<p>The safe and reliable usage of compact bipolar lead-acid batteries requires accurate estimation of their state of health. Designing state of health estimation frameworks based on the initial charging segments of a battery presents a significant challenge. In this study, an integrated gray wolf optimization algorithm-based hybrid estimation framework in combination with sample entropy, localized voltage area, and fuzzy entropy is developed to accurately estimate the state of health of bipolar lead-acid batteries. Partial charging profiles of bipolar lead-acid battery are utilized to extract and validate the useful battery health feature attributes based on gray relational grades to study battery health deterioration. The study also validates the better performance of the suggested hybrid model. The proposed hybrid models are developed utilizing two pairs of battery health attributes, such as localized voltage area paired with either fuzzy entropy or sample entropy. The average means absolute error and average root mean squared error values are below 1.02% and 1.5%, respectively, for the localized voltage area and fuzzy entropy health attribute pair. This confirms the effectiveness of the hybrid model as a health status estimation framework for the bipolar lead-acid batteries.</p>