Graphormer-VAE Model for Twin Load Estimation of Hydraulic Presses Using Multiphysics Simulation and Strain Data

Source abstract

Direct measurement of the distributed forming load in a large hydraulic press is difficult, particularly when die contact is asymmetric and frame strain is affected by temperature and support compliance. This study develops a Graphormer-VAE digital-twin estimator that combines a compact mechanical graph, multiphysics finite-element response descriptors, and sparse strain measurements to infer total vertical load and eccentric moment. Graph-biased attention encodes structural distance, edge class, and sensor centrality, while a variational latent layer provides a distribution over load states. The model was evaluated with 1,260 production-like strokes from a 20 MN four-column press, including centered loading, 60 and 120 mm lateral offsets, asymmetric die contact, and thermal-drift cases. Its mean absolute total-load error was 1.82% of rated capacity, and its eccentric-moment error was 3.7%. The corresponding errors for a graph convolutional baseline were 2.39% and 5.1%. The nominal 95% prediction interval achieved 94.1% empirical coverage, and mean inference latency was 18.6 ms per stroke window, below the 20 ms acquisition period used in this study. Removing multiphysics residual conditioning increased load error by 0.91 percentage points; removing graph-distance bias increased moment error by 1.4 percentage points. The estimator therefore links spatially sparse measurements to both load magnitude and load imbalance while expressing uncertainty. Its evidence is limited to the tested press, sensor layout, and operating cases, so transfer to other machines requires separate validation.