Implementation of real-time hybrid simulation using a large shake table with onboard actuators

Real-time hybrid simulation (RTHS) is a promising cyber-physical technique for the experimental evaluation of civil infrastructure systems subject to extreme dynamic loading. It allows for simulation of highly complicated civil infrastructure systems in a cost effective manner by partitioning them into numerical and physical substructures. And the coupling at the interface is achieved by enforcing equilibrium and compatibility at real-time. In RTHS, development of some systematic and random errors in the physical substructure are inevitable and can have substantial impacts on the quality of the simulation results. It has been shown that the reliability of RTHS results is highly dependent upon how successfully these sources of error in the physical substructure are mitigated. Some significant sources of error in RTHS are transfer system dynamics, e.g. dynamics of hydraulic actuator, and time delay, e.g. communication and computation delays. In this paper, we will show how a multi-degree of freedom (MDOF) RTHS system can be modeled with delay differential equations (DDE). Afterwards, a 4-story RTHS will be used as an illustrative numerical example to delineate how this DDE model can capture some important features of RTHS. Finally, the effects of transfer system dynamics on the quality of RTHS results will be shown for a 2-story structure and then the DDE model will be verified.

Gain-margin based discrete-continuous method for the stability analysis of real-time hybrid simulation systems

This paper demonstrates a real-time hybrid substructuring (RTHS) shake table test to evaluate the seismic performance of a base isolated building. Since RTHS involves a feedback loop in the test implementation, the frequency dependent magnitude and inherent time delay of the actuator dynamics can introduce inaccuracy and instability. The paper presents a robust stability and performance analysis method for the RTHS test. The robust stability method involves casting the actuator dynamics as a multiplicative uncertainty and applying the small gain theorem to derive the sufficient conditions for robust stability and performance. The attractive feature of this robust stability and performance analysis method is that it accommodates linearized modeled or measured frequency response functions for both the physical substructure and actuator dynamics. Significant experimental research has been conducted on base isolators and dampers toward developing high fidelity numerical models. Shake table testing, where the building superstructure is tested while the isolation layer is numerically modeled, can allow for a range of isolation strategies to be examined for a single shake table experiment. Further, recent concerns in base isolation for long period, long duration earthquakes necessitate adding damping at the isolation layer, which can allow higher frequency energy to be transmitted into the superstructure and can result in damage to structural and nonstructural components that can be difficult to numerically model and accurately predict. As such, physical testing of the superstructure while numerically modeling the isolation layer may be desired. The RTHS approach has been previously proposed for base isolated buildings, however, to date it has not been conducted on a base isolated structure isolated at the ground level and where the isolation layer itself is numerically simulated. This configuration provides multiple challenges in the RTHS stability associated with higher physical substructure frequencies and a low numerical to physical mass ratio. This paper demonstrates a base isolated RTHS test and the robust stability and performance analysis necessary to ensure the stability and accuracy. The tests consist of a scaled idealized 4-story superstructure building model placed directly onto a shake table and the isolation layer simulated in MATLAB/Simulink using a dSpace real-time controller.

Impedance matching control design for the benchmark problem in real-time hybrid simulation

The technology of real-time hybrid simulation (RTHS), which is one of the methods to test the performance of train operation on bridge in recent years, has strict real-time requirements. Combined with the fixed-point iteration (FPI) algorithm, this paper developed an off-line iterative hybrid simulation (OIHS) method, avoiding real-time synchronization between numerical and physical parts in RTHS to reproduce train–track–bridge coupling-vibration (TTBV) of high-speed railway in laboratory. In OIHS, the physical train model was installed on the shake table, while the response of the numerical track–bridge structure was simulated. To improve the test reproduction accuracy of the TTBV in high-speed railway, based on the shake table inherent off-line iterative control which is reproduce the commands issued to the shake table, an outer loop off-line iterative controller was designed to form a double-layer off-line iterative control framework to correct the response error between the subsystems. Compared with traditional finite element analysis, the accuracy and efficiency of the OIHS method were validated by numerical simulation and shake table test. The results demonstrated that the OIHS method can solve the dynamic convergence problem of the train–track–bridge on high-speed railway accurately and efficiently.

