":"2025-04-15 11:38:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":36885,"visible":true,"origin":"","legend":"\u003cp\u003eRandom Forest algorithm model\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6310092/v1/47ee01e9eee7c0cc379ede15.png"},{"id":80629970,"identity":"79e1cbe6-74c1-4fd9-bcbc-de23116b603f","added_by":"auto","created_at":"2025-04-15 11:38:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":23631,"visible":true,"origin":"","legend":"\u003cp\u003eLong Short-Term Memory algorithm model\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6310092/v1/11f2791adcc32e5e29676924.png"},{"id":80629933,"identity":"421f297b-1336-46aa-bff6-482c6d45881f","added_by":"auto","created_at":"2025-04-15 11:38:17","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":19435,"visible":true,"origin":"","legend":"\u003cp\u003eBidirectional Long Short-Term Memory algorithm model\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6310092/v1/d769b61aa7f10f92ee81a5b9.jpeg"},{"id":80631120,"identity":"cd05389b-09b2-465e-bf4b-4d545f91476b","added_by":"auto","created_at":"2025-04-15 11:46:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":128099,"visible":true,"origin":"","legend":"\u003cp\u003e(a) RF model, (b) LSTM model and (c) Bi-LSTM model for predicting SOH of single LIB.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6310092/v1/3e640d329ea9c6d6fec4c89d.png"},{"id":80629937,"identity":"68a76990-aaf6-4526-9fbd-7fe4a24b1914","added_by":"auto","created_at":"2025-04-15 11:38:17","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":104647,"visible":true,"origin":"","legend":"\u003cp\u003e(a) RF model, (b) LSTM model and (c) Bi-LSTM model for predicting SOH of single LIB with charge-discharge rate and plateau voltage introduced.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6310092/v1/35d3db9799fc2b160d59c7b8.png"},{"id":80629948,"identity":"7f117211-15f4-44dc-a243-e5abb95ac273","added_by":"auto","created_at":"2025-04-15 11:38:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":142214,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Cycle aging SOH change curve of battery module; (b) RFmodel (c) LSTM model (d) Bi-LSTM model for predicting SOH of lithium-ion battery module\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6310092/v1/457e47da8dd23009ed5ae48a.png"},{"id":107351706,"identity":"291c39cc-3559-45d4-9e24-28df7d6b4430","added_by":"auto","created_at":"2026-04-20 16:11:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":658233,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6310092/v1/0c26a6e8-d5d5-4047-9478-e31e56ff27f5.pdf"},{"id":80629944,"identity":"b0fba575-365f-41a0-bdd9-ba6e4499588e","added_by":"auto","created_at":"2025-04-15 11:38:17","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":84102,"visible":true,"origin":"","legend":"","description":"","filename":"SupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-6310092/v1/b37172bac77c351dfcfe5c21.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Machine learning-driven time series analysis for SOH prediction of lithium-ion batteries","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe increasing integration of renewable energy sources, such as wind and solar power, into the global energy landscape has necessitated advanced solutions to address challenges associated with energy storage and grid stability. Energy storage batteries, especially lithium-ion batteries (LIBs) serve as critical components, mitigating power fluctuations, enhancing supply quality, and enabling peak-load shifting \u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e. However, these batteries face performance degradation over time, including capacity loss and increased internal resistance, which pose risks to both efficiency and safety. Accurate and real-time State of Health (SOH) prediction models are essential for ensuring the reliability and longevity of these systems \u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e. SOH prediction not only supports timely maintenance and replacement but also optimizes charge-discharge strategies, extending battery life and reducing operational costs \u003csup\u003e[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eExisting research on SOH prediction models has seen significant progress through the application of machine learning and deep learning techniques. Traditional machine learning models, such as Support Vector Machines (SVM) and Random Forest (RF), offer robust performance on small datasets but often struggle with generalizing across diverse battery types \u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e. On the other hand, advanced deep learning models, including Long Short-Term Memory (LSTM) networks and their variants, effectively capture complex nonlinear relationships and temporal dependencies in time-series data \u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e. Despite these advancements, several challenges remain. Limited data quality and quantity, computational inefficiencies, and the inability of models to generalize across different battery chemistries and operating conditions continue to hinder practical deployment \u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e. Furthermore, achieving real-time prediction capabilities with high accuracy remains a critical bottleneck for many current methodologies.\u003c/p\u003e \u003cp\u003eTo address these challenges, this study develops and evaluates SOH prediction models using three machine learning and deep learning approaches: RF, LSTM, and Bidirectional LSTM (Bi-LSTM). The research involves extensive data preprocessing, including normalization and time-series segmentation, to prepare high-quality inputs for model training. Models are trained on datasets comprising key battery health indicators, such as voltage, current, temperature, and additional features like discharge time and median voltage. Performance evaluation is based on metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and R\u0026sup2;, providing a comprehensive comparison of the models' predictive capabilities. The findings offer valuable insights into the effectiveness of these models, particularly Bi-LSTM, in advancing SOH prediction for energy storage systems, paving the way for more reliable and efficient battery management solutions.