Data-efficient crack quantification in lithium-ion cathodes using foundation model transfer
Authors: Thorsten Tegetmeyer-Kleine, Thomas Schmitt, Phillip Aquino, Christiane Rahe, Dirk Uwe Sauer, Weihan Li
Organizations: Junior Professorship for Artificial Intelligence and Digitalization for Batteries, Institute for Power Electronics and Electrical Drives (ISEA), RWTH Aachen University, Campus-Boulevard 89, Aachen, 52074, Germany · Center for Aging, Reliability and Lifetime Prediction of Electrochemical and Power Electronic Systems (CARL), RWTH Aachen University, Campus-Boulevard 89, Aachen, 52074, Germany · Juelich Aachen Research Alliance, JARA-Energy, Templergraben 55, Aachen, 52056, Germany · Honda Research Institute Europe GmbH, Carl-Legien-Strasse 30, Offenbach/Main, 63073, Germany · Zenules GmbH, Landgraf-Georg-Str. 4, Darmstadt, 64283, Germany · Honda Research Institute USA, Inc., 21001 State Route 739, Raymond, OH, 43067, United States · Chair for Electrochemical Energy Conversion and Storage Systems, Institute for Power Electronics and Electrical Drives (ISEA), RWTH Aachen University, Campus-Boulevard 89, Aachen, 52074, Germany · Helmholtz Institute Muenster (HI MS), IMD-4, Forschungszentrum Juelich, Germany
Battery lifetime is central to sustainable electrification, yet the particle cracking that drives lithium-ion cathode aging is hard to measure: quantitative microscopy of this degradation is bottlenecked by annotation, because each destructive electron-microscopy cross-section spans hundreds of megapixels and pixel-level expert labelling requires hours per image. We show that a frozen self-supervised vision-transformer encoder, combined with a lightweight trainable decoder and iterative model-assisted annotation, turns this sparse labelling budget into population-scale degradation measurements. Applied to three 120-megapixel NMC cathode cross-sections representing initial, cycled-aged and calendar-aged states, the framework distinguishes intragranular cracks from early- and late-stage intergranular cracks and yields per-particle distributions of crack width, tortuosity and area fraction. Late intergranular crack coverage reaches 4.6% in the cycled sample versus 0.5% in the initial and calendar-aged samples, forming more tortuous, higher-coverage networks, consistent with degradation from repeated electrochemical cycling rather than elevated-temperature storage alone. A single destructive image yields the population-level statistics needed for lifetime-extending design, aging assessment and second-life decisions.
Figures & tables
Figure 1: Cathode degradation and multi-class crack dataset. (a–c) Representative regions from raw SEM images (ca. 17k×7k px, 22.3 nm/px) of NMC cathode cross-sections: (a) initial, (b) cycled-aged, and (c) calendar-aged. The three samples exhibit visibly different SEM contrast, brightness, and crack density. (d) Crack classification scheme: intragranular cracks (within primary grains), early intergranular cracks (typically < 120 nm at grain boundaries), and late intergranular cracks (typically > 150 nm and often widened with high-contrast deposits). (e) Dataset composition: 482 expert-corrected tiles distributed as 79 fully manual seed tiles (all drawn from the cycled-aged image) plus 403 model-assisted tiles (160 cycled-aged, 81 calendar-aged, 162 initial), across three samples and crack classes. (f) Tiling strategy with 1024 × 1024 px windows and 50% overlap for seamless image reconstruction.
