Capitalizing on the potential of this innovative battery design, a recent study published in ENGINEERING Chemical Engineering puts forward a sophisticated method for accurately estimating the state of health (SOH) of bipolar lead-acid batteries. This parameter, which reflects the battery’s ability to store and deliver charge relative to its original capacity, is critical for ensuring battery reliability, optimizing maintenance schedules, and preventing unexpected failures in real-world applications. The research focuses on enhancing SOH estimation accuracy, a task complicated by the intricate electrochemical behaviors unique to bipolar battery configurations.

The experimental phase of the study involved the production of six 6-volt bipolar lead-acid battery prototypes. What sets this fabrication apart is the use of fused filament fabrication (FFF) to create acrylonitrile butadiene styrene (ABS) components combined with spot-welded multilayered lead foils serving as bipolar substrates. This multilayer approach allowed precise pasting of positive and negative active materials, replicating authentic bipolar battery structures. Batteries were subjected to rigorous cycling tests at a steady 25 degrees Celsius, employing a consistent 0.3-ampere charge and discharge current until the voltage dropped to a cutoff of 5.25 V, iterating until each battery’s SOH declined below 60 percent.

To accurately capture degradation states during cycling, the study employed partial charging profiles from the tested batteries. From these profiles, researchers extracted three critical health indicators: localized voltage area, sample entropy, and fuzzy entropy. The localized voltage area was calculated over a voltage-time window between 6.45 V and 6.70 V, representing a nuanced voltage region sensitive to degradation phenomena. Sample entropy quantified the uncertainty and irregularity within the sequential voltage data, serving as a proxy for the stability and repeatability of voltage-time patterns. Fuzzy entropy further measured the complexity inherent to the voltage signals, evaluating degrees of randomness and subtle variations linked to battery aging.

Validation of these health features was rigorously performed using gray relational analysis, a method particularly suited for evaluating correlations in multi-variable systems riddled with noise and uncertainty. Impressively, all three attributes demonstrated strong correlations with battery SOH, registering gray relational grades exceeding 0.83. This high level of correlation substantiates that partial charging profiles can indeed reveal deep insights into battery degradation, enabling reliable health monitoring without necessitating full charge-discharge cycles.

Building on these insights, the study proposed a hybrid modeling framework that intertwines machine learning algorithms for SOH estimation. The first stage combines the strengths of Lasso regression—a technique that performs automatic feature selection and regularization—with support vector regression (SVR), known for its robustness in handling nonlinear relationships. The outputs from these two models served as input features for a second-stage random forest regression model, which delivers powerful ensemble learning capabilities by averaging results from numerous decision trees. Notably, the hyperparameters of the random forest model—such as the number of trees, maximum tree depth, and minimal sample split thresholds—were optimized through a nature-inspired algorithm known as the gray wolf optimizer (GWO), enhancing model adaptivity and predictive accuracy.

The research experimented with two pairs of health attributes for model input: localized voltage area combined first with fuzzy entropy and then with sample entropy. Training datasets comprised data from four prototype batteries (named BLAB01 to BLAB04), while two separate batteries (BLAB05 and BLAB06) were designated for testing. Among these configurations, the model leveraging localized voltage area alongside fuzzy entropy produced remarkable results—achieving a mean absolute error (MAE) below 1.02 percent and root mean squared error (RMSE) under 1.5 percent in SOH prediction. Even amidst irregular fluctuation patterns during testing, relative estimation errors remained under 6.2 percent, with 88 percent of predictions falling within a more stringent threshold of 3.5 percent error.

For benchmarking, the study compared its gray wolf-optimized hybrid framework against conventional machine learning and deep learning models, including Gaussian process regression (GPR), deep neural networks (DNN), recurrent neural networks (RNN), and long short-term memory (LSTM) networks. While these models have shown success in battery SOH estimation individually, the hybrid approach excelled with slightly better overall performance metrics. Such comparative analysis signifies the hybrid model’s ability to amalgamate complementary strengths, yielding consistent and precise SOH predictions that surpass individual models.

The robustness of the model was further tested for long-term SOH estimation by systematically increasing the proportion of initial training data from 50 to 70 percent. Encouragingly, the RMSE improved significantly as more data became available, decreasing from 2.08 percent down to 1.27 percent. This showcases the framework’s scalability and adaptability to extended battery operating conditions, vital for lifecycle management in practical deployment environments.

The implications of this research are profound. By demonstrating that partial charge profiles alone—captured without exhaustive discharge cycles—can fuel highly accurate SOH models, the study paves the way for real-time health monitoring systems that are less intrusive and energy-intensive. Integrating a gray wolf-optimized hybrid regression approach introduces an innovative computational paradigm that harnesses nature-inspired heuristics alongside ensemble learning, ensuring rapid convergence and global solution optimization while maintaining interpretability.

Ultimately, this research offers a powerful methodological blueprint for future battery management systems (BMS) tasked with handling emerging bipolar lead-acid battery technologies. Accurate and timely state of health estimation facilitates proactive maintenance strategies and optimizes battery usage by preventing premature failures or untimely replacements. As industries increasingly demand compact, high-power-density energy solutions, such breakthroughs in SOH estimation become pivotal enablers for reliability, sustainability, and economic viability of advanced lead-acid energy storage systems.

The study’s success in coupling experimental fabrication with advanced data-driven modeling illustrates the evolving landscape of battery research—one that merges materials science with artificial intelligence to harness next-generation functionalities in energy storage. Moving forward, further extension of the hybrid framework to incorporate multi-source sensing data or online adaptive learning could enrich SOH diagnostics, pushing battery technology closer to its full potential in electrification, renewable integration, and beyond.