\u003c/p\u003e"},{"header":"2. Model selection and construction","content":"\u003cp\u003eDeep learning methodologies, particularly neural network-based models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and their variants, including LSTM networks, have demonstrated remarkable efficacy in processing nonlinear and high-dimensional data \u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e. These models excel in capturing intricate patterns within time-series datasets. For instance, LSTM networks address the gradient vanishing or exploding issues inherent in traditional RNNs by incorporating gating mechanisms, thereby enabling the model to account for a broader temporal range of historical information when predicting battery SOH \u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e. Moreover, deep learning models possess the capacity to autonomously extract meaningful features from raw data, significantly enhancing their generalization capability and robustness. Leveraging these advancements, researchers have developed a variety of SOH prediction frameworks by integrating diverse and heterogeneous datasets, including voltage, current, and temperature data derived from battery charge-discharge processes. These models not only provide precise predictions of Remaining Useful Life (RUL) but also identify critical factors contributing to battery performance degradation, offering a scientific basis for effective battery maintenance and fault diagnosis \u003csup\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eConversely, traditional machine learning algorithms, such as SVM, RF, and Gradient Boosting Trees (GBT), have also played a pivotal role in predicting battery health \u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e. These approaches typically require manually engineered features but exhibit strong adaptability and interpretability when applied to small datasets, making them well-suited for scenarios with limited data availability or constrained computational resources. Studies have shown that ensemble learning techniques, which integrate multiple machine learning algorithms, can further enhance predictive accuracy and stability \u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e. For instance, stacked generalization, a method where primary models (e.g., SVM, RF) conduct preliminary analysis on battery data, followed by a secondary model (e.g., a neural network) synthesizing the outputs has been shown to yield more precise SOH predictions \u003csup\u003e[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e. Additionally, to address challenges like data imbalance commonly encountered in real-world applications, strategies such as oversampling, under sampling, and cost-sensitive learning have been explored to ensure reliable predictions across varying SOH levels \u003csup\u003e[\u003cspan additionalcitationids=\"CR21\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e. This study adopts RF, LSTM, and Bi-LSTM networks to construct SOH prediction models for energy storage batteries, systematically comparing their accuracy to identify the most effective approach.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Random Forest Model\u003c/h2\u003e \u003cp\u003eThe RF regression algorithm, a powerful ensemble learning method, enhances predictive accuracy and model generalization by combining multiple decision trees constructed through bootstrap sampling, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e \u003csup\u003e[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]\u003c/sup\u003e. In time-series forecasting, RF improve model performance by capturing nonlinear relationships and interaction effects, making them particularly effective for time-series data with complex patterns. By incorporating lagged features, such as past observations or seasonal indicators, RF can leverage this information to boost predictive power \u003csup\u003e[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/sup\u003e. Furthermore, RF exhibit strong robustness to outliers and noise, which makes them highly effective in handling real-world data that often contains uncertainty and irregularities. However, the application of RF regression in time-series forecasting also presents certain challenges \u003csup\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFirstly, RF lack explicit modeling of the inherent temporal order and dependencies in time-series data, which can result in the model's inability to fully exploit temporal information, thereby compromising the accuracy of long-term predictions \u003csup\u003e[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]\u003c/sup\u003e. Secondly, compared to traditional time-series models, such as ARIMA or state-space models, RF offer limited interpretability and struggle to provide clear causal explanations. This represents a significant limitation in fields where understanding the dynamic relationships between variables is crucial \u003csup\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/sup\u003e. Furthermore, when handling long sequences or high-frequency data, RF can become computationally demanding, particularly in real-time prediction scenarios, where the speed of model training and prediction may become a bottleneck \u003csup\u003e[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Long Short-Term Memory Model\u003c/h2\u003e \u003cp\u003eIn RNNs, when the time-series data becomes excessively long, the network encounters issues such as gradient vanishing or explosion during training, which impedes the effective updating of the network parameters \u003csup\u003e[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/sup\u003e. To address these challenges, significant research has been conducted, culminating in the development of Long Short-Term Memory (LSTM) networks by Hochreiter and Schmidhuber in 1997. LSTM networks are a variant of RNNs, specifically designed to overcome the limitations of traditional RNNs by incorporating memory cells and gating mechanisms. These innovations allow LSTM networks to learn