An Explainable Hybrid Opt-GRU-KAN Architecture for Lithium-Ion Battery Health Prediction

1  Introduction

The rising demand for electric vehicles (EVs) is primarily driven by significant technological advancements. With growing environmental awareness, more people are opting for eco-friendly transportation alternatives [1]. A critical factor in this shift is the efficiency of battery-operated vehicles, which convert most electrical energy directly into wheel power [2]. Central to the performance of these vehicles is the battery, with lithium-ion batteries being the most widely used due to their rechargeable nature and portability [3]. However, the consistent recharging of these batteries inevitably leads to ageing, resulting in a decline in their energy storage capacity. This ageing process reduces reliability, power output, and the ability to hold a charge [4]. Monitoring critical parameters is essential to ensure the efficient use of Li-ion batteries, with the State of Health (SoH) being the most important. SoH is a key metric for assessing battery performance, as it provides crucial insights into capacity degradation and ensures safe driving conditions [5]. Accurately estimating SoH, however, is challenging due to the gradual nature of battery degradation [6]. As the number of charge cycles increases, data-driven methods outperform model-based approaches in predicting SoH over extended battery lifespans. Conversely, while model-based methods may initially provide accurate predictions, they often need help maintaining precision over numerous cycles due to the complexities and non-linearities involved.

Moreover, machine learning emerged as a powerful tool for developing accurate and reliable prediction models. Vakharia et al. [7] introduced a novel approach to estimating the discharge capacity of lithium-ion batteries by combining optimised XAI with stacked long short-term memory (LSTM) models and utilising the jellyfish optimisation algorithm to enhance prediction accuracy. In contrast to the findings of [7], Jafari and Byun [8] presented an innovative method for estimating the Remaining Useful Life (RUL) of lithium-ion batteries in electric vehicles. This approach integrates measurable features, such as discharge time and temperature, with advanced machine learning techniques, emphasising the role of XAI in ensuring model transparency and trustworthiness. Moreover, Zhang et al. [9] provided additional insights by showing an improved transformer model optimised with a Stacked Denoising Autoencoder (SDAE) for predicting the RUL of lithium-ion batteries under varying charging and discharging conditions. This model leverages diverse NASA datasets, integrating multiple health factors and employing Principal Component Analysis (PCA) for data fusion to enhance prediction accuracy [10].

Although Wang et al. [11] emphasised on a hybrid model combining Empirical Mode Decomposition (EMD), Variance Contribution Ratio (VCR), GRU, and RF to estimate battery SoH. The estimation method uses a combination of machine and deep learning models. The model has not been validated for different battery chemistries. In a related study, Zhao and Behdad [12] proposed a framework for estimating electric vehicle batteries’ SoH using transformer-based neural networks. The research highlights the necessity of comprehensive datasets to capture real-world variability in battery usage and suggests future research directions to enhance model robustness and adaptability. An extension of this idea can be found in Gu et al. [13] where a novel method for SoH estimation of lithium-ion batteries using a convolutional neural network (CNN)-Transformer framework, emphasising the importance of data preprocessing techniques, such as the Pearson correlation coefficient (PCC) and PCA, to improve model efficiency, has been presented.

Moreover, Chen et al. [14] developed a new algorithm for SoH estimation of lithium-ion batteries using a regression vision transformer (RVIT) network. Based on the transformer model, this network effectively captures the temporal and spatial information embedded in battery data and has been trained and tested on NASA and CACLE datasets. Similarly, Jia et al. [15] proposed a hybrid model that integrates a bidirectional gated recurrent unit with a transformer utilising a multi-head attention mechanism. This model extracts time series features from indirect health indicators (HI), demonstrating improved accuracy, robustness, and generalisation, as evidenced by experiments on NASA’s PCoE lithium-ion battery data.

