Uncertainty Quantification in Transmissibility-Derived Features Used for Fault Detection

Abstract

A common feature used in system identification procedures is transmissibility, which is the frequency-domain ratio between any two outputs and is formally defined as the relative admittance between those two measurements; it is often interpreted as the response normalized by a reference response instead of by the actual input. Several researchers have used the transmissibility, or other features derived from changes in it, for various structural health monitoring applications. In this paper, we consider a SIMO identification model and regard the change in transmissibility as a feature correlating with damage occurrence. Both inherent randomness due to the estimation process and external sources of noise contamination are included as sources of uncertainty in the transmissibility. Quantification of this uncertainty is necessary to group-classify the measurements into either undamaged or damaged (binary) conditions with a clearer understanding of Type I/II trade-offs in a way that facilitates proper decision-making. The paper uses Receiver Operating Characteristic (ROC) curves for individual frequency lines as the key performance metric across the entire frequency domain and use Area Under Curve (AUC) as the metric to quantify the performance of the ROC. The paper proves that regions near resonance will have the best hypothesis test performance in terms of sensitivity and specificity.