Source-linked AI summary
Real-Time State-of-Health Estimation and Online Degradation Prognosis from Partial Battery Discharge Using Physics-Informed Neural Networks
Begoña Ispizua, Serio Gil-López, Leire Arrizabalaga, Ibai Laña
TL;DR
Accurate battery SOH estimation is challenging when charge or discharge curves are incomplete and when degradation transitions must be tracked in real time. This paper combines physics-informed learning from arbitrary discharge segments with continuously updated degradation prognosis, achieving MAPE below 4% across discharge segments.
Problem
SOH estimation is challenging when charge or discharge curves are incomplete, while the most informative phase for degradation prediction remains unsettled.
Method
The framework estimates SOH from arbitrary charge or discharge segments and continuously updates cell-specific degradation trajectories to identify knee-points and EoL.
Results
MAPE remained below 4% for every discharge segment, with the PINN consistently outperforming the conventional NN across evaluation metrics.
Takeaways & Limitations
The approach provides battery-agnostic, real-time degradation characterization that incorporates every predicted SOH value without prior battery information.
Takeaways & Limitations
Future work should evaluate generalization to more heterogeneous datasets and batteries operating under different current profiles.
Abstract
from arXiv · showhide
With the increasing integration of renewable energy sources, energy storage systems have become essential, making the accurate estimation of their State of Health (SOH) and degradation behavior critical. In this work, we propose a physics-informed deep learning approach for lithium-ion battery SOH prediction using incomplete discharge curves extracted from arbitrary voltage ranges, thereby reflecting realistic and heterogeneous operating conditions. The proposed method combines data-driven learning with physically motivated degradation dynamics to ensure consistent and reliable SOH estimation from partial discharge information, achieving a MAPE below 4$\%$. In addition, a real-time degradation trend estimation strategy is introduced to detect key aging transitions without requiring prior knowledge or historical data, making it applicable to a wide range of batteries. Overall, our approach enables SOH estimation from arbitrary discharge segments and a real-time degradation forecast that continuously integrates all usage, overcoming previous methods that rely on fixed protocols or early, non-adaptive predictions.
1. Introduction
The introduction motivates practical battery SOH estimation by highlighting the limitations of existing physics-based and data-driven methods under partial, heterogeneous operating data. It presents a physics-informed framework for arbitrary charge or discharge segments and a continuously updated, cell-specific degradation prognosis strategy.
- Motivation: Battery degradation is central to ESS management, particularly for accurate RUL estimation within BMS.The expansion of renewable energy, electric mobility, and battery use has increased the importance of advanced storage technologies.
- Existing methods: Physics-based models provide physical interpretability and generalizability without training data but are computationally expensive for real-time estimation.Data-driven methods offer lower computational costs and faster response times, but often require substantial, standardized data.
- Practical limitations: Existing approaches often require large datasets, complete or equal charge-discharge segments, or fixed regions, limiting use when arbitrary cycle portions are available.Purely data-driven methods may also struggle to generalize beyond their training distribution.
- Proposed framework: The proposed physics-informed framework estimates lithium-ion battery SOH from arbitrary charge or discharge segments by identifying the voltage region and selecting a dedicated model.The study first examines whether charge or discharge data provide more informative SOH inputs.
- Degradation prognosis: The proposed real-time prognosis framework continuously updates each cell’s degradation trajectory from available SOH estimates without predefined degradation models or battery-specific parameters.Adaptive linear regression uses the evolving trajectory to identify the degradation knee-point and related transitions.
2. Materials and Methods
The methodology comprises three stages: processing partial discharge curves and extracting features, predicting SOH with a neural network, and estimating degradation tendency from the predicted SOH. Experiments use 122 lithium-ion batteries cycled to End of Life under specified voltage, capacity, current, and charging conditions.
- Methodology workflow: The methodology first processes different curve sections to extract features, then uses a neural network to predict SOH, and finally estimates degradation tendency from the approached SOH.These steps form three main stages addressed in dedicated subsections.
- Dataset: The dataset contains 122 lithium-ion batteries cycled until End of Life, each with 1.1Ah nominal capacity and 3.3V nominal voltage.The dataset is from Severson et al. (2019).
