Brandon M. Greenwell

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

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 a 90 | 95 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 a 90 | 95 value.

Inverse Estimation for Damage Assessment in SHM: Moving Beyond the Probability of Detection

SHM systems are built to detect and estimate damage. For such systems, the detection of damage should be, inevitable. It is no longer conceivable that the system will regularly fail to detect damage. Instead, researchers should focus on methods to predict the extent of damage and feasible ranges of the signals that correspond to such damage. We refer to the application of such methods as the reliability of detection. Specifically, this paper considers SHM systems monitoring a particular region of interest. We no longer estimate the probability of detection (POD), but instead, use aspects of the POD process in order to determine the range of signal values that are statistically associated with the damage of interest. That is, instead of using the two step process in MLHNBK-1823 which converts regression results into probability estimates for damage detection, we examine directly the relationship between the signals and the level of damage. Then, using inverse estimation techniques, we estimate the range of signal values associated with a particular level of damage. We maintain the notion of statistical confidence and compute only the range of signal values that correspond to the confidence level of interest. Because signal data structure varies, we demonstrate several methods to construct the inverse estimate and its confidence interval. We applied these techniques in order to estimate damage from experimental data. Our experiment consisted of an array of PZT sensors adhered to a wing spar which was then fatigued on a test bed until crack lengths of 0.7mm were observed. Crack lengths were measured directly by pausing the test bed after a fixed number of cycles. Features were extracted from the waveforms received by the PZT sensors and associated with crack length through the estimation of a functional form. For a particular crack length of interest, inverse estimation on the functional form between the signal features and the crack length allowed us to estimate the associated signal value and 95% confidence interval. The inverse estimation techniques prove useful in estimating the signal values associated with a particular crack length. Further development of this application includes adjustments for environmental conditions. doi: 10.12783/SHM2015/331