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Real-time Hybrid Simulation (RTHS) is a technique wherein a structural system is divided into an analytical and an experimental substructure. The former is modeled numerically while the latter is physically present in the laboratory. The two substructures are kinematically linked together at their interface degrees of freedom (DOFs) and the equations of motion are solved in real-time to determine the structure’s response. One of the main challenges of RTHS is to include the effects of soil–foundation–structure interaction (SFSI), which can have a substantial effect on the overall response. The soil domain cannot be modeled experimentally due to the large payload size. On the other hand, modeling the soil domain numerically, using a continuum-based approach, in real-time is challenging due to the associated computational cost. To address these issues, this paper presents a framework for seismic RTHS of SFSI systems using a Neural Network (NN)-based macroelement model of the soil–foundation system. A coupled SFSI model is used to train the NN model and the loss function is based on dynamic equilibrium at the interface between the foundation and the structure. The framework is demonstrated using a three-story building with the lateral load resisting system comprised of moment resisting and damped brace frames. The proposed framework ensures a stable and accurate RTHS, accounting for SFSI by incorporating: (a) spring elements at the output DOFs of the NN model to remove rigid body modes; (b) dashpot elements at the output DOFs of the NN model to mitigate spurious higher frequencies of vibration; and (c) regularization in the NN model’s architecture with data augmentation to reduce overfitting. 

ABSTRACT Real‐time hybrid simulation (RTHS) is an experimental testing methodology that divides a structural system into an analytical and an experimental substructure. The analytical substructure is modeled numerically, and the experimental substructure is modeled physically in the laboratory. The two substructures are kinematically linked together at their interface degrees of freedom, and the coupled equations of motion are solved in real‐time to obtain the response of the complete system. A key challenge in applying RTHS to large or complex structures is the limited availability of physical devices, which makes it difficult to represent all required experimental components simultaneously. The present study addresses this challenge by introducing Online Cyber‐Physical Neural Network (OCP‐NN) models–neural network‐based models of physical devices that are integrated in real‐time with the experimental substructure during an RTHS. The OCP‐NN framework leverages real‐time data from a single physical device (i.e., the experimental substructure) to replicate its behavior at other locations in the system, thereby significantly reducing the need for multiple physical devices. The proposed method is demonstrated through RTHS of a two‐story reinforced concrete frame subjected to seismic excitation and equipped with Banded Rotary Friction Dampers (BRFDs) in each story. BRFDs are challenging to model numerically due to their complex behavior which includes backlash, stick‐slip phenomena, and inherent device dynamics. Consequently, BRFDs were selected to demonstrate the proposed framework. In the RTHS, one BRFD is modeled physically by the experimental substructure, while the other is represented by the OCP‐NN model. The results indicate that the OCP‐NN model can accurately capture the behavior of the device in real‐time. This approach offers a practical solution for improving RTHS of complex structural systems with limited experimental resources. 

Abstract 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.