A novel feature-based probability of detection assessment and fusion approach for reliability evaluation of vibration-based diagnosis systems

Abstract

Structural health monitoring systems are based on suitable sensor techniques allowing online and offline supervision of technical systems. The quantification of sensors/measurement devices is a key issue for qualifying their effectiveness and efficiency and therefore to ensure safe operations. Probability of detection serves as a performance measure for quantifying the reliability of conventional nondestructive testing procedures taking into account statistical variability of sensor-based measurements. For vibration-based supervision approaches and fault detection and isolation methods, the probability of detection approach cannot be applied similarly. This results mainly from the complexity of the dynamical behavior of systems monitored in relation to faults, sensors position (observability), and the related feature extraction or monitoring task. In this contribution, probability of detection evaluation of vibration-based fault detection of elastic mechanical structures to be monitored is developed. Beside a principal discussion of the problem serving as introduction, an example using different sensor types in combination with mechanical modifications of an elastic beam is presented. The a90/95-criteria representing probability of 90% detection at a confidence level of 95% is examined to the measurements and related outcomes. Based on the analysis of a suitably chosen feature (like eigenfrequency or band power) and dependent on the mechanical modes considered, the efficiency and deficiency of the different combinations are shown. Based on the proposed approach, a new insight into the usefulness of different sensor type and fault position combination becomes possible. To improve the detection quality, suitable assumptions in combination with sensor/information fusion are applied to feature-based analysis as detection task using vibration measurements. In addition, based on an experimental evaluation, it can be concluded that a suitable fault-feature probability of detection analysis can be successfully implemented as a new reliable measure for vibration-based fault detection and isolation approaches. Furthermore, decision fusion as the combination of different measurements will allow the improvement of results. Dependent on noise analysis, a trade-off between flaw size detection and probability of falsely characterizing a fault with a90/95 reliability level can be attained.

Probability of detection, localization, and sizing: The evolution of reliability metrics in Structural Health Monitoring

“…Four possible combinations can be used: (i) â vs a, (ii) â vs log(a), (iii) log(â) vs a, and (iv) log(â) vs log(a). 56 A good practice would be to plot all the four possible graphs and choose the one with the best fit. 52 Considering the â vs a case (the same procedure can be extended to the remaining three cases), the two variables are related to each other with the following regression equation…”

“…Four possible combinations can be used: (i) â vs a, (ii) â vs log(a), (iii) log(â) vs a, and (iv) log(â) vs log(a). 56…”

“…Ameyaw et al proposed a methodology in which, rather than fusing all the POD curves into a single POD curves, several belief values are computed using the Bayesian Combination Rule (BCR). 56,173,174 In this approach, all the possible sensor combinations are considered. For example, a certain damage could be detected (i.e., signal higher than the threshold value) only by certain sensors (each sensor with its own POD curve).…”

“…Ameyaw et al applied the concept of POD curves to vibration based fault detection and isolation (FDI). 56,173,174 It was found that, depending on the sensor type, position and damage location, different POD curves are generated. Therefore, it was considered reasonable to develop a strategy to combine different POD curves related to different sensors.…”

New Metric for Evaluation of Deep Neural Network Applied in Vision-Based Systems

“…No effort was made to relate detectability with size quantitatively because aircraft size was irrelevant. Contemporary applications, as demonstrated in the areas of nondestructive testing [15,16] and structural health monitoring [17], are concerned with how the characteristics of the target influence the probability of detecting it. The PR curve has been proposed as an alternative and more effective in dealing with highly skewed datasets [18,19].…”