Method to Find Accurate Solutions in System Identification

Abstract

This paper describes a method to find accurate mass and stiffness matrices in system identification. A set of simultaneous linear equations is solved to identify the mass and stiffness matrix of structures. An exact solution cannot necessarily be found because the coefficientmatrix in the equation is sometimes ill-conditioned. The singularvalue decomposition is used to find an approximate solution. The proposedmethod introduces the projected norm as an indicator to determine howmany singular values should be considered for identifying accuratemass and stiffness matrices. Anumerical example is given to demonstrate that the proposedmethod is effective for system identification. The system identification method was previously developed by the author and the contribution of the paper is a method to select singular values. It is found that the proposed method identifies mass and stiffness matrices that can accurately predict the dynamic characteristics and the mass properties of structures.