Deployment-Oriented Lithium-Ion Battery Remaining Useful Life Prediction with adaptive History Selection and Parameter-Efficient Updating

Dongxiao Ren; Xinyu Zhong; Zixiang Ye; Xing-Liang Xu

doi:10.20944/preprints202603.2447.v1

3. Method

This section describes the proposed method under the representative online-transfer setting introduced above. To keep the formulation relevant to deployment-oriented battery prognostics, we first define the causal online prediction setup, then describe the baseline, and finally present the two constrained strategies considered in this work: parameter-efficient updating and adaptive history selection.

3.1. Problem Setup

For each cell, the data arrive as a time-ordered sequence of charge–discharge cycles. At online step t, the predictor receives an input constructed only from information available up to that step and produces updated estimates of the target health variables under a strictly causal protocol. The exact rule used to construct the input sequence is described later together with the baseline and the adaptive history-selection mechanism.

The model predicts two quantities simultaneously: RUL and a capacity-based SOH proxy, represented here by discharge capacity (mAh).

Formally, let

f (\cdot; θ)

denote the predictor. Given the sampled input

x_{t}

at step t, the model outputs

{\hat{y}}_{t}^{rul}

and

{\hat{y}}_{t}^{soh}

, which correspond to the predicted RUL and capacity, respectively. As noted above, both prediction and adaptation at step t use only observations available up to that step.

3.2. Backbone Model and Baseline Setting

As the baseline, we use the same backbone architecture adopted in the representative online transfer learning framework [8]: a CNN–LSTM predictor with two output heads for RUL and SOH, where SOH is represented by capacity. For online battery prognostics under deployment constraints, the input size is fixed: the model [8] always takes 10 sampled recent cycles as input in this work. This setting ensures a fair comparison because all methods use the same input length and the same backbone structure.

Under the representative baseline, the model always receives 10 sampled cycles constructed from a fixed recent-history span, and online adaptation updates only the LSTM parameters while the CNN and prediction heads remain frozen [8]. This baseline is retained here as the reference setting. The two modifications examined in this work are introduced separately in Section 3.3 and Section 3.4.

3.3. Parameter-Efficient Online Personalization

Online fine-tuning can be costly and unstable when only limited target data are available, which is a practical concern for deployment-oriented battery management. To reduce the online update cost and improve stability, we freeze the CNN–LSTM backbone and update only a small set of parameters during online personalization. We achieve this by introducing a lightweight adapter module into the network. The adapter is placed after the LSTM encoder and before the prediction heads, allowing it to adjust the shared latent representation with only a small number of additional parameters. Given the latent feature

h

, the adapter produces

h^{'} = h + W_{u p} σ (W_{d o w n} h),

(1)

where

W_{d o w n} \in R^{d_{a} \times d}

and

W_{u p} \in R^{d \times d_{a}}

, with

d_{a} ≪ d

, and

σ (\cdot)

is a nonlinear activation function. Here, d denotes the feature dimension (hidden size) of the LSTM output, and

d_{a}

denotes the adapter bottleneck dimension.

During online adaptation on a target cell, we minimize a multi-task objective:

L = L_{r u l} + λ L_{s o h} .

(2)

During this process, only the adapter and the auxiliary SOH head are updated, while the backbone and the RUL head remain fixed. The RUL loss is still back-propagated through the shared representation, allowing the adapter to improve RUL prediction without re-tuning the heavy recurrent backbone. As a result, online optimization is restricted to a small set of parameters, which helps limit update cost and reduces the risk of overfitting when target-cell data are limited.

3.4. Adaptive Temporal Windowing

A fixed history window may not be equally suitable for different degradation rates in online battery prognostics. If degradation is fast, a long history may include outdated information and make adaptation less responsive; if degradation is slow, relying only on a short history may introduce noise. We therefore adopt an adaptive temporal window while keeping the model input length fixed.

The mechanism consists of two steps. At each online step, the method first determines the amount of recent history to use, denoted by

W_{t}

, and then converts that history into a fixed-length input through strided sampling, so that the model still receives

T = 10

sampled cycles. In the present implementation, three candidate spans,

{10, 20, 30}

, are used, corresponding to strides

{1, 2, 3}

. To select among them without relying on the model’s own predictions, the recent degradation rate is estimated from measured capacity changes. We then choose a sampling stride:

s_{t} = \{\begin{matrix} 1, & g_{t} \geq τ_{h i g h} (fast degradation) \\ 2, & τ_{l o w} \leq g_{t} < τ_{h i g h} \\ 3, & g_{t} < τ_{l o w} (slow degradation) \end{matrix}

(3)

The most recent

W_{t}

cycles are then selected, and every

s_{t}

-th cycle is sampled, so that the model always receives exactly

T = 10

input cycles. Faster degradation leads to denser sampling of recent history, whereas slower degradation corresponds to a longer effective history span under the same fixed-input requirement.