long-term dependencies within time-series data while mitigating the problems of gradient vanishing and explosion \u003csup\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/sup\u003e. The architecture of an LSTM network unit is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAn LSTM neural network comprises a series of identical LSTM unit structures \u003csup\u003e[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]\u003c/sup\u003e. Each unit is composed of three gating mechanisms: the forget gate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{f}}_{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e), the input gate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{i}}_{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e), and the output gate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{O}}_{\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e). The specific functions and effects of the three gating mechanisms are elaborated in the supporting literature. These gates dynamically regulate the learning, forgetting, and retention of historical sequence information. LSTM networks effectively address the issues of gradient explosion and vanishing that commonly hinder traditional RNNs, thereby enabling the modeling of long-term dependencies in sequential data \u003csup\u003e[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Bidirectional Long Short-Term Memory Model\u003c/h2\u003e \u003cp\u003eBi-LSTM networks represent an advanced extension of RNN architectures, designed to enhance representational capacity by simultaneously processing forward and backward information in a time sequence \u003csup\u003e[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]\u003c/sup\u003e. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the core of Bi-LSTM lies in its bidirectional structure, which integrates a forward LSTM layer that processes data in the natural sequence and a backward LSTM layer that handles the same sequence in reverse \u003csup\u003e[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/sup\u003e. This bidirectional mechanism enables Bi-LSTM to access both preceding and succeeding contextual information at any given time step \u0026#119905;t, facilitating a more comprehensive understanding of the dependencies within the sequence. Leveraging memory cells and gating mechanisms, including the input gate, forget gate, and output gate, Bi-LSTM effectively controls the storage and flow of information, ensuring robust modeling of complex sequential data \u003csup\u003e[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe choice of Bi-LSTM for SOH prediction models in LIBs stems from its unique advantages. First, the health status of LIBs in energy storage system is influenced by multiple factors, including charge-discharge history, environmental temperature, and usage frequency. These factors are not only tied to the current state but can also be impacted by future operational patterns. For instance, frequent high-current discharges over a short period can negatively affect battery health. Bi-LSTM\u0026rsquo;s ability to simultaneously consider historical and future data features enhances its accuracy in predicting battery health \u003csup\u003e[\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]\u003c/sup\u003e. Secondly, battery performance degradation is a gradual process involving complex dynamic changes over extended time scales. Traditional machine learning methods or unidirectional LSTM networks may struggle to capture such long-term dependencies. Bi-LSTM, leveraging its memory cells, effectively retains long-range information, making it particularly well-suited for modeling the battery aging process \u003csup\u003e[\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eMoreover, as battery operations generate substantial amounts of time-series data, Bi-LSTM efficiently processes these sequences, extracting features critical for health status evaluation. Finally, compared to other deep learning models, such as CNNs, Bi-LSTM is more adept at handling one-dimensional time-series data. While CNNs excel in two-dimensional data tasks like image recognition, they require additional architectural adjustments to preserve temporal information when applied to time-series data. Bi-LSTM\u0026rsquo;s inherent design eliminates this need, making it a more natural fit for SOH prediction \u003csup\u003e[\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cp\u003eThe SOH prediction of LIBs, based on the RF, LSTM and Bi-LSTM algorithm, aims to accurately assess the current state of the battery by analyzing its historical operational data. This process begins with the collection of extensive historical data, including, but not limited to, charge/discharge current, voltage, and temperature, typically derived from prior foundational research. Data preprocessing is a crucial step, encompassing tasks such as outlier removal, imputation of missing values, and data normalization to ensure the quality and reliability of model training. The construction of the LIBs health status prediction model involves three key frameworks: a single-cell time-series SOH prediction model, a single-cell time-series SOH prediction model incorporating environmental factors, and a battery module time-series SOH prediction model.\u003c/p\u003e \u003cp\u003eData preprocessing begins with visualizing the SOH variation curve of single-cell battery cycling data, specifically over 1000 cycles, to support time-series prediction as shown in Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eTo effectively predict the SOH of batteries, the raw SOH data was first subjected to min-max normalization. Specifically, the MinMaxScaler method was employed to map the SOH data to a range of [-1, 1], ensuring numerical stability during model training and improving convergence speed. This normalization process eliminates the influence of differing data scales, enhancing the comparability of data features and facilitating the accelerated learning of subsequent neural network models.