A Repeated Measurements Approach to SOH Battery Modelling of Cyclic Aged Data in a Laboratory Environment

Evaluating battery cyclic ageing usually involves tracking state of health metrics repeatedly over time under controlled laboratory stress conditions. Traditional analysis approaches often overlook the natural hierarchical structure of longitudinal data, which contains both within-cell measurement noise and between-cell variation. This paper addresses this gap by developing a robust, two-component variance model for battery state of health profiling that captures both intra-individual and inter-individual variability.

The authors formulate a two-stage nonlinear hierarchical model. At the first stage, the intra-cell ageing trajectory of each individual battery cell is represented using a simple power law expression. At the second stage, inter-cell variation driven by different charging currents is modeled using a single-knot cubic B-spline. Parameter identification is achieved through a novel regularized iterative generalized least squares procedure, paired with an information-theoretic criterion to optimally re-estimate tuning hyper-parameters. Furthermore, the framework integrates automated outlier detection via least trimmed squares to improve robustness against aberrant test observations.

Applied to laboratory cycling data gathered from nickel-cobalt-aluminum cells, the proposed power law model provides an excellent fit to individual capacity loss profiles. The iterative estimation algorithm converges rapidly within a few iterations. The fully trained hierarchical model predicts battery capacity fade with a root mean square error of 0.191 percent across the evaluated state of health range, effectively handling experimental noise and cell-to-cell differences.