Linking Calendar and Cycle Ageing in Lithium-Ion Batteries through Consistent Parameterisation of an Electrochemical-Thermal-Degradation Model
Pith reviewed 2026-05-10 16:44 UTC · model grok-4.3
The pith
A P2D model with consistent parameters for SEI growth, lithium plating and material loss predicts NMC cell capacity fade under calendar and combined ageing.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The work parameterises SEI growth, lithium plating and active-material loss in both electrodes from degradation-mode analysis and inserts the resulting constants into a P2D electrochemical-thermal-degradation model. The model then predicts capacity-fade trajectories, state-of-health, remaining-useful-life and internal degradation modes for an NMC cell under pure calendar ageing and under combined calendar-cyclic ageing at 81 operating points (three temperatures, three C-rates, three rest SoCs, three DoDs). Cycle life to 75 % SoH ranges from 0.8 to 14 years, and the simulations reveal competing calendar-versus-cyclic effects that produce sub-linear, linear or sup-linear fade.
What carries the argument
P2D electrochemical-thermal-degradation model whose SEI-growth, lithium-plating and active-material-loss parameters are fixed once from degradation-mode analysis data and then used without refitting across all conditions.
If this is right
- The same parameter set generates both pure-calendar and combined-calendar-cyclic trajectories without separate fitting.
- Capacity fade changes from sub-linear to sup-linear according to the specific combination of temperature, C-rate, rest SoC and DoD.
- Predicted cycle life to 75 % SoH spans more than an order of magnitude (0.8–14 years) across the 81 cases.
- Internal degradation-mode contributions can be extracted for any operating point, showing how calendar and cyclic mechanisms compete or reinforce each other.
Where Pith is reading between the lines
- Battery-management algorithms could embed the same model for online SoH and RUL estimation across mixed usage profiles.
- The released simulation dataset offers a ready benchmark for testing other degradation models that claim to cover both calendar and cyclic regimes.
- If the consistent-parameter approach generalises, it reduces the experimental effort needed to characterise new cell formats or chemistries.
Load-bearing premise
A single set of parameters for SEI growth, lithium plating and active material loss remains valid across the full range of temperatures, C-rates, rest SoCs and DoDs without any further adjustment.
What would settle it
Capacity and degradation-mode measurements on the same NMC cell at one or more of the 81 tested condition combinations that deviate markedly from the model's predicted fade curve.
Figures
read the original abstract
Parameterisation of coupled degradation mechanisms in lithium-ion batteries is a major challenge. Interactions between the mechanisms depend on usage conditions: C-rate, rest state-of-charge (SoC), depth-of-discharge (DoD) and temperature. This work presents a framework to consistently parameterise key degradation modes--solid-electrolyte interphase (SEI) growth, lithium plating, and active material loss in both electrodes--using insights derived from degradation mode analysis data. The work predicts capacity fade trajectories of a NMC-based lithium-ion cell under both calendar and combined calendar-cyclic ageing, using a P2D electrochemical-thermal-degradation model. The work predicts state-of-health (SoH), remaining-useful-life (RUL) and internal degradation modes of the cell--under 81 combinations of temperature (10$^o$C, 25$^o$C, 40$^o$C), C-rate (0.1 C, 0.3 C and 1.0 C), rest SoC (10%, 60%, and 100%) and DoD (50%, 70%, and 90%)--using PyBaMM. The predicted cycle-life varies between 0.8 to 14 years to reach 75% of SoH. The work provides mechanistic insights into competing effects between calendar and cyclic ageing, during cycling. The model demonstrates sub-linear, linear, and sup-linear/accelerated capacity fade based on the usage conditions. The simulated dataset for all the cases is made available.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper presents a framework for consistently parameterizing key degradation modes (SEI growth, lithium plating, and active material loss in both electrodes) in a P2D electrochemical-thermal-degradation model for NMC-based lithium-ion cells. Drawing on degradation mode analysis (DMA) data, it uses PyBaMM to predict capacity fade trajectories, SoH, RUL, and internal degradation modes under 81 combinations of temperature (10–40 °C), C-rate (0.1–1 C), rest SoC (10–100 %), and DoD (50–90 %) for both calendar and combined calendar-cyclic ageing. The work reports cycle lives ranging from 0.8 to 14 years to 75 % SoH, demonstrates sub-linear to super-linear fade behaviors, provides mechanistic insights into competing ageing effects, and releases the full simulated dataset.
Significance. If the single consistent parameter set derived from DMA data remains valid without condition-specific adjustments, the work would provide a useful advance for mechanistic prediction of mixed ageing in Li-ion batteries, with open data release and PyBaMM implementation aiding reproducibility. The ability to link calendar and cyclic contributions mechanistically could inform RUL estimation and usage optimization.
major comments (2)
- [Parameterization framework (methods section describing DMA-to-parameter mapping)] The central claim rests on a single fixed parameter vector for SEI growth rate constant, Li plating rate constant, and electrode active-material loss rates (positive and negative) that is valid across all 81 condition combinations. No cross-validation is described in which parameters are identified from a subset of DMA conditions and then applied without adjustment to held-out combinations of T, C-rate, rest SoC, and DoD. This test is required to confirm that the model's built-in temperature/voltage dependencies suffice and that no residual condition-specific effects necessitate post-hoc refitting.