\u003c/p\u003e \u003cp\u003eThe normalized SOH data was subsequently used to construct input-output sequences for the time-series prediction model. A fixed-length time window (set to 10-time steps in this study) was defined, and a sliding window technique was applied to extract continuous data segments as input sequences, with the data point following each segment serving as the corresponding output label. This process not only preserves the temporal dependencies within the data but also provides the model with the opportunity to learn long-term dependencies, which is critical for accurately predicting SOH.\u003c/p\u003e \u003cp\u003eFurthermore, to evaluate model performance and mitigate the risk of overfitting, the constructed sequence dataset was divided into training and testing sets, with 80% of the data used for model training and the remaining 20% reserved for assessing the model's generalization capability.\u003c/p\u003e \u003cp\u003eThe battery SOH time-series prediction experiment employed evaluation metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and R\u0026sup2; to assess the performance of the models. The specific calculation formulas of MAE, MSE and R\u003csup\u003e2\u003c/sup\u003e are described in detail in the supporting information.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the results of predicting the SOH status of a single LIB using the RF model, LSTM model and Bi-LSTM model. The evaluation results of all models are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe evaluation results show that the RF model achieves MAE, MSE, and R\u0026sup2; values of 0.0523, 0.0159, and 0.8960, respectively. In comparison, the LSTM model demonstrates slightly improved performance, with MAE and MSE values slightly reduced and R\u0026sup2; increased to 0.9057, indicating better predictive accuracy than the Random Forest model. The Bi-LSTM model delivers the best prediction results, with MAE as low as 0.0073, MSE at 0.0045, and R\u0026sup2; reaching 0.9231. These results highlight that Bi-LSTM has a distinct advantage in capturing long-term dependencies within time-series data and utilizing contextual information, making it particularly well-suited for tackling complex SOH prediction problems.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePrediction results of various models for SOH of LIBs\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSingle LIB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8960\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0089\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9057\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBi-LSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9231\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eSingle LIB with Parameters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0515\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9020\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0225\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9136\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBi-LSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9253\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eLIB Module\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0535\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0165\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8760\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0225\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0092\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8852\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBi-LSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0078\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9023\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo enhance the model's predictive capabilities, this study incorporates two critical parameters into the model inputs: charge-discharge rate and plateau voltage. The charge-discharge rate is crucial for understanding the degradation of lithium-ion battery health. Under high-rate charge-discharge conditions, the accelerated internal electrochemical reactions lead to rapid declines in battery capacity and SOH. The inclusion of plateau voltage further aids in uncovering trends in the battery's internal chemical reactions, such as electrolyte decomposition and active material detachment. By integrating these additional parameters, the predictive model achieves a more comprehensive understanding of battery aging mechanisms, significantly improving its accuracy and reliability.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the prediction results of the models after incorporating critical influencing parameters. The evaluation metrics summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, which include charge-discharge rate and plateau voltage as additional input features, demonstrate a significant improvement in the predictive accuracy of all three models. This indicates that by integrating these additional features, the models can more accurately capture the dynamic changes occurring during the battery aging process, thereby markedly enhancing the precision and reliability of SOH predictions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn addition to investigating the time-series SOH prediction for single LIB with integrated influencing factors, this study further explores the application of models in predicting the SOH of battery modules to evaluate their generalizability and adaptability. A battery module, comprising multiple single cells, has its overall performance influenced by the states of individual cells. Consequently, SOH prediction for battery modules presents greater challenges, requiring a comprehensive consideration of the interactions and variances among individual cells. This study applies RF, LSTM and Bi-LSTM models to battery module SOH prediction to assess their robustness and generalization capabilities in handling complex battery systems.