New Model Tracks EV Battery Charge Under Vibration-Induced Degradation

Lithium-ion batteries in electric vehicles spend their working lives being shaken. Road roughness, engine mounts and chassis dynamics expose every onboard pack to continuous mechanical loading, and that vibration quietly accelerates internal degradation, eroding the energy storage capacity over time. A new open-access study published in Discover Electronics on 27 September 2026 presents a modeling-based state of charge estimation framework that explicitly folds this vibration-induced capacity degradation into the estimation process, rather than ignoring it as most conventional methods do.

The research team, led by Yuanyuan Xie with Jonghoon Kim, Shuo Wu and Woonki Na, developed what they call an SPM-EKF approach: an electrochemical single particle model coupled with an extended Kalman filter. The key innovation is that the effective battery capacity is treated as a dynamic state variable influenced by vibration intensity, updated in real time alongside the state of charge itself. According to the authors, simulation and experimental validation results demonstrate that the proposed method achieves high SOC estimation accuracy for commercial cells of different chemistries even when vibration-induced capacity variation is present.

State of charge is a critical parameter for battery management in electric vehicles, and model-based approaches using the extended Kalman filter have long been favored because they are robust against measurement noise and can handle nonlinear battery dynamics. In the literature, however, these filters are almost always paired with equivalent circuit models, simplified electrical networks that are computationally cheap but physically shallow. The authors note that such models typically cannot fully capture the internal transport processes and electrochemical behavior of lithium-ion cells, and have very limited applicability under vibration conditions where complex degradation mechanisms and capacity loss significantly affect battery behavior.

The single particle model takes a different route. Its central assumptions are that the reaction current is uniformly distributed along the electrode thickness and that the electrolyte behaves as a lumped solution resistance, approximations the authors say are generally valid for the thin, highly conductive electrodes found in today’s EV batteries. Under these assumptions, the charging and discharging of an entire cell can be represented by a single intercalation particle of the electrode active material, with lithium-ion transport described by Fick’s second law of diffusion within a sphere. The cell’s SOC is derived analytically from the positive electrode, whose stoichiometric variation mainly reflects charge-discharge behavior, and the terminal voltage follows from the difference between the two electrode potentials minus overpotential and ohmic losses.

To make the framework vibration-aware, the researchers extended the conventional EKF state vector, which normally contains only SOC and transient polarization states, with a third entry: the effective capacity under vibration impact. A degradation equation updates this capacity at every time step, driven by the measured vibration intensity and an empirical degradation coefficient. The process noise covariance matrix is also adjusted according to vibration intensity, so the filter adaptively increases its uncertainty about the capacity state under heavy mechanical loading, keeping the estimator stable and responsive despite increased model mismatch. Measured current, terminal voltage and vibration signals all serve as inputs, and the EKF continuously corrects the predicted states against terminal voltage measurements.

The experimental campaign used commercial 18650 cylindrical cells in three chemistries: NCA, NMC and LFP, all provided by Samsung. Testing was performed on a BT-Lab platform at 25 degrees Celsius in a temperature-controlled chamber, with cutoff voltages of 4.2 V and 2.5 V for the NCA and NMC cells and 3.6 V and 2.0 V for the LFP cells. Discharge tests ran at 0.125 C, 0.25 C, 0.5 C and 1 C, followed by a long-term cycling test at 1 C for approximately 50 full charge-discharge cycles. The cycled cells were then mounted on a mechanical shaker and subjected to two hours of random vibration in the 10 to 100 Hz frequency range, after which additional charge-discharge cycles quantified the damage. Reference SOC values were constructed by Coulomb counting, with the reference capacity recalibrated through full 0.1 C discharges to account for cycling and vibration effects.

The results paint a consistent picture. Estimated voltage profiles matched the experimental discharge curves across all four C-rates, and when the team deliberately introduced initial voltage estimation errors of 10, 20 and even 50 percent, the filter converged back toward the measured profiles, demonstrating robustness against poor initialization. During the 50-cycle test on NCA cells, the estimated SOC tracked the experimental reference over the whole period, with the largest deviations appearing near abrupt transitions between 1 C charging or discharging and rest, where rapid voltage relaxation and polarization effects are not fully captured by the model. Initial SOC errors of up to 50 percent were likewise corrected within the first cycle.

The vibration experiments confirmed that mechanical loading measurably degrades capacity, and that the damage is chemistry dependent. After the two-hour random vibration test, the NCA cells showed the largest loss, about 2.1 percent on average across eight identical cells, while the NMC and LFP cells lost around 1.4 and 1.5 percent respectively. The authors suggest this variation reflects differences in cell structure, manufacturing and design, and note that even cells of the same chemistry may respond differently because of internal structural and assembly differences. In post-vibration estimation, the model captured the major charging and discharging voltage profiles for NMC and NCA cells well, while the LFP cells showed somewhat larger fitting errors around the transitions between their flat voltage plateaus, where the voltage-SOC relationship becomes nearly insensitive and weakens the EKF correction.

A final sensitivity analysis probed how errors in the vibration model itself propagate into SOC estimates. When the degradation coefficient was overestimated by 10 to 50 percent, the SOC error stayed below roughly 0.1 percent for NCA and NMC cells, while LFP showed slightly larger sensitivity, exceeding 0.15 percent at 50 percent overestimation. Overestimating the vibration intensity proved more consequential: errors for all three chemistries were higher than for the degradation coefficient, and LFP again led, with SOC error climbing to nearly 0.39 percent under 50 percent overestimation. The authors conclude that accurate vibration measurement matters more than precise calibration of the empirical degradation coefficient, and caution that vibration profiles with similar RMS acceleration but different power spectral densities may produce different degradation behavior. In practice, they suggest, reliable accelerometer placement, signal filtering and RMS vibration extraction are critical for maintaining accurate vibration-aware SOC estimation.

For the electric vehicle industry, the significance lies in closing a gap between laboratory-grade state estimation and the mechanically messy reality of the road. By combining a physics-based electrochemical model with an adaptive filter that watches capacity fade as it happens, the SPM-EKF framework offers a route to battery health monitoring that remains accurate under the very conditions that degrade the pack. The authors position it as a useful tool for battery state and performance estimation in practical operating environments, with the relatively low computational complexity needed for real-time onboard implementation.

Subject of Research: State of charge estimation for commercial EV lithium-ion batteries under vibration-induced capacity degradation

Article Title: Modeling based SOC estimation for commercial EV Li-ion batteries under vibration conditions

Article References: Xie, Y., Kim, J., Wu, S., & Na, W. (2026). Modeling based SOC estimation for commercial EV Li-ion batteries under vibration conditions. Discover Electronics, 3(1), Article 137. https://doi.org/10.1007/s44291-026-00291-y

Image Credits: AI Generated

DOI: 10.1007/s44291-026-00291-y

Keywords: lithium-ion batteries, electric vehicles, state of charge, extended Kalman filter, single particle model, vibration, capacity degradation, battery management, NCA, NMC, LFP, 18650 cells