3.5. Overall Workflow of the Proposed Online Personalization Framework

Figure 1 shows the PEAT workflow under the representative online-transfer setting. The method operates in an offline stage followed by an online stage. Offline, a CNN–LSTM predictor is trained on source cells and then reused for all target cells. Online, the input is constructed from a fixed number of sampled cycles, while the effective history span is adjusted according to recent target-cell behavior. The frozen backbone generates the predictions, and only the lightweight adaptation path is updated. The figure summarizes the workflow corresponding to the design choices described in Section 3.1, Section 3.2, Section 3.3 and Section 3.4.

4. Experiments and Results

PEAT is evaluated on 22 test cells under the same online setting as the representative baseline [8]. The evaluation examines average performance after online adaptation, the associated online update cost, and the effect of per-cell variation together with conservative safeguards on practical deployment.

4.1. Dataset and Setup

We use the same dataset and train–test split as the representative baseline study [8]. It contains degradation trajectories from 77 lithium-ion cells cycled under 77 different multi-stage discharge protocols, while the fast-charging protocol and ambient temperature are kept constant. Following the standard split used in the dataset, 55 cells are used as source cells for offline training, and the remaining 22 cells, which follow unseen discharge protocols, are used as test cells for online evaluation. For each test cell, end-of-life is defined by a capacity threshold, and the RUL target is the number of cycles remaining until that point.

We evaluate these 22 test cells in an online setting. For each cell, we first use a pre-trained CNN–LSTM model to predict RUL and SOH, and then perform online adaptation on the same cell using only the data observed up to that point. We denote the results as Before (without online adaptation) and After (with online adaptation).

To ensure a fair comparison, all methods use the same backbone, the same fixed input length of 10 sampled cycles, and the same training schedule. The comparison differs only in two experimental factors: the online update rule and the way recent history is selected to construct the 10-cycle input. Their detailed definitions have already been provided in Section 3 and are not repeated here.

Four experimental groups are considered under the same online setting: the representative baseline, the full PEAT method, and two component variants in which one of the two constrained design choices is removed. The purpose is not to claim broad generalization across multiple frameworks but to compare how different update and history-selection policies affect online personalization for battery prognostics under the same backbone and fixed-input setting.

Baseline: fixed history span $W = 30$ with stride $s = 3$ (30 cycles → 10 sampled cycles); online fine-tuning updates only the LSTM parameters while keeping the CNN and prediction heads frozen (74,880 trainable parameters) [8].
PEAT (full): adaptive temporal windowing with candidate spans ${10, 20, 30}$ (strides ${1, 2, 3}$ ); parameter-efficient online adaptation updates only the adapter and SOH head while keeping the backbone and RUL head frozen (2,193 trainable parameters).
PEAT without adaptive windowing (A-only): fixed history span $W = 30$ and $s = 3$ ; online adaptation updates only the adapter and SOH head (2,193 trainable parameters).
PEAT without parameter-efficient adaptation (B-only): adaptive temporal windowing with candidate spans ${10, 20, 30}$ ; Ma-style online fine-tuning updates only the LSTM parameters (74,880 trainable parameters).

The full PEAT setting combines both design choices, whereas the last two groups each remove one of them for ablation comparison.

4.2. Metrics

For RUL prediction, we adopt the root mean square error (RMSE), coefficient of determination (

R^{2}

), and mean absolute percentage error (MAPE). RMSE quantifies the average magnitude of prediction errors in the same unit as RUL (i.e., number of cycles), with smaller values indicating better predictive performance.

R^{2}

evaluates the goodness of fit between the predicted curves and the ground-truth trends, with higher values indicating better agreement between the predictions and the experimental observations. MAPE is reported as a percentage and is calculated using the same normalization protocol as in the baseline setting [8]: the absolute prediction error is normalized by a cell-level scalar (i.e., the cycle life corresponding to RUL), thereby ensuring the stability of the metric even when the RUL becomes small near battery end-of-life.

