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Degradation-Aligned Self-Supervised Learning for State of Health Estimation of Lithium-Ion Batteries under Label Sparsity

Jiaqi Yao, Julia Kowal

arXiv:2608.16612v1eess.SPcs.AIcs.LG

TL;DR

Sparse, uneven SOH labels make battery-health estimation difficult because full-lifespan calibration is costly, while unlabeled cycling data are plentiful. The paper uses cycle-order ranking to pretrain a CNN-GRU on unlabeled charging curves, and reports satisfactory SOH estimation across 1%–100% label ratios on the test cell after SSL pretraining.

  • Problem

    Data-driven SOH estimation relies on costly, lifespan-wide labeled cycling data, but practical battery-aging datasets are sparse in both label quantity and coverage.

  • Method

    The framework pretrains a CNN-GRU with intra-cell cycle-order ranking on unlabeled charging curves to learn degradation-aligned representations before fine-tuning.

  • Results

    SSL-pretrained models provide satisfactory SOH estimation across 1%–100% labeled-data ratios over the test cell’s entire lifespan, unlike pure supervised learning below 40%.

  • Takeaways & Limitations

    The framework supports SOH estimation with limited labels by using unlabeled charging data in practical settings where labels are sparse in quantity and coverage.

  • Takeaways & Limitations

    The evaluation samples fine-tuning labels uniformly above the 80% SOH threshold, limiting the tested label-distribution scope.

Abstract

from arXiv · show

An accurate estimation of the state of health (SOH) underpins a safe and optimized use of the battery system. Although compelling, data-driven SOH estimation models typically require large amounts of high-quality labeled cycling data, while in practice such labels are often sparse in both quantity and coverage. Therefore, in this work, we propose a degradation-aligned self-supervised learning (SSL) framework based on a convolutional neural network-gated recurrent unit (CNN-GRU) model, which learns aging-consistent representations from unlabeled data through a cycle-order ranking objective as the pretext task for pretraining, thereby enabling robust SOH estimation after fine-tuning on sparsely labeled data. Test results showcase that the proposed ranking-based SSL approach proves to endow the pretrained model with degradation-aligned information from unlabeled data, and after fine-tuning the model can carry out accurate, robust SOH estimation, even when only an extremely limited amount of 1% of unevenly distributed labeled training data is available, where the MAE of 1.718% and RMSE of 2.329% can be achieved on the test cell. In addition, in-depth analyses are presented regarding the influences of label distribution of battery degradation data. We believe this work could shed new light on SOH estimation of lithium-ion batteries under label sparsity in real-world applications.

Degradation-Aligned Self-Supervised Learning for State of Health Estimation of Lithium-Ion Batteries under Label Sparsity

The work proposes a ranking-based self-supervised learning framework for SOH estimation under label sparsity, using a CNN-GRU model with local feature fusion and analyzing label-distribution effects.

  • A ranking-based self-supervised learning framework is proposed for SOH estimation under label sparsity.
  • A CNN-GRU model with local feature fusion is developed for SOH estimation.
  • The study examines how the label distribution of degradation data influences SOH estimation.

1. Introduction

Battery SOH is difficult to measure directly and data-driven estimation requires scarce, costly labels. This work addresses label sparsity with degradation-aligned ranking-based self-supervised pretraining and a CNN-GRU model, while analyzing label-distribution effects.

  • Motivation: SOH is a degradation metric that is difficult to measure directly, so it must be estimated from measurable operational information.Capacity-based SOH is used in this work.
  • Motivation: Data-driven SOH estimation depends on extensive high-quality labels, but standardized calibration tests are costly, time-consuming, and rarely feasible during deployment.Late-life SOH labels are also limited in practical settings.
  • Proposed approach: Reconstruction-based SSL captures general data patterns but may not align representations with battery degradation, whereas cycle-aging order provides a task-relevant signal.The relative aging order between cycles is proposed as the self-supervised signal.
  • Proposed approach: The proposed ranking-based SSL framework pretrains on unlabeled constant-current charging curves using cycle-order ranking, then supports robust SOH estimation with sparse labels.The learned representations are intended to be degradation-consistent.
  • Proposed approach: A CNN-GRU model extracts and sequentially integrates local charging-curve patterns for SOH estimation and self-supervised pretraining.The same model architecture serves both estimation and pretraining.
  • Study scope: The study analyzes how the distribution of labeled battery-degradation data influences SOH estimation.This analysis addresses label-distribution effects under sparse supervision.

