Evaluating Load-Conditional Convergence in Lithium-Ion Battery Degradation: A Matched-Group Statistical Framework

Abstract

The rate of capacity fade in a lithium-ion battery following a transition to a new discharge current is widely assumed to equal that of a battery that has always operated at the destination current, an implicit premise referred to here as load-conditional convergence. Despite its routine incorporation into reduced-order lifecycle and prognostic models, this assumption has not, to our knowledge, been subjected to formal statistical evaluation against matched constant-load reference data. This paper proposes a convergence gap framework in which the signed difference between the post-transition fade slope of a recommissioned pack and the natural fade slope of a matched reference pack quantifies deviation from the convergence assumption. A zero gap is consistent with convergence; a nonzero gap indicates that prior load history has measurably shifted subsequent degradation kinetics in a direction and magnitude that present-state models cannot capture. The framework combines automated load-transition detection from raw current signals, Gaussian Process Regression for trajectory smoothing, Theil—Sen bootstrap slope estimation, and a three-axis sensitivity analysis spanning transition-boundary placement, bootstrap sample size, and GPR kernel specification. Applied to a pilot cohort of six matched pairs from a single laboratory and a single NMC chemistry within the NASA accelerated life testing dataset, five of six pairs reject the null hypothesis of a zero convergence gap under Bonferroni correction at an adjusted threshold of 0.0083, with departures occurring in both directions, two faster and three slower than the natural rate. The remaining pair produces a gap statistically indistinguishable from zero, showing that convergence, while not general, is attainable. These outcomes are stable under all three sensitivity analyses. Because the cohort is small and drawn from a single laboratory and chemistry, the findings are hypothesis-generating rather than confirmatory. The framework is designed as a reusable measurement instrument for systematic convergence testing across future datasets with broader chemistries and cohort sizes.