15 Rapid Seismic Risk Assessment of Structures with Gaussian Process Regression 161 15.3 Case Study Results and Discussion 15.3.1 Model Description The structure model which has been used in this paper is consisted to be a multi-story steel frame building. A five story shear frame with the same steel columns for all stories was tested experimentally before at [11] and a numerical model was fitted to its components using the Bouc-Wen nonlinear model. Based on the calibrated nonlinear model, four different structures with the same components but a different number of stories such as a 3-story, a 5-story, a 7-story, and a 9 story model, are considered here. The height of stories are about 0.17 m and the weight of each story is 23.2 kg. Newmark Beta has been used for nonlinear time history analysis of the structures and the time step is considered to be 0.001 s for all time history analyses. Damage state of a structure is best reflected in the maximum experienced drift ratio. Since the drift ratio can be obtained from relative displacement of each story normalized to the story height, damage states can be defined directly on a hysteresis loop of a typical component. In this case, four different damage states are defined, namely none, slight, moderate, and collapse damage. The hysteresis behavior of the nonlinear model subjected to a cyclic pushover test and the abovementioned damage states are shown in Fig. 15.1. The limit state of slight damage s, is considered as the yielding point of the component which is about 1.2 cm. The collapse damage state c is considered as 5 cm, and the moderate damage state mis taken as half of the displacement of the collapse damage. The considered limit states are shown in Fig. 15.1 and described in Table 15.1. 15.3.2 Prediction Objective Since in real life we get a limited chance to rapidly identify the extent of damage in different areas, the training set size is considered to be a small fraction of the whole data. In this case, out of 592 ground motion records available, 100 randomly selected records (∼17%) are used for training purposes and the rest remain untouched to test the model. We might not have Fig. 15.1 The hysteresis behavior of the component subjected to a cyclic pushover test Table 15.1 Definition of damage states Inter-story displacement (m) Drift ratio Damage state ID<0.012 DR<0.07 None 0.012 < ID < 0.025 0.07 < DR < 0.15 Slight 0.025 < ID < 0.05 0.15 < DR < 0.29 Moderate 0.05< ID 0.29<DR Collapse
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