This paper presents a reduced-order electrochemical battery model designed for the online implementation of battery control systems. The model is based on porous-electrode and concentrated-solution theory frameworks and is able to predict voltage as well as the internal electrochemical variables of a battery. The reduction of the model leads to a physics-based one-dimensional discrete-time state-space reduced-order model (ROM), which is especially beneficial for online systems. Models optimized around different operational setpoints are combined to predict cell variables over a wide range of temperatures and state of charges (SOCs) using the output-blending method. A sigma-point Kalman filter is further used to manage inaccuracies generated by the reduction process and experimental-related issues such as measurement error (noise) in the current and voltage sensors. The state-estimation accuracies are measured against a full-order model (FOM) developed in COMSOL. The whole system is able to track the internal variables of the cell, as well as the cell voltage and SOC with very high accuracy, demonstrating its suitability for an online battery control system.

Battery management systems (BMSs) are required to estimate many non-measurable values that describe the actual operating condition of batteries; such as state of charge (SOC) or state of health (SOH). In order to improve accuracy, many physical states and parameters can be estimated using physics-based models (PBMs). These estimates could be used to improve the control and prognosis of batteries. In a series of papers, we propose a new method to estimate internal physical states, SOC, SOH and other electrode-specific state of health (eSOH) parameters of a lithium-ion battery, using interconnected sigma-point Kalman filters (SPKFs) and a single-particle model with electrolyte dynamics (SPMe). This second paper focuses on the estimation of the eSOH parameter. Simulation results show that the method is capable of estimating the eSOH parameters and key degradation modes that can occur inside a lithium-ion battery cell using only cell voltage and current measurements.

Battery management systems (BMSs) are required to estimate many non-measurable values that describe the actual operating condition of batteries; such as the state of charge (SOC) or the state of health (SOH). In order to improve this evaluation, many physical states and parameters can be estimated using physics-based models (PBMs). These estimates could be used to improve the control and prognosis of batteries. In a series of papers we propose a new method to estimate the internal physical states, the SOC, the SOH and the electrode-specific state of health (eSOH) parameters of a lithium-ion battery, using interconnected sigma-point Kalman filters (SPKFs) and a single-particle model with electrolyte dynamics (SPMe). This first paper focuses on state estimation for non-aged cells. To begin, we describe and validate our electrochemical model against a high-fidelity P2D model. The interconnected SPKF algorithm is then described and the observability of our system is analyzed, showing that the interconnected estimator approach improves an observability measure of the system. Finally, the results of the estimator are discussed, comparing the estimated variables with the truth values under initialization, measurement and modeling uncertainties. The results show that the algorithm can estimate the internal battery states with high accuracy.

This article presents a novel framework for onsite estimation of lithium-ion battery electrochemical parameters by combining physics-informed neural networks (PINNs) with transfer learning (TL). Unlike conventional physics-based models that require costly offline parameterization or extensive experimental tests, the proposed two-phase strategy first trains a PINN using only the governing equations of the single particle model, and then fine-tunes selected electrochemical parameters with field voltage measurements while keeping most network weights frozen. This enables efficient adaptation to ageing and cell-to-cell variability with minimal data requirements. The approach achieves high accuracy in estimating key parameters such as diffusion coefficients and active material volume fractions under different degradation conditions. Under a simulation environment, the method reconstructs voltage responses with a root-mean-square error of 8.94 mV and estimates active material fractions with an average relative error below 2.2% across 400 study cases, significantly outperforming classical optimization-based estimators. Experimental validation on an aged NMC cell (82.09% nominal capacity) implemented on a Raspberry Pi 5, demonstrates practical feasibility, yielding a relative error of 3.89% in estimating volume fractions with a computational cost of 106 ms per iteration. These results confirm that the proposed TL-based PINN framework offers an accurate, computationally efficient, and easily deployable solution for real-time battery management systems.