3.1.1 Support vector machine (SVM)-based

SVM exhibits excellent generalization capabilities for small sample sizes, nonlinearities, and high-dimensional data. Its introduction to battery SOH assessment dates back to the early 2000s [59]. Using kernel functions, SVM projects data into a high-dimensional feature space. Subsequently, it constructs either an optimal separating hyperplane for classification or a regression function, designated as support vector regression (SVR), for SOH estimation [72]. In recent years, ever-increasing requirements for estimation accuracy, robustness, and engineering practicality have become the primary drivers of SVM research. These requirements have propelled the field beyond single-model applications. Instead, the current trend is toward deep integration of SVM with optimization algorithms, electrochemical mechanisms, and DL. The field thus continues its forward progress [73]. The overall framework of the SVR-based LIB SOH estimation method is illustrated in Figure 3.

Figure 3 Framework for SVM-based SOH estimation

To improve SVR performance using optimization algorithms, research has focused on intelligent strategies for automatically tuning two key SVR parameters: the penalty factor ϲ and the kernel function parameter γ. This line of research aims to overcome the limitations of traditional grid search methods, including low efficiency and a tendency to fall into local optima. Several representative studies illustrate this progress. Zhi et al. [74] developed a GA-Particle Swarm Optimization (PSO)-SVR hybrid optimization algorithm. This algorithm combines the strengths of the GA and PSO to optimize SVR parameters. On the NASA dataset, their method achieved higher estimation accuracy and faster convergence. In a similar vein, Li et al. [73] introduced the Ant Lion Optimizer (ALO). Comparative experiments showed that the ALO outperformed both grid search and GA-optimized benchmark models. Furthermore, Xing et al. [75] proposed an Improved Aquila Optimizer (IAO) to avoid local optima. This improvement enhanced the generalization capability and prediction accuracy of the SVR model when handling complex battery degradation patterns.

In the domain of model structure innovation and multi-model fusion, modifications to the SVM structure have been made to improve estimation stability and to address practical challenges such as battery pack inconsistency. A representative approach is the ensemble SVR model proposed by Guo et al. [76]. The outputs of multiple SVR submodels are integrated, effectively smoothing the estimation error of a single submodel. As a result, both overall accuracy and robustness are significantly enhanced. This ensemble strategy suggests that structural design aimed at greater model fault tolerance and adaptive capability represents an important direction for the engineering application of SVM.

In the context of combining battery-mechanism features for enhanced interpretability, research efforts have focused on integrating SVM with the physical characterization of battery aging. For instance, ICA-derived peak and area features were employed as SVM inputs in [77, 72], effectively combining physical interpretability with data-driven modeling. An effective connection is established between data-driven methods and electrochemical mechanisms.

Furthermore, with the rise of DL, SVM has been combined with Deep Neural Network (DNN) architectures to form complementary hybrid models. A Residual Network-SVR (ResNet-SVR) model was constructed in [78]. This model uses ResNet to extract high-dimensional temporal features and then feeds them to SVR for regression, combining the advantages of deep feature extraction with the generalization capability of shallow models on small samples. A comprehensive solution was developed that combines a Diffusion Convolutional Recurrent Neural Network (DCRNN) with SVM-RFE for feature selection and SOH prediction [79]. These fusion models indicate that SVM serves as a core component within more complex intelligent estimation frameworks, continuously expanding its application boundaries.

In summary, SVM for battery SOH estimation has evolved from early direct applications into a diverse system centered on optimization, fusion, and mechanism integration. Its advantages in handling small-sample and nonlinear problems enable continuous renewal by integrating it with optimization algorithms, ensemble strategies, and deep networks. Future directions include lightweight hybrid models, online updates, and embedding into onboard BMS for reliable real-time health management, paving the way for large-scale engineering applications. A systematic comparison of the above methods is presented in Table 4.

3.1.2 Gaussian process regression-based

GPR is a nonparametric Bayesian model widely used for battery SOH estimation. It provides both point predictions and full probability distributions, which are essential for uncertainty assessment and risk management. The performance of GPR is determined by its mean function and covariance function, where the kernel defines the similarity between data points and thus shapes the capacity degradation curve. Efforts to improve the performance of GPR for estimation focus on three aspects: feature engineering, model structure improvements, and optimization strategies. The overall technical workflow is depicted in Figure 4.

Figure 4 Framework for GPR-based SOH estimation

At the feature engineering level, research focuses on extracting features that are strongly correlated with battery aging and readily obtainable online. Traditional methods directly extract HFs from charge-discharge curves. However, these approaches suffer from high dimensionality and redundancy. To address these limitations, various feature selection and dimensionality reduction techniques have been introduced. To illustrate, Qian et al. [80] reported a strategy where features were first extracted from DTV curves under CC–CV charging conditions, followed by the application of canonical correlation analysis (CCA) to remove redundant information and improve feature quality. Reddy et al. [81] extracted a larger set of 26 features from charge-discharge curves, and PCA was then employed to reduce this set to three key dimensions for a GPR model. Furthermore, Chen et al. [82] accounted for the complexity of real-world applications. Multiple indirect health factors were jointly extracted from the stages of CC charging, CV charging, and CC discharging, while also considering the effect of temperature on aging. Dimensionality reduction was performed with SCC and PCC, resulting in a more robust input set for the model. Beyond these efforts, more advanced work has explored novel feature sources. The DRT method was adopted in [83] to extract effective features from EIS. Another notable contribution comes from Zhou et al. [84], who innovatively derived HFs from the geometric shape of mid- to high-frequency EIS Nyquist plots. This approach circumvents the time-consuming and unstable nature of traditional low-frequency EIS testing.

