Sodium-ion batteries (SIBs) have emerged as a promising alternative to lithium-ion batteries (LIBs) due to the abundant availability of sodium, lower costs, and comparable electrochemical performance characteristics. A thorough understanding of their performance features is essential for the widespread adoption and application of SIBs. Therefore, in this study, we investigate the output characteristics and electrochemical impedance spectroscopy (EIS) features of sodium-ion batteries (SIBs) under various states. The research results show that, unlike conventional lithium iron phosphate (LFP) batteries, SIBs exhibit a strong linear relationship between state of charge (SOC) and open-circuit voltage (OCV) across various SOC and temperature conditions. Additionally, the discharge capacity of the battery remains relatively stable within a temperature range of 15 °C to 35 °C; when the temperatures are outside this range, the available capacity of the sodium-ion battery reduces significantly. Moreover, the EIS profiles in the high-frequency region are predominantly influenced by the ohmic internal resistance, which remains largely unaffected by SOC variations. In contrast, the low-frequency region demonstrates a significant correlation between SOC and impedance, with higher SOC values resulting in reduced impedance, indicated by smaller semicircle radii in the EIS curves. This finds highlights that EIS profiling can effectively monitor SOC and state of health (SOH) in SIBs, offering a clear correlation between impedance parameters and the battery’s operational state. The research not only advances our understanding of the electrochemical properties of SIBs but also provides a valuable reference for the design and application of sodium-ion battery systems in various scenarios.

Vehicle body crashworthiness is crucial in a traffic accident. It can protect passengers from serious injury or death and reduce vehicle damage. To provide a more effective design framework for ensuring crash safety, a reliability-based design optimization (RBDO) method for vehicle body crashworthiness considering complex parametric correlation is developed by integrating copula functions. An RBDO model is formulated for the vehicle body crashworthiness problem based on a finite element model of a vehicle crash. Taking into account the correlation of random parameters, the optimal copula function is selected by the Bayesian method to model parametric correlation and build the joint probability distribution function. An efficient solution strategy is provided to perform the reliability analysis and optimization design of crashworthiness. The results demonstrate that the proposed method is reliable and has a high accuracy for crashworthiness design.