Output-only structural modal parameter estimation under non-white excitations based on response transmissibility

In cases of output-only modal parameter estimation for operational engineering structures, such as aerospace structures, the non-white excitations lead to non-physical modes being not able to be identified. For these cases, the recently developed response transmissibility-based methods of modal parameter estimation were studied and an improved poly-reference response transmissibility-based output-only approach of modal parameter estimation was proposed. Firstly, the parametric model of the poly-reference response transmissibility was introduced, it was presented by the left matrix fraction polynomials, the formulations of the least square estimation for unknown parameters were proposed, and the normal equation of the least square estimation was reduced by using the block property of the corresponding Jacobian matrix, it largely decreases the computational costs. Secondly, based on the high-dimensional accompany matrix method, the eigenvalue problem of the matrix polynomials was solved, it led to the solution to the modal parameters. In addition, the original constraints between the number of loading conditions and the number of references were removed by using the pseudo inverse of matrix. Finally, two numerical examples validated the proposed method. The results illustrated that the proposed method can be used to estimate the modal parameters very well and has the advantage of avoiding the influence of harmonics, so the problem due to non-white excitations is solved.