## 1 Introduction
The basic idea of the method based on an empirical model is to use battery experimental data to summarize the law of battery parameter change and model the relationship between battery capacity degradation and battery cycle times or cumulative ampere-hours, ambient temperature, charge/discharge ratio, and DOD. The established model is tested under different decline conditions, the decline factor is used as the parameter of the model, and a large amount of test data are used to fit into the mathematical expression. Generally speaking, the more complex the expression, the more decline factors corresponding to the model and the higher the accuracy of the model. Such methods rely on a large number of offline experiments under different working conditions, hardly conduct in-depth research on the nature of battery capacity loss in charge/discharge cycles, and possess poor adaptability to working conditions that cannot be covered by experiments [20]. The method based on the data-driven model refers to the use of Gaussian process regression or machine learning methods to deeply explore the life decay behavior of the battery, by training the battery degradation data set, finding the battery aging factor as a performance index, and establishing the battery aging model. Although this method does not require analytical mathematical models, it conducts modeling based on a large amount of battery experimental test data, extracts external characteristic parameters, learns the degradation rule from historical information, and realizes the capacity degradation assessment and the prediction of batteries, which requires a high amount of experimental data [27]. In summary, the existing battery capacity degradation model and its research mainly suffer from the following three shortcomings:Although existing battery capacity degradation models can consider many factors affecting capacity degradation, these models are mostly suitable for new batteries until the end of their life, that is, the capacity degradation to about 80%. The capacity degradation mechanism of new batteries and retired batteries is significantly different, so these capacity degradation models for new batteries cannot be used to simulate the capacity degradation of batteries directly. Because most of the model parameters are either fitted under laboratory conditions or provided by the manufacturer, the performance decline mode of the power battery is complicated, which leads to inaccurate estimates of the capacity of the retired battery. 2. Most of the existing models of retired battery capacity degradation only consider factors such as the number of battery charge/discharge cycles, operating temperature, DOD, charge/discharge rate, etc. Few models can consider the influence of the battery state of charge (SOC) range on capacity degradation, and hence the decline factors are not fully considered. In most practical applications, charge/discharge cycles are performed only in an SOC range. A DOD of the battery can correspond to multiple SOC ranges, the test results under a single DOD experimental condition are not suitable for all the SOC ranges, and the resulting capacity errors will be amplified in subsequent applications, thus hindering the research and analysis of retired battery echelon applications. 3. Most existing empirical models for capacity degradation of retired batteries only give the fitting model under specific battery operating conditions, and the model is not flexible. In the echelon utilization scenario of retired batteries, it is necessary to optimize and control their operating conditions reasonably, and a single operating parameter of the battery cannot fully meet the requirements of operation optimization. Therefore, there is an urgent need for a model that can predict the capacity degradation of retired batteries under multiple operating conditions with different charge/discharge rates, temperatures, DODs, and SOC ranges to support the research on the echelon utilization of retired batteries. Modeling research cannot be separated from data support.