## 1 Introduction  
Lithium-ion batteries are commonly employed in electronics, new energy vehicles, and power source systems owing to their high energy density, long life cycle, and low self-discharge rate [1, 2]. However, as the number of charge-discharge cycles increases, performance degradation will occur for the battery, such as a decrease in the maximum available capacity and an increase in internal resistance [3]. If the battery is not replaced promptly, great safety risks will be posed to the equipment, seriously affecting the stability and reliability of the power systems [4, 5]. Accurately estimating battery status is essential for effective battery management, and the state of health (SOH) and remaining useful life (RUL) of lithium-ion batteries are critical indicators for evaluating battery performance, which can effectively quantify the degree of aging [6]. In the field of battery health assessment, SOH is a widely used macro indicator to measure the overall health of a battery. In addition to SOH, the micro-health parameters of the battery are also important aspects in assessing the health status, including the volume fraction of negative electrode active materials, solid-phase diffusion coefficient, electrolyte concentration, and so on. Micro-health parameters are for the performance of the active material and electrolyte inside the battery, and changes in micro-health parameters can present the internal health state of the battery [7]. Although micro-health parameters can provide more detailed information about the internal state of the battery, their measurement and evaluation processes are relatively complex and require advanced models and algorithms. In contrast, SOH is more easily assessed by battery capacity, internal resistance, and other parameters. Therefore, in this study, SOH is chosen as the primary indicator for assessing battery health and the mainstream definition of SOH describes it as the ratio of maximum usable capacity to rated capacity [8]. As the number of charge-discharge cycles increases, the SOH will continuously decrease. When SOH decreases to 70%-80%, the battery is typically recognized as the end of life (EOL), and the number of cycles to degradation from the current state to EOL is called the RUL of the battery [9; 10]. In addition, there is a correlation between estimating SOH and predicting RUL, as both can be obtained by estimating battery capacity. Model-based and data-driven methods are included in the main research methods [11]. Model-based methods can be classified as equivalent circuit models and electrochemical models, each based on distinct modeling mechanisms. In the equivalent circuit model, intricate physical and chemical processes within the battery are simplified and basic electronic components are used to simulate battery output [12]. [PERSON] et al. [13] introduced a recursive least square weighted decoupling method to enhance parameter estimation accuracy across various dynamic regimes. [PERSON] et al. [14] used recursive least squares with variable forgetting factors to identify parameters of the equivalent circuit model, achieving internal impedance identification and capacity estimation. [PERSON] et al. [15] developed an equivalent circuit model using the constant voltage charging current curve to predict battery SOH by determining relevant circuit model features. However, establishing a precise model of battery aging is challenging owing to the intricate internal reaction mechanism [16]. Electrochemical models model the dynamics of battery performance degradation by simulating physical and chemical processes within the battery [17]. [PERSON] et al. [18] simulated the battery charging and discharging process by establishing an electrochemical model to analyze the affected factors of battery capacity degradation, thereby predicting RUL. [PERSON] et al. [19] designed an enhanced single-particle model capable of predicting battery aging states using aging research data from LMO-NMC-cathode graphite-anode batteries.