Additionally, Wang et al. [16] introduced method for lithium-ion battery SOH estimation using an Enhanced Whale Optimization Algorithm for feature selection and Support Vector Regression (SVR). Key features are selected from charge data, with improved accuracy through dynamic thresholding and random forest-based weighting. The method faces limitations in generalisation and lacks comparison with advanced deep learning models. Moreover, Dong et al. [17] proposed a robust RUL prediction framework for lithium-ion batteries using a CNN-LSSVR model optimised by mutation particle swarm optimisation. It introduces discharge energy as a novel RUL indicator and leverages Multi-Resolution Singular Value Decomposition (MRSVD) for effective noise reduction. The approach addresses small-sample and high-noise challenges in battery prognostics.

Furthermore, Yao et al. [18] introduced a mechanism-empowered feature engineering approach for accurate Li-ion battery SoH estimation. It integrates mechanistic signal analyses—IC, DV, QV, and a novel ICD method—with statistical techniques like PCC, GRA, and MRMR to extract robust and interpretable features. The model relies on controlled datasets and handcrafted features, limiting adaptability to real-world conditions and diverse battery chemistries. Lastly, Lu et al. [19] proposed an estimation method based on a deep learning neural network with fine-tuned transfer learning. This approach addresses the limitations of conventional machine learning models that assume identical data distributions across training and testing sets.

The examined literature shows considerable advances in battery health estimation utilising machine learning, particularly transformer-based designs. However, critical research gaps given in Table 1 remain: limited exploration of model generalisation across diverse battery chemistries and operational conditions, inadequate integration of real-world variability in datasets, particularly regarding long-term ageing effects, lack of standardisation in preprocessing techniques leading to inconsistent performance across studies, and limited focus on enhancing the transparency of deep learning models beyond basic explainability. This encourages additional research into developing robust, interpretable models that can generalise across multiple battery types and environmental circumstances while utilising standardised data fusion and preprocessing methodologies to increase accuracy and consistency in health and longevity forecasts.

Contributions and Structure of the Paper

The main contributions of this study can be summarised as follows:

•   Integrating the GRU-KAN hybrid architecture for SoH estimation effectively addresses the constraints of previous methodologies, considerably enhancing prediction accuracy while minimising reliance on large training datasets when compared to traditional neural network techniques.

•   The embedded XAI framework overcomes the interpretability challenges in battery health estimation, providing actionable insights into degradation mechanisms that enable proactive maintenance strategies and targeted interventions before a critical failure occurs.

•   The Optuna-based hyperparameter optimisation framework demonstrates superior adaptability and efficient model training across diverse operating conditions, proving the model’s performance remains robust regardless of variations between training and target battery characteristics.

•   Module ablation analysis confirming the hybrid model’s superior accuracy and generalisation capabilities in capturing both non-linear degradation patterns and temporal dependencies critical for reliable state of health predictions.

The subsequent sections are structured as follows: Section 2 explains the proposed methodology. Sections 3 and 4 present results. Section 5 provides comparative analysis. Section 6 concludes.

2  Model Development

2.1 Experimental Data and Setup

The Toyota Research Institute dataset has been chosen to train selected algorithms. Real-time data and CALCE data [20] have been utilised to validate the proposed model given in Table 2. The minimum hardware requirement to implement the work is Windows 11 with an Intel i5-1135G7 CPU and 8 GB RAM. Jupyter Notebook with Python 3.9 has been used to train and test the proposed model.

2.1.1 Toyota Data

The dataset comprises 124 commercial LFP cells manufactured by A123 Systems, cycled under different charge-discharge conditions. The cells have a nominal voltage of 3.3 V and a capacity of 1.1 Ah and have been cycled in a temperature chamber of 30∘C. End of life was defined as several cycles till 80% of the nominal capacity and results from 124 batteries with cycle life from 150 to 2300, and 72 fast charging conditions were gathered. According to the manufacturer’s suggested fast charging rate, charging rates were from 3.6 C to extreme fast-charging (XFC) settings of 6 C. A total of 10 batteries have been selected for testing, namely b1c0, b1c1, b2c0, b2c1, b3c0, b3c1, b1c3, b2c3, b3c3, and b1c5. The batteries were chosen so that some have degradation from 0–500 cycles; some have 500–1000, and others have 1000–1500 and above 2000 cycles to have variability in the data.