SOH estimation is evaluated using the same three metrics, namely RMSE,

R^{2}

, and MAPE. For MAPE, the absolute capacity-estimation error is normalized by a cell-level scalar, specifically the initial nominal capacity of the battery cell, and is then reported as a percentage.

4.3. Experimental Results for RUL

Table 1 reports the mean RUL results for the 22 test cells. For PEAT, both the pre-update results (Before) and the post-update results (After) are reported under the same evaluation pipeline. For the representative baseline, only the post-update results are available because the original paper reports only the After results (Task A in [8]).

Table 1 shows that, under the same backbone and fixed-input setting, PEAT achieves better average RUL metrics after online adaptation than the representative baseline. This comparison should be read together with the efficiency analysis in Section 4.5, because deployment depends not only on average error but also on the update cost required to obtain that gain. In the present setting, a lighter online update path still preserves the average benefit of personalization, rather than indicating uniform advantage in every aspect.

4.4. Component Study and Complementary Roles

To examine how the two design choices relate to the two deployment bottlenecks identified earlier, we compare PEAT with variants in which one component is removed at a time. Table 2 reports the mean RUL results after online adaptation. Removing adaptive windowing increases the average RMSE to 168.26, while replacing the adapter-based update with Ma-style LSTM updating increases it to 169.30. The full method achieves the best mean RMSE and

R^{2}

among the tested variants, but the more important point for deployment-oriented battery prognostics is that neither design choice alone is sufficient in the current setting.

This pattern is consistent with the roles of the two components. Adaptive windowing mainly addresses temporal-context mismatch by allowing the sampled history to track the recent degradation rate, whereas parameter-efficient adaptation mainly addresses update cost and update risk by limiting the number of trainable parameters used during online adaptation. When only one of these design choices is retained, the remaining bottleneck may still weaken online personalization for part of the test set. The full method should therefore be interpreted less as a claim of synergy and more as evidence that these two deployment bottlenecks are coupled in practice: a lighter update path is more effective when the input context is better matched, and a better-matched context is more useful when the update itself remains controlled.

4.5. Efficiency and Accuracy–Cost Trade-off

Online personalization should be evaluated not only by average prediction accuracy, but also by the update cost required to achieve that gain. Relative to the representative baseline [8], PEAT reduces the number of trainable parameters involved in online updating from 74,880 to 2,193 and decreases the average update time per step from 2.54 s to 2.29 s. For battery-management deployment, this reduction matters because repeated updating must remain computationally manageable if personalization is to be used during operation. Figure 2 places the tested methods on a simple accuracy–cost plane, with online update time on the x-axis and post-adaptation RUL RMSE on the y-axis. Points closer to the lower-left corner correspond to lower average error achieved with less update time. Under this comparison, the full PEAT setting lies closer to that corner than the representative baseline. The purpose of the figure is therefore not to claim an absolute advantage, but to show that the average benefit of personalization is still preserved when the update path is made lighter. For deployment, however, this average trade-off is only a first step; the next question is whether the gain is distributed safely across cells or is accompanied by harmful adaptation in a vulnerable subset.

4.6. Per-Cell Error Change Under PEAT

Average results can mask substantial cell-to-cell variation, which is critical for battery-management decisions based on online prognostics. To make this variation explicit, we examine the change in RMSE for each cell under PEAT. For a given cell, we define

Δ

RMSE as RMSE(After) minus RMSE(Before). A negative

Δ

RMSE indicates that online adaptation reduces the error, whereas a positive value indicates that it increases the error.

Figure 3 shows the

Δ

RMSE values for the 22 cells. The full method reduces RMSE in 14 cells and increases RMSE in 8 cells. At the cell level, the gain is not uniform: cells with larger errors before adaptation tend to benefit more from personalization, whereas cells that are already predicted reasonably well are more likely to deteriorate after updating. Online personalization should therefore not be treated as a uniform update step for all cells in battery prognostics.

The full RUL trajectories of the 22 test cells are further visualized in Figure 4. The figure shows the ground-truth and predicted RUL curves before and after online adaptation, with the cells ordered by

Δ

RMSE. This visualization links the average result to trajectory-level changes and provides context for the robustness analysis in Section 4.7 and the case studies in Section 4.8.

