Li-ion battery state-of-health (SOH) diagnosis in real-world operating environments remains a challenge. Equivalent circuit models (ECMs) commonly employed by battery management systems suffer from a loss of accuracy over the full range of operating conditions faced in real-life operation. This is because some circuit parameters are functions of the internal states, such as SoC, as well as operating conditions such as applied current and temperature. This state-dependence of model parameters also affects the reliability of ECMs when applied to model-driven SOH diagnosis. As an alternative, physics-based models for diagnosis may offer improved accuracy over ECMs, but they also present challenges as they rely on prior knowledge of a large number of battery parameters, plus the absence of a reference electrode in commercial cells limits model identifiability. Therefore to improve the accuracy and generalisation of ECMs in SOH diagnosis, we propose a hybrid approach combining an ECM with a probabilistic machine learning approach in order to estimate the functional dependency of ECM parameters on battery states and operating conditions. Specifically, we employ computationally efficient Gaussian process regression  to simultaneously retrieve battery states and model parameters as functions of operating conditions directly from drive cycle data. We demonstrate how a 1st order RC circuit (representing diffusion dynamics) may be fully parameterized using this method, making ECMs both more accurate in predicting voltage as well as more robust when applied to SOH diagnosis. The framework is also battery chemistry and construction agnostic, making it applicable from cell to pack level in a variety of applications .
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