<p>In practical industrial systems, dynamic fluctuations in operating conditions readily lead to imbalanced data distributions. New or sudden operating scenarios introduce data from unknown domains, resulting in an insufficient model generalisation and adaptability. While existing transfer learning methods attempt to address cross-domain prediction challenges, they remain constrained by weak generalisation capabilities in open-set scenarios and the difficulty in balancing online computational efficiency with prediction accuracy. Therefore, an offline-online multi-level transfer learning framework is proposed for open-set RUL prediction across multiple target domains. In the offline phase, multi-source domains are utilized to pre-train the model. In the online phase, the Dynamic Time Warping (DTW) method is utilized to determine the relationship between the uncertain original test data and multiple target domains firstly, forming a preliminary mixed target domain; an online weighted Maximum Mean Discrepancy (MMD) is designed to complete the transfer from the source domains to the mixed target domain; and a joint optimization strategy is devised for fine-tuning of the model. The strategy of offline pre-training combined with online fine-tuning achieves a balance between execution efficiency and predictive accuracy. Experiments on three open-access datasets demonstrate excellent transferable RUL prediction performance even though the test data differ greatly from the source and target domain data, helping to maintain the equipment reliably under complex conditions.</p>