IDEAS home Printed from https://ideas.repec.org/a/eee/appene/v377y2025ipbs0306261924018798.html
   My bibliography  Save this article

Perspective modelling and measuring discharge voltage on truncated data of long-term stored Li-ion batteries based on functional state space model

Author

Listed:
  • Koláček, Jan
  • Vališ, David
  • Fuksová, Mária
  • Hlinka, Jiří
  • Procházka, Petr

Abstract

The subject of battery sources and electrical energy accumulators is currently very topical. Moreover, the possibilities of reusing already discarded sources are being explored as so-called “second-life batteries”. This article is concerned with studying and modelling the behaviour of a battery in an electric aircraft in operation — the voltage during discharge. Outcomes from extensive experiments on real long-term stored batteries have provided statistically robust sets of data on both long-term stored and new batteries; some of the data, however, are truncated. A modern approach that neglects the truncated issues and is based on functional data analysis and modified with a specific time series is used to model the process. This suggested model is much more accurate than the model used previously as it can effectively process truncated data. It also allows a certain degree of generalization. The aim is to determine the probability density of the time when the battery reaches the critical value, including the numerical statistics, for both stored and new batteries. The results are compared using the specific statistical Kullback–Leibler divergence approach to determine the degree of difference. The proposed model applies to similar issues where battery voltage is modelled in a time domain while the data form is truncated. It is proved, however, that further use of the stored batteries does not disrupt the safe and reliable operation of an electric airplane in terms of their functionality.

Suggested Citation

  • Koláček, Jan & Vališ, David & Fuksová, Mária & Hlinka, Jiří & Procházka, Petr, 2025. "Perspective modelling and measuring discharge voltage on truncated data of long-term stored Li-ion batteries based on functional state space model," Applied Energy, Elsevier, vol. 377(PB).
    • Handle: RePEc:eee:appene:v:377:y:2025:i:pb:s0306261924018798
    DOI: 10.1016/j.apenergy.2024.124496
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0306261924018798
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.apenergy.2024.124496?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    2. Hyndman, Rob J. & Booth, Heather, 2008. "Stochastic population forecasts using functional data models for mortality, fertility and migration," International Journal of Forecasting, Elsevier, vol. 24(3), pages 323-342.
    3. Wang, Shunli & Fan, Yongcun & Jin, Siyu & Takyi-Aninakwa, Paul & Fernandez, Carlos, 2023. "Improved anti-noise adaptive long short-term memory neural network modeling for the robust remaining useful life prediction of lithium-ion batteries," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    4. Chuanlong Wang & Akila C. Thenuwara & Jianmin Luo & Pralav P. Shetty & Matthew T. McDowell & Haoyu Zhu & Sergio Posada-Pérez & Hui Xiong & Geoffroy Hautier & Weiyang Li, 2022. "Extending the low-temperature operation of sodium metal batteries combining linear and cyclic ether-based electrolyte solutions," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    5. Fang Liu & Rong Xu & Yecun Wu & David Thomas Boyle & Ankun Yang & Jinwei Xu & Yangying Zhu & Yusheng Ye & Zhiao Yu & Zewen Zhang & Xin Xiao & Wenxiao Huang & Hansen Wang & Hao Chen & Yi Cui, 2021. "Dynamic spatial progression of isolated lithium during battery operations," Nature, Nature, vol. 600(7890), pages 659-663, December.
    6. Seger, Pedro V.H. & Rigo-Mariani, Rémy & Thivel, Pierre-Xavier & Riu, Delphine, 2023. "A storage degradation model of Li-ion batteries to integrate ageing effects in the optimal management and design of an isolated microgrid," Applied Energy, Elsevier, vol. 333(C).
    7. Alexander Aue & Diogo Dubart Norinho & Siegfried Hörmann, 2015. "On the Prediction of Stationary Functional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 378-392, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuan Gao & Han Lin Shang, 2017. "Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates," Risks, MDPI, vol. 5(2), pages 1-18, March.
    2. Elías, Antonio & Jiménez, Raúl & Shang, Han Lin, 2022. "On projection methods for functional time series forecasting," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Rob Hyndman & Heather Booth & Farah Yasmeen, 2013. "Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 261-283, February.
    5. Fang, Lei & Härdle, Wolfgang Karl, 2015. "Stochastic population analysis: A functional data approach," SFB 649 Discussion Papers 2015-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Umberto Amato & Anestis Antoniadis & Italia Feis & Irène Gijbels, 2025. "Functional time series forecasting: a systematic review," Statistical Papers, Springer, vol. 66(1), pages 1-47, January.
    7. Ahbab Mohammad Fazle Rabbi & Stefano Mazzuco, 2021. "Mortality Forecasting with the Lee–Carter Method: Adjusting for Smoothing and Lifespan Disparity," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 97-120, March.
    8. Hong Li & Johnny Siu-Hang Li, 2017. "Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements," Demography, Springer;Population Association of America (PAA), vol. 54(3), pages 1073-1095, June.
    9. Kosiorowski Daniel & Mielczarek Dominik & Rydlewski Jerzy P. & Snarska Małgorzata, 2018. "Generalized Exponential Smoothing In Prediction Of Hierarchical Time Series," Statistics in Transition New Series, Statistics Poland, vol. 19(2), pages 331-350, June.
    10. Haixu Wang & Jiguo Cao, 2023. "Nonlinear prediction of functional time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    11. Israel Martínez‐Hernández & Marc G. Genton, 2021. "Nonparametric trend estimation in functional time series with application to annual mortality rates," Biometrics, The International Biometric Society, vol. 77(3), pages 866-878, September.
    12. Feng, Lingbing & Shi, Yanlin & Chang, Le, 2021. "Forecasting mortality with a hyperbolic spatial temporal VAR model," International Journal of Forecasting, Elsevier, vol. 37(1), pages 255-273.
    13. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    14. Chang, Yoosoon & Choi, Yongok & Kim, Chang Sik & Miller, J. Isaac & Park, Joon Y., 2021. "Forecasting regional long-run energy demand: A functional coefficient panel approach," Energy Economics, Elsevier, vol. 96(C).
    15. Cees Diks & Bram Wouters, 2023. "Noise reduction for functional time series," Papers 2307.02154, arXiv.org.
    16. Ana Debón & Steven Haberman & Francisco Montes & Edoardo Otranto, 2021. "Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model," IJERPH, MDPI, vol. 18(4), pages 1-16, February.
    17. Daniel Kosiorowski & Dominik Mielczarek & Jerzy P. Rydlewski & Małgorzata Snarska, 2018. "Generalized Exponential Smoothing In Prediction Of Hierarchical Time Series," Statistics in Transition New Series, Polish Statistical Association, vol. 19(2), pages 331-350, June.
    18. Won-Ki Seo, 2020. "Functional Principal Component Analysis for Cointegrated Functional Time Series," Papers 2011.12781, arXiv.org, revised Apr 2023.
    19. Han Lin Shang & Yang Yang, 2021. "Forecasting Australian subnational age-specific mortality rates," Journal of Population Research, Springer, vol. 38(1), pages 1-24, March.
    20. Won‐Ki Seo, 2024. "Functional principal component analysis for cointegrated functional time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 320-330, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:appene:v:377:y:2025:i:pb:s0306261924018798. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/405891/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.