ECCOMAS 2024

Reduced order modeling of road structures in a digital twin

  • Kehls, Jannick (RWTH Aachen University)
  • Reese, Stefanie (RWTH Aachen University)
  • Brepols, Tim (RWTH Aachen University)

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Studying structural problems in engineering fields is crucial in ensuring the safety and longevity of structures. This especially holds for critical infrastructure such as roads. Having real-time sensor data available is of course a necessity for the prediction of e.g. structural failure. In the best case, the real-time sensor data is used to predict quantities of interest in the future. Therefore, finite element (FE) simulations are used within a digital twin, incorporating real-time sensor data that shall predict the structural behavior [1]. A problem with this predictive process can occur when the simulation has a large number of degrees of freedom, which easily happens when either the desired simulated geometry is big, or a fine discretization needs to be used in order to ensure a good agreement of the simulation and the real-world measurements. The finite element simulation can take a long time and a large amount of computational resources, which in some cases might lead to the point where the simulation loses its predictive value. To counteract the complexity of the simulations, projection-based model order reduction techniques can be used. First, results of full order simulations capturing the expected structural behavior are sampled and then used to construct a reduced order model. In case of the proper orthogonal decomposition (POD), a singular value decomposition of the sampled solution states is used to construct the POD projection matrix [2]. This projection matrix can be used to reduce the dimensions of the linear system of equations that has to be solved in the FE simulation leading to a reduction in computation time. Because the POD is only able to reduce the time to solve the system of equations, further methods have to be used to reduce the time to construct the system of equations, which can take up a lot of time in nonlinear problems [3]. These methods are called hyper-reduction methods. Applying the proposed methodology to an exemplary structural simulation of a road, the simulation time can be massively reduced without sacrificing the validity of the results. [1] M. Kaliske and I. Wollny, Bautechnik 100(7): 374-382, 2023 [2] A. Radermacher and S. Reese, Int. J. Numer. Methods Eng. 107(6): 477-495, 2016 [3] J. A. Hernandez, M. A. Caicedo and A. Ferrer, Comput. Methods. Appl. Mech. Eng. 313: 687-722, 2017