Minimum Localizable Damage for Stochastic Subspace-based Damage Diagnosis

This article describes an approach to evaluate the minimum localizable damage for stochastic subspace-based damage diagnosis. Localizability is defined as the sensitivity to small and local damages (detectability), the ability to narrow down the exact damage location (localization resolution) and the test response of undamaged parameters (false localization alarms). For the analysis, damage is defined as a change in model-based design parameters, for example, material constants or cross-sectional values in a finite element model. Subsequently, the parameter changes are linked to changes in the global damage-sensitive features using sensitivity vectors, and inherent uncertainties (due to stochastic loads and measurement noise) are quantified. This way, local structural parameters can be tested for changes using statistical hypothesis tests, such as the general likelihood ratio and the statistical minmax localization test. Due to the numerical conditioning of the damage localization problem, the sensitivity vectors have to be clustered before damage can be localized. Sensitivity clustering corresponds to a substructuring of the finite element model, where the number of clusters (the localization resolution) is a user-defined input parameter. The main results of this paper are mathematical criteria to calculate the damage detectability and the false alarm susceptibility for different localization resolutions. Moreover, an automated substructuring routine is described that finds the optimal substructure arrangement as a compromise between high damage detectability, high localization resolution, and low false alarm susceptibility. For proof of concept, a numerical case study is presented, where the damage localizability is determined and validated for a cable-stayed bridge.