In this paper, a loop substructure identification method is proposed to estimate the parameters of any story in a shear structure with measurements of only limited number of acceleration floors and unknown structural mass. A shear structure is divided into substructures consisting of a series of similar two-story standard substructures; two identification problems are formulated for the standard substructure using the cross power spectral densities (CPSD) of structural responses, each of which identifies the parameters of one story given that the parameters of the other are known. A loop identification scheme is proposed by connecting the two identification problems in a loop manner, forming a sequence of estimation problems to directly identify both story parameters of the standard substructure. If the structural masses are unknown, this loop identification method can still be applied to estimate mass normalized structural parameters as well as the relative mass distribution of the structure. The convergence condition is derived for the loop substructure identification, showing that the loop identification sequence is conditionally converged and some structural responses play a crucial role in determining the convergence. To achieve convergent identification results, a reference selection method is proposed, which uses a synthesized response, formed by a linear combination of the measured structural responses, as the reference response to calculate the CPSD and perform the loop substructure identification. A 20-story shear building is used to verify the convergence condition and to demonstrate that the proposed reference selection method does provide the converged and accurate estimation results.
In the authors’ previous work, an inductive substructure identification method was proposed for shear structures, which utilizes the frequency responses (Fourier transforms) of floor accelerations to formulate a series of inductive substructure identification problems, estimating the structural parameters from top to bottom iteratively. However, the simulation results show that the proposed method can only obtain relatively accurate results if measurement noise is not large. In order to improve the identification accuracy, an uncertainty analysis of the parameter identification errors is conducted for this method in this paper, revealing the important factors that influence the identification accuracy. Based on this result, a new substructure identification method is proposed herein, in which the cross power spectral densities (CPSDs) of structural responses, computed via multi-taper method, are utilized to formulate the substructure identification problems. A similar uncertainty analysis of the identification errors is carried out for the new method, illustrating why the new method could significantly improve the identification accuracy. Finally, a numerical example of 8-story shear building structure is utilized to verify the effectiveness of the new multi-taper based substructure method on enhancing the identification accuracy.