How much data does a memory kernel need? Measurement requirements for fractional models of battery and corrosion degradation
Abstract
How much data does a memory kernel need before a fit is meaningful? For a distributed-order model, the answer is about 3.1 decades of observation, more than standard battery-degradation tests provide. Battery capacity fade and corrosion-film growth depend on their history, so they are often modelled using general fractional calculus (GFC), where memory is described by an arbitrary Sonine kernel rather than a single power law. We tested this using two mechanistic models without fractional operators and de Levie's porous-electrode model, whose high-frequency order is exactly 0.5; our estimator recovered 0.500. A single aging curve can recover an effective order, alpha, to within 5% noise using a weak formulation, while separating the tempered parameters (alpha, lambda) requires several Arrhenius conditions, with errors improving from (0.25, 0.43) with one condition to (0.04, 0.07) with four. A distributed-order memory needs 3.1 decades of data to be resolved to 90%; below that, a two-order memory can collapse into one intermediate order that fits the data better than the true spectrum. For saturating passivation, however, a general kernel improves the fit substantially, raising R2 from 0.862 to 0.998. Across 20 cells from two public datasets, observation windows span only 1.23 to 2.24 decades, making the 3.1-decade result a practical design rule: it defines what must be measured before fitting a memory kernel, not only what cannot be fitted.
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BibTeX
@misc{feugmo2026much,
title = {{How much data does a memory kernel need? Measurement requirements for fractional models of battery and corrosion degradation}},
author = {Conrard Giresse Tetsassi Feugmo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05426},
eprint = {2611.05426},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05426},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - How much data does a memory kernel need? Measurement requirements for fractional models of battery and corrosion degradation
AU - Conrard Giresse Tetsassi Feugmo
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.05426
UR - https://arxiv.org/abs/2611.05426
AB - How much data does a memory kernel need before a fit is meaningful? For a distributed-order model, the answer is about 3.1 decades of observation, more than standard battery-degradation tests provide. Battery capacity fade and corrosion-film growth depend on their history, so they are often modelled using general fractional calculus (GFC), where memory is described by an arbitrary Sonine kernel rather than a single power law. We tested this using two mechanistic models without fractional operators and de Levie's porous-electrode model, whose high-frequency order is exactly 0.5; our estimator recovered 0.500. A single aging curve can recover an effective order, alpha, to within 5% noise using a weak formulation, while separating the tempered parameters (alpha, lambda) requires several Arrhenius conditions, with errors improving from (0.25, 0.43) with one condition to (0.04, 0.07) with four. A distributed-order memory needs 3.1 decades of data to be resolved to 90%; below that, a two-order memory can collapse into one intermediate order that fits the data better than the true spectrum. For saturating passivation, however, a general kernel improves the fit substantially, raising R2 from 0.862 to 0.998. Across 20 cells from two public datasets, observation windows span only 1.23 to 2.24 decades, making the 3.1-decade result a practical design rule: it defines what must be measured before fitting a memory kernel, not only what cannot be fitted.
ER -