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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

Data-driven battery SOH estimation relies on costly, lifespan-wide labels that are sparse in practice. The paper pretrains a CNN-GRU using cycle-order ranking on unlabeled charging curves and reports satisfactory estimation across labeled-data ratios from 1% to 100% on its test cell.

  • Problem

    Data-driven SOH estimation relies on high-quality labels from costly lifespan-wide calibration tests, while real-world battery-aging data are often sparse in quantity and coverage.

    Source: §1 · p. 6, §5 · p. 33

  • Method

    The framework pretrains a CNN-GRU on unlabeled charging curves with an intra-cell cycle-order ranking objective to learn degradation-aligned representations for SOH estimation.

    Source: §2.2 · p. 13

  • Results

    SSL-pretrained models carried out satisfactory SOH estimation on the test cell across labeled-data ratios from 1% to 100%.

    Source: §4.2 · p. 25

  • Takeaways & Limitations

    Cycle order provides an ordinal self-supervision signal aligned with battery aging even without explicit SOH labels.

    Source: §2.2 · p. 13

    The label-sparsity evaluation samples labels uniformly only from data above 80% SOH, leaving deep-degradation labels outside that setup.

    Source: §4.2 · p. 25

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.

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

The paper highlights a ranking-based self-supervised framework and a CNN-GRU model with local feature fusion for SOH estimation under label sparsity, alongside analysis of how label distribution affects degradation data.

Highlights

1. Introduction

The introduction frames SOH estimation as important for safe battery use but difficult under sparse, unevenly distributed labels. It proposes cycle-order self-supervision and a CNN-GRU model to learn degradation-aligned representations from unlabeled charging data.

Introduction

  • SOH quantifies battery degradation and supports remaining-life assessment, maintenance scheduling, and safe, optimized battery use, but it must generally be estimated from operational measurements.The introduction says SOH can be defined using capacity or internal resistance and uses the capacity-based definition in this work.Source: §1 · p. 4
  • Battery SOH labels are costly and difficult to collect, especially late in life, leaving practical aging datasets sparse in quantity and coverage despite abundant unlabeled cycling data.Standardized checkup tests require time, expense, and extensive cycling to obtain deep-degradation labels.Source: §1 · p. 6
  • Cycle-order ranking pretraining on unlabeled CC charging curves is proposed to learn degradation-consistent representations for SOH estimation with sparse labels.The pretrained model is fine-tuned on limited labeled data; the authors describe this as the first use of intrinsic cycle-order information for self-supervised battery SOH estimation.Source: §1 · p. 8
  • Prior battery SSL includes reconstruction-based methods and contrastive learning with mask reconstruction, but reconstruction objectives may not align learned representations with degradation.The introduction motivates relative cycle age as a more task-relevant self-supervised signal because battery aging is ordered.Source: §1 · pp. 7–8
  • A CNN-GRU model uses convolutional layers to extract local charging-curve patterns and recurrent units to integrate them sequentially for SOH estimation and pretraining.The same model architecture supports both self-supervised pretraining and downstream SOH estimation.Source: §1 · p. 8
  • The paper presents in-depth analyses of how the label distribution of battery degradation data influences SOH estimation.Source: §1 · p. 8

2. Methodology

The methodology combines a CNN-GRU encoder with an intra-cell cycle-order ranking objective to learn degradation-aligned representations from unlabeled charging curves. The pretrained encoder is then frozen while a new regression head is fine-tuned on sparse SOH labels.

2.1.1. Convolutional Neural Networks

  • CNNs extract local aging-related patterns from battery cycling curves, treated as structured one-dimensional signals with correlated adjacent measurements.Source: §2.1.1 · p. 10

2.1.2. Gated Recurrent Units

  • The GRU integrates CNN-extracted local patterns over time, using gating to selectively combine current inputs with historical information for degradation-related representation learning and SOH estimation.Source: §2.1.2 · p. 11

2.1.3. CNN-GRU Model

  • The CNN-GRU model uses two convolution-ReLU blocks to extract charging-curve features, a GRU to model their temporal dependencies, and a two-layer fully connected head for pretraining or SOH regression.The same head architecture serves both tasks with different output sizes and loss functions; the model takes the CC charging voltage segment as input.Source: §2.1.3 · pp. 11–13

2.2. Cycle-Order Ranking for Degradation-Aligned SSL

  • Cycle-order pretraining ranks sufficiently separated cycles within each cell, avoiding cross-cell comparisons and encouraging aging scores to follow degradation order.Pairs with identical cycle numbers or gaps below dmin are excluded because their order may be unclear or affected by capacity recovery.Source: §2.2 · pp. 13–15

2.3. Degradation-Aligned SSL Framework

  • The framework pretrains on unlabeled charging data, then transfers the encoder and fine-tunes a new SOH-regression head on labeled data while keeping the encoder frozen.The data are preprocessed and split into training, validation, and test sets; only the new head is updated during fine-tuning.Source: §2.3 · pp. 16–17

3. Experimental Setup

The experiments use four CALCE cells, with preprocessing and a degradation-spanning train/validation/test split designed to evaluate cross-cell generalization. The setup compares frozen-encoder self-supervised approaches with supervised learning and evaluates both SOH regression and whether pretrained aging scores track degradation.