Subject of Research: Not applicable
Article Title: State of health estimation for bipolar lead-acid batteries based on gray wolf optimized hybrid regression technique
News Publication Date: 15-Feb-2026
Web References: http://dx.doi.org/10.1007/s11705-025-2613-7
Image Credits: HIGHER EDUCATION PRESS

Keywords

Bipolar lead-acid battery, state of health estimation, partial charging profile, gray wolf optimizer, hybrid regression model, Lasso regression, support vector regression, random forest, battery cycle testing, entropy, gray relational analysis, battery management system

The research, conducted by Jin, Ming, and Wei, delves into the intricacies of lithium-ion battery management systems. With the increasing reliance on battery technology in electric vehicles, grid storage, and portable electronic devices, accurately assessing the health of lithium-ion batteries is crucial. The study emphasizes that traditional methods of SOH estimation often fall short due to limited sensor data or partial observations, which can lead to significant inaccuracies and suboptimal performance predictions.

The PINN framework proposed by the authors acts as a powerful tool that bridges the gap between data-driven machine learning techniques and the underlying physics governing battery operation. By integrating physical laws with statistical learning, the PINN approach not only enhances the estimation accuracy of SOH but also provides insight into the complex degradation processes occurring within the battery cells, resulting in a more comprehensive understanding of battery performance.

One of the standout features of this study is its innovative handling of sparse sensor data. In practical applications, obtaining exhaustive readings from battery systems can be challenging due to cost constraints, operational environments, and technological limitations. The researchers developed a method that compensates for these deficiencies by synergizing limited data with a physics-informed model. This combination overcomes the uncertainties associated with sparse observations and provides a robust framework for real-time SOH monitoring.

The authors conducted extensive experiments to validate their proposed methodology. By utilizing empirical data from different battery cells undergoing various operating conditions, they demonstrated that the PINN framework can accurately predict the SOH in cases where traditional methods struggled. This ability holds immense potential for industries dependent on battery performance, allowing for more informed decision-making regarding maintenance and replacement strategies.

Moreover, the implications of this research extend beyond mere performance metrics. The ability to accurately estimate battery SOH can lead to improved battery management systems, resulting in enhanced safety, efficiency, and longevity of energy storage technologies. For instance, more precise SOH assessment can facilitate optimal charging practices, reducing the risk of overheating or degradation, which often plagues lithium-ion batteries.

The researchers also address the scalability of their approach. The PINN framework, while initially developed for specific battery chemistry, can be adapted to various other energy storage systems. This adaptability suggests that the model has the potential to revolutionize SOH estimation across multiple applications, from consumer electronics to large-scale renewable energy grids.

In conjunction with environmental considerations, the authors discuss the broader implications of their findings in the context of sustainable energy solutions. As nations strive to reduce carbon footprints and transition towards renewable energy sources, the need for reliable energy storage systems becomes increasingly pressing. By enhancing the SOH estimation capabilities of lithium-ion batteries, this research contributes significantly to the longevity and reliability of systems that underpin these renewable technologies.

Furthermore, the synergy between PINNs and battery technology also opens doors to subsequent research avenues. Future studies may explore the incorporation of additional variables, such as thermal management or external load conditions, into the PINN framework. This can lead to even more refined models capable of predicting long-term battery behavior and informing better operational strategies.

The study also invites academia and industry to collaborate on real-world applications of this innovative methodology, fostering a multi-disciplinary approach to advance battery technology. The fusion of physicists, data scientists, and engineers can catalyze the development of smarter, safer, and more efficient batteries, essential for meeting global energy demands.

In summary, the research conducted by Jin, Ming, and Wei presents a significant advancement in the field of lithium-ion battery management technology. By employing a Physics-Informed Neural Network for SOH estimation amid partial observability, the authors offer an insightful and practical approach that promises to reshape how we understand and manage battery systems. Given the ongoing demand for efficient energy storage, their contribution is likely to garner attention and acclaim within both scholarly circles and industry applications.

As we progress further into the 21st century, advancing battery technology will remain a cornerstone of sustainable development, and studies such as this will play a critical role in defining the landscape of energy storage solutions. The potential for enhanced longevity, safety, and efficiency in lithium-ion batteries not only benefits individual consumers and industries but contributes to the broader goals of global sustainability and renewable energy integration.

In conclusion, the innovative approach presented in this research signifies a vital leap towards addressing the challenges associated with lithium-ion batteries. It stands as a testament to the power of combining advanced computational techniques with fundamental scientific principles, ultimately paving the way for next-generation energy solutions that align with the pressing demands of our time.

Subject of Research: Lithium-ion battery state-of-health estimation using Physics-Informed Neural Networks.

Article Title: Physics-Informed neural SOH Estimation method for Lithium-ion battery under partial observability and sparse sensor data.

Article References:

Jin, M., Ming, X., Wei, D. et al. Physics-Informed neural SOH Estimation method for Lithium-ion battery under partial observability and sparse sensor data.
Ionics (2025). https://doi.org/10.1007/s11581-025-06805-0

Image Credits: AI Generated

DOI: 10.1007/s11581-025-06805-0

Keywords: Lithium-ion batteries, state-of-health estimation, Physics-Informed Neural Networks, sparse data, energy storage solutions, machine learning, battery management, renewable energy, performance optimization.