Identification of Tall Shear Buildings under Unknown Seismic Excitation with Limited Output Measurements

Abstract

Due to the fact that some structural external excitations such as earthquakes and wind forces can not be accurately measured under actual operating conditions, it is necessary to investigate algorithms for structural identification under unknown earthquakes. In this paper, an algorithm based on the extended Kalman estimator approach is proposed for the identification of structural parameters and unknown excitation of tall shear-type buildings with only partial measurements of structural absolute acceleration responses. The equation of motion of a tall shear building under ground motion is established in the absolute co-ordinate system, in which the ground-motion input is applied to the 1st floor of the building as an unknown excitation. Based on substructure approach, the tall building is decomposed into substructures. For each substructure above the 1st floor, substructural relative responses and parameters are identified by extended Kalman estimator. For the substructure containing the 1st floor, it is proposed that substructural extended state vector is firstly identified by the extended Kalman estimator and the unknown excitation is subsequently estimated by least-squares estimation. Then, the 1st story stiffness is estimated based on structural eigenvalue equation and the expansion of the determinate of the structural eigen-matrix. The unknown ground motion is identified by the Newmark-β method. A numerical simulation example demonstrates the efficiency of the proposed algorithm.

Identification of flexible buildings with bending deformation and the unmeasured earthquake ground motion

“…In order to estimate k 1 , frequency spectra of the measured translational acceleration response are analyzed to obtain the vibration frequencies of the building [19]. With an estimated value of the frequency of the building i ω and its frequency equation,…”

“…where det( ) A denotes the determinant of matrix A. k 1 can be estimated by the expansion of the determinant of the structural eigen-matrix  2 i A = K ω M and the formulation of the stiffness and mass matrices [19]. After the estimation of the unknown excitation time history 1 ( ) u t f and the estimated value of k 1 , the unknown ground acceleration motion can be estimated from eq.…”

“…After the estimation of the unknown excitation time history 1 ( ) u t f and the estimated value of k 1 , the unknown ground acceleration motion can be estimated from eq. (7) by solving a first-order differentiation equation based on the Newmark- [19] …”

“…Substructure approach is usually adopted for the identification of a tall building [19,[25][26][27][28][29].…”

“…Zhao et al [18] proposed a hybrid identification approach in the absolute co-ordinate system for multi-story shear-type buildings under earthquake excitations. Recently, the authors presented an algorithm for the identification of shear-type buildings subject to unknown earthquake excitations with partial output measurements [19]. However, shear-type buildings are the simplified structure models with only the translational degrees of freedom.…”