Capistrán, Marcos A.Infante Del Río, Juan AntonioRamos del Olmo, Ángel Manuel2023-06-222023-06-2220231. Ramos, A.M.: On the well-posedness of a mathematical model for lithium-ion batteries. Appl. Math. Model. 40(1), 115–125 (2016). https://doi.org/10.1016/j.apm.2015.05.006 2. Díaz, J.I., Gómez-Castro, D., Ramos, A.M.: On the well-posedness of a multiscale mathematical model for lithium-ion batteries. Adv. Nonlinear Anal. 8(1), 1132–1157 (2019). https://doi.org/10.1515/anona2018-0041 3. Richardson, G.W., Foster, J.M., Ranom, R., Please, C.P., Ramos, A.M.: Charge transport modelling of lithium-ion batteries. Eur. J. Appl. Math. (2021). https://doi.org/10.1017/S0956792521000292 4. Oden, T., Moser, R., Ghattas, O.: Computer predictions with quantified uncertainty, part i. SIAM News 43(9), 1–3 (2010) 5. Guo, M., Sikha, G., White, R.E.: Single-particle model for a lithium-ion cell: thermal behavior. J. Electrochem. Soc. 158(2), A122–A132 (2011) 6. Raijmakers, L.H.J., Danilov, D.L., Eichel, R.A., Notten, P.H.L.: A review on various temperatureindication methods for li-ion batteries. Appl. Energy 240, 918–945 (2019) 7. Li, Y., Ralahamilage, D., Vilathgamuwa, M., Mishra, Y., Farrell, T., Choi, S.S., Zou, C.: Model order reduction techniques for physics-based lithium-ion battery management: A survey. IEEE Ind. Electron. Mag. 2021, 256 (2021) 8. Capistrán, M.A., Christen, J.A., Daza-Torres, M.L., Flores-Arguedas, H., Montesinos-López, J.C.: Error control of the numerical posterior with bayes factors in bayesian uncertainty quantification. Bayesian Anal. 1(1), 1–23 (2021) 9. Spantini, A., Solonen, A., Cui, T., Martin, J., Tenorio, L., Marzouk, Y.: Optimal low-rank approximations of bayesian linear inverse problems. SIAM J. Sci. Comput. 37(6), A2451–A2487 (2015) 10. Bui-Thanh, T., Willcox, K., Ghattas, O.: Model reduction for large-scale systems with high-dimensional parametric input space. SIAM J. Sci. Comput. 30(6), 3270–3288 (2008) 11. Ning, G., Popov, B.N.: Cycle life modeling of lithium-ion batteries. J. Electrochem. Soc. 151(10), A1584 (2004) 12. Santhanagopalan, S., Guo, Q., Ramadass, P., White, R.E.: Review of models for predicting the cycling performance of lithium ion batteries. J. Power Sourc. 156(2), 620–628 (2006) 13. Kumaresan, K., Sikha, G., White, R.E.: Thermal model for a li-ion cell. J. Electrochem. Soc. 155(2), A164 (2007) 14. Cai, L., White, R.E.: Mathematical modeling of a lithium ion battery with thermal effects in. comsol incmultiphysics (mp) software. J. Power Sourc. 196(14), 5985–5989 (2011) 15. Marcicki, J., Yang, X.G.: Model-based estimation of reversible heat generation in lithium-ion cells. J. Electrochem. Soc. 161(12), A1794 (2014) 16. Bizeray, A.: State and parameter estimation of physics-based lithium-ion battery models. In: PhD thesis, University of Oxford (2018) 17. Tagade, P., Hariharan, K.S., Basu, S., Verma, M.K.S., Kolake, S.M., Song, T., Oh, D., Yeo, T., Doo, S.: Bayesian calibration for electrochemical thermal model of lithium-ion cells. J. Power Sourc. 320, 296–309 (2016) 18. Chen, S.C., Wan, C.C., Wang, Y.Y.: Thermal analysis of lithium-ion batteries. J. Power Sourc. 140(1), 111–124 (2005) 19. Grandjean, T.R.B., Li, L., Odio, M.X., Widanage, W.D.: Global sensitivity analysis of the single particle lithium-ion battery model with electrolyte. In: 2019 IEEE vehicle power and propulsion conference (VPPC), IEEE, pp. 1–7 (2019) 20. Vazquez-Arenas, J., Gimenez, L.E., Fowler, M., Han, T., Chen, S.K.: A rapid estimation and sensitivity analysis of parameters describing the behavior of commercial li-ion batteries including thermal analysis. Energy Convers. Manage. 87, 472–482 (2014) 21. Edouard, C., Petit, M., Forgez, C., Bernard, J., Revel, R.: Parameter sensitivity analysis of a simplified electrochemical and thermal model for li-ion batteries aging. J. Power Sourc. 