For Real-time hybrid simulation (RTHS) to be stable and accurate, it is essential to address the time desynchronization issue between the numerical and physical substructures. Desynchronization is primarily caused by time delays, inherent dynamics of the control plant, system uncertainties, and noises. While existing adaptive compensators have shown effective tracking performance in single-input single-output (SISO) RTHS, their effectiveness in multi-input multi-output (MIMO) RTHS has not been fully demonstrated. MIMO-RTHS presents additional challenges due to its larger solution space, and significant dynamic coupling between actuators. To address these challenges, this study introduces an adaptive compensation framework for MIMO-RTHS. The proposed framework utilizes a control law based on the inverse dynamics of the control plant, incorporating real-time adaptive parameter updates through Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) methods. Both the transfer function (TF) and discrete-time state-space (SS) models of the plant are employed in distinct parameter estimation cases. The performance of the proposed compensation is validated through a multi-axial RTHS (maRTHS) benchmark problem. Extensive simulations on the maRTHS incorporating various earthquake inputs, sensor noise, and model uncertainties, demonstrated an excellent tracking performance and strong robustness across four parameter estimation cases (EKF-TF, UKF-TF, EKF-SS, and UKF-SS). The use of UKF with SS model (UKF-SS) achieved superior performance, effectively managing nonlinearities and noise without requiring low-pass filtering.

In this paper, a new experimental method of full scale real time shaking table test of structural element is introduced. The main feature of this experimental method is characterized by the use of the inertial loading equipment. The inertial loading equipment consists of a loading frame, a counter weight and isolators. The loading frame supported by the isolators was set on the shaking table. Specimens used in this experimental method were partial frames taken out from full scale building structures. The test set-up was composed of a specimen, the inertial loading equipment and loading beam which transmits the horizontal force to the specimen from the inertial loading equipment. This test set-up, regarded as a single degree of freedom system, makes it easy to understand the dynamic behavior of the test set-up including a specimen. Furthermore, the natural period of the experimental system corresponds to the fundamental natural period of existing building structures. So, full scale and real time dynamic loading test of partial frame can be realized. This method was developed for the existing large scale shaking table and the effectiveness has been already verified through many experiments. Further development of the experimental method adjusted to the 3-D largest shaking table under construction at present is also described.

Real-time hybrid simulation (RTHS) combines physical experimentation with numerical simulation to evaluate dynamic responses of structures. The inherent characteristics of integration algorithms change when simulating numerical substructures owing to the response delay of loading systems in physical substructures. This study comprehensively investigates the effects of integration algorithms on the delay-dependent stability and accuracy of multiple degrees-of-freedom RTHS systems. Seven explicit integration algorithms are considered; and the discrete-time root locus technique is adopted. It is found that the stability of RTHS system is mainly determined by the time delay rather than the integration algorithms, whereas its accuracy mainly depends on the accuracy characteristic of the applied integration algorithm itself. An unconditionally stable integration algorithm cannot always guarantee good stability performance; and the inherent accuracy or numerical energy dissipation of integration algorithms should be taken into account in RTHSs. These theoretical findings are well verified by RTHSs.

High performance compensation using an adaptive strategy for real-time hybrid simulation

