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Graph-based two-way multi-task Gaussian process model for full-field reconstruction in complex mechanical structures
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DOI：10.1007/s00158-025-04118-4.png)
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Abstract
En 中文
Full physical field reconstruction is a challenging problem in design and digital twin modeling that has garnered significant attention in recent years. This paper addresses the reconstruction of physical fields for complex mechanical structures using finite element method (FEM) by proposing a novel graph-based two-way multi-task Gaussian process (GT-MTGP) model. In this approach, loads are defined as state inputs, while nodes from the FEM are treated as task inputs. The GT-MTGP framework constructs both state and task correlation functions, enabling the prediction of responses for both unknown loads and nodes. This allows the model to evaluate the full physical field using sparse points from the structure. Furthermore, to enhance the model’s representation of complex structures, a graph-based distance metric is introduced for the task correlation function, leveraging the FEM mesh. This distance is defined as the shortest path between nodes in the graph structure, offering a more reasonable measure than coordinate-based distance, particularly in complex structures where connectivity is a critical factor. To validate the proposed method, experiments are conducted on three typical mechanical structures: a cracked plate, a cylindrical shell with a rectangular hole, and a solid spoke in a head sheave. The results demonstrate that the GT-MTGP model outperforms single-task models and highlight the effectiveness of the graph-based distance metric in handling complex mechanical structures.
Keywords:
Full physical field reconstruction
Surrogate model
Multi-task Gaussian process
Graph-based distance
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