Toward Data-Driven Dynamic Substructuring in Frequency Domain

The aim of this work is to integrate a machine-learning (ML)-based meta-model into a conventional structural vibration model in a componentwise manner using dynamic substructuring. In dynamic substructuring, the finite element (FE) method is one of the popular ways of modeling substructures. In this study, we theoretically examine dynamic substructuring formulations for cases where an ML-based meta-model replaces an FE substructure of an assembled global structure. In dual assembly and frequency domain, vibration features of a substructure acting on the other substructure can be independently defined as an interface dynamics stiffness matrix and an interface effective force vector. This substructural information can be described as the ML-based meta-model. Consequently, a hybrid modeling technique of the FE model and ML-based meta-model can be achieved in the proposed formulation. In this study, a feed-forward neural network (FNN) with supervised learning is employed to define the ML-based meta-model, which can predict the interface effective force and the interface dynamic stiffness of a substructure from various input parameters, such as material properties, geometry, and loading conditions. Two FNNs are then utilized to handle the complex numbers caused by damping, with separate training for real and imaginary parts. An additional attractive feature of the proposed hybrid method is that it can handle nonmatching mesh problems with ease. The performance of the proposed FE-ML hybrid method is illustrated through numerical examples.