Lithium batteries, one of the most versatile energy storage technologies, play a pivotal role in the global transition from fossil fuels to renewable energy sources. With advantages such as high voltage, high energy density, and relatively low manufacturing costs, these batteries have found widespread application in fields such as aerospace, power grids, automotive, and robotics. With the rapid expansion of lithium battery applications, their reliability and longevity have become increasingly crucial. Consequently, the development of precise and effective battery management systems (BMSs) is an urgent concern. The state of charge (SOC) is a particularly important indicator monitored by the BMS because it reflects the available capacity within the battery and serves as a critical measure of its endurance and capability to sustain operation. Accurately estimating the SOC not only enhances operational efficiency but also plays a significant role in improving the safety and lifespan of lithium batteries. To ensure the safe operation of batteries, fiber Bragg grating (FBG) sensors have been gradually incorporated for the SOC estimation of lithium batteries to monitor their state variations during the charging and discharging processes. However, most studies primarily focus on introducing FBG and do not specifically determine the influence of strains at various spatial positions on SOC estimation.

This study investigates the effect of strain measurements at three different positions on the surface of an 18650 lithium battery on the accuracy of SOC estimation. First, a lithium battery strain-monitoring system based on FBG sensors is developed, wherein three FBG sensors are strategically placed near the negative terminal, positive terminal, and central region of the battery. These sensors continuously monitor the strain at different positions on the battery surface under different conditions. To estimate the SOC, the strains at different positions, currents, and voltages are used as state features. A convolutional neural network-gated recurrent unit (CNN-GRU) model is employed to estimate the SOC. By incorporating the strain data from various positions, we can compare the influence of different strain positions on the SOC estimation accuracy. Finally, both static and dynamic conditions are applied to validate the impact of strain at different positions as input features for SOC estimation, demonstrating that strain position can significantly affect SOC estimation for lithium batteries.

The battery monitoring system based on FBG strain sensing collects data from different positions, as well as voltage and current measurements. Under static conditions, as shown in Fig. 4, the strains at all three positions initially increase, then decrease, and finally increase again. The most pronounced strain trend is observed at the central position, whereas the trends near the positive and negative terminals are less noticeable. Under dynamic conditions, as shown in Fig. 6, the strains at all three positions exhibit an upward trend, with the strain at the central position exhibiting the most significant changes, followed by the strain near the negative terminal, and finally, the strain near the positive terminal with the weakest trend. By combining different features and inputting them into the CNN-GRU model, the results indicate that the strain at the central position provides the strongest auxiliary effect for SOC estimation under static conditions, with a root mean square error (RMSE) and mean absolute error (MAE) of 0.59% and 0.46%, respectively. Under dynamic conditions, the central position strain achieves an RMSE and MAE of 1.17% and 0.81%, respectively.

To address the challenge of accurately estimating the SOC of lithium-ion batteries, this study proposes a battery-monitoring system based on FBG strain sensing. The FBG sensors are attached at different positions on the battery surface—near the negative terminal, positive terminal, and central position—to enable real-time strain monitoring. By inputting the strain from different positions, along with the voltage and current, into the CNN-GRU deep learning model, experimental data are collected, and SOC estimation under both static and dynamic operating conditions is performed. The experimental results indicate that during the charging and discharging processes, the strains at all three positions vary. Although the overall trends are similar, the strain at the central position exhibits the most pronounced variation, followed by the strain near the negative terminal, with the strain near the positive terminal exhibiting the least noticeable change. The consideration of the strain from each position as an auxiliary feature alongside electrical parameters results in a notable improvement in SOC estimation accuracy. However, the impact of the strain on the SOC estimation accuracy varies by position, with the strain at the central position contributing the most significant enhancement, whereas the strains near the positive and negative terminals have a weaker effect. This study demonstrates the importance of using FBG sensors for strain measurement on the battery surface and reveals the differential impact of strain at various positions on the accuracy of SOC estimation. This provides new insights and possible methodologies for the improved integration of FBG sensors into battery management systems. Based on the current findings, future research may further explore several directions, including the optimization of the FBG sensor placement, multimodal data fusion, and investigations of different battery models and types.