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Abstract This paper addresses the parameter estimation problem for lithium-ion battery pack models comprising cells in series. This valuable information can be exploited in fault diagnostics to estimate the number of cells that are exhibiting abnormal behaviour, e.g. large resistances or small capacities. In particular, we use a Bayesian approach to estimate the parameters of a two-cell arrangement modelled using equivalent circuits. Although our modeling framework has been extensively reported in the literature, its structural identifiability properties have not been reported yet to the best of the authors’ knowledge. Moreover, most contributions in the literature tackle the estimation problem through point-wise estimates assuming Gaussian noise using e.g. least-squares methods (maximum likelihood estimation) or Kalman filters (maximum a posteriori estimation). In contrast, we apply methods that are suitable for nonlinear and non-Gaussian estimation problems and estimate the full posterior probability distribution of the parameters. We study how the model structure, available measurements and prior knowledge of the model parameters impact the underlying posterior probability distribution that is recovered for the parameters. For two cells in series, a bimodal distribution is obtained whose modes are centered around the real values of the parameters for each cell. Therefore, bounds on the model parameters for a battery pack can be derived.
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This content will become publicly available on November 1, 2026
A mathematical framework for validating stage-promoting self-contained sleep models
Mathematical models of neuronal networks play a crucial role in understanding sleep dynamics and associated disorders. However, validating these models through parameter estimation remains a significant challenge. In this work, we introduce an automated parameter estimation framework for sleep models that satisfy two key assumptions: (i) they consist of competing neuronal populations, each driving a distinct sleep stage (stage-promoting), and (ii) their dynamics evolve independently of weakly observed variables or external inputs (self-contained). We apply our method to a system of coupled nonlinear ordinary differential equations (ODEs) representing three interacting neuronal populations. Direct firing rates of these populations are typically unobservable, and hypnograms provide only the dominant sleep stage at each time point. Despite the limited information available in hypnograms, we successfully estimate ODE parameters for the underlying neuronal population model directly from hypnogram data. We use a smoothed winner-takes-all strategy within a constrained minimization framework, reformulate the problem in an unconstrained setting through the Lagrangian, and derive the corresponding optimality conditions from state and adjoint equations. A projected nonlinear conjugate gradient scheme is then used to estimate the parameters numerically. We validate our approach by accurately reconstructing 111 out of 139 hypnograms from the Sleep-EDF database. The inferred population-level parameters provide insights into sleep regulation by capturing interaction strengths, timescale constants and non-rapid eye movement-related variability.
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- PAR ID:
- 10646175
- Publisher / Repository:
- Royal Society
- Date Published:
- Journal Name:
- Royal Society Open Science
- Volume:
- 12
- Issue:
- 11
- ISSN:
- 2054-5703
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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