Bipolar lead-acid batteries have emerged as a promising advancement in energy storage technology, offering significant improvements over conventional valve-regulated lead-acid (VRLA) batteries. These improvements are driven by a fundamentally different architectural design that places the cathode and anode on opposite faces of a bipolar substrate, enabling electrons to flow seamlessly between adjacent cells without the need for external conductive elements like tabs or straps. This compact design not only boosts active material utilization but also enhances power density, making bipolar lead-acid batteries an attractive solution for various high-demand applications.
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