3.1. Data Preparation

  • CX2-37 and CX2-38 train the models, CX2-36 is used for validation, and CX2-34 is held out for testing within the training degradation range.The study uses CALCE cells CX2-34, CX2-36, CX2-37, and CX2-38, which have LCO cathodes and a rated capacity of 1.35 Ah; charging uses 0.5 C CC-CV to 4.2 V and discharging uses 1 C CC to 2.7 V [18]. CC charging voltage curves are resampled to 300 points, and outliers are removed using current/voltage anomalies and rolling MAD of CC segment lengths.Source: §3.1 · pp. 17–19

3.2. Experiment Settings

  • All CNN-GRU variants share a two-layer CNN and one-layer GRU encoder, while task-specific heads map latent features to aging score, SOH, or a reconstructed 300-point curve.The CNN uses kernel size 7 and channels 1→32→64; the GRU maps input size 64 to output size 128. Batch size is 256, and Optuna with TPE tunes learning rates using validation performance.Source: §3.2 · pp. 19–20
  • SSL-Rank uses a minimum cycle gap of 50; SSL-Recon reconstructs charging curves, SSL-MO combines reconstruction and ranking, and each pretrained encoder is frozen while a new head adapts to limited labels.Ordinary supervised models trained on the limited labeled data serve as the baseline.Source: §3.2 · p. 20

3.3. Evaluation Metrics

  • SOH regression is evaluated with MAE, RMSE, MAX, and R2, while Spearman’s ρ assesses the monotonic relationship between pretrained aging scores and ground-truth SOH.MAE summarizes average error magnitude, RMSE weights larger errors more, MAX captures the worst-case deviation, and R2 measures fit to overall label variation; ρ ranges from −1 to 1.Source: §3.3 · pp. 20–21

4. Results and Discussion

Ranking-based self-supervised pretraining produced aging-aligned scores and enabled strong SOH estimation with sparse labels; estimation performance also depended on where labels covered the degradation trajectory.

4.1. Evaluation of the Pretrained Model via Degradation Alignment

  • Across all four cells, pretrained aging scores tracked degradation and had Spearman correlations with SOH of -0.997, -0.998, -0.996, and -0.997 for CX2-37, CX2-38, CX2-36, and CX2-34, respectively.The scores captured capacity-recovery dips on the validation and test cells, despite some local fluctuations and divergence.Source: §4.1 · pp. 22–24, Figure 6 · p. 23

4.2. Model Performance Comparison under Label Sparsity

  • All three SSL models estimated SOH across 1%–100% label ratios, whereas SSL-Rank outperformed SSL-Recon and SSL-MO throughout; pure SL failed below 40% labels.Labels were sampled from the above-80%-SOH region; even with 50% or 100% labels, SL was outperformed by the SSL models, while SSL-Recon showed greater oscillations.Source: §4.2 · pp. 25, 27, Figure 7 · p. 26, Figure 8 · p. 27
  • SSL-Rank led all four evaluation metrics across label ratios, with MAEs of 1.715%, 1.722%, 1.692%, and 1.718% at 100%, 50%, 10%, and 1%, respectively.It maintained an R2 above 0.970 across test scenarios.Source: §4.2 · pp. 27–29, Table 2 · p. 28

4.3. Analysis on the Influence of Label Distribution

  • With random rather than uniform labels, R2 fell from 0.979 to 0.977 at 10% labels and from 0.981 to 0.977 at 5%; early-only labeling failed at 5%.Early-stage curves had limited diversity, and sampling only above 90% SOH at 10% labels also failed; larger label quantity partly compensated for limited diversity.Source: §4.3 · pp. 29–31, Figure 9 · p. 30
  • Late-only labels yielded the lowest MAE at every budget: 1.320%, 1.369%, 1.369%, and 1.350% with 10%, 5%, 2%, and 1% labeled data, respectively.Late-life charging curves show stronger aging-related variation, providing informative supervision; late-only labels also reduced errors below 60% SOH while increasing error above 90% SOH.Source: §4.3 · pp. 31–32, Table 3 · p. 33

5. Conclusion

The study proposes degradation-aligned self-supervised learning to support lithium-ion battery SOH estimation when labeled cycling data are sparse. On the CALCE dataset, the approach learns aging-consistent representations from unlabeled charging curves and achieves accurate estimation after fine-tuning with limited labels.

Results

  • With 1% of unevenly distributed labeled training data, SSL-Rank achieved a test-cell MAE of 1.718% and RMSE of 2.329%.The learned aging scores also had Spearman’s correlation coefficients extremely close to -1 with ground-truth SOHs.Source: §5 · p. 34

Framework

  • A cycle-order ranking pretext task learns aging-consistent representations from unlabeled CC charging curves before fine-tuning on sparse labels.The framework targets label sparsity in both quantity and coverage, where lifespan-wide calibration tests are time-consuming and costly despite abundant unlabeled operational cycling data.Source: §5 · pp. 33–34

Model

  • The CNN-GRU extracts local charging-curve patterns with convolutional layers and integrates them sequentially through recurrent units for SOH estimation and self-supervised pretraining.The framework was evaluated on the CALCE battery aging dataset.Source: §5 · p. 34

Analysis and future work

  • The study analyzes how label distribution influences battery degradation data, but evaluates only one cell model under one cycling condition.Future work is proposed to extend the framework across cells and cycling conditions to better reflect real-world variability.Source: §5 · p. 34

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