\u003c/p\u003e \u003cp\u003eThe comprehensive SOH time-series variation for the battery module is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, compared to the prediction metrics for single-cell batteries, all models exhibit slightly higher MAE and MSE values and a decrease in R\u0026sup2; when predicting the SOH of battery modules. This indicates that the models perform less effectively for battery modules than for single cells. The reduced performance is primarily due to the increased complexity of battery modules, which are influenced by a broader range of factors. For instance, variations in the series-parallel configurations of individual cells and initialization differences among cells can significantly impact the SOH of the module.\u003c/p\u003e \u003cp\u003eDespite this slight decline in predictive performance for battery modules, all models still demonstrate robust predictive capabilities. Future research could improve the accuracy of SOH predictions for battery modules and even entire battery packs by adopting strategies such as performance balancing and incorporating critical influencing parameters.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis study presents a comprehensive exploration of SOH prediction for LIBs across various contexts, leveraging RF, LSTM, and Bi-LSTM models. The research introduces innovative contributions, such as incorporating critical parameters (charge-discharge rate and plateau voltage), to enhance prediction accuracy by capturing dynamic battery aging processes. Bi-LSTM consistently demonstrated superior performance across single cells, single cells with additional parameters, and battery modules, achieving the highest predictive accuracy.\u003c/p\u003e \u003cp\u003eThe findings underline Bi-LSTM\u0026rsquo;s ability to effectively model long-term dependencies and handle complex systems like battery modules, where performance is influenced by intercell interactions and configuration variations. Despite the reduced accuracy in battery module predictions due to increased complexity, all models showcased robust capabilities. This work not only highlights the critical role of enriched feature sets in enhancing model efficacy but also provides a solid foundation for future research aimed at improving battery health management, optimizing system design, and ensuring the safety and reliability of energy storage systems.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eY. Zhang wrote the main manuscript text.X. Bi, S. Wang and B. Tao prepared figures 1-6.All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThe authors declare that no external funding or financial support was received for this research.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and analysed during the current study are not publicly available due the confidentiality of the data used but are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJing Xie, Yichun Lu, A retrospective on lithium-ion batteries[J]. Nature Communications, 2020, 11, 2499.\u003c/li\u003e\n\u003cli\u003eRunwei Mo, Xinyi Tan, Fan Li, et al. Tin-graphene tubes as anodes for lithium-ion batteries with high volumetric and gravimetric energy densities[J]. Nature Communications, 2020, 11, 1374.\u003c/li\u003e\n\u003cli\u003eVignesh S, Hangseng Che, Jeyraj Selvaraj, et al. 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Journal of Manufacturing Systems, 2025, 378, 124763.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Lithium-ion battery, State of health, Machine learning","lastPublishedDoi":"10.21203/rs.3.rs-6310092/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6310092/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEnergy storage batteries are essential for stabilizing renewable energy systems and ensuring power grid efficiency. However, challenges such as capacity degradation, inadequate data quality, and the need for real-time predictions highlight the importance of accurate State of Health (SOH) models. This study explores Random Forest(RF), Long Short-Term Memory (LSTM) and Bidirectional LSTM (Bi-LSTM) for SOH prediction across single lithium-ion battery, batterywith environmental factors and battery modules. Bi-LSTM demonstrated superior performance in evaluation indicators, achieving lower MAE, MSE and R² value closest to 1, with further accuracy gains through additional features like discharge time and median voltage. The results underscore Bi-LSTM’s effectiveness in capturing long-term dependencies and its potential to enhance battery health management, contributing to reliable and sustainable energy storage systems.\u003c/p\u003e","manuscriptTitle":"Machine learning-driven time series analysis for SOH prediction of lithium-ion batteries","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-15 11:38:10","doi":"10.21203/rs.3.rs-6310092/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-05-26T05:53:00+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-20T11:17:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-15T20:14:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"159985993255637561795065788955387161027","date":"2025-05-09T10:17:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"6388703250223980424381066055453164813","date":"2025-04-30T13:13:00+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-28T01:21:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-28T01:20:21+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-03-27T09:30:59+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-03-27T08:19:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-03-26T08:05:09+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"533f0428-dab7-4553-b7eb-6b2ccd544d59","owner":[],"postedDate":"April 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":46940214,"name":"Physical sciences/Energy science and technology/Energy storage/Batteries"},{"id":46940215,"name":"Physical sciences/Energy science and technology/Energy storage"}],"tags":[],"updatedAt":"2026-04-20T16:08:08+00:00","versionOfRecord":{"articleIdentity":"rs-6310092","link":"https://doi.org/10.1038/s41598-025-33725-w","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-04-14 15:57:45","publishedOnDateReadable":"April 14th, 2026"},"versionCreatedAt":"2025-04-15 11:38:10","video":"","vorDoi":"10.1038/s41598-025-33725-w","vorDoiUrl":"https://doi.org/10.1038/s41598-025-33725-w","workflowStages":[]},"version":"v1","identity":"rs-6310092","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6310092","identity":"rs-6310092","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}