Graph-based dual-attention model for multi-bend tube forming quality prediction with basis spline cross-sectional fitting

Spatial multi-bend tubes are widely used in high-end equipment because they provide flexible spatial routing and lightweight structural integration. However, their forming quality is difficult to predict because the deformation of each bend influences the subsequent bends, leading to cumulative axial and cross-sectional errors. This study proposes a graph-based dual-attention framework for predicting the forming quality of spatial multi-bend tubes under given process parameters. A closed basis spline representation in a polar-coordinate cross-sectional frame is introduced to describe continuous cross-sectional deformation, while a kinematics-based key-point representation is adopted to characterize axial forming accuracy. A hierarchical graph attention module is used to capture intra-section and inter-segment geometric dependencies, and a segment-to-tube decoder integrates cross-sectional features with process parameters for axial prediction. The framework is trained on finite-element data generated for rotary draw bending of 316L stainless steel tubes and is further examined using physical bending experiments. The results show that the proposed method provides accurate prediction of both cross-sectional deformation and axial forming accuracy, demonstrating its potential for data-driven quality evaluation in multi-bend tube manufacturing.