SUMMARYIt has been shown that the operator-splitting method (OSM) provides explicit and unconditionally stable solutions for quasi-static pseudo-dynamic substructure testing. However, the OSM provides only an explicit target displacement but not an explicit target velocity, so that it is essentially an implicit method for real-time substructure testing (RST) when the velocity-dependent restoring force is considered. This paper proposes a target velocity formulation based on the forward di erence of the predicted displacements so as to render the OSM explicit for RST. The stability and accuracy of the resulting OSM-RST algorithm are investigated. It is shown that the OSM-RST is unconditionally stable so long as the non-linear sti ness and damping are of the softening type (i.e. the tangent sti ness and damping never exceed the initial values). The stability of the OSM-RST for structures with inÿnite tangent damping coe cient or sti ness is also proved, and the stability of the method for MDOF structures with a non-classical damping matrix is demonstrated by an energy criterion. The e ects of actuator delay and compensation are analysed based on the bilinear approximation of the actuator step response. Experiments on damped SDOF and MDOF structures verify that the stability of the OSM-RST is preserved when the experimental substructure generates velocity-dependent reaction forces, whereas the stability of real-time substructure tests based on the central di erence method is worsened by the damping of the specimen.

SUMMARYHybrid simulations that combine numerical computations and physical experiment represent an effective method of evaluating the dynamic response of structures. However, it is sometimes impossible to take all the uncertain or nonlinear parts of the structure as the physical substructure. Thus, the modeling errors of the numerical part can raise concerns. One method of solving this problem is to update the numerical model by estimating its parameters from experimental data online. In this paper, an online model updating method for the hybrid simulation of frame structures is proposed to reduce the errors of nonlinear modeling of numerical substructures. To obtain acceptable accuracy with acceptable extra computation efforts as a result of model parameter estimation, the sectional constitutive model is adopted, therein considering axial-force and bending-moment coupling; moreover, the unscented Kalman filter is used for parameter estimation of the sectional model. The effectiveness of the sectional model updating with the unscented Kalman filter is validated via numerical analyses and actual hybrid tests on a full-scale steel frame structure, with one column as the experimental substructure loaded by three actuators to guarantee the consistency of the boundary conditions.

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