2. Methodology

The proposed CNN-GRU framework combines convolutional extraction of local charging-curve patterns with gated sequential integration, then applies a shared task head for ranking-based self-supervised pretraining and SOH regression. Its intra-cell cycle-order objective uses relative cycle order to learn degradation-aligned representations from unlabeled charging data.

  • Feature extraction: CNNs extract local patterns from charging curves treated as structured one-dimensional signals with strong correlations between adjacent measurements.The convolutional design uses local receptive fields and shared trainable kernel parameters, while same padding preserves sequence length.
  • Sequential integration: GRU gating selectively combines current inputs, historical information, and candidate hidden states to sequentially integrate extracted local patterns.The reset gate controls historical-information retention, while the update gate controls fusion of the previous and candidate hidden states.
  • CNN-GRU architecture: The encoder contains two stacked CNN blocks and one GRU layer, while the head uses two fully connected layers with ReLU activation.The CNN extracts local patterns from charging curves, and the GRU integrates these features to capture temporal dependencies.
  • Task head: The same head architecture supports self-supervised pretraining and SOH estimation, with task-specific output sizes and loss functions.Ranking pretraining predicts an aging score, reconstruction pretraining reconstructs the input charging curve, and downstream estimation performs SOH regression.
  • Ranking-based pretraining: Battery cycle order provides ordinal self-supervision because later cycles generally represent deeper degradation than earlier cycles.The intra-cell cycle-order ranking objective is designed to learn degradation-aligned representations from unlabeled charging data.
  • Ranking-based pretraining: The ranking algorithm groups samples by cell, forms pairs from distinct cycles separated by at least dmin, and averages ranking losses across valid cell groups.Groups with fewer than two samples are skipped, and the objective returns no ranking supervision when no valid group exists.

3. Experimental Setup

Experiments use CALCE’s public aging dataset with four CX2 cells, standardized partial charging curves, and cleaned SOH labels. CNN-GRU models are pretrained with ranking, reconstruction, or multi-objective SSL and evaluated using regression and monotonicity metrics.

  • Data and cycling protocol: Experiments use CALCE’s public battery aging dataset and cells CX2-34, CX2-36, CX2-37, and CX2-38.The cells are prismatic lithium cobalt oxide cells subjected to the described charging and discharging protocols.
  • Data preprocessing: BatteryML preprocesses raw cycling data, after which CC-charging voltage curves are extracted and resampled to 300 points.SOH labels use full discharge capacity, while further cleaning removes anomalies in current, voltage, and charging-segment lengths.
  • Model configuration: CNN-GRU models share architectural hyperparameters across pretraining and SOH estimation, with task-specific fully connected heads.Ranking pretraining and SOH regression reduce latent dimensions from 128 to 64 to 1, whereas reconstruction expands them from 128 to 256 to 300.
  • Self-supervised pretraining: The proposed SSL-Rank uses a minimum cycle gap of dmin = 50 and is compared with SSL-Recon and SSL-MO.SSL-Recon is described as reconstruction-based SSL, while SSL-MO is a multi-objective SSL approach.
  • Evaluation metrics: SOH regression is evaluated with MAE, RMSE, MAX, and R2, while Spearman’s rank correlation coefficient ρ assesses degradation-aligned aging scores.MAE measures average error magnitude, RMSE emphasizes large errors, R2 evaluates overall fit, and ρ measures monotonicity with ground-truth SOH.