4.7. Robustness Analysis of Conservative Online Updating

An additional robustness study is conducted with a conservative online update policy, without changing the main PEAT design. This policy combines an update trigger, hold-out early stopping, and rollback. Section 4.6 shows that average improvement does not ensure safe personalization at the cell level. Relative to the no-adaptation reference used in the per-cell analysis, the original PEAT reduces the RUL RMSE on 14 of the 22 test cells but still increases it on the remaining 8. Its average RUL RMSE decreases from 168.10 to 160.58, whereas the worst-case degradation reaches 52.69.

To this end, we introduce a conservative online updating strategy that combines an update trigger, hold-out early stopping, and rollback. Online adaptation is activated only when the pre-update capacity mismatch exceeds a threshold calibrated on source-side validation cells. Once adaptation is triggered, the current target chunk is divided into an adaptation subset and a hold-out validation subset, and early stopping is monitored on the latter. If the post-update validation mismatch does not improve sufficiently, the model is rolled back to its pre-update parameters. This design leaves the basic PEAT mechanism unchanged, but makes the online updating policy more selective in deployment-oriented battery prognostics.

Table 3 summarizes the comparison between the original PEAT and Robust PEAT. Robust PEAT achieves an average RUL RMSE of 162.91, which is slightly higher than the 160.58 obtained by the original PEAT, indicating that part of the average gain is sacrificed. The number of degraded cells relative to the no-adaptation reference decreases from 8 to 6, one cell becomes unchanged, and the worst-case degradation is reduced from 52.69 to 35.22. Compared with the original PEAT, Robust PEAT gives up part of the average gain in exchange for fewer harmful updates and lower worst-case degradation.

Figure 5 presents a cell-level comparison between the original PEAT and Robust PEAT. Cells below the diagonal have lower RUL RMSE under the conservative policy, whereas cells above the diagonal lose part of the larger gains achieved by the original PEAT. The distribution shows that Robust PEAT does not improve all cells uniformly. Instead, its benefit is concentrated on cells that are more vulnerable to harmful adaptation.

Figure 6 shows the per-cell change in RUL RMSE relative to the no-adaptation reference. Relative to the original PEAT, the conservative variant shortens the positive tail of the

Δ

RMSE distribution and shifts some degraded cells to neutral or improved outcomes. This pattern matches the reduction in degraded cells from 8 to 6 and the decrease in worst-case degradation from 52.69 to 35.22.

The average SOH RMSE decreases from 5.74 to 4.18 for the original PEAT and further to 3.58 for Robust PEAT, while the number of cells with improved SOH RMSE increases from 16 to 20. These changes suggest that the capacity-based trigger and rollback mechanism also helps stabilize the auxiliary SOH output, in addition to the RUL prediction.

Figure 7 reports the chunk-level statistics associated with this behavior. Among the 2036 total chunks, 1006 are skipped by the trigger, 987 are updated and retained, 34 are rolled back after adaptation, and 9 short chunks are not updated. The counts show that online updating is not activated for nearly half of the chunks, and that only a small fraction of attempted updates are later rejected. These results suggest that online personalization does not need to be performed at every opportunity. Instead, a selective policy can retain much of the average benefit while reducing exposure to harmful updates.

The robustness analysis is included because deployment-oriented evaluation in battery prognostics depends on more than average performance alone. Under the same backbone setting, lightweight online personalization improves the average result and supports a more selective update policy, with lower worst-case degradation and reduced risk of harmful adaptation.

4.8. Case Studies

Figure 4 includes cells that illustrate both post-adaptation improvement and deployment risk. Figure 8 corresponds to a cell with clear improvement. For cell 7-5, the RMSE decreases from 152.93 (Before) to 110.79 (After). After adaptation, the predicted curve follows the ground-truth trend more closely. This cell is consistent with the pattern noted in Section 4.6, where online personalization is more helpful when the pre-adaptation mismatch remains large.

Figure 9 corresponds to a cell whose prediction error increases after online adaptation. For cell 6-8, the RMSE rises from 225.07 (Before) to 277.75 (After). The local trajectory appears noisier and may not be fully captured by the recent input context, so even a lightweight online update may move the shared representation in an unfavorable direction when only limited observations are available. Together, these two cells illustrate the broader per-cell heterogeneity reported in Section 4.6 and help explain why the conservative update policy in Section 4.7 is needed.

