efficiency improvement of the structural system identification by reducing singularity of the response matrixes in inverse solution of equations of motion

this paper presents a method for identification of linear system physical parameters (structural mass, damping and stiffness matrices) using the inverse solution of equation of motion in the frequency domain, by focus on the reducing the illconditioning effect. the method utilizes the measured responses from the forced vibration test of structure in order to identify the system properties and detect the probable damages. inputs and outputs data is gathered in an augmented matrix [a|b], that large number of this data is caused to ill condition problem. moreover, as an inevitable problem, there is a noise in the measurement and makes discrepancy in result of identification. ill conditioning causes instability in the result of identification, the instability and noisy result reduce validity of the results and accordingly will be valueless statistic methods in the system identification (si). this paper is presented an algorithm to improve the ill conditioning problem that is a special upper triagularization matrix method. the proposed algorithm can identify parallel and pseudo parallel vectors in coefficient matrix of linear equations. by removing these linearly dependent vectors and thus reducing singularity of the matrix, stabilization is resulted which is a key objective in numerical linear algebra. in order to optimal estimation of identification results, least-squares and penalty function methods is used. the validity and efficiency of the reduce singularity of matrix method is tested on a eight non shear story frame structure by using direct model updating method. aforementioned structures have a non-proportional damped matrix and subjected to sweep harmonic forces. the results show that the proposed algorithm improves the stability of the estimation and the answer is quite useful.