- Dataset: The cells use 3.6V upper and 2V lower cut-off voltages and are discharged at a constant current of 4C, while charging protocols vary.The passage states that different charging protocols are applied.
2.1. Data processing
The data-processing workflow selects the more informative operating phase, defines bend-point capacity as the SOH ground truth, and enables SOH estimation from arbitrary partial discharge segments. Segment-specific processing extracts voltage–capacity, statistical, and incremental-capacity features from independently computed local measurements.
- Phase selection: The workflow compares charging and discharging data using Random Forest, XGB, and Feedforward Neural Network models evaluated by MAPE to identify the more informative phase for SOH estimation.Charging is associated with consistency and stability, whereas discharging reflects real load conditions; the study notes no consensus on which phase contains stronger degradation signatures.
- SOH definition: The capacity at the discharge-curve bend point is adopted as the SOH health indicator and used as ground truth for training and validating the PINN models.The bend point is identified with the Kneedle algorithm, which detects maximum curvature from the greatest perpendicular distance to the endpoint-connecting line.
- Partial-discharge segmentation: SOH is estimated from limited discharge portions across arbitrary voltage regions rather than requiring complete discharge curves.Each discharge curve is divided into 8 uniformly distributed sections, each representing a 5% nominal-capacity decrement.
- Segment processing: Each discharge segment is treated as an independent sample, with its capacity computed locally because cumulative discharge capacity is unavailable for individual segments.The approach reflects real-world operation, where only local measurements over limited time intervals are typically available.
- Feature extraction: Segment-specific features include voltage–capacity geometry, current and voltage statistics, and incremental-capacity descriptors for SOH estimation.Geometric descriptors comprise arc length, slope, and enclosed area; statistical indicators comprise mean, variance, kurtosis, and skewness.
2.2. SOH estimation
The SOH estimator uses a Verhulst physics-informed neural network driven by segment-level features and constrained by battery degradation dynamics. It incorporates multidimensional health indicators and combines data-fitting with physical-consistency losses, using MAPE, RMSE, and R^2 for validation.
- Model formulation: A Verhulst PINN estimates battery SOH from segment-level features extracted during data processing.The network is selected specifically to perform SOH estimation after feature extraction.
- Model formulation: The Verhulst degradation model represents capacity loss as u(t) = 1 − SOH(t), with degradation rate r and finite upper bound K estimated from cycle-indexed data.Here, t denotes the cycle number, with each cycle defined as a full charge-discharge process.
- Health indicators: Latent variables x = [x_1, … , x_n] ∈ R^n are introduced as multidimensional health indicators to distinguish degradation trajectories across batteries.This formulation allows monitoring data and extracted features to supplement time-dependent degradation modeling.
- Physics-informed training: A surrogate neural network is embedded in the PINN, whose output u(x, t) and automatically differentiated temporal derivative are constrained by Verhulst dynamics.The Verhulst parameters r, K, and C are unknown and optimized during training; identical batteries share these parameters in this study.
- Physics-informed training: The training objective combines a data-driven loss with a physical-consistency loss, while MSE trains the model and MAPE, RMSE, and R^2 evaluate validation accuracy.The relative weights of data and physical consistency are controlled by λ_u and λ_f.
2.3. Degradation estimation
The degradation estimator continuously updates a least-squares trend and its confidence interval as new SOH estimates become available. It detects the knee-point through consecutive confidence-interval violations, then models the subsequent degradation regime and supports adaptive application without battery-specific calibration.
- Linear regression: The degradation trend is fitted online from the second SOH prediction onward and continuously updated after each completed discharge.The knee-point is unknown a priori, so least-squares parameters are updated as SOH estimates arrive.
- Confidence interval: A sliding-window deviation of slope variations defines the confidence interval, which is updated each cycle and progressively narrows as data accumulate.The deviation tracks changes in the slope trend and supports uncertainty bounds for the fitted degradation line.
- Knee-point detection: The knee-point alarm is triggered when γ consecutive SOH predictions fall outside the confidence interval, with γ evaluated from 1 to 70.The threshold is selected through validation-battery sensitivity analysis by comparing estimated and true knee-point cycles.
