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The paper proposes a method based on kernel principal component analysis (KPCA) and multi-scale temporal convolution network (MTCN) for identifying faults in lithium-ion batteries, which is crucial for ensuring the safe and stable operation of energy-storage systems. Lithium-ion batteries are the primary component of energy storage units. The method involves the following steps: First, fault data are normalized, and KPCA is used for dimensionality reduction and single fault detection to reduce computational complexity and improve data reliability. According to the different types of overcharge faults and unknown faults, KPCA is used to reduce the data from the original dimension to 2 or 4 dimensions. The KPCA model is trained using the normal data corresponding to the two groups of fault data, and the fault data are inputted as the test data. The results show that the SPE statistic and the T2 statistic considerably exceed the control limit, verifying the reliability of the data. Then, the data are labeled according to the fault type: the overcharge data are labeled as D0 (normal) and D1 (fault), and the unknown fault data as F0 (normal) and F1 (fault). The labeled data are divided into training and test sets according to a specific proportion. Afterward, the MTCN model is trained with the training dataset, and its hyperparameters are optimized with the frost algorithm to improve model accuracy. Finally, the trained MTCN model is used to classify the test dataset. The method is validated on two groups of data: overcharge fault data and unknown fault data. The results show that the frost algorithm can optimize the hyperparameters after about 20 iterations. Compared with LSTM and CNN, which are also optimized by the frost algorithm, MTCN achieves a higher classification accuracy, reaching 99.265% and 99.688%, on the overcharge fault dataset and unknown fault dataset, respectively, while maintaining comparable performance to Xception and ResNet50. Additionally, to verify the influence of the training data amount, the training and test sets are divided according to different proportions, and the three algorithms are tested. KPCA verifies the reliability of charging fault and unknown fault data, and the results show that MTCN has the highest classification accuracy, especially on the overcharge fault dataset. Owing to the low dimensionality of the original data set, LSTM and CNN exhibit poor classification performance. In contrast, MTCN can extract more temporal information, achieving high classification accuracy. These results demonstrate the effectiveness and superiority of the method in fault diagnosis of lithium-ion batteries.