At the model structure improvement level, research aims to enhance GPR's ability to model complex degradation patterns, such as long-term trends and local regeneration. To address the limitations of a single kernel in capturing mixed patterns, Wang et al. [85] proposed a composite kernel. This kernel combines a linear kernel with a square-exponential kernel to capture long-term decay and fluctuations. Furthermore, to overcome the limitations of a single GPR model, Yang et al. [86] developed a hybrid framework integrating a DNN with GPR. In this framework, the DNN leverages its powerful nonlinear mapping capabilities to learn deep representations from heterogeneous, multi-source features, such as IC curves, IR, and discharge energy. These representations are then fed into GPR for probabilistic estimation, enabling a more comprehensive characterization of the aging mechanisms.

At the optimization strategy level, research focuses on automated model configuration to improve performance and efficiency. The choice of kernel functions and hyperparameters critically determines GPR performance, yet manual tuning is time-consuming and experience-dependent. To address this issue, Chen et al. [87] proposed an evolutionary framework based on encoding strategies and GA to automatically discover optimal combinations and configurations of the GPR kernel. Zhao et al. [88] introduced a chaos-enhanced metaheuristic algorithm to optimize GPR hyperparameters. Binary variables are used for feature selection. The proposed solution effectively avoids the local-optimal trap of traditional optimization algorithms while achieving joint optimization of feature subsets and model parameters.

Despite significant progress, GPR-based methods still face several common challenges. For example, the robustness of most models needs further validation in complex scenarios, such as varying temperature conditions, missing early-cycle data, or weak correlations between early-cycle features and SOH. In addition, the generalization of models trained on specific battery data to other battery types remains an area for improvement. A detailed comparison of the methods is shown in Table 5. Future research trends may focus on developing more adaptive online learning GPR frameworks, exploring physics-informed semi-physical GPR models, and leveraging transfer learning to enhance cross-battery generalization, thereby promoting more reliable application of GPR in onboard BMS.

3.1.3 Ensemble learning and sparse probabilistic model-based

Beyond SVM and GPR, other ML paradigms have been explored, among which ensemble learning and sparse probabilistic models demonstrate unique value. Ensemble methods combine multiple weak learners to enhance prediction robustness and nonlinear fitting capability, while sparse probabilistic models seek model sparsity and probabilistic output within a Bayesian framework. Although fewer in number than mainstream approaches, they provide useful supplements for addressing specific challenges in data-driven SOH or remaining useful life (RUL) prediction. The complete technical framework is shown in Figure 5.

Figure 5 Framework for SOH estimation based on ensemble learning & sparse probabilistic models

Ensemble learning methods, such as random forest (RF) and gradient boosting machine (GBM), have attracted widespread attention for their excellent ability to handle high-dimensional features and nonlinear relationships. A key advantage of these methods is their ability to automatically evaluate feature importance while maintaining good tolerance to data noise. CatBoost is an effective implementation of a gradient-enhanced decision tree framework, which uses techniques such as ordered enhancement and symmetric tree structure to effectively alleviate gradient bias and overfitting. It demonstrates strong performance on multi-dimensional datasets. For example, Yin et al. [89] proposed a complete pipeline that includes feature compression, interpolation, and regularisation. They fed the processed health factor sequences into a CatBoost model. This approach achieved excellent predictive accuracy (R² > 0.98) on public datasets and demonstrated robustness in noisy environments. Zhang et al. [90] made a further advancement in feature engineering. They integrated multi-domain features, including time-domain, frequency-domain, and entropy features. They then applied discriminant correlation analysis (DCA) for dimensionality reduction. Furthermore, the CatBoost hyperparameters are optimized with the Sparrow Search Algorithm (SSA). This strategy significantly improved the generalization of cross-battery SOH prediction. RFs have been applied in real-world scenarios due to three factors: ease of implementation, ability to handle heterogeneous data, and a certain degree of interpretability. Mawonou et al. [91] utilized seven years of real-world electric vehicle operating data to build an RF-based data-driven aging predictor, which achieved an average error of 1.27%. The model mechanisms were also used to rank and analyze key factors affecting aging. However, ensemble learning methods are black-box models that cannot quantify uncertainty in their predictions. This limitation restricts their direct application in battery safety management scenarios that require risk assessment.