2.1.2 CALCE Data

The CALCE battery dataset consists of two CS2 batteries: CS2_36 and CS2_37. The charging of the batteries was done at a constant current (CC) mode at a 1C rate until the voltage reached 4.2 V. Further, the batteries have been charged at constant voltage (CV) mode at 4.2 V until the current dropped below 0.05 A [21].

2.1.3 Real-Time Data

Real-time data was acquired from an NMC battery deployed in the E-Scooter at Thapar Institute, India. The complete battery pack comprises 14 series-connected cells with a nominal voltage of 51.8 V and 28 Ah capacity (3.7 V, 2.0 Ah per cell), charged in CC-CV mode. The data has been fetched through an IoT module in the BMS and a cloud interface at 3-s intervals across 30 measured parameters, providing cell-level insight into degradation behaviour under variable operational loads [20,22].

2.2 Proposed Model

In this paper, a hybrid GRU-KAN model with Optuna has been proposed, for which the methodology is shown in Fig. 1. The model consists of four parts: data pre-processing, GRU and KAN model building, Optuna hyperparameter optimisation, and model explainability. Module ablation analysis has been done to find the contribution of each model for SoH estimation.

Figure 1: Flow chart of the proposed model.

2.2.1 Data Pre-Processing

The battery cycling data had three batches, and it was necessary to preprocess it to obtain quality data and organise it properly. The detailed pre-processing has been given in Algorithm 1. Among batch 1, five cells declared to have failed to reach 80% capacity, namely b1c8, b1c10, b1c12, b1c13, and b1c22, were excluded from further consideration. All measurements were merged with batch1 (b1c0–b1c4) cells in batch2 (b2c7, b2c8, b2c9, b2c15, b2c16), resulting in an extension of 662, 981, 1060, 208, and 482 cycles in cycle life, respectively. Six cells (b3c37, b3c2, b3c23, b3c32, b3c42, b3c43) were removed from batch 3 due to noisy measurements. The dataset was partitioned into a train set (odd-indexed cells, batches 1–2), a primary test set (even-indexed cells and battery 83), and a secondary test set (remaining batch 3 cells). The discharge capacity (Qd) was monitored in each battery cycle, deteriorating to end-of-life at 0.8 Ah (80% nominal capacity).

2.2.2 GRU-KAN Model

The algorithm of the proposed model is given in Algorithm 2, and the layered architecture has been shown in Fig. 2. The GRU model adapts the recurrent neural network that intends to resolve the vanishing gradient problem. GRU has a gating mechanism with fewer parameters than LSTM and can deal with long-term sequences capturing time-series data. GRU incorporates two gates: the update gate and the reset gate [23]:

zt=σ(Wz⋅[ht−1,xt]+bz),rt=σ(Wr⋅[ht−1,xt]+br)(1)

where zt and rt represent update and reset gates, σ is the sigmoid function, Wz, Wr are weight matrices, and bz, br are biases.

Figure 2: Node-level architecture of the proposed GRU-KAN model.

