Deep learning to estimate lithium-ion battery state of health without additional degradation experiments

Lithium-ion batteries are widely deployed due to high energy density and responsiveness, but their components degrade over time, causing capacity and power fade. Accurate estimation of state of health (SOH), often defined as present capacity relative to initial capacity, is vital for safe and efficient battery management but cannot be directly measured during operation. Traditional SOH estimation relies on lifelong degradation experiments and labeled data from the target battery type, which are time- and resource-intensive and impractical for rapid technology iteration. Feature-engineered methods and recent deep neural networks can map operating data to SOH, but both typically require target-labeled data. Transfer learning alleviates data needs by fine-tuning with some target labels, yet still demands substantial target-domain labeling (often 25–30% of life), keeping the experimental burden. Unsupervised domain adaptation in other fields shows that models can learn domain-invariant features without target labels. Motivated by this, the study asks whether SOH can be accurately estimated across different battery types without any target labels by leveraging domain adaptation and ensemble deep learning.

Prior SOH estimation approaches extract engineered features—electrical, electrochemical, acoustic, mechanical, and thermal—and map them to SOH, but require extensive labeled degradation data for each target battery. Deep neural networks have shown strong performance by learning features from raw charging data, yet still depend on target-domain labels. Transfer learning methods for SOH using retraining or fine-tuning reduce but do not eliminate labeled target data needs, typically requiring at least 25–30% labeled life data. In contrast, label-agnostic cross-domain learning using domain adaptation has been successful in visual recognition, where models jointly optimize for prediction and domain invariance. For LIB SOH, methods without target labels are rare; recent works explore domain adversarial or multi-source adaptation but still often leverage some labels or differ in setup. The paper positions its contribution as a target label-agnostic SOH estimation framework combining domain adaptation with a swarm of DNNs, and addresses issues like source–target distribution mismatch and source distribution skewness.

Framework: A swarm of deep neural networks (DNNs) is trained with domain adaptation to transfer knowledge from a labeled source dataset to an unlabeled target dataset. Each DNN shares the same architecture and hyper-parameters but different random initialization; their outputs are later filtered and averaged for reliable SOH estimation. Input and preprocessing: Partial charging curves (capacity vs. voltage segments) from constant-current charging are used as inputs. For both source and target domains, curves are normalized by nominal capacity and gridded over a voltage sampling window with 10 mV intervals. In cross-dataset validation, a 500 mV window is used: 3.5–4.0 V for datasets #1–#4 and 3.1–3.6 V for dataset #5. Architecture: The input sequence is processed by stacked 1D CNN layers to extract feature vectors. For source samples, flattened features feed a shared terminal fully connected (TFC) layer to regress SOH. For target samples, flattened features first pass through a middle fully connected (MFC) layer to reconstruct features, which then feed the same TFC for SOH pre-estimates. ReLU activations follow all convolutional and fully connected layers; a sigmoid scales outputs to [0,1]. All DNNs use He initialization. Domain adaptation and loss: Training jointly minimizes (i) source-domain SOH regression loss (mean squared error between predictions and labels), (ii) maximum mean discrepancy (MMD) between source features and reconstructed target features to encourage domain invariance (Gaussian kernel), and (iii) target-domain first-cycle regression loss assuming SOH=1 for fresh cells (first-cycle partial charging curves are assumed available). The composite loss E uses weights k1=1, k2=0.1, k3=1. Source distribution trimming: To mitigate source–target distribution mismatch and domain imbalance effects, the source SOH label distribution is trimmed to reduce skewness. Source samples are binned by SOH (bin width 2%); an optimization selects the number of remaining samples per bin to (a) drive skewness toward zero and (b) discard as few samples as possible, with constraints to keep a comparable range and a unimodal distribution, and to bound inter-bin count differences (epsilon 4.5%). This yields a more balanced source domain before training. Training protocol: N=300 DNNs are trained independently using Adam (learning rate 0.001), mini-batch size 20, on an NVIDIA Tesla V100 GPU. In each sub-training, two-thirds of source samples form the training set and one-third the validation set. Early stopping occurs when both training and validation RMSE drop below 5% or after 2000 epochs (minimum 500 epochs). Estimation (inference) and model selection: For a target batch, all trained DNNs produce SOH pre-estimates. Due to training variability, performance is diverse; the framework selects DNNs whose pre-estimate means are in the upper quartile and standard deviations in the lower quartile across the swarm. The final SOH estimate is the average of selected DNN outputs. Analysis shows strong negative correlation between mean and RMSE and positive correlation between standard deviation and RMSE, justifying this unsupervised selection. Data and validation design: Five datasets from distinct manufacturers and chemistries (LCO, LCO/NCO blend, NMC, NCA, LFP) totaling 65 cells and 71,588 samples are used. Two datasets (#3 PANASONIC, NCA/Graphite; #5 GOTION, LFP/Graphite) are generated in-house; three are public (CALCE, SANYO, KOKAM). Cross-dataset experiments pair each dataset as source/target, yielding 20 combinations. Each combination is tested under four target SOH lower bounds (95%, 90%, 85%, 80%), simulating varying degradation levels without target labels, totaling 80 cases. Impact of voltage window and hyper-parameters is analyzed in supplementary notes. Battery cycling protocols for in-house datasets: #3 charged CC 0.3C to 4.2 V then CV to 0.03 A; discharged at 2C; #5 charged CC 1C to 3.65 V then CV to 1.35 A; discharged at 1C; tests at 20°C and 45°C, respectively; charging curves extracted from CC phase.