In contrast to GPR, the relevance vector machine (RVM) offers a sparser Bayesian solution: it retains only a small subset of relevance vectors, enabling faster online inference for embedded deployments—at the cost of higher training complexity and kernel sensitivity. However, RVM performance heavily depends on the choice of kernel functions and hyperparameters, and its training is computationally expensive. To optimize its performance, Chen et al. [92] introduced the Bat Algorithm (BA) to automatically optimize the RVM kernel parameters and constructed a dynamic ensemble framework comprising multiple RVMs with wavelet kernels as sub-models. The framework fuses sub-models by dynamically updating their weights, improving the accuracy and generalization of online SOH estimation. To address the complex degradation patterns caused by cell inconsistency within battery packs and the burden of separately estimating SOH and RUL, Lyu et al. [93] proposed a unified RVM-based framework. They constructed a hybrid kernel RVM (HKRVM) that integrates global and local kernels and employed a Genetic Gray Wolf Optimizer (GGWO) to determine optimal kernel parameters and weights. In addition, the metabolic extreme learning machine (MELM) was introduced to synergistically predict SOH and RUL probabilities. Despite the theoretical advantages of RVM in sparsity and probabilistic output, its complex training and tuning process, along with uncertainty regarding its performance advantage on real-world battery data. This is the main reason it has not been as widely adopted as GPR.

In summary, ensemble learning methods such as CatBoost and RF perform strongly at mining complex feature interactions and handling noisy real-world data, but their black-box nature and lack of uncertainty quantification are major drawbacks. Sparse probabilistic models such as RVMs offer uncertainty quantification and fast inference, making them suitable for embedded scenarios, yet their application is limited by high training costs and complex hyperparameter tuning. In the future, key directions for advancing these two types of methods in battery health management may include exploring hybrid architectures that combine the predictive power of ensemble learning with the uncertainty quantification advantages of probabilistic models, or developing more efficient adaptive RVM training algorithms. A detailed comparison of the two types of methods is presented in Table 6.

To present an intuitive comparison, Table 7 groups the aforementioned representative traditional ML methods by dataset and error metric.

Traditional ML methods remain effective when data are scarce. SVM and GPR are preferred in small-sample settings due to their simple architecture and strong regularisation, but they extrapolate poorly beyond the training range. For cross-battery transfer, GPR learns generic degradation patterns via automatic relevance determination kernels. SVM, in contrast, overfits to battery-specific features and transfers poorly. Random forest handles cell-to-cell variability moderately well through its feature importance mechanism. Extreme conditions like low temperature, fast charging, or deep discharge are problematic for all traditional ML methods, as such data are rarely available for training, and the feature-SOH relationships change substantially. Overall, traditional ML suits stable operating profiles with well-understood degradation. For dynamic or extreme conditions, physical priors or transfer learning are necessary to improve performance.

3.2.1 Convolutional Neural Network (CNN)-based

CNNs are built on three principles: local connectivity, weight sharing, and hierarchical stacking. With inherent strengths in local feature extraction, temporal information mining, and parameter-efficient learning, CNNs have become a core component of data-driven methods for battery SOH estimation. Based on six representative studies, CNN-based SOH estimation has evolved into three paradigms: hybrid architectures for deep feature mining, end-to-end lightweight modeling, and mechanism integration with engineering validation. These paradigms cover high-accuracy estimation, practical deployment, and reliability assurance.

The hybrid architecture paradigm for deep feature mining centers on integrating local feature extraction with global dependency modeling. Within this paradigm, CNNs typically function as front-end modules in hybrid networks, working in conjunction with models such as transformers and Long Short-Term Memory (LSTM) networks to achieve high-accuracy SOH estimation across multi-scale data. When processing raw time-series data from a single unit, one-dimensional (1D) convolution captures local features, including voltage fluctuations and current ripples, thereby providing structured input to the transformer [99]. In battery pack scenarios, CNNs are combined with PCA for dimensionality reduction and feature aggregation, enabling the extraction of spatiotemporal correlations from multi-source features that serve as branched inputs to enhance the model's representation [100]. For high-precision tasks involving fused sensor data, CNNs convert multi-physical images into high-dimensional feature representations and collaborate with GPR to jointly estimate SOH and state of charge (SOC) [101]. Finally, within systematic automated modeling frameworks, CNNs are cascaded with improved LSTM networks to extract both local spatial features and long-term temporal dependencies, thereby enabling the joint prediction of SOH and RUL [102].

The end-to-end lightweight modeling paradigm prioritizes engineering practicality by establishing a direct mapping from raw data to SOH via lightweight networks. In this way, it avoids both manual feature engineering and complex preprocessing. A representative example comes from Tian et al. [103], who employed a CNN that directly takes raw charging-voltage sequences of arbitrary duration and starting point as input. Using deep 1D convolutions, the network autonomously learns hierarchical features and simultaneously outputs core indicators, such as maximum and remaining capacity. When compared with hybrid architectures, this paradigm requires less data and adapts well to fragmented charging profiles and non-standardized collection scenarios. Therefore, it offers a lightweight solution that is well-suited for large-scale SOH estimation deployment.