Figure 2: Foundation model architecture and model-assisted annotation workflow. (a) Encoder-decoder architecture combining a frozen DINOv3 ViT-B/16 backbone with a trainable DeepLabV3+ decoder for 3-class semantic segmentation. The frozen encoder supplies dense per-patch features while the lightweight decoder adapts to the domain with minimal annotated data and reduced training compute. (b) Model-assisted labelling workflow: 79 expert hand-annotated tiles (cycled-aged image) train an initial model. The model then generates provisional pixel-wise crack-class masks for 403 additional tiles (160 cycled-aged, 81 calendar-aged, 162 initial), which are expert-corrected and added back into training to yield the final model. (c) Image-scale inference: sliding windows with 50% overlap produce per-tile 3-class sigmoid predictions (intragranular, early intergranular, late intergranular), stitched by visit-count normalisation to eliminate boundary artefacts. (d) Mean-Dice comparison between the seed model (79 manual tiles, 0.49) and the final model (482 expert-corrected tiles, 0.58), an 18% relative improvement ( Δ=+0.09 ). (e) Representative output linking segmentation to geometric quantification: raw SEM ROI, predicted late-intergranular mask overlay, and combined distance- and width-transform overlay (full ROI walkthrough in Supplementary Figure S1 ). (f) Per-class morphometric summary previewing the full analysis in Fig. 4 : kernel density estimate of mean crack width and tortuosity distributions for intragranular (I), early intergranular (EI), and late intergranular (LI) cracks.
Figure 3: Multi-class segmentation performance. (a–c) Representative segmentation results for each sample condition showing input SEM images and model predictions (overlay). Despite the visible contrast and brightness differences among the three SEM images, the model detects the crack classes in all conditions. (d) Normalized confusion matrix aggregated across the expert-corrected tile set ( n=482 tiles; threshold τ=0.1 ). (e) Per-class segmentation metrics. The model achieves Dice scores of 0.575 (intragranular), 0.513 (early intergranular), and 0.653 (late intergranular) (mean Dice 0.580; mean clDice 0.587).
Figure 4: Automated morphometric quantification of crack characteristics. Three rows show intergranular cracks (a–d, combining early and late classes), intragranular cracks (e–h), and all cracks combined (i–l). Each row contains four panels: violin plots of area fraction (a, e, i), mean crack width (b, f, j), tortuosity (c, g, k), and width probability distributions (d, h, l). Brackets indicate statistically significant pairwise differences (two-sided Mann–Whitney U test); significance levels: *** q<0.001 , ** 0.001≤q<0.01 , * 0.01≤q<0.05 , ns q≥0.05 , where q is the Benjamini–Hochberg false-discovery-rate-adjusted p -value across the family of 27 pairwise tests (3 subsets × 3 metrics × 3 condition pairs); see Methods. Cycled-aged samples show significantly higher late intergranular crack area fraction and tortuosity than initial and calendar-aged samples; mean crack width is only slightly larger and not statistically significant (panel j).
Figure 5: Statistical analysis of degradation patterns. Rows: intergranular (a–c), intragranular (d–f), and all cracks combined (g–i). Columns: ECDFs of mean crack width with 95% Dvoretzky–Kiefer–Wolfowitz bands and median markers (a, d, g); orientation rose diagrams (b, e, h); area fraction vs. mean width (c, f, i). The cycled-aged width distributions (red) show only a slight, non-significant shift toward larger widths relative to initial (blue) and calendar-aged (green); the statistically significant cycled-aged increases are in area fraction and tortuosity (panel j). (j) Mann–Whitney U tests on late intergranular cracks with Cliff’s δ ; q -values are Benjamini–Hochberg-adjusted within the 9-test intergranular-late sub-family (see Methods and Supplementary Methods §S7).
Figure 6: Proposed mechanism of crack evolution in NMC cathodes. (a–d) Schematic illustration of characteristic crack types, shown as a generalized progression; in practice, these mechanisms may overlap temporally and coexist depending on local microstructural conditions: (a) Initial polycrystalline NMC particle with coherent grain boundaries. (b) Intragranular cracks form within primary particles due to anisotropic lattice strain during H2 → H3 phase transition. (c) Intergranular cracks nucleate at grain boundaries under repeated mechanical stress from volume changes. Intragranular cracks from (b) persist but are omitted for visual clarity. (d) Late-stage degradation with widened cracks ( > 150 nm), rock-salt phase formation, and electrolyte infiltration pathways. Intragranular cracks remain present but are not shown to highlight intergranular crack progression. (e) Generalized trend of crack morphology metrics correlated with electrochemical capacity retention, suggesting crack width as a quantitative degradation marker. The depicted sequence represents a predominant tendency rather than a strict temporal order.