- Knee-point detection: After knee-point detection, a second least-squares regression models the new degradation regime until a user-defined capacity threshold, commonly 80% of nominal capacity.The second fitted line and its confidence interval are used to determine the cycle associated with the selected minimum capacity.
- Online applicability: The methodology adapts continuously to degradation changes across datasets, charging and discharging protocols, and operating voltage ranges without prior battery-specific information or calibration.If SOH estimates are unavailable, the framework’s first stage can generate them for the degradation estimator.
3. Results
Results on a 10-battery validation set show that discharge data and segment-specific physics-informed models enable accurate SOH estimation from partial discharge curves. The framework also tracks degradation trends, detects the knee point, and approximates battery EoL.
- Experimental setup: 10 batteries were reserved exclusively for validation, while the remaining cells supported training and analysis.All reported results refer to this validation set.
- Data modality comparison: Discharge data consistently produced lower MAPE than charge data for knee-point and EoL prediction across all evaluated models and targets.Discharge curves were therefore selected for SOH-based degradation forecasting.
- Segment classification: 0.99 validation accuracy was achieved by the XGBoost classifier assigning unseen discharge segments to voltage-range categories and corresponding SOH models.This validated the pipeline’s segment-routing stage.
- Feature selection: Different voltage segments required different predictive features, with 4 or 5 significant features generally retained and only the VQ-curve slope retained for segment 6.Segment 6 is near the knee point and represents the most linear discharge region.
- SOH estimation: 1.52% MAPE, 0.016 RMSE, and 0.952 R2 were achieved by segment 6, the most accurate segment, using only the VQ-curve slope.Across all segments and metrics, PINNs outperformed conventional NNs, and no segment exceeded 4% MAPE.
- Degradation prognosis: 34 consecutive SOH predictions outside the confidence interval minimized mean knee-point error and was selected to declare transition to accelerated degradation.The framework also detects degradation-trend changes and approximates battery EoL.
4. Conclusions
The study presents a physics-informed framework that estimates SOH from arbitrary discharge segments and uses those estimates for real-time degradation prediction. It generalizes across voltage ranges while providing battery-agnostic degradation characterization without prior information.
- Framework: The framework estimates battery SOH from arbitrary discharge segments across different voltage ranges and uses those estimates for real-time degradation prediction.Multiple deep learning models were developed for different discharge-voltage segments.
- Physics-informed modeling: Physics-informed models combine the Verhulst degradation equation with a loss term penalizing error between predicted and ground-truth SOH.This formulation promotes convergence toward the ground truth while preserving physical consistency.
- SOH estimation: The voltage segment centered around 3.14 V achieved the highest accuracy because it lies near the informative discharge-curve knee and depends only on curve slope.The result supports robustness and generalization across voltage segments.
- Degradation trend estimation: Least-squares regression fits predicted SOH values, and its confidence interval identifies the degradation knee and the endpoint of the second degradation regime.The second regime is estimated to end when the confidence interval intersects the minimum valid capacity.
- Degradation trend estimation: The real-time estimator applies to individual batteries without prior information and incorporates every predicted SOH value to adaptively characterize evolving degradation trajectories.The approach is described as accurate and battery-agnostic.
Future work
Future work should optimize how discharge curves are segmented and assess whether the pipeline generalizes across more heterogeneous battery datasets and operating current profiles.
- Future work: Investigate the optimal number of discharge-segment models needed to cover the entire discharge curve.This includes determining the optimal length of each segment.
- Future work: Evaluate the proposed pipeline on more heterogeneous battery datasets.
- Future work: Assess performance on batteries operating under different charging and discharging current profiles.
CRediT author statement
The CRediT statement assigns Begoña Ispizua primary responsibility for conceptualization, investigation, methodology, and manuscript writing. Sergio Gil-López contributed conceptualization, methodology, and supervision; Leire Arrizabalaga handled software; and Ibai Laña contributed conceptualization, supervision, and writing review and editing.
- Begoña Ispizua contributed conceptualization, investigation, methodology, and writing of the original draft, review, and editing.
- Sergio Gil-López contributed conceptualization, methodology, and supervision.
- Leire Arrizabalaga contributed software development.
- Ibai Laña contributed conceptualization, supervision, and writing review and editing.