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The dynamic responses of wind turbine towers subjected to earthquakes and winds are very complex and might cause significant damages. However, the reproduction of the dynamic response in a laboratory is not easy because the specimen shall be scaled very small to meet the space limits of wind tunnels and shaking tables. Real-time hybrid testing (RTHT) is an appealing option to solve this difficulty, which takes part of a structure as the specimen, while treats the rest numerically so that large scale specimen could be used. However, the application of RTHT to a wind turbine tower requires more complex boundary coordination to reproduce the coupled shear and bending behavior. This paper proposes a shaking-table substructure testing framework, where the lower part of the tower is fixed on the shaking table at the bottom and the top of the specimen is simultaneously loaded by a two-degree-of-freedom loading device. The loading facilities communicate in real time with the numerical substructure, and the superstructure including the wind turbine and blades is numerically simulated under the external excitations. Displacements and forces at the boundary are transferred between the numerical and physical substructures to realize boundary compatibility and equilibrium. A novel boundary loading device controls two masses to realize bending and shear equilibrium at the same boundary surface. Enhanced three-variable control is proposed to improve the performance of boundary coordination and the error-response negative feedback compensation method is proposed to reduce error transmission in RTHT, as demonstrated and introduced in a series of simulations and conceptual study.

Real-time hybrid simulation (RTHS) is recently applied to study the vibration of the vehicle–bridge coupling system, where bridges and the vehicle are the numerical and experimental substructures respectively. Inevitable time delay of the boundary loading imposed to the experimental substructure will greatly affect the accuracy and stability of RTHS. To minimize the time delay effects, this paper proposes a recursive prediction optimal (RPO) compensator based on optimal control and recursive least squares. The numerical simulation of the RTHS of the vehicle–bridge coupling system is conducted using MATLAB/Simulink. The performance of the RPO method is compared with three traditional time delay compensation methods (i.e. the polynomial extrapolation (NI), the inverse compensation (IC) and the derivative feedforward (DF)) through both open-loop and RTHS simulations. The RPO method shows the best compensation performance in the frequency range up to 20[Formula: see text]Hz.

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.