KAN models are an application of the Kolmogorov-Arnold representation theorem. Unlike MLPs, KAN has learnable activation functions between neurons [24,25]. For any continuous function f:

f(x1,…,xn)=∑i=12n+1ψi(∑j=1nϕij(xj))(2)

where ϕij and ψi are inner and outer transformation functions learnt via B-splines. Applied to battery input x=[V,I,T,IR,Cycle], KAN decomposes the SoH relationship as:

hi=∑j=1dϕij(xj),SoH=∑i=02dΦi(hi)(3)

The GRU hidden state integrates temporal patterns via the update gate zt (long-term degradation) and reset gate rt (selective forgetting after rest periods). The SoH prediction layer is:

y^SoH=WSoHht+bSoH(4)

2.2.3 Optuna Optimiser

Optuna dynamically constructs the hyperparameter search space and minimises a validation objective using Bayesian optimisation, tree-structured Parzen estimators, and pruning of unpromising trials [26]:

θ∗=arg⁡minθ∈Θf(θ)(5)

where θ is the hyperparameter vector, Θ the search space, and f(θ) the validation loss.

2.2.4 Explainability

XAI bridges the gap between predictive accuracy and model transparency in DL-based SoH estimation [27]. SHAP, a game-theory-based post-hoc method, assigns each feature a contribution score by evaluating all feature coalitions [28]. Kernel SHAP provides an efficient approximation:

g(z′)=ϕ0+∑j=1Mϕjzj′(6)

where g is the explanation model, z′∈{0,1}M is the coalition vector, and ϕj is the Shapley value for feature j.

2.3 Module Ablation Analysis

Each core module (GRU, KAN, Optuna) was removed or replaced in isolation to quantify its contribution [29]. Replacing GRU with Conv-GRU degraded temporal tracking; removing KAN reduced non-linear modelling capacity; omitting Optuna lowered prediction accuracy. RMSE, MSE, and R2 results confirm all three components are necessary for optimal performance.

2.4 Evaluation Metrics

Performance is evaluated using RMSE, MSE, MAE, MAPE, and R2:

RMSE=∑(SoHtrue−SoHpred)2n,MSE=∑(SoHtrue−SoHpred)2n(7)

MAE=∑|SoHtrue−SoHpred|n,R2=1−∑(SoHtrue−SoHpred)2∑(SoHtrue−SoHmean)2(8)

3  Results and Performance Evaluation

Eight architectures were evaluated on battery cycling data up to 2000 cycles; full quantitative results are in Table 3. Figs. 3 and 4 show the baseline and proposed model prediction results, respectively.

Figure 3: SoH estimation results for baseline models (a) Conv-GRU (b) GRU (c) KAN (d) Optuna GRU.

Figure 4: SoH estimation results for proposed Optuna GRU-KAN.

The Conv-GRU (Fig. 3a) shows moderate accuracy but fails to track degradation between cycles 500–1000. The standard GRU (Fig. 3b) tracks capacity changes more precisely, though it remains unreliable at high cycle counts. Standalone KAN (Fig. 3c) exhibits the weakest baseline performance with systematic overestimation early in cycling, confirming that temporal modelling elements are essential. The Optuna GRU (Fig. 3d) achieves strong alignment but shows minor underprediction outliers in the 1.06–1.07 Ah range.

The proposed Optuna GRU-KAN (Fig. 4) maintains consistent accuracy from cycle 1 to 2000, accurately capturing gradual fade, rapid knee-point transitions, and temporary capacity recovery at cycles 1000–1500—a direct result of integrating GRU’s temporal memory with KAN’s non-linear function modelling. The model also demonstrates robustness to cell-to-cell variability, a critical requirement for practical BMS deployment.

Explainability Results

The SHAP analysis (Fig. 5) provides local and global explanations. Locally (Fig. 5a), for Sample 42, internal resistance, cycle number, and minimum temperature positively influence the prediction, while average temperature and charge capacity reduce it, yielding f(X) = 0.385 against baseline E[f(X)] = 0.371. Globally (Fig. 5b), charge capacity, cycle number, and internal resistance are the dominant SoH features; Tavg, Tmin, and QD show minimal impact, guiding feature selection and model refinement.

Figure 5: Explainability results (a) local SHAP waterfall for sample 42 (b) global feature importance.

