# Lithium Battery SOH Estimation Based on Manifold Learning and LightGBM
## 1 Introduction
extracted eight degradation parameters, such as equal time interval voltage difference, equal voltage drop discharge time, and root mean square of discharge voltage value from voltage, current, and temperature profiles to jointly predict the RUL of Li-ion batteries but ignored the redundancy and deficiency among the degradation parameters [21]. [PERSON] et al. proposed a gray wolf optimization support vector regression method to build a degradation model based on the life cycle data of sample batteries to achieve the evaluation and prediction of the degradation state of Li-ion batteries, but the battery capacity is difficult to measure directly and does not have real-time functionality [22]. In addition, although PCA (principal component analysis), LDA (linear discriminant analysis) and NMF (non-negative matrix factorization) are more effective in feature extraction applications, they are all linear. However, they are linear models that can only discover the global features of the data, and LDA is supervised and requires a given label information during training. Recently, a large amount of research has started to focus on the unsupervised domain. Researchers in different fields have found that data points in high-dimensional space lie approximately on a sub-flowform in the embedded low-dimensional space. To discover the nonlinear structure of the high-dimensional data space, some researchers have proposed kernel methods, but they are computationally intensive and do not take into account the intrinsic manifold structure of the original high-dimensional data. However, the manifold-based methods can effectively solve the above problems. To this end, this paper proposes an SOH estimation and RUL prediction algorithm for lithium-ion batteries based on manifold learning and the LightGBM model, which integrates each cycle curve of the battery to establish feature engineering. In this paper, we choose to extract a total of three types of features from different perspectives, which are capacity degradation features, entropy value features, and correlation coefficient features. Among them, the capacity degradation features extract different feature parameters for the discharge voltage curves in charge/discharge cycles, including the average voltage decay and IC curve feature parameters; the entropy value features are the generalized multiscale sample entropy of each attribute using the algorithm described in the previous paper to measure the information uncertainty; finally, the autocorrelation coefficient and partial autocorrelation coefficient are extracted in the time domain. Then, the L-ISOMAP manifold learning algorithm is used to dimensionally reduce the input feature set to solve the dimensional explosion problem. Finally, LightGBM prediction models are established to perform SOH prediction on different datasets, and multidimensional model superiority assessment is performed, including the selection of different prediction models, the comparison of the selection of different manifold learning methods, and model generalization validation experiments. The approximate structure of this paper is as follows. Section 2 shows the algorithms used for SOH prediction. It includes the algorithms used in data preprocessing, as well as the principle of the generalized multiscale sample entropy algorithm, L-ISOMAP algorithm, and the LightGBM regression prediction model. Section 3 shows the flow-based learning and LightGBM prediction process constructed in this paper. Section 4 is an example validation of the datasets from different sources using specific battery data examples, combined with the prediction model built in Section 3, and the analysis of the obtained prediction results. Section 5 sets up multiple sets of experiments to validate the multidimensional superiority of the model proposed in this paper. Section 6 concludes by summarizing the whole paper.