Real-time hybrid simulations using large-scale magnetorheological (MR) dampers were conducted to evaluate the performance of various structural control strategies to control the seismic response of a three-story steel-frame building. Magnetorheological dampers were installed in the building to limit the story drift to less than 1.5% under the design-basis earthquake (DBE). The laboratory specimens, referred to as experimental substructures, were two individual MR dampers, with the remainder of the building modeled as a nonlinear analytical substructure. The experimental technique enables an ensemble of ground motions to be applied to the building, resulting in various levels of damage, without the need to repair the experimental substructures because the damage will be within the analytical substructure. Five different damper control algorithms, including passive and semiactive control algorithms, were selected. An ensemble of five ground motions scaled to the DBE was used for the real-time hybrid simulations to obtain statistical responses of the structure for each control. The real-time hybrid simulation results show that the MR dampers can control the drift, enabling the performance objective of 1.5% maximum story drift to be achieved. Although some semiactive controllers show better performance for a specific ground motion, the response statistics from the real-time hybrid simulations show that the overall performance of the semiactive control algorithms with the selected user-defined parameters is similar to that for the passive controller for the three-story building used in this study. A comparison of real-time hybrid simulation results with numerical simulation results using OpenSees was conducted to further gain insight into the performance of the damper control algorithms observed in the real-time hybrid simulations.

Real-time hybrid simulation combines experimental testing and numerical simulation by dividing a structural system into experimental and analytical substructures. Servohydraulic actuators are typically used in a real-time hybrid simulation to apply command displacements to the experimental substructure(s). Servohydraulic actuators may develop a time delay due to inherent actuator dynamics that results in a desynchronization between the measured restoring force(s) and the integration algorithm in a real-time hybrid simulation. Inaccuracy or even instability will occur in a hybrid simulation if actuator delay is not compensated properly. This paper presents an adaptive compensation method for actuator delay. An adaptive control law is developed using an error tracking indicator to adapt a compensation parameter used in the proposed compensation method. Laboratory tests involving large-scale real-time hybrid simulations of a single degree of freedom moment resisting frame with an elastomeric damper are conducted to experimentally demonstrate the effectiveness of the proposed adaptive compensation method. The actuator tracking capability is shown to be greatly improved and exceptional experimental results are still achieved when a good estimate of actuator delay is not available.

Adaptive model reference control method for real-time hybrid simulation

Seismic performance assessment of a low-rise thin reinforced concrete wall building with unconnected fiber reinforced elastomeric isolators using real-time hybrid simulations

Magneto-rheological (MR) fluid dampers can be used to reduce the traffic induced vibration in highway bridges and protect critical structural components from fatigue. Experimental verification is needed to verify the applicability of the MR dampers for this purpose. Real-time hybrid simulation (RTHS), where the MR dampers are physically tested and dynamically linked to a numerical model of the highway bridge and truck traffic, provides an efficient and effective means to experimentally examine the efficacy of MR dampers for fatigue protection of highway bridges. In this paper a complex highway bridge model with 263 178 degrees-of-freedom under truck loading is tested using the proposed convolution integral (CI) method of RTHS for a semiactive structural control strategy employing two large-scale 200 kN MR dampers. The formation of RTHS using the CI method is first presented, followed by details of the various components in the RTHS and a description of the implementation of the CI method for this particular test. The experimental results confirm the practicability of the CI method for conducting RTHS of complex systems.

Model-based feedforward–feedback tracking control has been shown as one of the most effective methods for real-time hybrid simulation (RTHS). This approach assumes that the servo-hydraulic system is a linear time-invariant model. However, the servo-control closed-loop is intrinsically nonlinear and time-variant, particularly when one considers the nonlinear nature of typical experimental components (e.g., magnetorheological dampers). In this paper, an adaptive control scheme applying on a model-based feedforward–feedback controller is proposed to accommodate specimen nonlinearity and improve the tracking performance of the actuator, and thus, the accuracy of RTHS. This adaptive strategy is used to estimate the system parameters for the feedforward controller online during a test. The robust stability of this adaptive controller is provided by introducing Routh’s stability criteria and applying a parameter projection algorithm. The tracking performance of the proposed control scheme is analytically evaluated and experimentally investigated using a broadband displacement command, and the results indicates better tracking performance for the servo-hydraulic system can be attained. Subsequently, RTHS of a nine-story shear building controlled by a full-scale magnetorheological damper is conducted to verify the efficacy of the proposed control method. Experimental results are presented for the semi-actively controlled building subjected to two historical earthquakes. RTHS using the adaptive feedforward–feedback control scheme is demonstrated to be effective for structural performance assessment.