A vacuum pump is a widely used vacuum device and a key component of the space environment simulator. Aiming at the problem of fault diagnosis and state assessment of the vacuum pump, this paper proposes a complete set of empirical mode decomposition [Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)] based on adaptive noise and support vector machine optimized by particle swarm optimization (PSO-SVM). The CEEMDAN method can adaptively decompose the acoustic emission signal of the vacuum pump to obtain several eigenmode functions [Intrinsic Mode Functions (IMFs)] and residuals. The normalized energy values of the IMF component are extracted as the eigenvector. The PSO algorithm is used to optimize the key parameters of the SVM, and the samples are used for training to establish a fault diagnosis model. The vacuum pump overload fault and vacuum pump with different working states are judged by experiments. The results show that the method has an accuracy of more than 97.0% and can effectively realize fault diagnosis and state assessment of vacuum pump equipment.