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 1: ∣ Precision–recall curves and threshold selection. (a) Per-class PR curves with average precision (AP) values; filled circles mark the operating point at τ=0.1 . (b) Per-class and mean Dice score vs. decision threshold τ ; the selected threshold is annotated. The low optimal τ reflects extreme foreground–background imbalance ( < 1% crack pixels).
Figure 2: ∣ Morphometric threshold sensitivity. Area fraction, mean crack width, and tortuosity (mean ± std across ROIs) as a function of the decision threshold τ∈{0.05,0.1,0.2,0.3,0.5} for each crack class and sample condition. Area fraction decreases monotonically with increasing τ as stricter thresholds suppress low-confidence crack pixels; mean width and tortuosity are more stable because skeleton-based statistics average over retained crack pixels. The relative ordering of conditions is preserved across all τ tested: the cycled-aged cross-section consistently shows the highest late intergranular area fraction, width, and tortuosity, while calendar-aged late-crack coverage remains comparable to the initial state throughout. Within τ∈[0.05,0.2] the absolute morphometric values closely track the main-text numbers; outside this range the relative ordering is preserved but absolute values deviate more substantially. The operating point τ=0.1 used throughout this study is highlighted.
Figure 3: ∣ Zero-shot SAM2 vs. fine-tuned DINOv3 on the NMC crack validation set. Columns: raw tile; expert 3-class reference (intragranular red, early intergranular green, late intergranular blue); SAM2 in automatic mode ( 64×64 point grid, no prompts); SAM2 prompted with Otsu-derived dark-region centroids and area-bounded lowest-mean-intensity multi-mask selection; fine-tuned DINOv3-DeepLabV3+. Per-prediction binary Dice values are annotated below each prediction column. The inset on the SAM2-auto column of row 1 shows the unfiltered output before geometric and intensity post-processing, illustrating the oversegmentation failure mode on textured SEM matrix. The 3-class reference is collapsed to a single crack vs. background target because SAM2 is class-agnostic; this typology gap is the structural reason fine-tuning is required for the cycled/initial late-intergranular comparison.
Figure 4: ∣ Per-cross-section segmentation metrics by aging condition. Mean per-class scores for Dice, clDice, IoU, Precision, and Recall (with standard-deviation error bars) computed separately for the initial, cycled-aged, and calendar-aged cross-sections. Crack classes are abbreviated as I (intragranular), EI (early intergranular), and LI (late intergranular). The relative ranking of per-class scores is preserved across aging conditions: the frozen DINOv3 encoder transfers across the three aging states despite substantial differences in SEM contrast, brightness, and late-crack density.
Method
Binary Dice ↑
Binary IoU ↑
3-class capable?
DINOv3-DeepLabV3+ (ours, binary)
0.77
0.65
✓ (via 3-class output)
SAM2-auto (zero-shot)
0.019
0.010
—
SAM2-prompted (Otsu)
0.025
0.013
—
Appendix
Table 1: ∣ Zero-shot SAM2 baselines vs. fine-tuned DINOv3 (binary segmentation). SAM2 sam2.1-hiera-large in two configurations evaluated on the same 482-tile reference set as the main DINOv3 result. Binary Dice and IoU were computed after collapsing the 3-class reference to crack-vs-background. For each SAM2 configuration the higher of the with- and without-filter values was retained per tile. The 95% CIs are non-paired bootstrap with n=1000 resamples.
Sample
Class
ROIs
Area (%)
Width (nm)
Length ( μ m)
Tortuosity
Initial
Intragranular
446
10.34±7.54
107±33
0.8±0.6
0.95±0.31
Initial
Intergran. early
97
1.66±0.76
91±10
8.6±5.7
1.38±0.53
Initial
Intergran. late
97
0.52±1.29
159±22
1.5±3.4
1.55±0.63
Cycled-aged
Intragranular
610
9.25±7.17
107±32
1.1±0.9
0.97±0.31
Cycled-aged
Intergran. early
69
1.30±1.23
98±15
7.3±7.4
1.58±0.73
Cycled-aged
Intergran. late
69
4.58±3.60
167±39
14.2±10.5
2.40±1.00
Appendix
Table 2: ∣ Morphometric statistics by sample and crack class. Mean ± std across ROIs, supporting the per-condition morphometric comparisons in the main article. Bold: highest values within each metric column. Pixel size: 22.3 nm.