4. Results and Discussion

The pretrained model learns aging-aligned representations from unlabeled charging data, enabling robust SOH estimation with sparse labels. Results also show that label distribution affects performance, especially when labels cover only early degradation stages.

  • Aging-aligned representations: Predicted aging scores generally follow monotonic capacity fade and capture capacity-recovery events despite local fluctuations.This alignment is observed for validation cell CX2-36 and test cell CX2-34, including recovery near the 1300th and 1150th cycles.
  • Aging-aligned representations: Normalized aging scores exhibit monotonic trends with ground-truth SOH, increasing as the battery degrades.Spearman’s rank correlation coefficients are used to quantify the association for each cell.
  • SOH estimation under label sparsity: SSL models provide satisfactory SOH estimation from 1% to 100% labeled data, whereas the unpretrained SL model fluctuates strongly under sparse labeling.Labels are sampled from data above the 80% SOH threshold, with approximately 1200 training samples at 100%.
  • SOH estimation under label sparsity: 1.715%, 1.722%, 1.692%, and 1.718% are the SSL-Rank model’s MAEs at labeled-data ratios of 100%, 50%, 10%, and 1%, respectively.SSL-Rank leads across all four evaluation metrics in every testing scenario.
  • SOH estimation under label sparsity: R2 remains over 0.970 for SSL-Rank in all test scenarios, while the SL baseline collapses to MAEs around 12% with fewer labeled samples.The largest errors occur in the deepest-degradation regime, where aging accelerates significantly.

5. Conclusion

The work addresses sparse SOH labels by pretraining a degradation-aligned SSL framework on abundant unlabeled charging data, then fine-tuning it with limited labeled data for robust estimation.

  • 5. Conclusion: Sparse SOH labels arise in both quantity and coverage because standardized checkup tests must span the batteries’ entire lifespan under controlled conditions.These labeling constraints limit conventional data-driven SOH estimation models, which rely on large amounts of high-quality labeled cycling data.
  • 5. Conclusion: The proposed framework learns aging-consistent representations from unlabeled CC charging curves using a cycle-order ranking objective during pretraining.It is designed for practical settings where lifespan-wide SOH calibration tests are time-consuming and costly, while unlabeled operational cycling data are abundant.
  • 5. Conclusion: The pretrained representations enable robust SOH estimation after fine-tuning on only a limited amount of labeled data.This design leverages unlabeled operational cycling data to reduce dependence on costly lifespan-wide calibration tests.

CRediT Authorship Contribution Statement

Jiaqi Yao led the study’s conception, methods, implementation, analysis, investigation, resources, data curation, drafting, revision, and visualization. Julia Kowal contributed to manuscript review and editing and provided supervision.

  • Jiaqi Yao handled conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, original drafting, review and editing, and visualization.
  • Julia Kowal contributed to writing—review and editing and supervision.

Abbreviations

This section defines the manuscript’s abbreviations for battery systems, modeling methods, neural networks, degradation mechanisms, and lithium-ion battery materials.

  • Battery terminology: The abbreviations include battery lifecycle and management terms such as BMS, BOL, and EOL, alongside CC and CV charging modes.BMS means Battery Management System; BOL and EOL mean Beginning of Life and End of Life; CC and CV mean Constant Current and Constant Voltage.
  • Modeling methods: The manuscript abbreviates neural-network architectures and related computational models as CNN, DNN, FC, GRU, ECM, and EKF.These denote Convolutional Neural Network, Deep Neural Network, Fully Connected, Gated Recurrent Unit, Equivalent Circuit Model, and Extended Kalman Filter.
  • Diagnostics and degradation: Battery diagnostics and degradation mechanisms are represented by ICA, LAM, and LLI.ICA denotes Incremental Capacity Analysis, while LAM and LLI denote Loss of Active Material and Loss of Lithium In…
  • Applications and materials: The abbreviation list also includes EV and LCO for Electric Vehicle and Lithium Cobalt Oxide.The supplied passage identifies EV as Electric Vehicle and LCO as Lithium Cobalt Oxide.
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