Professional Report
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Preview · Only 1/3Professional Experimental Report on Collaborative Estimation of SOC and SOH for Lithium-Ion Batteries
1 Introduction
State of Charge (SOC) and State of Health (SOH) in lithium-ion batteries cannot be measured directly and must be estimated using model-based and data-driven methods. This report establishes a second-order RC equivalent circuit model within the VoltLab research platform and employs Adaptive Extended Kalman Filtering (AEKF) for joint SOC and capacity (SOH) estimation. Building on this unified true-value joint estimation, two forward-looking initiatives are implemented as independent analyses: first, decoupled updates of SOC (minute-scale) and SOH (cycle-scale) within a multi-time-scale framework; second, integration of Physics-Informed Neural Networks (PINN) with new thermal and impedance observation channels to enhance cross-battery generalization and Uncertainty Quantification (UQ) capabilities.
2 method
A second-order RC equivalent circuit model characterizes terminal voltage, while ampere-hour integration under known initial SOC and rated capacity constructs the reference SOC. SOH is derived from capacity calibration as C_now/C_new. An AEKF adaptively tunes noise covariance to enhance robustness against current transients and initial value deviations. As an extension, this report outlines a multi-timescale update scheme and key modeling considerations for PINN/new observation channels, enabling the estimation framework to maintain a unified true-value closed loop while supporting online scalability.
3 Data Sources and Ground Truth Construction
All estimates assume access to a ground truth: SOC is derived from ampere-hour integration, the OCV-SOC relationship is calibrated via low-current tests (residual < 5 mV), and capacity calibration provides SOH labels. Figures 3 and 4 illustrate the calibration relationships and aging sequences.
| Cell | Rated/Ah | T/°C | C-rate | Regime | Note |
|---|---|---|---|---|---|
| Cell-A | 2.5 | 25 | 1 | CC-CV / DST | NASA-style reference |
| Cell B | 2.5 | 25 | 2 | HPPC / US06 | high C-rate |
| Cell-C | 2.5 | 40 | 1 | BBDST | elevated T |
| Cell-D | 2.5 | 10 | 0.5 | Daylight Saving Time | low T |
| SOC band | R₀/mΩ | R₁/mΩ | C₁/F | R² |
|---|---|---|---|---|
| 0–20% | 27.5 | 12 | 1800 | 0.9818 |
| 20–40% | 28.7 | 11.2 | 1680 | 0.9846 |
| 40–60% | 31.2 | 10.4 | 1560 | 0.9826 |
| 60–80% | 31.9 | 9.6 | 1440 | 0.9844 |
| 80–100% | 33.6 | 8.8 | 1320 | 0.9827 |
7 Multi-timescale decoupled SOC (minute-level) and SOH (cycle-level) updates
Multi-timescale decoupling addresses the fundamentally different evolution rates of SOC and SOH: SOC fluctuates violently at the second-to-minute scale with current, making it suitable for rolling updates via adaptive filtering (e.g., AEKF); SOH drifts slowly over cycles due to capacity degradation, warranting batch updates through capacity calibration. Figure 9 displays the trajectories of SOC (minute-scale) and SOH (cycle-scale) on the same time axis, demonstrating their clear decoupling without cross-contamination: high-frequency SOC fluctuations do not enter the SOH channel, while slow SOH drift does not corrupt real-time SOC estimates. This decoupling is a prerequisite for subsequently introducing PINNs and multi-channel observation.
10 Metric Item and Data Requirements
To enhance the value of professional reports and clarify acceptance criteria, this section translates the aforementioned outlook into quantifiable metrics and specifies the sufficient and necessary battery data that the communication module must read and process. The metrics are categorized into six types: ① Multi-time-scale decoupling – SOC is updated on a minute-by-minute rolling basis, while SOH is updated in batches per cycle; the two are decoupled in time scale and do not contaminate each other. ② Physics-Informed Neural Networks (PINN) – Equivalent circuit or electrochemical constraints are applied as soft regularization, ensuring outputs satisfy physical consistency such as terminal voltage residuals, SOC monotonicity, and energy conservation. ③ Thermal observation channel – Multi-channel temperature, temperature rise rate, and hotspot detection. ④ Impedance observation channel – Online internal resistance and evolution of impedance spectrum (EIS) features. ⑤ Cross-battery generalization – Error drift and domain adaptation across cell types and chemistries. ⑥ Uncertainty Quantification (UQ) – Confidence intervals, calibration error, and predictive entropy. The table below lists the sufficient and necessary data and sampling requirements for each metric. As long as the communication module satisfies the fields listed in this table (timestamp, multi-string voltage, current, multi-channel temperature, cycle count, capacity calibration, online internal resistance/impedance, SOC/SOH labels, operating conditions, and chemistry labels), it constitutes the "sufficient and necessary" minimum dataset.
| Metric Items | Sufficient and Necessary Data (Read by Communication Module) | Time Scale / Sampling Requirements | Satisfy criteria |
|---|---|---|---|
| Multi-timescale Decoupling (SOC: Minute-level / SOH: Cycle-level) | Timestamp t, Current I(t), Voltage V(t), Cycle Count cycle, Capacity Calibration C | SOC ≥1 Hz rolling; SOH per cycle / every N cycles batch | SOC and SOH update channels are independent, with no residual coupling. |
| Physics-Informed Neural Networks (PINN) | V(t), I(t), temperature T, OCV-SOC relationship, equivalent circuit parameters | Synced with SOC (≥1 Hz) | Terminal voltage fitting residual below threshold; energy conservation and SOC monotonicity satisfied. |
| Thermal observation channel | Multi-channel temperature Tᵢ, ambient temperature T_amb, thermal boundary | ≥0.1 Hz (slow thermal inertia) | Temperature rise rate, ΔT distribution, and hotspot detectability |
| Impedance Observation Channel | Online internal resistance R₀, impedance spectrum Z(f), or pulse impedance | SOH Level (Per Cycle / Periodic) | Trackable internal resistance trends and spectral peak shifts |
| Cross-battery generalization | Cell ID / Chemistry Label, Cross-Battery SOH Label | Loop Level | Cross-domain RMSE drift and domain adaptation error reduction |
| Uncertainty Quantification (UQ) | Dispersion of repeated samples or ensemble predictions under identical operating conditions | On-demand | Confidence intervals cover the true value (calibrated) and prediction entropy is low. |