A deep-learning method for modeling geometric deviations of complex surfaces

Parts with complex surfaces have become increasingly exploited due to advanced manufacturing processes. The extensive use of these complex parts in industry in recent years has led to new challenges within the design process when simulating their geometric defects for function assessment, quality control and tolerance analysis. Compared to mechanical parts with regular geometric surfaces and well-established geometrical specification standards, the geometry of complex surfaces is often difficult to be represented by explicit parameters or processed by feature operations, which poses challenges to the modelling and simulation of geometric deviations. Skin Model Shapes (SMSs) enable a discrete representation of surface deviations that allows the storage, simulation and analysis of shapes' geometric variations, and have been successfully applied for canonical geometries. In this paper, a method for generating geometric deviations on parts with complex surface based on deep learning is proposed. Laplace-Beltrami Operator (LBO) is exploited to encode geometric deviations as manufacturing signature and deviations patterns. After pre-processing steps, deviation patterns selected from modal decomposition are used as training data for the mesh Convolutional Neural Networks (CNN), which establishes the links between patterns and parts' manufacturing factors, and transferred to target shapes. Geometric deviations are generated on target shapes by linear combination of the transferred patterns with respect to manufacturing signature. A case study is implemented from an open dataset to illustrate the proposed method. The simulated geometric deviations show their effectiveness and potential to improve the design process and the manufacturing accuracy of parts with complex surfaces.