The mechanism integration and engineering bou-ndary validation paradigm addresses the blind decision-making that often accompanies data-driven models and places particular emphasis on the reliability of CNNs. In this paradigm, CNNs function as classic health feature extractors. Through tests that involve various fast-charging aging strategies and deep aging stages, researchers have clarified where CNNs offer generalization advantages, specifically in mild aging stages, and where their limitations emerge, namely in deep aging scenarios. These findings establish guidelines for the application of data-driven methods [104]. In a related effort, Li et al. [101] integrated a CNN with a traditional machine learning model, namely GPR. The integration not only improves estimation accuracy but also quantifies the associated uncertainty, thereby striking a balance between performance and reliability.

The application of CNNs in battery SOH estimation has evolved into a diverse technical system. The hybrid architecture paradigm for deep feature extraction prioritizes accuracy, enabling precise estimation in complex scenarios. The end-to-end lightweight modeling paradigm focuses on practicality, adapting to real-world operating conditions. The mechanism integration and engineering boundary validation paradigm targets reliability, enhancing controllable management of technical applications. As summarised in Table 8, the three paradigms evolve synergistically to advance CNN-based SOH estimation from the laboratory to industrialization. Future trends will center on lightweight, automation, and physics-informed fusion, achieving deep integration of data and mechanism-driven methods.

3.2.2 Recurrent neural network-based

Battery aging is a continuous dynamic process with strong historical dependency. Specifically, the current SOH is the cumulative result of electrochemical stress, side reactions, and microstructure degradation over all previous cycles. The long-term dependency limits static estimation methods. To address this issue, Recurrent Neural Networks (RNNs) and their variants [105, 106], which process sequential data and memorize historical information via internal states, have become key technologies for characterizing battery aging and bridging health diagnosis to life prediction. In practice, RNNs formulate SOH estimation as the dynamic modeling of capacity-fading sequences or multivariate time series, thereby opening new pathways for understanding long-term degradation. However, due to the vanishing and exploding gradient problems in standard RNNs, LSTMs and gated recurrent units (GRUs) have become core solutions. In recent years, RNN research for SOH estimation has shown a trend toward integration and engineering applications. The following discussion focuses on LSTM and GRU.

LSTM-based: LSTM addresses the vanishing gradient problem of traditional RNNs through its input, forget, and output gates. It captures nonlinear, time-varying patterns in battery aging, achieving higher accuracy and generalization. Thus, LSTM is widely used for LIB SOH estimation, providing effective solutions across basic applications, structural optimization, parameter tuning, hybrid models, and multi-task expansion.

Early studies focused on basic LSTM architectures. Researchers combined the native temporal feature extraction capability of LSTMs with simple feature engineering and data preprocessing to validate the feasibility and superiority of LSTMs for SOH estimation. These works [107–109] typically used real-world full-lifecycle data or public datasets, adopting features such as ohmic resistance and IC curve characteristics. The results showed that LSTMs outperform traditional ML methods with low deployment barriers, thereby establishing a solid benchmark for subsequent model improvements. Nevertheless, this line of approaches struggled to adapt to complex and dynamic real-world scenarios.

With the advancement of research, addressing inherent limitations of native LSTM, such as missing unidirectional temporal information, equal weighting of input features, and low computational efficiency on long sequences, researchers have improved single-network models by restructuring network architectures or integrating attention mechanisms. Bidirectional LSTM (Bi-LSTM) [110–112] traverses time steps in both forward and backward directions, effectively avoiding unidirectional information loss and significantly improving stability in small-sample and complex temporal scenarios. The introduction of attention mechanisms [113] enables focus on key stages of the charging curve and critical aging time steps. In particular, local-global dual attention [114] captures global temporal dependencies while reducing computational complexity for long sequences, achieving substantial gains in SOH estimation accuracy. However, increased model complexity reduces real-time performance, and most models rely on manual or fixed parameter tuning, leaving considerable room for improvement in extreme-condition adaptation and cross-scenario generalization.

Alongside network structure optimization, intelligent hyperparameter optimization has emerged as an important complementary direction. It addresses several issues inherent in native LSTM, including the need for subjective manual tuning, susceptibility to local optima, and the risk of overfitting or underfitting. Researchers have employed SOH estimation error as the fitness function when combining LSTM with a variety of optimization algorithms, including the Differential Evolution Grey Wolf Optimizer (DEGWO), the Improved Quantum Particle Swarm Optimization (IQPSO), and the classical PSO. This integration achieves global hyperparameter optimization, thereby improving SOH estimation performance. The optimized models reported in [115, 116] achieved estimation errors below 1% on public datasets from NASA and MIT. Furthermore, the models demonstrated an accuracy improvement of at least 5% compared with traditional LSTM [117, 118]. Despite these advances, several limitations remain. Most methods focus primarily on core hyperparameters, such as the number of neurons in the hidden layer and the learning rate, which reflects a lack of comprehensive optimization. In addition, the iterative optimization process is time-consuming, and the stability of optimization when applied to noisy data requires further improvement.

