The probability of detection for structural health monitoring systems: Repeated measures data

Abstract

The United States Air Force currently relies on schedule-based inspections using nondestructive evaluation methods for ensuring airframe integrity. The sensitivity of a nondestructive evaluation method is quantified statistically using a probability of detection process. The purpose of the probability of detection process is to generate a metric for a given nondestructive evaluation technique and corresponding defect (e.g. crack). This process could be conducted under various inspection conditions and defect sizes. The set of factors varied in the process is controlled to allow each nondestructive evaluation inspection to be treated as statistically independent. Current United States Air Force structural inspections are performed at time intervals that adhere to the independence assumption. However, the United States Air Force plans to service airframes based on their actual condition instead of the current schedule-based approach. Accordingly, there is emphasis on developing advanced health management technologies, such as structural health monitoring systems, which provide an automated and real-time assessment of a structure’s ability to serve its intended purpose. Therefore, structural health monitoring is considered to be equivalent to an in situ nondestructive evaluation structural inspection device. With a structural health monitoring system, the time interval between inspections will be much smaller than the time intervals between nondestructive evaluation inspections. Since structural health monitoring measurements are from the same sensors, in the same location, the independent measurement assumption used to analyze nondestructive evaluation methods is invalid. In this article, we present a statistical method consistent with current probability of detection process, yet designed to appropriately analyze dependent data. We demonstrate this method first with simulated data and then with experimental data from three test specimens of a representative aircraft structural component. This method leverages the advantages of a structural health monitoring system through its frequent measurements while maintaining its usefulness through appropriately computed probability of detection values. Furthermore, we present a numerical method for estimating the number of test specimens needed to achieve a desired value.