Forecasting Electrode State of Health (eSOH) for Managing Battery Lifetime Using Domain-Knowledge-Informed Machine Learning
Authors: Roy Apoorva , Alghalayini Maher , Movahedi Hamidreza , Siegel Jason , Harris Stephen J , Stefanopoulou Anna 
Published: December 2024

Lithium-ion batteries (LIBs) degrade the least compared to other battery chemistries but are sensitive to operational limits corresponding to physical degradation processes in each electrode. As LIBs age, their capacity fades and this is observable from the decrease in their range when they operate within fixed maximum and minimum terminal voltage limits (Vmin and Vmax). There is rich literature on a variety of physics-based, data-driven and empirical models that have been developed to track degradation indicators like capacity fade and resistance growth. However, capacity and resistance alone do not provide insights into individual electrodes' internal health. Therefore, it is valuable to track any four out of the six “electrode state-of-health” eSOH parameters = [Cp, Cn, x100, y100, x0, y0] as defined in [1,2,3] that allow us to limit the operation of each electrode within safe limits and slow down degradation. In this study, the eSOH parameters are the electrode capacities – Cp for cathode/positive and Cn for anode/negative – and lithium stoichiometric windows – x0, x100 in LixC6 and y0, y100 in LiyNiMnCO – in the negative and positive electrodes, respectively. Note that the capacity C can be derived using four independent eSOH parameters.
Due to aging caused by the loss of cyclable lithium (due to SEI formation, plating, and cathode metal (Mn) dissolution) and loss of active material (LAM, as a result of particle fracture), the electrodes' stoichiometric windows shrink and shift (see Figure 1 panel (a)) with time along with a reduction in their cyclable capacities. These intrinsic degradation mechanisms at the electrode particle level govern the observable capacity fade that is achieved when the cell terminal voltage is between Vmin and Vmax. When fresh, operating between Vmin/Vmax protects the electrodes from reaching damaging overpotentials such as anode overpotential which can lead to plating. However, as the eSOH shrinks and shifts, the Vmin and Vmax limits might force one or both electrodes to operate at damaging overpotentials, making it necessary to apply individual eSOH limits in order to achieve fast charging against plating and Mn dissolution in an electric vehicle as shown in Figure 1 panel (b). Estimating eSOH and programming the battery management system (BMS) to impose operational limits as shown in Figure 1 panel (b) can avoid unsafe operation and/or accelerated degradation:

The BMS should limit the maximum anode stoichiometry to prevent lithium plating. Plating usually occurs at low temperatures and high charging C-rates when the battery's average particle state of charge is already high.

The BMS should limit the minimum of the cathode stoichiometry as high cell voltages can also cause cathode metal dissolution when the cathode has low stoichiometry.

Forecasting the four eSOH parameters [Cp, Cn, x100, y0] leverages Gaussian process regression (GPR) on positive and negative eSOH parameters and thermodynamic capacity to predict future capacity fade for up to 80 cycles. To ensure accurate extrapolation, domain knowledge is integrated into GPR modeling by selecting a suitable prior mean function. Two representative cells have been selected from the experimental dataset presented in [4] to demonstrate the performance of the GP model. Results for one cell depicted in Figure 1 panel (c) show that capacity forecasted using positive and negative eSOH parameters is consistent with that of thermodynamic capacity, with RMSE being less than 1.6%.
References:
[1] Mohtat, P., et al. "On identifying the aging mechanisms in li-ion batteries using two points measurements," American Control Conference (ACC), 2017.
[2] Lee, S., et al. (2020). “Electrode state of health estimation for lithium ion batteries considering half-cell potential change due to aging”. J-ECS.
[3] Lopetegi, I., et al . (2024). “A new battery SOC/SOH/eSOH estimation method using a PBM and interconnected SPKFs: Part ii. SOH and eSOH estimation”. J-ECS.
[4] Mohtat, P., et al (2022). “Comparison of expansion and voltage differential indicators for battery capacity fade”. Journal of Power Sources.

Figure 1