To overcome the limitations of a single LSTM and reduce noise, feature redundancy, and data dependence in SOH estimation, researchers have developed various fusion models that leverage complementary advantages. Studies [119, 120] combined signal processing methods such as empirical mode decomposition (EMD) and nonlinear state space reconstruction (NSSR) with LSTM, effectively separating noise from the true aging trend in capacity sequences, stabilizing temporal data, and addressing estimation deviations caused by capacity regeneration and cell inconsistency. Li et al. [121] and Kumari et al. [122] respectively integrate DL models, namely Temporal Convolutional Networks (TCN) and the Residual Network with 110 layers (ResNet110), to achieve collaborative extraction of local temporal features and global temporal correlations. Specifically, the method proposed by Li et al. [121] improves estimation accuracy by over 14% compared with the single LSTM model on public datasets. Integration with transfer learning [123] and federated learning [124] has addressed data dependency and battery data privacy issues, respectively. However, these approaches significantly increase model complexity and prolong training and inference times, while some fusion methods suffer from mode mixing and reconstruction complexity.

Researchers have exploited the inherent coupling relationships between battery SOH and other state parameters, such as SOC, RUL, and IR, to design LSTM-based architectures that leverage the temporal modeling advantage of this network. Examples include dual LSTMs in series [125] and an encoder-decoder structure with LSTM [126]. These architectures enable the joint estimation of multiple parameters, a capability that effectively avoids the error accumulation commonly observed in single-task estimation. Moreover, they require no additional dedicated measurement equipment. As a result, this approach offers strong engineering feasibility and enhances both the integration and real-time performance of BMS. Nevertheless, several limitations persist. These methods suffer from weak generalization across different data sources and battery types. In addition, the trade-off in accuracy among multiple parameters remains a challenge, making it difficult for these methods to fully adapt to complex and dynamic real-world operating conditions.

In summary, LSTM and its improved models for LIB SOH estimation have evolved from basic feasibility validation to multi-dimensional optimization, addressing core issues such as temporal modeling, parameter optimization, feature extraction, and engineering adaptation. This has improved accuracy, generalization, and engineering feasibility, providing technical pathways and theoretical support for accurate LIB SOH estimation. A detailed comparison of the aforementioned LSTM-based methods is shown in Table 9. However, existing methods still have limitations. Future research should focus on extreme-condition adaptability, cross-scenario generalization, balancing model complexity with real-time performance, and ease of engineering deployment to promote the large-scale application of LSTM models in LIB SOH estimation.

Gated recurrent unit-based: the GRU is a simplified variant of LSTM that reduces parameter count and computational complexity while retaining the ability to capture temporal dependencies, making it more suitable for real-time applications such as embedded BMS and industrial online monitoring. Recent research shows that GRU follows a development trajectory similar to LSTM's in SOH, but with greater emphasis on efficiency. The complete technical framework is illustrated in Figure 7.

Figure 7 Application-oriented GRU-based technical framework for SOH estimation

Early work primarily validated the effectiveness of GRU as a basic regressor for processing HF sequences extracted from voltage and current data [127, 128]. Later research focused on structural optimization and efficiency improvement. For example, a bidirectional GRU (Bi-GRU) was adopted to better utilize the sequential context [129], and comparative experiments [130, 131] consistently confirmed that GRU typically reduces training time by 20%–30% and parameter count by over 25% while maintaining prediction accuracy comparable to LSTM, highlighting its superior efficiency advantage. Regarding the evolution from a single model to a hybrid architecture, GRU has been combined with Savitzky-Golay filters to improve input data quality [132]. It is cascaded with transformers to achieve local-global complementarity and combined with EMD to adapt to the deterministic trend of capacity degradation [99, 130]. To meet the stringent reliability requirements of BMS, GRU research has also advanced to enhance robustness and reduce prediction volatility. This has been achieved by integrating attention mechanisms (AMs) to dynamically focus on key features and time steps [128], or by using robust loss functions, such as mixture correntropy loss, to suppress noise and outliers [127]. Meanwhile, the transition of GRU from static modeling to dynamic adaptation is also a frontier research focus. For example, Shi et al. [133] used intelligent algorithms to optimize its hyperparameters.

In summary, the development of GRU is driven by the core principles of efficiency priority, hybrid innovation, and practical reliability. Although GRU theoretically offers lower state-space complexity and less refined control over information flow than LSTM, it holds irreplaceable value in engineering-oriented deployment research. Together with LSTM, they form a complete technical spectrum that covers from algorithm research to industrial applications.

3.2.3 Autoencoder-based

The CNN and RNN models described earlier in this chapter primarily follow the supervised learning paradigm, aiming to establish an accurate end-to-end mapping from battery measurements to SOH labels. In contrast, autoencoders (AEs) and their variants employ unsupervised or semi-supervised learning to extract intrinsic aging-related health features from data, addressing key challenges in SOH estimation, such as label scarcity, variable operating conditions, and cell-to-cell variability. The technical development framework of autoencoder-based SOH estimation is illustrated in Figure 8.

Figure 8 Development of Autoencoder-based SOH estimation technology

From a technological evolution perspective, the application of AEs in SOH estimation has advanced from feature extraction to the integration of mechanisms. Early research primarily utilized AEs as unsupervised feature extractors, automatically learning low-dimensional dense representations of data through encoder-decoder pre-training. For instance, sparse autoencoders (SpAEs) extract critical aging features via L1 regularisation, while denoising autoencoders (DAEs) enhance feature robustness in noisy environments by recovering clean signals. These more discriminative features can significantly simplify the complexity of subsequent regression models, effectively improving the stability of SOH estimation in scenarios with inconsistent data quality and significant cell-to-cell variability [134].

