Modern industries require efficient and reliable machinery. To ensure the stability of industrial equipment and avoid unnecessary downtime, it is important to gauge a machine's remaining useful life (RUL) accurately. This has been done using deep learning-based approaches. In particular, deep neural networks are considered promising in this regard. These include recurrent neural networks (RNNs), convolutional neural networks (CNNs), or hybrid networks.

Bi-layer metallic tube (BMT) plays an extremely crucial role in engineering applications, with rotary draw bending (RDB) the high-precision bending processing can be achieved, however, the product will further springback. Due to the complex structure of BMT and the high cost of dataset acquisi-tion, the existing methods based on mechanism research and machine learn-ing cannot meet the engineering requirements of springback prediction. Based on the preliminary mechanism analysis, a physical logic enhanced network (PE-NET) is proposed. The architecture includes ES-NET which equivalent the BMT to the single-layer tube, and SP-NET for the final predic-tion of springback with sufficient single-layer tube samples. Specifically, in the first stage, with the theory-driven pre-exploration and the data-driven pretraining, the ES-NET and SP-NET are constructed, respectively. In the second stage, under the physical logic, the PE-NET is assembled by ES-NET and SP-NET and then fine-tuned with the small sample BMT dataset and composite loss function. The validity and stability of the proposed method are verified by the FE simulation dataset, the small-sample dataset BMT springback angle prediction is achieved, and the method potential in inter-pretability and engineering applications are demonstrated.