Supplementary Figure S1: Skeleton-based morphometric extraction. The skeleton-based extraction procedure applied within each ROI, illustrated for an example intergranular late ROI. (a) Raw SEM image of the region of interest. (b) Multi-class segmentation overlay fused with a semi-transparent highlight of the single-class crack mask (white: 16.1% of pixels, 17 666 px; black: 83.9%, 91 895 px). (c) Medial-axis skeleton overlaid on the raw SEM image, with branch points (orange) and endpoints (cyan) classified from the 3×3 neighbour-degree topology and the principal orientation (172.6°) derived from the leading eigenvector of the skeleton coordinate covariance matrix; the network comprises 74 branches and 30 endpoints, with tortuosity 5.39, anisotropy 1.51, and roughness 64.76 px. (d) Fused distance-transform map (cividis colour scale) and per-skeleton-pixel width heatmap w(xs)=2d(xs) (inferno colour scale), both overlaid on the raw ROI. (e) Crack width histogram (mean 10.69 px, median 10.39 px, std 4.43 px, range 2.00–27.57 px). (f) Empirical cumulative distribution function of crack width with P25 , P50 , and P75 percentiles indicated. Together, panels (c)–(f) document that the pipeline reliably extracts centrelines even for branched, tortuous crack networks and yields stable width estimates along elongated crack segments.
Supplementary Figure S2: Per-tile boundary-F1 distribution at 1 px and 2 px tolerance. Per-tile boundary-F1 (BF1) score distributions at 1-pixel and 2-pixel Euclidean boundary tolerance for each crack class. The median BF1 at 1-pixel tolerance (0.45–0.46 per class) rises to 0.58–0.62 at 2-pixel tolerance, approaching the clDice level. The improvement from 1 px to 2 px confirms that 1–2-pixel boundary misalignment dominates the moderate pixel-exact Dice. For crack structures only 2–5 pixels wide at the imaging resolution of 22.3 nm/px, this boundary uncertainty corresponds to sub-50 nm localisation error, comparable to the precision achievable by human annotators tracing approximate crack centrelines.
Supplementary Figure S3: Method-by-method diagnostic on tile 100_0000_00038 (the Fig. 1 sample tile). Row a (predictions): columns left-to-right are the raw tile, the 3-class expert reference (intragranular red, early intergranular green, late intergranular blue), SAM2-auto, SAM2-prompted, and fine-tuned DINOv3; each prediction cell is annotated with its binary Dice. Row b (error maps): same column order; cyan = true positive, magenta = false positive, amber = false negative, black = true negative. Row c (inputs): for each SAM2 column, the prompts the method sees: Otsu-derived dark mask overlay (column 1), Otsu centroids (column 2, SAM2-prompted inputs), the 64×64 dense point grid (column 3, SAM2-auto inputs), and one prompt zoom showing SAM2’s 3 multi-mask candidates with the area-bounded lowest-mean-intensity selection bordered in green (column 4); column 5 shows the DINOv3 sigmoid heatmap (maximum over the 3 crack classes) before binarisation, with the colour bar indicating P(any crack) per pixel.
Supplementary Figure S4: Region-of-interest detection pipeline. The automated ROI-extraction workflow that defines the spatial units used for the morphometric analysis in the main article, illustrated for the cycled-aged image (intergranular late class). (a) Binary threshold mask at decision threshold τ . (b) Post-merge mask after morphological closing merges spatially proximal crack fragments belonging to the same secondary particle. (c) Rejected sub-particle components below the minimum-area threshold, suppressed to remove artefacts. (d) Final detected ROI windows: each surviving component is enclosed by its axis-aligned bounding box, expanded by a fixed margin to ensure full particle coverage. The resulting ROI windows are sorted in raster order (top-to-bottom, left-to-right) and used as the spatial units for all downstream morphometric statistics reported in the main article.