As the demand for model interpretability grows, research has embedded electrochemical knowledge into AE frameworks to construct physics-informed hybrid models. By simultaneously optimizing the data reconstruction loss and the residuals of the physical equations, physics-informed AEs guide networks to learn HFs that fit the data while adhering to physical laws. For example, Xu et al. [135] incorporated ECM equations as soft constraints into the loss function, thereby ensuring the monotonicity and rationality of capacity-decay trajectories. This enables high-precision predictions with limited data and robust resistance to sudden shifts in operating conditions. More advanced work has developed disentangled autoencoders (DisAEs), in which distinct latent variable dimensions correspond to specific aging mechanisms, such as SEI growth and lithium plating, thereby achieving mechanistic interpretability.

To mitigate the challenges posed by dynamic operating conditions and cross-battery generalization, the AE paradigm has been extended to extract domain-invariant HFs. The encoder-decoder architecture helps to quickly adapt to new scenarios. It either integrates physical priors from online parameter identification or uses adversarial training to align latent-space distributions across different conditions. Consequently, precise estimation is achievable through fine-tuning only a subset of network layers, providing a unified framework for online adaptation and transfer learning [136]. Furthermore, variational autoencoders (VAEs) characterize the probabilistic distribution of latent variables, enabling both synthetic data generation to address data scarcity and uncertainty quantification to support risk-aware battery management.

For industrial deployment, AE-based methods face engineering challenges, including lightweight edge implementations, online adaptation, and safety certification. Researchers have proposed various solutions to address these issues. Model compression techniques such as knowledge distillation and neural architecture search reduce the computational burden on edge devices. Incremental learning strategies that handle concept drift during long-term battery operation enable the model to adapt over time. Meanwhile, deterministic inference schemes have been developed to comply with functional safety standards. Although challenges remain in network design, training complexity, and integration with complex aging mechanisms, AEs serve as a critical bridge between data-driven approaches and battery physics. By fulfilling this bridging role, they represent a core technical route toward an interpretable, adaptive, and reliable BMS. Future research should establish more comprehensive evaluation protocols that systematically compare accuracy, efficiency, generalization, and uncertainty quantification on public benchmarks. Such efforts would promote standardization and engineering maturity across the field, a goal essential for widespread industrial adoption.

3.2.4 Hybrid neural network-based

In the field of battery SOH estimation, single DL models such as CNNs, LSTMs, GRUs, and AEs have demonstrated superior feature extraction and temporal modeling capabilities compared to traditional ML methods. However, single models have inherent limitations. To address this, hybrid neural networks integrate complementary network architectures, achieving a transition from manual feature engineering to automatic feature extraction and from simple temporal modeling to refined spatiotemporal feature fusion. This effectively improves the accuracy and robustness of estimation under practical scenarios such as complex operating conditions, fragmented data, and cell inconsistency, making hybrid neural networks a mainstream research direction in LIB SOH estimation.

Feature extraction is a prerequisite for LIB SOH estimation. By combining AEs and temporal networks, hybrid neural networks drive the evolution from manual design to unsupervised automatic extraction, enabling end-to-end model training. Zhu et al. [137] proposed the convolutional autoencoder-Bi-LSTM (CAE-Bi-LSTM) fusion architecture, which achieves unsupervised feature extraction and bidirectional temporal modeling of charging data, maintaining high estimation accuracy even under capacity-fluctuation scenarios. Obregon et al. [138] fused convolutional autoencoder (CAE) and DNN to autonomously extract high-dimensional features from EIS data, thereby adapting to temperature-varying conditions. In contrast, Wu et al. [139] employed a dual-autoencoder architecture that combines a CAE and a representation autoencoder (RAE) , thereby achieving complementary extraction of local and long-range temporal features. Excellent performance is obtained in small-sample scenarios.

LIB charge-discharge data exhibits both spatial local and temporal features. The hybrid architecture that combines CNNs with temporal networks has become the fundamental paradigm for spatiotemporal feature mining, evolving from simple serial fusion to multi-scale, multi-channel, and bidirectional designs to adapt to fragmented real-world data and varied operating conditions. In the basic architecture, local spatial features are first extracted by CNNs and are then passed into temporal networks, where long-term capacity degradation is captured. In this way, the limitations inherent in single models are compensated. For deep networks, skip connections were introduced by Xu et al. [140] to optimize the gradient flow, thereby mitigating feature degradation. To enhance spatial feature extraction, researchers have developed CNN variants. Multi-scale CNNs use kernels of different sizes to simultaneously extract fine- and coarse-grained features, thereby avoiding information loss [141]. Dilated CNNs use different dilation rates to expand the receptive field without increasing parameters or relying on pooling operations, thereby preserving feature information [142]. Multi-channel CNNs integrate health information from incomplete data segments via multiple input channels for fragmented real-world data [143]. Parallel CNNs extract independent features from voltage, current, and temperature data, thereby improving feature comprehensiveness [144, 145]. For temporal modeling, Bao et al. [142] replaced unidirectional LSTMs and GRUs with Bi-GRUs to capture both forward and backward temporal dependencies, enabling more accurate characterization of full-cycle battery degradation.

