Generative adversarial networks and hessian locally linear embedding for geometric variations management in manufacturing

Geometric variations and uncertainty are generally observed on every manufactured workpiece and have a critical influence on the functional performance of mechanical parts. In computer-aided tolerancing, the Skin Model Shapes framework is recognized as a novel paradigm to embed the expected and observed geometric variations of mechanical products based on discrete geometry representation schemes. Currently, the generation of Skin Model Shapes is still limited due to the lack of knowledge-based parameter settings in the design process, and the consideration of enriched simulation and measurement data. In this paper, a novel method based on two distinct techniques, namely Generative Adversarial Networks (GAN) and Hessian Locally Linear Embedding (HLLE), is proposed to generate Skin Model Shapes without any explicitly defined parameters. A Wasserstein GAN structure is trained for generating patterns of geometric deviations based on simulation data. Geometric deviations on planar and cylindrical surfaces are considered in a training process since both types of surfaces are widely used in mechanical engineering. HLLE is used in the paper to extend the implementation of the proposed deviation mapping process from planar/cylindrical surfaces to other types of surfaces scattered in 3D space. The proposed Skin Model Shapes generation process enables the efficient generation of part representatives with geometric deviations without the need for extensive deviation modeling. Meanwhile, the proposed method overcomes the common limitation of simulating different types (e.g. rotational and freeform) of non-ideal surfaces on Skin Model Shapes. The implemented case studies show that our method can be used to generate hundreds of distinct Skin Model Shapes within seconds while the distributions of simulated geometric deviations on the surfaces are consistent with the measurement results. Meanwhile, the generated Skin Model Shapes can be used for further applications such as assembly simulation and tolerance analysis to obtain more realistic simulation results.