Statistical Methods for Probability of Detection in Structural Health Monitoring

Abstract

There is much interest in the potential to use Structural Health Monitoring (SHM) technology to augment traditional Nondestructive Evaluation (NDE) methods to improve safety, increase asset availability, and reduce maintenance and inspection costs. SHM has the potential to be used in many areas of application including critical components in aircraft and pipelines. Probability of detection (POD) plays a critical role in aircraft structural integrity programs. As such, there has been a high interest in developing methods that can be used to assess POD in SHM applications. In contrast to traditional NDE laboratory experiments to assess POD that involve a set of specimens with cracks, SHM sensors are fixed and SHM data are acquired over time as cracks grow or otherwise evolve. Traditional statistical methods for assessing POD (e.g., as described in MIL-HDBK 1823A 2009) have to be extended to properly handle repeated-measures data. This purpose of this paper is to review the basic statistical concepts of probability of detection (POD) and to show how these concepts can and should be applied to SHM POD studies by modifying and extending existing methods for estimating POD. The methods presented here are applicable when there is a scalar damage index or other response that will be used to make a detect decision. The paper compares a simple model based on length at detection and a random effects model to describe repeated measures data.

Ultrasonic Methods

“…SHM is a technique used for monitoring the integrity of in-service structures of aircraft, bridges, piplines and other components which are continuously exposed to operational load and environmental influence. The goal of SHM technology is to complement NDE techniques to improve reliability of the structure and reduce inspection and repair costs (Meeker et al 2019;Etebu and Shafiee 2018). Thus, performance of the SHM system is characterized by the quality of sensors, their mounting and reliability of measurements.…”

“…In the case of ultrasonic inspection the system provides a response from the defect whose amplitude is dependent on it's size. Signal response approach is able to estimate and build POD curve using greatly smaller amount of data comparing to Hit/Miss analysis (Meeker et al 2019;Chapuis et al 2018b). Generally, this approach has a linear model and is expressed as following (Chapuis et al 2018b):…”

“…Another complexity to define a thres is a dependent measurement of SHM. Due to a large degree of variability the measurement response can be classified as damage even if there is none in accordance with prior measurements (Meeker et al 2019;Fisher and Michaels 2009;Cobb et al 2009).…”

“…There is a risk to overestimate the POD of smaller size defects and underestimate the PFA in the case of missing important influential sources. Factors of SHM system which could affect the signal are as follows (Meeker et al 2019;Mandache et al 2011):…”

Monitoring Tasks in Aerospace

“…Currently, guidelines to develop PoD curve for NDI are provided in (MIL-HDBK-1823A 2009), but may not be generalized in its entirety for SHM application. PoD curves have been developed for SHM application but for specific cases (Roach 2015) (Meeker et al 2019). Developing a PoD curve for a general SHM sensor setup would likely require a large experimental program with multiple reference samples, with and without damages, in a representative environment translating into a very costly effort.…”