The introduction of AM adds a feature enhancement layer to hybrid architectures, enabling refined spatiotemporal feature fusion. After AM is incorporated into the basic spatiotemporal fusion framework, adaptive weighting is applied to the hidden states of temporal networks, the channel features of CNNs, or the time steps. Consequently, the model is enabled to focus on core aging features. For example, Zhao et al. [146] weighted the hidden states of temporal networks to highlight the contributions of key cycle stages, thereby improving robustness to cell inconsistency. Tian et al. [147] enhanced the feature interval that is highly correlated with SOH, thereby further reducing estimation errors by weighting bidirectional temporal features. Through attention-weighted data reconstruction, Liu et al. [148] effectively suppressed noise interference in raw data. In addition, a self-attention mechanism was adopted by Wang et al. [149] and Yang et al. [150] to enable global feature correlation analysis, compensating for incomplete local data.

Hybrid neural networks achieve high estimation accuracy but are complex, making them unsuitable for real-time online LIB SOH estimation. To address this issue, a complementary fusion of pure temporal networks was employed, thereby reducing model parameters while preserving accuracy and enabling lightweight network design. This architecture integrates multiple temporal networks to complementarily model long- and short-term features. LSTM typically serves as the primary network. Its gating mechanism overcomes the vanishing gradient problem of traditional RNNs, enabling accurate capture of long-term dependencies and capacity degradation over multiple cycles. Meanwhile, RNN or secondary LSTM/GRU networks serve as auxiliaries, modeling short-term temporal features within a single charge-discharge cycle to compensate for the limitations of LSTM. For example, the basic LSTM-RNN architecture proposed by Liu et al. [151] can be directly adapted for real-world online estimation. The improved LSTM-RNN architecture by Li et al. [152] integrates a parameter optimization algorithm that enhances the model's adaptability to nonlinear and non-Gaussian aging data. While maintaining a lightweight structure, the estimation accuracy is further optimized.

To overcome the limited generalization of single-stream hybrid neural networks, the hierarchical multi-stream feature fusion architecture uses a Hierarchical Feature Coupling Module (HFCM) as its core. It extracts features in parallel through shallow and deep streams at different dimensions, then adaptively fuses them. This preserves raw data information while integrating deep multi-scale contextual features, enabling comprehensive mining of aging characteristics. The fused features are fed into an LSTM for temporal dependency modeling, thereby enabling effective adaptation to different battery types and complex operating conditions. This architecture achieves stable estimation accuracy across multiple datasets with higher training efficiency than traditional temporal networks [153].

In summary, as summarised in Table 10, hybrid neural networks have achieved high accuracy and adaptability in LIB SOH estimation, but still face poor interpretability, limited adaptability under extreme conditions, and a trade-off between lightweight design and accuracy. Future research may focus on few-shot and cross-battery transfer learning, interpretability enhancement, and adaptability optimization to promote engineering applications.

To present an intuitive comparison, Table 11 groups the aforementioned representative DL methods by dataset and error metric.

When data are scarce, deep models overfit easily. Their training requires large-scale cycle tests that are costly and time-consuming, making DL difficult in battery research. Transfer learning and fine-tuning help, but rely on sufficiently large pre-training datasets. For cross-battery generalization, hierarchical feature extraction can potentially learn domain-invariant representations. However, without physical constraints, models tend to use dataset-specific shortcuts that fail when battery chemistry or form factor changes. Domain adaptation and adversarial training improve generalization, but add complexity and training overhead. Under extreme operating conditions, data distribution shifts cause significant performance degradation, especially for RNNs. These models rely on patterns of benign aging, which differ from the nonlinear dynamics induced by low temperature or ultra-fast charging. Furthermore, deep models impose high computational demands that exceed the capacity of automotive-grade microcontroller units (MCUs), limiting onboard deployment. DL methods suit scenarios with diverse training data, sufficient cloud or edge resources, and relaxed latency constraints. For onboard use, techniques like pruning, quantization, and knowledge distillation are essential.

