## 1 Introduction  
In the context of today's increasing attention to sustainable development, renewable energy has become an important way to solve the energy crisis and environmental pollution. With the rapid development of the electric vehicle industry and electrochemical energy storage technology, lithium-ion batteries, as the main power source of electric vehicles, have entered the stage of large-scale retirement. According to the research of IDTechEx and TrendForce, by 2030, there will be over 6 million battery packs retiring from electric vehicles per year, and at the same time, the global power and energy storage battery recycling scale will exceed 1 TWh, of which the lithium iron phosphate battery recycling scale will account for more than 58% [1, 2]. Large quantities of power batteries continue to retire, and improper recycling will lead to resource waste and a series of environmental problems, and hence the sustainable development of energy has brought great challenges. Thus, the question of the utilization and recovery of retired lithium-ion batteries has been paid more and more attention [3, 4]. The average remaining capacity of such retired electric vehicle batteries is about 70-80% of their initial capacity, and although they are no longer suitable for high-power-demand scenarios such as electric vehicles, they still have a considerable energy storage capacity and good potential for reuse. After reasonable design and control, retired batteries can be used in other fields with good operating environments and relatively low battery performance requirements. From this point of view, compared with the new batteries, retired batteries have better environmental protection and economic value [5]. However, in the process of recycling, the battery will inevitably appear to have a performance decline and even unreliability and unsafety problems. Compared with new batteries, retired batteries have poor consistency, high performance dispersion, and a high security risk. In the process of layer-by-layer integration from battery cells, modules, and battery clusters to energy systems, the above problems will be superimposed and amplified, thus resulting in increased uncertainty in the overall performance of the system [6,7]. To realize the safe, reliable, large-scale, and multi-scenario echelon utilization of retired power batteries, it is necessary to accurately estimate the capacity degradation and life cycle of batteries. Therefore, it is of great significance to research the health decline law of retired batteries by studying suitable models and methods for the echelon utilization of retired batteries. In the process of using retired power batteries, there are many factors that affect the decline in battery capacities, such as the number of battery charge/discharge cycles, operating temperature, depth of discharge (DOD), SOC range, charge, discharge current, etc. [8]. Most of the existing studies on the capacity degradation of lithium batteries are based on the accelerated aging test data, which can be mainly divided into three types: electrochemical mechanism model [9, 10, 11, 12, 13], empirical model [14, 15, 16, 17, 18, 19, 20], and data-driven model [21, 22, 23, 24]. The method based on the electrochemical mechanism model involves the physical and chemical process of the battery and then researches the law of the influence of the aging process on state variables. This method can describe the aging process of the battery from the point of view of the essential mechanism, but many incentives affect the aging of the battery, so aging modeling is very difficult. Moreover, this model relies on the experimental data obtained under strict experimental conditions, which has a large gap with the actual operation of the battery, thus resulting in a significant error when applying such a model [25,26].