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Real-time hybrid simulation (RTHS) is a practical, cost-effective, and versatile experimental technique to evaluate structural performance under dynamic excitation. The simulated structure is commonly split into a physically tested rate-dependent substructure (PS) and a numerically simulated substructure (NS). A transfer system such as a servo-hydraulic actuator is used to impose boundary conditions on the PS. Consequently, efficient actuator control is necessary to guarantee reliable simulation results. However, time delay and uncertainties exist due to the dynamics of the actuator, which adversely influence the accuracy and stability of RTHS. Therefore, an innovative robust actuator dynamics compensation method is proposed in this study comprising three components, namely a mixed sensitivity-based robust H∞ controller to stabilize the actuator–specimen dynamics, a polynomial extrapolation module to further cancel the actuator delay, and an adaptive filter for displacement reconstruction of the actuator–specimen system. A detailed design procedure of the proposed strategy is presented. The efficacy of the proposed strategy is validated through a series of virtual tests on the benchmark problem for RTHS. Results show that the proposed method exhibits excellent tracking performance and robustness. In particular, the maximum values of the calculated time delay (TD), root mean square of the tracking error (RMSE), and peak tracking error (PE) are 0 ms, 2.56%, and 2.12%, respectively, whereas the maximum values of the standard deviation of TD, RMSE, and PE are 0 ms, 0.25%, and 0.33%, respectively.

Proposed in this paper is an online hybrid test framework using a static and dynamic separated model scheme, where the equations of motion are solved by the operator-splitting (OS) algorithm, while the restoring force is obtained from a static analysis or quasi-static test of substructures. One of the keys of a successful substructure online hybrid test is the boundary coordination between the numerical and physical substructures. This is easily determined for the dynamic boundary whose displacement target is determined by the displacement predictor of the OS algorithm. However, the coordination is not straightforward for boundaries associated with static forces. This paper proposes an approximate method to determine the compatibility of the boundaries of static degrees of freedom, where the numerical substructure is analyzed first with the static boundary at the displacement of the previous step. The reaction force is then acquired from the analysis results as the target force of the corresponding degree of freedom of the physical substructure. The measured displacement is used as the target for the numerical substructure in the next step. In this procedure, the numerical substructure and the physical substructure alternatively move forward. Therefore, it is call staggered coordination. This is not a rigorous method to analyze boundary compatibility and equilibrium. However, it does make the substructure online hybrid test much easier and more feasible. Here, the staggered coordination scheme is examined by a six-story RC frame equipped with BRBs through both numerical simulation and physical testing. An energy-based index shows that the error introduced by this method can be ignored and that the proposed framework of online hybrid test works precisely without any malfunction.

Shaking table substructure testing takes the substructure with complex behavior physically tested, with the behavior of the rest structural system being numerically simulated. This substructure testing allows the payload of a shaking table being fully utilized in testing of the most concerned part, thus significantly increases its loading capacity. The key to achieve a successful shaking table substructure test is to coordinate among the substructures, specifically, to satisfy compatibility, equilibrium, and synchronization at the boundary between numerical and experimental substructures. A number of studies have focused on the essential techniques of shaking table substructure testing, and several applications have been carried out. Nonetheless, its progress is still in the preliminary stage, because of the limited applications using multi-directional shaking tables on large-scale specimens. This paper reviews a series of shaking table substructure tests and their associated implementation aspects including hybrid testing frameworks, time integration algorithms, delay compensation methods, shaking table and actuator control schemes and boundary force measurement methods. The key techniques required for a successful test are also stressed, such as the force control of actuators to coordination among the substructures. Finally, challenges for future studies and applications are identified and presented.

During a real-time hybrid simulation (RTHS), inevitable time delay of actuators when responding to a command will reduce the accuracy of test results and sometimes even cause unstable testing. The inner-loop controller of an actuator is generally capable of eliminating the effects due to small time-delays. However, if a test specimen behaves nonlinearly, accuracy of RTHS results will be impaired. In addition to the uncertainty of test specimens and transfer system, measurement noises of the displacement and force sensors also require a robust external controller for RTHS. In this paper, a robust linear-quadratic-gaussian (LQG) controller with a Loop Transfer Recovery (LTR) procedure and a polynomial-based feedforward prediction (FP) algorithm is proposed to compensate the adverse effects due to time delay and uncertainties within the RTHS testing system. The stability and robustness of the proposed controller are analysed in the frequency domain using the Nyquist curve and the Bode diagrams. Numerical simulations are then carried out on the benchmark problem using both the proposed robust and the conventional LQG controllers and their performance is compared using the nine evaluation criteria. It is demonstrated that the robust LQG (RLQG) controller outperforms the conventional LQG controller in terms of compensating the parameter uncertainties in the testing system and achieving accurate RTHS results.

