Model Parametrization and Adaptation Based on the Invariance of Support Vectors With Applications to Battery State-of-Health Monitoring

Abstract

Support vector regression (SVR) algorithms have been applied to the identification of many nonlinear dynamic systems due to their excellent approximation and generalization capability. However, the standard SVR algorithm involves an iterative optimization process, which is often computationally expensive and inefficient. For applications such as the battery state-of-health (SOH) monitoring, where the identification algorithm needs to be applied repeatedly for multiple cells because of the variation in model dynamics (due to battery aging and cell-to-cell difference), the computational burden could pose difficulties for real-time or onboard implementation. In this paper, the battery $V{-}Q$ curve identification problem for SOH monitoring is studied. Based on experimental battery aging data, we develop a model parametrization and adaptation framework utilizing the simple structure of SVR representation with determined support vectors (SVs) so that the model parameters can be estimated in real time. Through mathematical analysis and simulations using a mechanistic battery aging model, it is shown that the SVs of the battery models stay invariant, even when the batteries age or vary. The invariance of the SVs is verified using experimental aging data. Consequently, the resulting model for the battery $V{-}Q$ curve can be directly incorporated into the battery management system (BMS) and adapted online for SOH monitoring. Moreover, the general characteristics of the data that could maintain the SVR invariance are identified. The proposed automated model parametrization process (via an optimization algorithm) can be extended to nonlinear dynamic systems with the given properties.