In the traditional method of blind source separation based parallel factor (PARAFAC), all matrices must contain the same factors to satisfy the uniqueness of PARAFAC decomposition. The shortcoming limits the application of PARAFAC. Therefore, PARAFAC needs to be extended to overcome the shortcoming. PARAFAC2 emerge as the times require. Only one pattern matrix with the same factors is required in the PARAFAC2 method, and the factors in other matrices can be different. If the mode of the dimension changes, the PARAFAC2 method is still valid, while the model of the traditional PARAFAC method must be re-established. Based on the PARAFAC2 method, a new blind source separation model for mechanical faults is proposed. In the proposed model, data tensors are generated by a time segmentation method. Then the tensors are decomposed by the PARAFAC2 method. The proposed method is applied to blind source separation of simulated signals. Compared with the performance index and similarity coefficient of traditional PARAFAC, those of the proposed method is superior. Finally, PARAFAC2 is applied to the blind source separation of mechanical faults. The results show that the blind source separation method based on PARAFAC2 is effective.

Extended Parallel Factor; Blind source separation; Tensor; Fault diagnosis