# Lithium Battery SOH Estimation Based on Manifold Learning and LightGBM
## 5 Instance Validation
### Multidimensional Superiority Assessment
#### 5.4.1 Comparison of the Effects of Different Models  
XGBoost provides an integrated decision tree-based learning method that excels in accuracy and automatically handles missing values and outliers, and which also supports parallel computation [33]. XGBoost's ability to process high-dimensional sparse data quickly and accurately with high operational efficiency and parallel processing makes it one of the very popular algorithms in the field of machine learning, performing well on multiple datasets. Random forest is an integrated learning method based on decision trees, which consists of multiple decision trees and is \"randomized\" to improve model performance and stability [34]. First, each base tree is sampled by \"bootstrap aggregating\" with put-back sampling, and second, each base tree uses \"feature randomization\" to randomly select only a portion of features for splitting when selecting nodes for splitting. This will reduce the correlation between each base decision tree and increase the stability of the algorithm. Random forests are widely used in modern machine learning in various fields, such as finance, healthcare, and natural language processing.  
As well as0 ensemble learning models, regression models commonly used in machine learning, such as ELM and LSTM, are also widely applied in the field of SOH prediction. An ELM (extreme learning machine) [35] is a fast neural network algorithm that differs from other neural network algorithms in that ELM no longer requires initialization and iterative optimization of weight parameters in the network. It directly transmits randomly generated input weights from the input layer to the hidden layer through matrix operations, and then forms output weights by linearly combining the output vectors generated by the input layer in the hidden layer, thereby achieving the classification, regression, or clustering of data samples. The LSTM (long short-term memory) is a recurrent neural network (RNN) commonly used to process sequential data. The LSTM algorithm uses a series of gates to filter the input and control the flow of information, effectively maintaining and updating the content and length of memory units, thus, avoiding the \"gradient disappearance\" and \"gradient explosion\" problems encountered in the training process of traditional RNN algorithms [36]. It improves the accuracy and generalization ability of the network when processing long sequence data.  
To verify the superiority of the LightGBM model selected in this paper, the ELM, LSTM, random forest, and XGBoost models were selected, and the capacity features obtained in the previous paper were input to compare the prediction results with the LightGBM model selected in this paper [37]. The next step is to compare the computational cost of each model and characterize the operational efficiency by calculating the model run time. The prediction results are shown in Table 4.  
From Table 4, it can be seen that the LightGBM, XGBoost, and random forest algorithms all have good regression prediction ability, and the goodness-of-fit and root mean square error of all three are relatively close, reflecting the good adaptability of the feature engineering in this paper. However, the average MSE value of LightGBM for the three batteries is \(2.5361\times 10^{-4}\), which is \(2.700\times 10^{-4}\) and \(0.9685\times 10^{-4}\) lower than that of the random forest and XGBoost, respectively. In addition, the prediction goodness-of-fit of the LightGBM model is improved. Therefore, the LightGBM method can effectively improve the SOH estimation accuracy and operation rate and has good SOH estimation performance.