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To address the problem that the faults in axial piston pumps are complex and difficult to effectively diagnose, an integrated hydraulic pump fault diagnosis method based on the modified ensemble empirical mode decomposition (MEEMD), autoregressive (AR) spectrum energy, and wavelet kernel extreme learning machine (WKELM) methods is presented in this paper. First, the non-linear and non-stationary hydraulic pump vibration signals are decomposed into several intrinsic mode function (IMF) components by the MEEMD method. Next, AR spectrum analysis is performed for each IMF component, in order to extract the AR spectrum energy of each component as fault characteristics. Then, a hydraulic pump fault diagnosis model based on WKELM is built, in order to extract the features and diagnose faults of hydraulic pump vibration signals, for which the recognition accuracy reached 100%. Finally, the fault diagnosis effect of the hydraulic pump fault diagnosis method proposed in this paper is compared with BP neural network, support vector machine (SVM), and extreme learning machine (ELM) methods. The hydraulic pump fault diagnosis method presented in this paper can diagnose faults of single slipper wear, single slipper loosing and center spring wear type with 100% accuracy, and the fault diagnosis time is only 0.002 s. The results demonstrate that the integrated hydraulic pump fault diagnosis method based on MEEMD, AR spectrum, and WKELM methods has higher fault recognition accuracy and faster speed than existing alternatives. [ABSTRACT FROM AUTHOR]