Evaluating the Probability of Detection Capability of Permanently Installed Sensors Using a Structural Integrity Informed Approach

Abstract

There is a growing interest in using permanently installed sensors to monitor for defects in engineering components; the ability to collect real-time measurements is valuable when evaluating the structural integrity of the monitored component. However, a challenge in evaluating the detection capabilities of a permanently installed sensor arises from its fixed location and finite field-of-view, combined with the uncertainty in damage location. A probabilistic framework for evaluating the detection capabilities of a permanently installed sensor is thus proposed. By combining the spatial maps of sensor sensitivity obtained from model-assisted methods and probability of defect location obtained from structural mechanics, the expectation and confidence in the probability of detection (POD) can be estimated. The framework is demonstrated with four sensor-component combinations, and the results show the ability of the framework to characterise the detection capability of permanently installed sensors and quantify its performance with metrics such as the $${\mathrm{a}}_{90|95}$$ a 90 | 95 value (the defect size where there is 95% confidence of obtaining at least 90% POD), which is valuable for structural integrity assessments as a metric for the largest defect that may be present and undetected. The framework is thus valuable for optimising and qualifying monitoring system designs in real-life engineering applications.

A probabilistic method for structural integrity assurance based on damage detection structural health monitoring data

“…It is therefore important to design a monitoring system with adequate area coverage to sufficiently cover all regions where defects may occur, such that the minimum detection capabilities are not too low, a concept which is explored in more detail in. 24…”

“…Systematic effects are especially acute in permanently installed sensors which are in a fixed location. 48,49 Most notably, the probability of detection may be highly dependent on the relative position between the installed sensor and the sought defect 49 ; if the sought defect happens to occur outside the field of sensitivity of the installed sensors, the probability of detection is going to be severely compromised. Other examples of sources of systematic uncertainty are any imperfections and dynamic responses of the beam that would alter the sensor output, defect morphology 50 and the quality of the coupling between the sensor and the component.…”

“…The distribution of POD curves can be produced with model-assisted methods, where different systematic effects are studied using computational parametric studies. This uncertainty quantification approach has been applied for permanently installed monitoring systems 24 and in commercial software for evaluating inspection techniques. 52 With a distribution of POD curves defined, the uncertainty in POD can be incorporated into the particle filtering method, whereby each sampled postulated defect is also assigned a sampled POD curve.…”

“…In practice, the effect of each systematic effect will have to be studied to obtain the actual distribution of POD curves. This can either be done experimentally, or a model-assisted approach can be devised as proposed in References 24 and 49 where computational models are used to evaluate the response of the permanently installed sensors for different combinations of systematic effects weighted against the likelihood of such a combination of systematic effects occurring.

Figure 16.Various amount of systematic uncertainty in detection capabilities of permanently installed monitoring systems, represented as POD curves in (a), (c) and (e); the corresponding life-cycle management results, represented with the plot of projected remaining cycles until POnormalFcrit against the number of cycles experienced by the component as shown in (b), (d) and (f).

…”

“…Previous work has demonstrated how to incorporate systematic uncertainties into a receiver operating characteristic (ROC) analysis to quantify the confidence in detection capabilities. 24 In this article, these POD curves are used in the particle filtering scheme to postulate possible defect extent.…”