In recent large earthquakes in Japan, a large number of wooden houses collapsed due to strong ground motions. In order to reduce the damage of buildings and loss of human life, it is important to enhance the seismic performance of wooden houses. To clarify the vibration properties of wooden houses such as a natural period and a damping ratio under a severe earthquake ground motion is an essential point to estimate and upgrade its seismic performance; however, it is generally difficult since the wooden house shows strong non-linearity on its vibration during strong ground motion due to the mechanical property at the connection of wooden members.
In this paper, the vibration properties of wooden houses are identified using subspace model identification method. The methods used in this paper are the PI-MOESP scheme and the PO-MOESP scheme proposed by Verhaegen. These two methods have different algorithms in terms of the assumption of the additive noise to the system. The PI-MOESP scheme is valid when the system has colored measurement noise, and the PO-MOESP scheme is valid when the system has white process and white measurement noise.
First, using the numerical model of a two-story unsymmetric-plan wooden house, we compared the characteristics of the PI-MOESP scheme and the PO-MOESP scheme. The numerical results show that the PI-MOESP scheme needs a large value of the line of block Hankel matrix to obtain a true identified value, and the PO-MOESP scheme can estimate the true value when the additive colored noise contains broadband frequency and has low amplitude compared with input-output data. It is also shown that the identified values for the data of non-linear vibration converge with increasing number of the line of block Hankel matrix.
Then, we identified the vibration properties of the full-scale two story wooden house, which was used as the test structure for the three-dimensional shake table test conducted in 2007, by the PI- and the PO-MOESP schemes. The identification results for the data obtained by white noise shaking shows that the damping ratio of the torsional mode is about 15%, which is approximately three times larger than that of the translational mode. From the identification results for the data obtained by earthquake shaking, it is shown that when the maximum story drift angle is about 1/50 rad, the natural period becomes about three times compared with the value under low-lever vibration and the damping ratio becomes about 20%.