Identification of dynamic systems from data composed by combination of their response compoments

A time domain method for identification of the equivalent system matrices M−1K and M−1ζ of structures from data composed of measured displacement, velocity and acceleration is proposed in this paper; where the matrices M, ζ and K are the mass, damping and stiffness matrices, respectively. The stochastic subspace algorithm is used to identify the system and output matrices of a continuous-time state-space system from the combined response measurements. A generalized transformation method has been derived to transform the identified system matrix into an equivalent system matrix, Ac, which has similar contents as the system matrix in the state equation of motion for structures. Then the natural frequencies and mode shapes in the damping free case can be calculated from the equivalent M−1K matrix that is the negative sub-matrix in the left lower part of Ac. The damping ratios and damped natural frequencies can be calculated from Ac. The procedure is also available for only one type of measurement for displacement, velocity or acceleration. be’s mass-spring model [AIAA Journal 23(9) 1985, p. 1431] with eight degrees of freedom is employed as a numerical example to validate the feasibility of this procedure. The algorithms are also applied to the NTU 5 floors frame structure model [J. Eng. Mech. 2000, p. 693] as an experimental study case.