Fuzzy logic–based estimation and topological ordering of pack-to-pack capacity variations in parallel-connected batteries

Reliable estimation of the State of Health (SOH) remains a key challenge for battery systems, as many established approaches rely on detailed battery models and aging-dependent parameters. In industrial applications, SOH values are often delivered by proprietary algorithms, motivating the need for independent cross-checking from the customer’s perspective. This work proposes a model-free method to infer relative capacity differences between parallel-connected battery packs using only measured current and voltage signals. Three probabilistic distributions derived from standard operational data are combined via a fuzzy logic-based pairwise comparison, and the resulting relations are aggregated into a global capacity ranking using topological ordering. The method requires neither battery modeling nor knowledge of absolute capacities and provides a logically consistent relative reference for SOH validation. Simulation studies show that the true capacity order is correctly identified across multiple load profiles, with increased uncertainty when higher-capacity packs simultaneously exhibit higher internal resistance. The approach is further validated using 26 months of real-world data from an electric city bus with five parallel-connected NMC battery packs, capturing evolving capacity differences, including a known pack replacement. The results show substantial agreement with a Kalman filter-based SOH estimation for most pack pairs, while also revealing cases of disagreement and delayed adaptation. The proposed method provides a scalable and transparent cross-check for SOH algorithms, enabling probabilistic validation of relative capacity estimates in multi-pack battery systems.