- [Results section on capacity fade predictions and dataset release] The abstract and results claim quantitative predictions of capacity fade trajectories and RUL, yet no validation metrics (RMSE, MAE, or similar), error bars on the simulated SoH curves, or direct comparisons against independent long-term experimental cycling data are reported. Post-hoc consistency checks on the DMA-derived rates versus the model's output fade curves are also not described, leaving open the possibility that the 'predictions' largely reproduce the input rates by construction.
minor comments (2)
- [Abstract and results summary] The reported cycle-life range (0.8–14 years) would benefit from explicit mapping to the extreme condition combinations and from any sensitivity analysis on the free parameters.
- [Figures and dataset description] Figure captions and text should clarify whether the simulated dataset includes any stochastic variability or is purely deterministic from the P2D model.
Simulated Author's Rebuttal
We thank the referee for their constructive and detailed review of our manuscript. We address each major comment point by point below, providing the strongest honest defense of the work while acknowledging areas where revisions can improve clarity and rigor.
read point-by-point responses
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Referee: [Parameterization framework (methods section describing DMA-to-parameter mapping)] The central claim rests on a single fixed parameter vector for SEI growth rate constant, Li plating rate constant, and electrode active-material loss rates (positive and negative) that is valid across all 81 condition combinations. No cross-validation is described in which parameters are identified from a subset of DMA conditions and then applied without adjustment to held-out combinations of T, C-rate, rest SoC, and DoD. This test is required to confirm that the model's built-in temperature/voltage dependencies suffice and that no residual condition-specific effects necessitate post-hoc refitting.
Authors: We appreciate the referee highlighting the value of cross-validation to demonstrate the robustness of the single fixed parameter set. The parameters for SEI growth, lithium plating, and active material loss were derived from DMA data spanning a range of conditions, with the P2D model then using its inherent physical dependencies (temperature via Arrhenius relations and voltage-dependent kinetics) to generate predictions for all 81 combinations without any condition-specific refitting. While an explicit cross-validation procedure (fitting on a DMA subset and testing on held-out conditions) was not described in the original manuscript, we agree this would strengthen the claims. In the revised version, we will add such an analysis to the methods section, splitting the DMA data where feasible to validate predictive performance on unseen combinations and confirm that the built-in dependencies are sufficient. revision: partial
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Referee: [Results section on capacity fade predictions and dataset release] The abstract and results claim quantitative predictions of capacity fade trajectories and RUL, yet no validation metrics (RMSE, MAE, or similar), error bars on the simulated SoH curves, or direct comparisons against independent long-term experimental cycling data are reported. Post-hoc consistency checks on the DMA-derived rates versus the model's output fade curves are also not described, leaving open the possibility that the 'predictions' largely reproduce the input rates by construction.
Authors: We thank the referee for this important point on validation. The capacity fade trajectories and RUL estimates are not direct reproductions of the input DMA rates by construction; they emerge from the full coupled solution of the P2D electrochemical-thermal-degradation equations in PyBaMM, which accounts for dynamic interactions, competing mechanisms, and condition-dependent effects during both calendar and cyclic operation. We agree that the results would be strengthened by quantitative metrics (e.g., RMSE or MAE where comparable data exist), error bars on SoH curves (e.g., from parameter sensitivity), and explicit post-hoc consistency checks between DMA-derived rates and simulated outputs. We will revise the results section to include these elements. Direct comparisons to fully independent long-term cycling datasets were not performed, as the study centered on consistent parameterization from DMA and broad simulation across conditions; the released dataset supports such external validations. revision: partial
Circularity Check
No significant circularity; parameterisation from DMA insights is independent of the forward predictions
full rationale
The derivation chain begins with degradation-mode-analysis data used to extract a single consistent parameter vector for SEI growth, lithium plating and active-material loss. These parameters are then inserted into the P2D electrochemical-thermal model whose temperature, voltage and C-rate dependencies are already present in the governing equations. The model is subsequently run forward to generate capacity-fade trajectories under 81 condition combinations. Because the DMA-derived rates are not re-adjusted to the same fade curves they are later asked to predict, and because no self-citation chain or uniqueness theorem is invoked to force the functional form, the predictions remain logically downstream of the inputs rather than equivalent to them by construction. The absence of reported cross-validation is a methodological limitation but does not constitute circularity in the derivation itself.
Axiom & Free-Parameter Ledger
free parameters (3)
- SEI growth rate constant
- Lithium plating rate constant
- Active material loss rate constants (positive and negative electrodes)
axioms (2)
- domain assumption The P2D electrochemical-thermal model equations accurately capture lithium transport, heat generation, and voltage response under the tested conditions.
- domain assumption Degradation mode analysis data provide independent, mechanism-specific information that can be mapped one-to-one onto the three rate constants without cross-talk or additional parameters.
Reference graph
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