- The framework achieves accurate cross-dataset SOH estimation without any target labels: absolute error <3% for 89.4% of samples and <5% for 98.9% of samples; maximum absolute error <8.87% across 71,588 samples and 80 cases. - Trimming the source SOH distribution improves performance: maximum absolute error reduced from 10.09% (no trim) to 8.87% (trim), and the proportion of large errors (>5%) decreases markedly. - Compared to traditional methods without target labels (GPR, RF, SVR, CNN), which show MAE >5.01% and maximum absolute error >17.91%, the proposed framework reduces MAE and maximum error by more than half; overall MAE ≤1.43% and maximum absolute error ≤8.87% without target labels. - Computational efficiency: with a swarm size of 300, training time is about 0.7 hours, avoiding thousands of experimental hours (datasets require roughly 644–8473 hours to generate labeled degradation data). - Ablations: Removing swarm-driven selection or domain adaptation (or both) degrades performance to levels comparable to existing methods, confirming both components are critical. - Swarm analysis: Pre-estimate RMSEs across DNNs are widely distributed before selection (some >10%); selecting DNNs by high mean and low standard deviation tightens RMSE bandwidth to ~4% and drops mean RMSE to ~2%. - Explanation maps show domain adaptation mitigates feature attribution discrepancies across datasets, enabling accurate transfer; without adaptation, strong misattributions near LFP voltage plateaus cause overestimation. - Hyper-parameters: Increasing swarm size improves accuracy; size ≥50 suppresses MAE below ~2%. ReLU outperforms Tanh, Sigmoid, and LogSigmoid. Multiple CNN layers help; channels fewer than 128 suffice for high accuracy.

The study demonstrates that accurate SOH estimation across different battery types is feasible without target-domain labels by combining domain-invariant feature learning with a swarm-based estimator selection. This directly addresses the bottleneck of needing costly target degradation experiments and enables rapid deployment of SOH estimators for new chemistries or manufacturers using only existing labeled datasets. Domain adaptation aligns feature representations between source and target, as evidenced by explanation maps that show reduced cross-domain discrepancies and improved estimates. The swarm-driven strategy leverages training variability to form a reliable committee, with unsupervised selection based on mean and variance of predictions correlating strongly with true RMSE, enabling robust aggregation without labels. Compared to standard regressors or single CNNs, the approach halves error metrics in target label-agnostic settings and essentially eliminates the need for thousands of experimental hours, highlighting significant practical relevance for battery management systems and data-driven health monitoring.

The paper introduces a deep learning framework for lithium-ion battery SOH estimation that operates without target-domain labels. It integrates domain adaptation within a DNN architecture and aggregates predictions from a swarm via unsupervised selection to yield reliable estimates. Validated across 65 cells, five manufacturers, and 80 cross-dataset cases, the method attains absolute errors <3% for 89.4% of samples and <5% for 98.9%, with a maximum error <8.87%, outperforming common baselines in unlabeled settings and doing so with minimal training time. The work provides insights into the roles of domain adaptation and ensemble selection, offers guidance on hyper-parameter choices (e.g., swarm size, activation functions, CNN depth), and proposes source distribution trimming to reduce skewness and improve transfer. Future work includes extending inputs and targets to other signals and SOH metrics, advancing trimming strategies, and scaling to large real-world BMS datasets that typically lack labels.

- As a data-driven approach, performance depends on the representativeness of the source domain; while trimming mitigates skewness, optimal trimming strategies could be further developed. - The framework assumes availability of first-cycle target data with SOH=1 to aid adaptation; scenarios lacking such data may require alternative constraints. - Validation uses partial charging curves under controlled CC conditions; although the framework is input-agnostic, performance on other signals or duty cycles requires further evaluation. - Hyper-parameter choices and selection thresholds (quartiles) are empirically determined; adaptive or theoretically optimized criteria could further improve robustness. - Real-world deployment on large, noisy field datasets is proposed but not demonstrated; robustness to sensor noise and operational variability remains to be fully assessed.