## 1 Introduction
This method provides 95% confidence intervals and probability density functions (PDFs) for RUL prediction results, effectively addressing the problem of insufficiently considering the lifespan information contained in multiple internal states of lithium-ion batteries. [PERSON] [15] proposed a deep learning approach that combines autoencoders with deep neural networks (DNNs) to extract multidimensional RUL information, enhancing prediction accuracy. [PERSON] [16] presented an RUL prediction method based on Multi-Channel Input (MCI) configuration and Recurrent Neural Network (RNN) algorithms, including both Single-Channel Input (SCI) and MCI configurations. Compared to the single channel-based method, this method significantly reduces prediction errors. [PERSON] [17] introduced a hybrid RUL prediction model based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and a bi-directional gated recurrent unit, along with genetic algorithm-based factor improvement and dynamic population weighting to accelerate algorithm convergence. [PERSON] [18] proposed a deep learning-based method trained on the widely used Oxford battery degradation dataset, utilizing Generative Adversarial Networks (GANs). The network architecture adopted long short-term memory (LSTM), hierarchical strategies, and custom loss functions, achieving accurate predictions for small-sample condition RUL. The above data-driven methods directly leverage historical sample data from lithium batteries to predict future aging trends by establishing statistical or machine learning models. These methods circumvent the need for intricate mathematical or physical modeling processes, significantly enhancing the generality of lithium battery lifespan prediction models. However, due to the differences in the manufacturing process, environmental factors, and the uncertainty during the degradation process, the difference between the degradation characteristics of different batteries (individual differences) may be great. Within the process of constructing predictive models using a set of historical samples, such approaches often fail to adequately account for individual differences. As a result, predictive models developed using the overall sample data struggle to accurately reflect the aging trends of in-service batteries, leading to the accumulation of predictive bias [19; 20]. In order to reduce the error caused by individual differences, this paper introduced a new proposed method. First, calculate the degradation rate of historical capacity data and target battery capacity data, and then use an extreme learning machine (ELM) to construct the relationship between the capacity degradation rate and the capacity of historical data and use the trained model on the target battery's existing degradation rate to predict the capacity data. After that, the adjusting factor can be obtained according to the differences in capacity obtained by ELM and the real capacity data. Finally, another transfer learning-based ELM is applied to predict the RUL according to the capacity data, and the adjusting factor is used to adjust the prediction result. The contributions of the method are as follows:  
1. Using the ELM model can reduce the required training time because compared with traditional neural networks, ELM does not need to follow a critical gradient descent process;
2. The proposed ELM-based transfer learning method can improve the stability of the traditional ELM method, reducing error caused by the inherent features of the ELM model in which the initial parameters are arbitrarily generated;
3. The adjusting factor can further enhance the precision and accuracy of RUL prediction by clearly identifying and evaluating individual differences. In general, compared with existing prediction models, our method has better performance in accuracy and efficiency. The remainder of this paper is organized as follows.