4.9. SOH Results and Trade-off

Table 4 indicates a limitation of the present deployment-oriented design. The full method improves its own average SOH RMSE after online adaptation, from 5.74 to 4.18, but this value remains higher than the After SOH RMSE reported in the representative baseline study (2.57). This result suggests that the shared lightweight adaptation path does not optimize RUL and SOH equally well. In the current pipeline, SOH mainly serves as an auxiliary signal that stabilizes the online update for RUL-oriented personalization rather than as the primary optimization target. This comparison indicates a remaining multi-task imbalance: the design choices that make online RUL adaptation lighter and more controllable do not necessarily produce the best standalone SOH result. A more task-aware weighting strategy or a partially decoupled update path may help reduce this gap, but these options are not studied in the present work.

4.10. Discussion

Under the fixed-backbone and fixed-input setting, PEAT does not aim to replace existing RUL predictors with a universally superior model. Its role is to provide a lighter online update path when a pre-trained global model remains mismatched to a target cell. In battery management, average improvement is meaningful only when it is obtained with manageable update cost and acceptable adaptation risk. The cell-level results further show that the gain is conditional rather than universal: cells with larger pre-adaptation mismatch tend to benefit more, whereas cells that are already well tracked or locally noisy may deteriorate after updating.

These results are better interpreted as trade-offs than as uniform dominance. Adaptation benefit, update cost, and the risk of harmful updates need to be considered together. Section 4.5, Section 4.6 and Section 4.7 show that PEAT improves the first two on average under the same basic setting, while the conservative variant in Section 4.7 reduces the third through selective updating. The SOH results add a further boundary condition: the shared lightweight adaptation path does not support RUL and SOH equally well. A deployment-ready personalization scheme for battery prognostics therefore requires lightweight adaptation together with update triggering, rollback control, and more careful multi-task balancing.

5. Conclusions

This work addresses a practical issue in deployment-oriented battery prognostics: how to make personalization less burdensome under a representative CNN–LSTM online-transfer setting without changing the backbone or fixed input length. The experiments suggest that this goal can be achieved to a useful but limited extent. PEAT reduces the number of trainable parameters involved in online updating, slightly shortens the per-step update time, and still improves the average RUL result after adaptation. At the same time, the evaluation shows that average improvement alone is not sufficient for battery-management deployment: some cells still deteriorate after updating, and the conservative variant indicates that part of the average gain can be traded for lower worst-case degradation and fewer harmful updates. These results indicate that under the same baseline setting, online personalization can move toward a better balance among accuracy benefit, update cost, and adaptation risk. The remaining SOH gap further indicates that more selective updating and better coordination between tasks are still needed.

Author Contributions

Conceptualization, D.R. and X.-L.X.; methodology, D.R. and X.Z.; software, X.Z.and Z.Y.; validation, X.Z.and Z.Y; formal analysis, D.R.; investigation, D.R.; writing—original draft preparation, X.Z.; writing—review and editing, D.R. and X.-L.X.; visualization, D.R.; supervision, X.-L.X.; project administration, X.-L.X.; funding acquisition, X.-L.X. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data Availability Statement: The HUST dataset used in this study is publicly available in Mendeley Data at DOI: 10.17632/nsc7hnsg4s.2. The dataset was used in accordance with the corresponding usage terms. The representative baseline study used for comparison is cited in Ref. [8].

Acknowledgments

The authors would like to thank Mingyuan Peng from Zhejiang Tailong Commercial Bank Co., Ltd. for his valuable guidance on key steps of data cleaning and feature engineering.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Overview of the proposed online personalization framework based on a representative online transfer learning baseline.

Figure 2. Accuracy–cost trade-off. The x-axis represents the online update time, and the y-axis represents the RUL RMSE after online adaptation.

Figure 3. Per-cell change in RUL RMSE under the full method.

Δ

RMSE = RMSE(After) − RMSE(Before); negative values indicate improvement.

Figure 3. Per-cell change in RUL RMSE under the full method.

Δ

RMSE = RMSE(After) − RMSE(Before); negative values indicate improvement.

Figure 4. Qualitative RUL predictions for all 22 test cells (sorted by

Δ

RMSE under PEAT). Each panel shows the ground-truth RUL curve and the predictions before (pre-trained) and after (online-adapted) personalization. The cells are ordered from the largest improvement (most negative

Δ

RMSE) to the largest degradation (most positive

Δ

RMSE).

