Real-time hybrid simulation of structural systems with soil-foundation interaction effects using neural networks

Real-time hybrid simulation (RTHS) involves dividing a structural system into numerical and experimental substructures. The experimental substructure is challenging to model analytically and is therefore modeled physically in the laboratory. Analytical substructures are conventionally modeled using the finite element method. The two substructures are kinematically linked, and the governing equations of motion are solved in real-time. Thus, the state determination of the analytical substructure needs to occur within the timestep, which is of the order of a few milliseconds. All structural systems are supported by a soil-foundation system and any evaluation of the efficacy of response modification devices placed in the structure should consider soil-foundation structure interaction (SFSI) effects. SFSI adds compliance to a structural system, thereby altering the natural frequencies. Additionally, nonlinear behavior in the soil can result in residual deformations in the foundation and structure, as well as provide added damping. These effects can occur under both wind and earthquake loading. To overcome the barrier of the large computational effort required to model SFSI effects in real-time using the conventional finite element approach, a neural network (NN) model is combined with an explicit-based analytical substructure and experimental substructure with dampers to create a framework for performing RTHS with SFSI effects. The framework includes a block of long-short term memory (LSTM) layers that is combined with a parallel rectified linear unit (ReLU) to form a NN model of the soil-foundation system. RTHS of a tall 40-story steel building equipped with nonlinear viscous dampers and subjected to a windstorm are performed to illustrate the framework. It was found that a number of factors have an effect on the quality of RTHS results. These include: (i) the discretization of the wind loading into bins of basic wind speed; (ii) the extent of the NN model training as determined by the root mean square error (RMSE); (iii) noise in the restoring forces produced by the NN model and its interaction with the integration algorithm; and, (iv) the bounding of outliers of the NN model's output. Guidelines for extending the framework for the RTHS of structures subjected to seismic loading are provided.