Train-track-bridge interactions (TTBIs) in high-speed railways affect the response of the train on the bridge and involve complicated dynamics. This study introduced an improved real-time hybrid simulation (RTHS) method, wherein a physical train model was tested on a shake table, while the dynamics of the track-bridge structure were determined numerically. The moving load convolution integral method (MLCIM) was proposed for the real-time calculation of the track-bridge structure dynamics independent of the complexity of the numerical model. The results obtained using the MLCIM were compared to those obtained using the traditional finite element method to verify its accuracy and efficiency. Next, the TTBI characteristics of a train moving across a seven-span simply supported bridge with the track structure were analyzed for cases of different girder stiffnesses and train speeds. The results demonstrated that the improved RTHS method using the MLCIM effectively represented the TTBI dynamics. The girder stiffness and train speed were shown to substantially influence the responses of the moving train. Further, a ride comfort evaluation confirmed the operational performance of a train on the studied track-bridge structure.

Shaking table tests (STTs) provide an effective method to realistically assess seismic performance of nonstructural components (e.g., ceilings, water pipe supports and hangers, and glass screen walls), whose damage losses have been found to exceed those of structural components in recent earthquakes. During a shaking table test, nonstructural components respond upon the floor motion of a supporting frame where nonstructural components are attached to. Accurately reproducing floor response spectra of the supporting frame is therefore critical to achieve consistent and high-quality test results. This paper proposes a multi-directional decoupling iteration (MDI) control method to achieve this demand. The principle of the proposed MDI method is explained first. The effectiveness of the proposed controller to overcome the dynamic coupling between the supporting frame and the shaking table and to accurately reproduce floor response spectra along multi-directions is validated through a series of STTs of water pipe supports and hangers.

Benchmark problem for real-time hybrid simulation (RTHS) is proposed to enable researchers assessing the robustness and performance of various tracking controllers in a uniform setting. In this paper, a controller combining the sliding mode controller (SMC) and an improved adaptive polynomial-based forward prediction (IAFP) algorithm is proposed. The SMC is adopted for its robustness to the uncertainties that may be experienced in an RTHS testing; while the IAFP is employed as a time delay compensator to stabilize RTHS with large time delay and reduce the time delay effects. Numerical simulations and physical experiments of the RTHS on a linear test specimen are conducted utilizing the program available through the benchmark problem. Time history responses obtained from RTHS are compared with those of the reference model and the nine evaluation criteria are computed, from which the robustness of the proposed controller and accurate RTHS results are demonstrated.

Real-time hybrid simulation (RTHS) is an innovative and versatile technique for evaluating the dynamic responses of structural and mechanical systems. This technique separates the emulated system into numerical and physical substructures, which are analyzed by computers and loaded in laboratories, respectively. Ensuring the boundary conditions between the two substructures through a transfer system plays a significant role in obtaining reliable and accurate testing results. However, measurement noise and the delay between commands and responses due to the dynamic performance of the transfer system are inevitable in RTHS. To address these issues and to achieve outstanding tracking performance and excellent robustness, this paper proposes an adaptive Kalman-based noise filter and an adaptive two-stage delay compensation method. In particular, in the novel noise filter strategy, adaptive inverse compensation with parameters updated by the least squares method is adopted to accommodate the amplitude and phase errors induced by a traditional Kalman filter. In the proposed delay compensation method, classic polynomial extrapolation and an adaptive inverse strategy are employed for coarse and fine compensation, respectively. Virtual RTHS on a benchmark problem reveals the satisfactory tracking performance and robustness of the proposed methods. Comparisons with polynomial extrapolation and single-stage adaptive compensation indicate the superiority of the proposed two-stage delay compensation method.