## 1 Introduction  
With the widespread application and technological advancement, lithium batteries have become important components in the fields of electronic devices, electric vehicles, aviation, and aerospace [1, 2]. Although lithium batteries have advantages, such as high energy density, a wide operating temperature range, and high charging efficiency [3], the degradation of the remaining capacity for lithium batteries may accelerate the aging of connected batteries, reduce the endurance of devices, influence the security, and may cause loss of property [4, 5]. In order to determine the possible remaining usage time for batteries before their remaining capacity reaches the failure threshold so that they can be replaced in time, the prediction of the remaining useful life (RUL) for lithium batteries is essential [6, 7, 8]. At present, RUL prediction is generally faced with the difficulty that the historical data used to construct battery prediction models often exhibit inherent stochastic biases compared to operational battery data, resulting in substantial uncertainties within the established predictive models. Consequently, accurately evaluating the RUL prediction of lithium batteries has become a challenging endeavor within the current landscape of lithium battery health assessment. In the field of lithium battery remaining lifespan prediction, experts and scholars from various countries have made substantial contributions. Currently, there are two main categories of methods: those based on physical models [9, 10] and those based on data-driven approaches [1, 2, 7]. For physical model-based prediction methods, the methods based on physical models establish battery aging models by analyzing internal physical or chemical changes. [PERSON] [4] discussed the limitations of predicting specific discharge capacities, proposing a paradigm shift toward excellence in data-driven approaches within the realm of materials research. [PERSON] [11] introduced the estimation of battery capacity using measurable parameters during battery discharge cycles that effectively prevent the continued use of batteries beyond their service life threshold, thereby mitigating a range of safety concerns. [PERSON] [12] presented a novel framework incorporating a deep neural network with memory features, achieving a balance between accuracy and computational complexity. However, due to the inherent complexity of internal reactions within batteries and the significant variations in the aging processes among different types of batteries, models constructed using this approach are generally applicable to a specific type and set of operating conditions of batteries. On the other hand, data-driven methods utilize historical operational data of batteries to construct aging prediction models. As these methods do not require a precise understanding of the exact physical and chemical mechanism parameters, leading to battery failure, they can directly uncover patterns of lithium battery performance degradation from electrical parameters, such as voltage and current. Consequently, this approach is more versatile and has gradually emerged as the predominant method for predicting the remaining lifespan of lithium batteries in various contexts in recent years. [PERSON] [13] proposed a novel Multi-Kernel Support Vector Machine (MSVM) based on multiple kernel functions (polynomial and radial basis kernel functions) and utilized a particle swarm optimization algorithm to search for MSVM model parameters, penalty factors, and weight coefficients. This approach effectively addresses issues related to the weak generalization of SVM and data transfer. [PERSON] [14] introduced a bidirectional long short-term memory (Bi-LSTM) network, dropout technique, and Bayesian variational inference to quantify the uncertainty in RUL prediction results.