Covariance of Limit Defining Pairs (CLDP): A Novel Approach to Establishing Detection Sensitivity for Structural Health Monitoring Data

Abstract

This paper explores a novel approach to establishing detection sensitivity for SHM. The proposed approach uses data associated with the largest flaw such that all smaller flaws were not detected and the smallest flaw such that all larger flaws were detected for that specimen. These points are termed “limit defining” because they directly contribute to defining the most valuable portion of the probability of detection (POD) curve. A POD curve can be efficiently built using a standard hit/miss analysis, and an upper confidence bound can be generated by calculating the Covariance of the Limit Defining Pair (CLDP) to take the dependence into account. A fatigue experiment was conducted on 60 aluminum bars using a carbon nanotube (CNT) based fatigue crack gauge. 100 data points were collected for each specimen as the crack grew to ~2mm. 1000 classic POD curves were generated by randomly selecting 1 point from each specimen to observe variability, and subsequently the same data was analyzed using the CLDP. Finally, random subsets of specimens were selected to simulate POD statistics associated with testing fewer specimens. Overall, CPLD has proven to be a robust and reliable alternative to traditional detection sensitivity evaluation for SHM sensors.