4  Correlation Analysis

Figs. 6 and 7 show correlation plots between actual and predicted discharge capacity. Conv-GRU (Fig. 6a) shows moderate alignment with noticeable scatter at both capacity extremes. GRU (Fig. 6b) improves alignment but remains inconsistent above 1.05 Ah. Standalone KAN (Fig. 6c) shows the weakest correlation with systematic underprediction above 1.025 Ah. Optuna GRU (Fig. 6d) achieves a strong linear relationship across the full range with only small outlier clusters near 1.06–1.07 Ah.

Figure 6: Prediction correlation plots for baseline models (a) Conv-GRU (b) GRU (c) KAN (d) Optuna GRU.

Figure 7: Prediction correlation plot for proposed Optuna GRU-KAN.

The proposed Optuna GRU-KAN (Fig. 7) achieves the tightest alignment across the full 0.875–1.075 Ah range with minimal outliers at all capacity levels, confirming its superiority. Across all evaluated models, correlation strength followed as KAN worst, followed by Conv-GRU variants, with the proposed hybrid consistently best.

5  Comparative Analysis

Table 3 and Fig. 8 present the full ablation results. Baseline KAN performed poorly (RMSE: 4.05%, R2: 29.53%); Conv-GRU was moderate (RMSE: 2.75%); GRU was the strongest baseline (RMSE: 0.63%, R2: 97.77%). Optuna LSTM closely matched GRU (RMSE: 0.62%). The proposed Optuna GRU-KAN surpassed all models on every metric (RMSE: 0.57%, MAE: 0.11%, R2: 98.56%). Table 4 and Fig. 9 confirm Optuna GRU-KAN (RMSE: 0.0020, MAE: 0.00040) substantially outperforms prior CNN-LSSVR, MRSVD-CNN-LSSVR, and MRMR-GPR4 methods.

Figure 8: Model evaluation plots (a) RMSE (b) MSE (c) MAE (d) R2.

Figure 9: Error comparison with previous work: (a) RMSE (b) MAE.

Validation of the Proposed Model

The model was validated on real-time EV battery data (Fig. 10), achieving RMSE of 0.49 and MSE of 0.0024, confirming robust generalisation to variable loads and environmental conditions. Validation on CALCE data (Fig. 11, Table 5) yielded RMSE below 0.010 for both CS2 batteries, further demonstrating cross-chemistry robustness.

Figure 10: SoH prediction for real-time data (a) real-time data plot (b) prediction plot.

Figure 11: Discharge capacity prediction for CALCE data (a) CS2_36 (b) CS2_37.

6  Conclusion

This paper presents a hybrid GRU-KAN framework optimised by Optuna for lithium-ion battery SoH estimation. The proposed architecture achieves superior results on all metrics (RMSE: 0.57%, MSE: 0.0033, MAE: 0.11%, R2: 98.56%), outperforming all baseline and optimised variants. Module ablation confirmed each component’s necessity. Validation across Toyota training data, real-time EV data, and the CALCE benchmark demonstrates strong generalisation across chemistries and operating conditions. The integrated SHAP-based XAI framework provides transparent, actionable insights into degradation mechanisms, offering significant potential for real-world deployment in intelligent battery management systems.

Acknowledgement: None.

Funding Statement: The authors gratefully acknowledge the Ministry of Electronics and Information Technology (MeitY), Government of India, Project Identification No. 25(2)/2021-ESDA.

Author Contributions: Conceptualization: Riya Sharma, Ashima Singh; methodology: Riya Sharma; validation: Riya Sharma, Ashima Singh, Mukesh Singh; formal analysis: Riya Sharma, Anju Bala; data curation: Anju Bala; writing—original draft: Riya Sharma, Ashima Singh; writing—review and editing: Mukesh Singh, Ashima Singh, Riya Sharma; supervision and project administration: Ashima Singh; funding acquisition: Mukesh Singh. All authors reviewed and approved the final version of the manuscript.

Availability of Data and Materials: Available from the corresponding author upon reasonable request.

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no competing interests.

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