# Lithium Battery SOH Estimation Based on Manifold Learning and LightGBM
## 1 Introduction  
As one of the most commonly used energy storage devices, lithium-ion batteries are widely used in aerospace, new energy vehicles, and portable electronic devices [1; 2; 3; 4; 5]. Due to the chemical reactions inside the battery and the influence of the external environment, the service life of the battery gradually ages or even fails with the use time. Therefore, timely prediction of the health condition and failure threshold of Li-ion batteries is beneficial for planning and managing batteries to ensure safe and reliable operation of devices. Therefore, accurate prediction of the state of health (SOH) and remaining useful life (RUL) of Li-ion batteries is of great significance in the field of Li-ion battery use [6; 7; 8]. In recent years, theories and technologies related to the fields of artificial intelligence, machine learning, and data mining have become more and more mature, and data-driven battery SOH prediction has received more and more attention. Researchers have used advanced machine learning and neural networks and other methods to establish the mapping relationships between battery SOH and RUL and features to achieve the prediction task [9; 10; 11; 12]. [PERSON] et al. used early battery cycling data, observed the discharge voltage-capacity degradation curve, and established a hybrid prediction model of a WOA-XGboost algorithm with input time series data to achieve SOH prediction on a time series [13]. In the research of [PERSON], the voltage during the charging process of Li-ion batteries served as an indirect health factor, and a model for predicting the RUL of Li-ion battery was built based on an artificial neural network (ANN). Nevertheless, fewer features were extracted, and the model generalization ability of the model withfewer features in the actual prediction should be verified [14]. [PERSON] et al. proposed a Gaussian regression-based, joint principal component analysis method to process the charging curve to obtain indirect health features, which was combined with a battery aging model and achieved high accuracy. [PERSON], [PERSON] et al. proposed constructing health indicators (HI) characterizing battery decline under dynamic operating conditions and introduced an ELM decline model for offline training of the whole battery life cycle by an extreme learning machine (ELM) to achieve SOH online estimation, which is more robust than the traditional estimation methods [15]. [PERSON] proposed a model based on incremental capacity analysis and a BP neural network to predict the SOH of batteries at different ambient temperatures. By analyzing the correlation between IC curve characteristics and SOH, the mapping relationship between temperature and IC curve characteristics was established by the least squares method to obtain the SOH prediction model at different temperatures [16]. [PERSON] combined the filtering algorithm with the autoregressive sliding average algorithm and used the fusion algorithm to build the remaining life prediction model for lithium-ion batteries, which effectively improved the training speed [17]. Due to the complexity of chemical reactions in actual lithium-ion batteries, various types of partial differential equations need to be established, and the parameters and matrix calculations involving the equivalent circuit model are relatively large, which makes it difficult to guarantee the accuracy of the model in practical applications. Furthermore, SOH cannot be directly measured, often relying on certain technical means for the correct extraction of the internal parameters and characteristic relationships of the battery to estimate SOH [18; 19; 20]. Data-driven and predictive model building-based approaches usually extract typical features from degraded data, and, using currently popular machine learning, models can construct state mapping relationships between degraded data and health states to overcome the problems of sample size and nonlinearity of data, thus, achieving SOH and RUL prediction tasks. [PERSON] et al.