Quantification of damage detection schemes using receiver operating characteristic (ROC) curves

Abstract

In this work we detect damage in a composite to metal bolted joint subject to ambient vibrations and strong temperature fluctuations. Damage to the joint is considered to be a degradation of the connection strength implemented by loosening the bolts. The system is excited with a signal that conforms to the Pierson-Moskowitz distribution for wave height and represents a possible loading this component would be subject to in situ. We show that as the bolts are loosened, increasing amounts of nonlinearity are introduced in the form of impact discontinuities and stick-slip behavior. The presence of the nonlinearity, hence the damage, is detected by drawing comparisons between the response data and surrogate data conforming to the null hypothesis of an undamaged, linear system. Two metrics are used for comparison purposes: nonlinear prediction error and the bicoherence. Results are displayed using Receiver Operating Characteristic (ROC) curves. The ROC curve quantifies the trade-off between false positives (type I errors) and false negatives (type II errors). Type I errors can be expressed as the probability of false alarm and 1 - type II error is the probability of detection. We demonstrate that ROC curves provide a unified quantifiable approach for directly comparing the merits of different detection schemes.