4.3.1 PPO-based

Compared with Q-learning and DQN, PPO offers advantages in continuous action-space adaptation, policy-update stability, and multi-objective optimization efficiency, making it better suited to the demanding requirements of nonlinearity, dynamics, and SOH protection in battery systems. PPO supports decision-making in continuous action spaces without discretization. For example, it can directly output continuous power distribution ratios [160] or dynamically adjust switch-combination strategies [161], thereby avoiding precision loss and operating-condition fluctuations caused by discretization and reducing irreversible damage to SOH. It strictly limits the amplitude of policy updates via a clipped objective function and combines generalised advantage estimation (GAE) to reduce training variance, thereby avoiding battery stress responses such as overheating and high-current charge-discharge caused by abrupt parameter changes, and improving the stability of SOH optimization. At the same time, it can efficiently integrate multi-objective rewards such as SOH attenuation, balance effect, and energy consumption, directly maximizing the cumulative reward through policy gradient optimization without the need to design a complex multi-objective coordination mechanism, thus meeting the comprehensive needs of SOH optimization. In the passive balancing SOH optimization of the LIB pack [161], DQN needs to discretize the 5 switches' on/off actions into 32 combinations. Even after filtering out invalid actions, its decisions are still not precise enough, leading to more switching than PPO does, which further damages battery health. As a policy gradient algorithm, PPO can adjust the switching strategy more smoothly, reducing switching costs while achieving an 83.1% reduction in SOC variance, thereby indirectly reducing SOH degradation caused by imbalance. It can also adapt to battery packs with different SOH states without fine-tuning, with robustness superior to DQN. In the power allocation of hybrid energy storage systems [160], the SOH optimization needs to dynamically output continuous power allocation ratios. The DQN's discretization process cannot accurately capture load fluctuations and battery aging patterns, whereas PPO directly outputs continuous actions through the actor-critic framework. By incorporating the aging loss into the reward function and using the electro-thermal coupling model, the battery aging loss is reduced by 0.3%–9.4% compared with traditional methods, and training time is shortened by 97%. Meanwhile, PPO's stable update mechanism avoids the common reward-oscillation problem in DQN training, ensuring the consistency of SOH protection strategies. When combined with the predictive safety filter (PSF), it further prevents battery health degradation caused by decision fluctuations, whereas DQN struggles to consistently maintain the effectiveness of SOH optimization in complex load scenarios due to training instability.

4.3.2 DDPG-based

DDPG shares the actor-critic framework with PPO, which is also applicable to decision-making problems in complex dynamic systems such as battery health optimization. Both algorithms aim to learn optimal policies through interaction with the environment. However, DDPG adopts a deterministic policy and ensures stability through soft updates of target networks, placing greater emphasis on the smoothness and temporal correlation of action outputs. In contrast, PPO employs a stochastic policy and constrains the magnitude of policy updates via trust-region clipping, without requiring a soft-update mechanism, thereby achieving higher sample efficiency and placing greater emphasis on training robustness and efficiency. Given this difference, DDPG offers unique advantages for SOH optimization. SOH degradation is directly related to continuous variables such as motor torque distribution and battery charge-discharge rates, and is a long-term cumulative process dependent on historical operating states. DDPG deterministic continuous action output enables fine-grained smooth adjustments, avoiding health state fluctuations. It can also flexibly integrate temporal modules such as GRU to capture historical dependencies, and its reward function can be directly linked to SOH degradation indicators, making it better suited to health optimization requirements. PPO, however, requires additional temporal modeling; its stochastic policy can introduce parameter uncertainty, and it is less effective at optimizing a single health indicator. Relevant literature provides strong support for this. Wu et al. [162] implemented DDPG embedded with a GRU and self-attention mechanism for SOH optimization of dual-motor electric vehicles, to achieve health-coordinated optimization of the dual motors and the battery through continuous torque distribution. Experimental results showed that the final SOH of the two motors reached 99.99929% and 99.99978%, respectively, while battery SOH performance achieved 96.83% of the globally optimal Dynamic Programming (DP) algorithm, with a significantly reduced SOH decay rate. Yin et al. [163] adopted DDPG to precisely optimize adaptive unscented Kalman filter (AUKF) parameters through continuous actions for LIB SOH estimation, reducing the MSE to 0.050, a 33% reduction compared with the traditional unscented Kalman filter (UKF). In contrast, the stochastic policy of PPO introduces uncertainty in parameter adjustment, making it difficult to achieve the stable accuracy required for SOH estimation under high-noise conditions. The evaluation of representative RL algorithms for battery SOH optimization management is presented in Table 12.

The primary bottleneck of RL in health management is sample efficiency. Q-learning and DQN require tens of thousands of training episodes to converge, each corresponding to a real charge-discharge cycle that cannot be physically repeated. This forces researchers to use degradation models for generating virtual data, and the model-reality discrepancy introduces bias that undermines policy reliability. Imitation learning and offline RL reduce the need for online interaction but depend heavily on the availability of high-quality expert demonstrations. For cross-battery transfer, degradation dynamics and state transitions differ significantly across chemistries. Policies are tightly coupled to specific batteries, making retraining or fine-tuning necessary for new types. Under extreme conditions, nominally trained policies may not have explored the extreme regions of the state space, and extrapolation errors during deployment can lead to unsafe actions. For instance, at low temperatures, the agent may overestimate battery tolerance and issue excessive power commands, risking thermal runaway. Computationally, RL inference is far cheaper than training, but still burdens automotive-grade controllers, especially when deep networks are used as function approximators. In summary, RL-based health management currently suits only scenarios with high-fidelity degradation models, well-defined operating conditions, and sufficient computational resources. For onboard deployment, improvements in sample efficiency, lightweight inference, and safety assurance are essential, with formal verification or conservative exploration needed before real-world use.