Hybrid Identification Method for Multi-story Buildings with Unknown Ground Motion

Simultaneous identification of both structural parameters and ground motion of an earthquake-excited structure by using measured structural response time histories only has received great interests in recent years. A hybrid identification method is proposed in this paper for the problem concerned. The hybrid identification method first identifies the structural parameters above the first floor of a multi-story shear building using the least-squares method. The minimum modal information is then introduced to find the structural parameter of the first floor of the building to eliminate the non-uniqueness problem. After all the structural parameters are identified, the unknown earthquake-induced ground motion is finally constructed by solving a first-order differentiation equation. A series of shaking table tests were also conducted on a building model under different kinds of ground motion to experimentally examine the proposed hybrid method. Absolute acceleration responses at all floors of the test building were measured and integrated to obtain velocity and displacement responses. All the measured and integrated responses are then analysed using the hybrid identification method with a shift-average procedure to identify the stiffness and damping parameters as well as to reconstruct the unknown seismic input. The experimental results indicate that the hybrid identification method is potentially a promising technique for structural parameter and seismic excitation identification of multi-story buildings using output measurements only. Y.L. Xu, Research Center for Urban Hazards Mitigation (RCUHM), The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong X. Zhao, Research Center for Urban Hazards Mitigation (RCUHM), The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong J.Chen, Research Center for Urban Hazards Mitigation (RCUHM), The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong J.Li, Department of Building Engineering, Tongji University, Shanghai, China INTRODUCTION System identification techniques using only measured structural responses to identify modal or structural parameters invoked great interests in the past a few decades since external excitations such as wind forces or earthquake loads cannot be obtained or accurately measured under actual operating conditions. This is particularly true for large civil engineering structures such as tall buildings, long bridges, and offshore platforms. Great efforts have now been exerted to identify both structural parameters and unknown external excitations in the time domain. Toki et al. (1989) proposed a time-domain identification technique by which structural parameters and ground motion of an earthquake-excited structure could be identified using measured structural responses only. The coda of measured structural response time histories, which was treated as free vibration response without ground motion, was first utilized to identify the structural parameters in the time domain with the Kalman filter. The input ground motion was then estimated from the measured structural responses and the identified structural parameters. Wang and Haldar (1994) developed an iterative least-squares method to identify simultaneously the structural parameters and ground motion of an earthquake-excited structure. Their method assumed that the ground motion at the first four time instances was zero so that the measured absolute structural responses at the first four time instances could be seen as the relative structural responses and the initial seismic forces could be evaluated. Using the initial seismic forces and the measured structural responses, the system parameters were then estimated using the least-squares method, and the seismic forces were re-evaluated from the estimated system parameters. Wang and Haldar (1997) also extended their identification method to the structures with limited observations. To reduce the sensitivity of the initial values of unknown structural parameters or ground motion to the identified results, Li and Chen (2003) proposed a statistical average algorithm based on the equation of motion established in the relative coordinate system. The aforementioned identification procedures are all based on the equation of motion established in the relative coordinate system for an earthquake-excited structure. Since the absolute structural responses other than the relative structural responses are often measured in practice, the relative structural responses cannot be obtained if the ground motion is unknown. Thus, there is a limitation for the aforementioned procedures to be implemented in practice. In recognition of this restriction, Hoshiya and Sutoh (1995) extended the Toki’s identification procedure to account for absolute structural responses by using an extended Kalman filter. The basic steps in their procedure are, however, the same as the Toki’s ones. That is, the coda of measured absolute structural response time histories was utilized to identify the structural parameters, and the input ground motion was then estimated from the measured absolute structural responses and the identified structural parameters. It is noted that in practice, the separation of coda part from the entire structural response time history recorded during an earthquake event is quite difficult. Even though it is approximately obtained, the duration of the coda (so-called free vibration) of the structural response is very short and the amplitude of the free vibration is very small compared with the earthquake-induced structural vibration. Therefore, the accuracy of identified results may be significantly affected because of short duration and the measurement noise may become a serious problem. Furthermore, one may note that the damping parameters determined from lowamplitude free or ambient vibration tests differ greatly from the damping parameters obtained from earthquake-induced structural responses though it may not true for stiffness parameters (Chopra, 1995). A hybrid identification method is proposed in this paper for the problem concerned. The hybrid identification method first identifies the structural parameters above the first floor of a multi-story shear building using the least-squares method. The minimum modal information is then introduced to find the structural parameter of the first floor of the building to eliminate the non-uniqueness problem. After all the structural parameters are identified, the unknown earthquake-induced ground motion is finally constructed by solving a first-order differentiation equation. A series of shaking table tests were also conducted on a scaled 3-story steel shear building under different kinds of ground motion to experimentally examine the proposed hybrid method. Absolute acceleration responses at all floors of the test building were measured and integrated to obtain velocity and displacement responses. All the measured and integrated responses are then analysed using the hybrid identification method with a shift-average procedure to identify the stiffness and damping parameters as well as to reconstruct the unknown seismic input. The identified structural stiffness is compared with the theoretical value computed from standard values of material and geometric properties, and the identified structural damping is compared with that obtained from the frequency domain identification method. The reconstructed seismic excitation is compared with that recorded during the shaking table test in both the frequency domain and time domain. HYBRID IDENTIFICATION METHOD The basic theory of the hybrid identification method is introduced in this section. The absolute response equation of motion of a shear building excited by ground motion can be expressed as ( ) ( ) ( ) ( ) t Y Y t t t g g 0 0 K C KY Y C Y M − − = + + & & & & (1) where , C , and M K are respectively the mass, damping, and stiffness matrix of the building, , , and are respectively the absolute acceleration, velocity, and displacement response vector of the building; , ( ) t Y& & ( ) t Y& ( ) t Y ( ) t Y0 & & ( ) t Y0 & , and ( ) t Y0 are respectively the absolute acceleration, velocity, and displacement of the foundation or the ground; and , [ ] 0 0 1 L c g − = C [ ] 0 0 1 L k g − = K (2) where and are respectively the damping and stiffness of the ith story. The right term of Eq. (1) has the following form i c i k ( ) ( ) ( ) ( ) ( ) [ ] g g t Y k t Y c t Y t Y t 0 0 0 1 0 1 0 0