Supplementary Figure S5: Per-class segmentation metrics versus crack density (full panel set). Per-tile Dice (top row) and IoU (bottom row) plotted against the foreground pixel fraction for intragranular ( a , d ), intergranular early ( b , e ), and intergranular late ( c , f ) cracks across all 482 expert-corrected tiles. Dashed lines show linear fits; Pearson correlation coefficients r are annotated in each panel ( r=0.21 – 0.32 ). The full multi-panel decomposition shown here supports the conclusion that pixel-exact agreement is principally limited by low-density tiles rather than by model failures on crack-rich regions, motivating the topology-aware and boundary-tolerant metrics (clDice, BF1) reported in the main article.
Accurate assessment of lithium-ion battery ageing is challenged by cell-to-cell variability, heterogeneous cycling protocols, and limited transferability of data-driven models across datasets. In particular, robust identification of degradation transitions, such as the knee point, and reliable early-life prediction of remaining useful life (RUL) remain open problems. This study proposes a unified framework for battery ageing analysis based on continuous representations of voltage-capacity and capacity-cycle trajectories learned from heterogeneous public datasets (NASA, CALCE, ISU-ILCC). The continuous formulation enables consistent extraction of degradation descriptors, including curvature, plateau length and knee-related metrics, while reducing sensitivity to dataset-specific discretisation. Across more than 250 cells, statistically significant correlations between knee onset and end-of-life (Pearson 0.75-0.84) are observed. Additional early-life analysis confirms that knee-related features retain predictive value when estimated from partial trajectories. Early-life models provide increasingly stable RUL predictions as the number of observed cycles increases, with meaningful predictive performance emerging within the first 5-20 cycles and remain robust under cross-dataset domain shift. The framework integrates continuous modelling, feature extraction and uncertainty-aware prediction, providing an interpretable and dataset-consistent approach demonstrating robustness across heterogeneous dataset types. Compared with conventional discrete or feature-based methods, the proposed representation reduces sensitivity to sampling resolution and improves cross-dataset consistency. The study is limited to laboratory-scale datasets and capacity-based end-of-life definitions.
Reliable early detection of lithium-ion battery degradation requires health indicators that are physically interpretable and computable from routine cycler telemetry without access to the degradation region. We introduce CausalHealth, a framework that applies causal graph discovery and k-nearest-neighbour transfer entropy to per-cycle voltage, current, temperature, and resistance time series, and organises twelve resulting anomaly scores into three signal-class bundles (Magnitude-shift, Predictive-residual, Complexity-entropy) -- with Isolation Forest reported separately as it falls below the bundle reliability threshold -- to characterise detection sensitivity across ten commissioning fractions (5--30,%). The Magnitude-shift class achieves 100,% detection across all seven tested cells spanning LFP (MIT--Stanford MATR) and LCO (NASA PCoE, CALCE CS2) chemistries, with a lead time of up to 402 cycles before conventional capacity-threshold failure on gradual-fade cells. A Reliability-Weighted Master Health Index (RWMHI) -- a cross-bundle fusion of five high-reliability detectors weighted by inverse coefficient of variation -- improves lead time by 15--52 cycles over the class median on long-lived cells while maintaining 100,% detection. Validation against electrochemical impedance spectroscopy on an NMC prismatic cell provides independent physical grounding: transfer entropy TE(R→V) correlates with charge-transfer resistance Rct (pooled r=+0.990; temperature-controlled partial r=+0.898), and an Arrhenius analysis of both quantities yields an activation energy consistent with published NMC charge-transfer kinetics. These results are evaluated on seven cells across three benchmark datasets.
Dieter W. Heermann, Hagen Heermann
Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, D-69120 Heidelberg, Germany · Intilion GmbH, Wollmarktstraße 115c, D-33098 Paderborn, Germany
An accurate estimation of the state of health (SOH) underpins 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 awareness 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 and cross-cell robustness. We believe this work could shed new light on label-efficient SOH estimation of lithium-ion batteries, addressing a practical need in battery management.
Jiaqi Yao, Julia Kowal
Department of Electrical Energy Storage Technology (EET), Technische Universität Berlin, Einsteinufer 11, 10587, Berlin, Germany