Figure 4. Qualitative RUL predictions for all 22 test cells (sorted by

Δ

RMSE under PEAT). Each panel shows the ground-truth RUL curve and the predictions before (pre-trained) and after (online-adapted) personalization. The cells are ordered from the largest improvement (most negative

Δ

RMSE) to the largest degradation (most positive

Δ

RMSE).

Figure 5. Cell-level RUL RMSE comparison between the original PEAT and Robust PEAT. The diagonal marks equal performance; points below it have lower RUL RMSE under Robust PEAT.

Figure 6. Per-cell change in RUL RMSE relative to the no-adaptation reference for the original PEAT and Robust PEAT. Negative values denote improvement after online adaptation, and positive values denote degradation relative to the reference.

Figure 7. Chunk-level decision distribution under Robust PEAT, including chunks skipped by the trigger, updated and retained, rolled back after adaptation, and short chunks not updated.

Figure 8. Case study (improvement). RUL prediction for cell 7-5 before and after online adaptation under the full method.

Figure 9. Case study (degradation). RUL prediction for cell 6-8 before and after online adaptation under the full method.

Table 1. Comparison of RUL results over 22 test protocols/cells. Baseline After values are from [8]; the corresponding Before results are not reported there.

	Before			After
Method	RMSE ↓	$R^{2} ↑$	MAPE (%) ↓	RMSE ↓	$R^{2} ↑$	MAPE (%) ↓
Ma et al. (2022) baseline [8]	–	–	–	186.00	0.804	8.72
PEAT (Full)	168.10	0.8451	8.22	160.58	0.8588	7.69

Table 2. Component study of RUL results (After only, mean over 22 test protocols/cells). The baseline values are quoted from [8].

Method	RMSE ↓	$R^{2} ↑$	MAPE (%) ↓
Ma et al. (2022) baseline [8]	186.00	0.804	8.72
PEAT without adaptive windowing	168.26	0.8556	8.05
PEAT without parameter-efficient personalization	169.30	0.8472	8.07
PEAT (Full)	160.58	0.8588	7.69

Table 3. Robustness comparison between the original PEAT and the conservative online updating variant (Robust PEAT). Panel (a) reports cell-level RUL stability relative to the no-adaptation reference. Negative mean

Δ

RMSE values indicate lower average RUL error than the reference, whereas positive worst

Δ

RMSE values indicate the most severe degradation case. Panel (b) summarizes the auxiliary SOH performance and the chunk-level update behavior of Robust PEAT.

Table 3. Robustness comparison between the original PEAT and the conservative online updating variant (Robust PEAT). Panel (a) reports cell-level RUL stability relative to the no-adaptation reference. Negative mean

Δ

RMSE values indicate lower average RUL error than the reference, whereas positive worst

Δ

RMSE values indicate the most severe degradation case. Panel (b) summarizes the auxiliary SOH performance and the chunk-level update behavior of Robust PEAT.

(a) RUL and stability summary
Method	RMSE ↓	$R^{2} ↑$	Improved cells	Degraded cells	Mean $Δ$ RMSE vs. no-adaptation reference	Worst $Δ$ RMSE vs. no-adaptation reference
No-adaptation reference (Before)	168.10	0.8451	–	–	0.00	0.00
PEAT	160.58	0.8588	14/22	8/22	-7.51	52.69
Robust PEAT	162.91	0.8535	15/22	6/22	-5.19	35.22
(b) SOH summary
Method			SOH RMSE ↓	$R^{2} ↑$	Improved SOH cells
No-adaptation reference (Before)			5.74	0.9953	–
PEAT			4.18	0.9972	16/22
Robust PEAT			3.58	0.9980	20/22

In Panel (a), Robust PEAT has one unchanged cell relative to the no-adaptation reference. Chunk-level update behavior of Robust PEAT: 2036 total chunks; 1006 chunks skipped by the trigger; 987 chunks updated and retained; 34 chunks rolled back after adaptation; and 9 short chunks not updated.

Table 4. SOH results (mean over 22 test protocols/cells). Baseline After values are from [8]; the corresponding Before results are not reported there.

	Before			After
Method	RMSE ↓	$R^{2} ↑$	MAPE (%) ↓	RMSE ↓	$R^{2} ↑$	MAPE (%) ↓
Ma et al. (2022) baseline [8]	–	–	–	2.57	0.999	0.176
PEAT (Full)	5.74	0.9953	0.420	4.18	0.9972	0.294

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