325, 482–494 (2016) 22. Li, W., Cao, D., Jöst, D., Ringbeck, F., Kuipers, M., Frie, F., Sauer, D.U.: Parameter sensitivity analysis of electrochemical model-based battery management systems for lithium-ion batteries. Appl. Energy 269, 115104 (2020) 23. Jokar, A., Rajabloo, B., Désilets, M., Lacroix, M.: An inverse method for estimating the electrochemical parameters of lithium-ion batteries. J. Electrochem. Soc. 163(14), A2876 (2016) 24. Rajabloo, B., Jokar, A., Désilets, M., Lacroix, M.: An inverse method for estimating the electrochemical parameters of lithium-ion batteries. J. Electrochem. Soc. 164(2), A99 (2016) 25. Li, J., Wang, L., Lyu, C., Liu, E., Xing, Y., Pecht, M.: A parameter estimation method for a simplified electrochemical model for li-ion batteries. Electrochim. Acta 275, 50–58 (2018) 26. Johnson, D.H.: Signal-to-noise ratio. Scholarpedia 1(12), 2088 (2006) 27. Saltelli, A.P., Annoni, I., Azzini, F., Campolongo, M., Ratto, Variance, T.: Based sensitivity analysis of model output design and estimator for the total sensitivity index. Comput. Phys. Commun. 181(2), 259–270 (2010) 28. Singh, V.P., Rajagopal, A.K., Singh, K.: Derivation of some frequency distributions using the principle of maximum entropy (pome). Adv. Water Resour. 9(2), 91–106 (1986) 29. Bui-Thanh, T.: A gentle tutorial on statistical inversion using the bayesian paradigm. I: Technical Report 12-18, Institute for Computational Engineering and Sciences, 01 (2012) 30. Howson, C., Urbach, P.: Scientific Reasoning: The Bayesian Approach. Open Court Publishing, Berlin (2006) 31. Bui-Thanh, T., Ghattas, O., Martin, J., Stadler, G.: A computational framework for infinite-dimensional bayesian inverse problems part i: the linearized case, with application to global seismic inversion. SIAM J. Sci. Comput. 35(6), A2494–A2523 (2013) 32. Cui, T., Martin, J., Marzouk, Y.M., Solonen, A., Spantini, A.: Likelihood-informed dimension reduction for nonlinear inverse problems. Inverse Prob. 30(11), 114015 (2014) 33. Christen, J.A., Fox, C., et al.: A general purpose sampling algorithm for continuous distributions (the t-walk). Bayesian Anal. 5(2), 263–281 (2010) 34. Roberts, G.O., Rosenthal, J.S.: Optimal scaling for various metropolis-hastings algorithms. Stat. Sci. 16(4), 351–367 (2001) 35. Anaconda software distribution (2020). https://www.anaconda.com/products/distribution1578-730310.1007/s13398-022-01340-3https://hdl.handle.net/20.500.14352/72986Acuerdo transformativoIn recent years, the sustained increase in the worldwide demand for lithium batteries goes side by side with the need for reliable methods to assess battery performance. Of particular importance is assessing Lithium-Ion cell’s thermal behavior given its role on hazard and aging of batteries. An essential task towards developing battery management systems is the estimation of physical parameters and their uncertainties in terms of both models and observations. Consequently, this paper analyzes the uncertainty in a thermal single particle model for a lithium-ion cell. In the first part of the manuscript, we explore the model adequacy by analyzing the forward and backward uncertainty propagation in the model in terms of diffusion coefficients, reaction rate constants, and observations of cell voltage. In the second part of the manuscript, we infer the cell’s reversible heat given the energy balance equation and the cell’s temperature observations. We argue that the methods proposed here may be extended to analyze other more general lithium-ion modelsengAtribución 3.0 Españajournal articlehttps://doi.org/10.1007/s13398-022-01340-3open access519.6517.9Li-Ion batteriesParameter identificationUncertaintyAnálisis numéricoEcuaciones diferenciales1206 Análisis Numérico1202.07 Ecuaciones en Diferencias