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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.
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This content will become publicly available on July 1, 2026
Multi-physics framework for seismic Real-time Hybrid Simulation of soil–foundation–structural systems
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.
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- Award ID(s):
- 2037771
- PAR ID:
- 10618623
- Editor(s):
- Yang, J
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Engineering Structures
- Volume:
- 334
- Issue:
- C
- ISSN:
- 0141-0296
- Page Range / eLocation ID:
- 120247
- Subject(s) / Keyword(s):
- Real-time hybrid simulation Seismic soil–structure interaction LSTM neural networks Macroelement modeling Real-time online model updating Nonlinear viscous dampers
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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