Enhanced hierarchical symbolic dynamic entropy and maximum mean and covariance discrepancy-based transfer joint matching with Welsh loss for intelligent cross-domain bearing health monitoring

Domain adaptation (DA) as a critical and valuable tool is devoted to minimizing the distribution discrepancy across domains, which has been successfully utilized in intelligent bearing health monitoring. In particular, transfer joint matching (TJM) is a promising transfer learning strategy, especially when the domains differ considerably. In the TJM, the maximum mean discrepancy (MMD) is usually employed to assess the discrepancy of distributions in reproducing kernel Hilbert space (RKHS). However, the MMD has been proved to lose some useful statistical information in the RKHS. Hence, an improved TJM approach, called maximum mean and covariance discrepancy-based transfer joint matching with Welsh loss (MMCD-WTJM), is proposed in this article. In MMCD-WTJM, maximum mean and covariance discrepancy (MMCD) instead of MMD is incorporated into the TJM to match more statistical information in RKHS. Meanwhile, the Welsh loss function is incorporated into the TJM to enhance the stability of the model. Besides, we develop enhanced hierarchical symbolic dynamic entropy (EHSDE) to extract a more useful feature representation. Eventually, a novel hybrid cross-domain bearing fault identification based on EHSDE and MMCD-WTJM is developed. The analysis results of eight transfer bearing fault identification tasks demonstrate that the developed approach has an excellent capacity in intelligent bearing health monitoring under varying operation conditions and different machines. Compared with the existing entropy-based fault feature extraction approaches and domain adaptation-based transfer fault diagnosis methods, the presented bearing health monitoring scheme has remarkable strengths in recognition accuracy.