Robust statistical damage localization with stochastic load vectors

Abstract

Summary The stochastic dynamic damage locating vector approach is a vibration‐based damage localization method based on a finite element model of a structure and output‐only measurements in both reference and damaged states. A stress field is computed for loads in the null space of a surrogate of the change in the transfer matrix at the sensor positions for some values in the Laplace domain. Then, the damage location is related to positions where the stress is close to zero. Robustness of the localization information can be achieved by aggregating results at different values in the Laplace domain. So far, this approach, and in particular the aggregation, is deterministic and does not take the uncertainty in the stress estimates into account. In this paper, the damage localization method is extended with a statistical framework. The uncertainty in the output‐only measurements is propagated to the stress estimates at different values of the Laplace variable, and these estimates are aggregated based on statistical principles. The performance of the new statistical approach is demonstrated both in a numerical application and a lab experiment, showing a significant improvement of the robustness of the method due to the statistical evaluation of the localization information. Copyright © 2014 John Wiley & Sons, Ltd.

Operational modal analysis with uncertainty quantification for SDDLV-based damage localization

“…While modal truncation and variance errors of the required modal parameters may perturb results, a consistent statistical analysis can at least in part compensate and improve the damage localization resolution. Further details of are found in [13,14].…”

“…In [13,14] the uncertainty propagation from system identification results to the computed stress vectors S(s i ) at the selected the Laplace variables s i was analyzed. In this section, these results are summarized and the respective statistical test is shown.…”

“…Then, these covariances are propagated to the stress vector as follows. Note that a more detailed description of this step is available in [13,14]. In a first step, the sensitivity of R(s) in (3) with respect to the system matrices A c and C c is obtained, yielding…”

“…Based on these considerations, a statistical extension of the SDDLV method was developed in [13] for the actual decision if an element is damaged. In [14] a more robust version has been developed, where a joint statistical evaluation of the stress computation is carried out at several Laplace domain variables s where the transfer function matrix difference is evaluated.…”

Rank-revealing QR decomposition applied to damage localization in truss structures

“…The DDLV method was further enhanced for the case of output‐only analysis , and this modification was called the stochastic dynamic DLV. The problem of empirically established thresholds required for the successful application of the DLV methods was addressed in the papers by Dohler et al and Martin et al , where statistical hypothesis testing approach was applied. An and Ou studied precise damage localization in a long‐span steel truss bridge model based on the SDLV method.…”