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.

域适应 (DA) 作为一种关键且有价值的工具，致力于最小化域间的分布差异，已成功用于智能轴承健康监测。特别是，转移联合匹配（TJM）是一种很有前途的转移学习策略，尤其是当领域差异很大时。在 TJM 中，通常使用最大平均差异 (MMD) 来评估再现核希尔伯特空间 (RKHS) 中分布的差异。然而，已经证明 MMD 在 RKHS 中丢失了一些有用的统计信息。因此，本文提出了一种改进的 TJM 方法，称为基于最大均值和协方差差异的转移联合匹配与威尔士损失 (MMCD-WTJM)。在 MMCD-WTJM 中，最大均值和协方差差异 (MMCD) 而不是 MMD 被纳入 TJM 以匹配 RKHS 中的更多统计信息。同时，在TJM中加入了Welsh损失函数来增强模型的稳定性。此外，我们开发了增强的分层符号动态熵（EHSDE）来提取更有用的特征表示。最终，开发了一种基于 EHSDE 和 MMCD-WTJM 的新型混合跨域轴承故障识别。八项传递轴承故障识别任务的分析结果表明，所开发的方法在不同运行条件和不同机器下的智能轴承健康监测方面具有出色的能力。与现有的基于熵的故障特征提取方法和基于域适应的转移故障诊断方法相比，