Analysis and mitigation of uncertainties in damage identification by modal-curvature based methods

The objective of this paper is to address and reduce the uncertainties associated with measurement noise and discretization in damage identification methods based on modal curvature analysis. The experimental case study considers the local reduction in the bending stiffness of a slender beam under free-free and simply supported boundary conditions. First, the analysis of error sources and their propagation is theoretically set up. Second, the mitigation of uncertainties in damage localization is pursued using a two-stage approach based on multiple hypothesis testing relative to the normalized indices and the definition of a combined macro-index. Finally, the Monte Carlo method is exploited to obtain the statistical error distribution of the experimental damage position and severity predictions by randomizing the numerical displacement mode shapes with the identified noise. The present analysis allows us to find the optimal number of sensors that minimizes the combination of bias and truncation errors, to highlight how sensor spacing and data noise affect damage localization, and to determine the uncertainty bounds of the predicted damage severity. The two-stage approach, enhanced by selecting thresholds related to real noise levels and tuned on SHM objectives, appears to improve identification accuracy compared to the separate use of damage indices based on absolute confidence levels.