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Although excellent progress has been made recently in powertrain fault diagnosis based on vibration signals, most of them are based on the assumption that the fault features of the training and test data are drawn from the same probability distribution. Due to the limitation of the domain shift phenomenon, the performance of the current intelligent fault diagnosis methods is significantly reduced. Even many existing transfer learning methods have the problem of low generalization ability. Inspired by sparse representation theory, a novel cross-domain fault diagnosis method based on K-means singular value decomposition (K-SVD) and long short-term memory network (LSTM) is proposed in this study. First, K-SVD can convert source domain data into a sparse dictionary and sparse coefficient. The domain-invariant features are explored in the sparse dictionary, which contains redundant features. The sparse coefficients are input into the LSTM to obtain a primary classifier.