Efficient two-step procedure for parameter identification and uncertainty assessment in model updating problems

The model updating procedures employed in vibration-based health monitoring need to be reliable and computationally efficient. The computational time is a fundamental task if the results are used to evaluate, in quasi-real-time, the safe or the unsafe state of strategic and relevant structures. The paper presents an efficient two-step procedure for the identification of the mechanical parameters and for the assessment of the corresponding uncertainty in model updating problems. The first step solves a least squares problem, providing a first estimate of the unknown parameters. The second (iterative) step produces a refinement of the solution. Moreover, by exploiting the error propagation theory, this article presents a direct (non-iterative) procedure to assess the uncertainty affecting the unknown parameters starting from the experimental data covariance matrix. To test the reliability of the procedure as well as to prove its applicability to structural problems, the methodology has been applied to two test-bed case studies. Finally, the procedure has been used for the damage assessment in an existing building. The results provided in this article indicate that the procedure can accurately identify the unknown parameters and properly localize and quantify the damage.