Organizations: Dynamics Research Group, School of Mechanical, Aerospace, and Civil Engineering, University of Sheffield, Sheffield, Mappin St, Sheffield, United Kingdom
The current paper introduces the GraphNARX model, a graph-based nonlinear autoregressive exogenous model for structural dynamics. The model is built to account for the geometry of structures and to model dynamic behaviour as the interaction between elements of the structure. Similar to other types of NARX models, GraphNARX is used for system identification. Nodal attributes of the graph encode past displacements and nodal forces, and the output of the model is the next-timestep displacement. The graph formulation of the model allows it to generalise to structures of different dimensions and degrees of freedom. Moreover, because graph-learning is performed locally between the nodes, the GraphNARX model can also learn to infer displacements of nodes for which data are not available, i.e.\ to perform virtual sensing. The proposed model's performance is evaluated in a system-identification framework and a virtual-sensing framework, and achieves good accuracy and exhibits generalisation capabilities to structures of different sizes.
Figures & tables
Figure 1: General graph example.
Figure 2: Example mass-spring system of ten degrees of freedom.
Figure 3: Graph representation of the mass-spring system of Figure 2 .
Figure 4: Input graph representation of mass-spring system for the proposed GraphNARX model.
ID
ϕe
ϕv
GNN 1
(ny,10,5)
(5+ny+nx,15,1)
GNN 2
(ny,15,7)
(7+ny+nx,20,1)
GNN 3
(ny,20,10)
(10+ny+nx,25,1)
Table 1: GNN network sizes considered in training
Figure 5: Example of actual displacements (blue curve) compared to multi-step-ahead predictions of the GraphNARX model (orange curve) for the sixth degree-of-freedom of the ten-degree-of-freedom system.
Figure 6: Average NMSE for different values of timestep-ahead predictions of the GraphNARX model for the testing dataset of the ten-degree-of-freedom system.
Figure 7: Example of actual displacements (blue curve) compared to multi-step-ahead predictions of the GraphNARX model (orange curve) for the tenth degree-of-freedom of the 20-degree-of-freedom system.
Figure 8: Average NMSE for different values of timestep-ahead predictions of the GraphNARX model for the testing dataset of the 20-degree-of-freedom system.
Figure 9: Example of actual displacements (blue curve) and predicted displacements (orange curve) for the virtual-sensing application for the sixth node of the ten-degree-of-freedom system, which was assumed to not have a sensor. The mask for the system was m=[1,0,1,0,1,0,1,0,1,0] , where 1 indicates an available sensor and 0 a missing sensor
Figure 10: Example of actual displacements (blue curve) and predicted displacements (orange curve) for the virtual-sensing application for the 11 th node of the 20-degree-of-freedom system, which was assumed to not have a sensor. The mask for the system was m=[0,0,1,0,0,1...0,0,1] , where 1 indicates an available sensor and 0 a missing sensor
R. B. Annis School of Engineering University of Indianapolis Indianapolis United States · Department of Civil Engineering National Yang Ming Chiao Tung University Hsinchu Taiwan