166 E. E. Bas et al. Fig. 16.2 (a) El-Centro ground motion acceleration; and brace results from pure analysis: (b) displacement history, and (c) force history where Mis the mass matrix, and Kis the stiffness matrix given by Eqs. (16.2) and (16.3). M=[m] (16.2) K=[ka +ke] (16.3) For this study, the story mass mis selected to be 1.75 kN-s2/mm, and the frame stiffness (k a) is determined from the frame sections to be 176.75 kN/mm. The axial brace stiffness, along its local axis, is 1224.1 kN/mm. The resulting natural period of the frame is 0.294 s. The structure is assumed to have an inherent damping of 2% modeled using Rayleigh damping. The equation of motion of the full system can be written as shown in Eq. (16.4). m¨x +c˙x +kx =−m¨ug (16.4) c is the inherent viscous damping of the structure; x(t), ˙x(t), and ¨x(t) are the displacements, velocity, and acceleration response, respectively, and ¨ug is the ground motion acceleration. For HS, the equation is rewritten such that ka is the frame stiffness representing the analytical substructure, and ke is the experimental stiffness which represents the brace stiffness. The brace stiffness is transformed into global coordinates. In the HS case, the feedback from the experimental substructure replaces the kexi term in Eq. (16.5). m¨xi +c ˙xi +(ka +ke)xi =−m¨ug (16.5) The pure analytical model that is developed in Simulink is using the Chang integration algorithm and uses a 1/2048 s time step [22]. The time step of the integration is selected to be the same as the controller time step to synchronize the data transfer. For the purpose of dynamic analysis, and later the HS seismic testing, a typical California ground motion is selected and used, which is the 1940 El-Centro ground motion excitation shown in Fig. 16.2a. From pure dynamic analysis, the brace displacement and brace force histories are obtained and shown in Fig. 16.2b and c, respectively. It is noted that such time history data is modified and used as the training data, to represent the feedback data, for the machine learning approach. To do so, a 28-time step delay is considered along with the pure analytical model data when used for the training and validation phases of pure analysis of the metamodel. As previously mentioned, metamodel is updated with the “real” feedback data that is obtained from free moving actuator. 16.5 Validation for RTHS with FE Model In this section, before getting into the HS test with metamodel, a brief summary of the validation tests that are conducted to validate the SCRAMNetGT card connection between the computers and the controller are presented. These tests were conducted in real-time, i.e. RTHS. For the offline validation test, the feedback from the experimental model was considered as it is coming from the command of the system. The displacement command was multiplied with the constant stiffness value of the specimen, and these validation tests were considered for linear elastic experimental material. Fig. 16.3a shows
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