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![Fig. 1. Pattern of real and ideal PoD curves [2].](profile/Germano-Padua/publication/221926704/figure/fig4/AS:668554391195656@1536407196505/Pattern-of-real-and-ideal-PoD-curves-2_Q320.jpg)
![Fig. 3. Example of PoD curve with 95% confidence level [2].](profile/Germano-Padua/publication/221926704/figure/fig2/AS:317035000156160@1452598442379/Example-of-PoD-curve-with-95-confidence-level-2_Q320.jpg)
![Fig. 5. PoD curves for defects LF and LP, respectively [2].](profile/Germano-Padua/publication/221926704/figure/fig5/AS:668554391191568@1536407196646/PoD-curves-for-defects-LF-and-LP-respectively-2_Q320.jpg)
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... equation 16, it is possible to determinate the number of simulations necessary to reach the error level wished. Details of Method Monte Carlo are provided by Carvalho [ 2] and Ang [6]. The ROC curves are well known in theory of signal detection and accessed on technical referenced of pattern recognition [7, 8, 9, 10]. These curves are result of relation between number of false positives (FP), abscissas axis, and number of true positives (TP), ordinates axis. Alike PoD, reliability is given by area under the curve. Reliability of technique is better as much as higher values of TP and lower values of FP. Ideal reliability is encompassed in a 100% of a square area, according to didactic example of figure ...
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O livro pretende-se uma contribuição para a área da biblioteconomia, por meio do caminho do ensino e da formação profissional de bibliotecários. É fruto da colaboração de professores e pós-graduandos do Departamento de Biblioteconomia e Documentação da Escola de Comunicações e Artes, que aceitaram participar da iniciativa de compartilharem conteúdo...
Citations
... This concept arose in the 1970s, in studies on discontinuity detection capabilities by NDT methods carried out in the aerospace industry [13][14][15][16][17][18]. The results of the inspections in representative samples allow obtaining reliable parameters that relate the probability of detection of the defect with its size, and quantify the capacity of the nondestructive testing method (NDT) to detect discontinuities [12,[19][20][21][22]. This methodology allows to compare capabilities of inspection methods and techniques in order to (1) evaluate the performance of inspectors, (2) validate inspection procedures, (3) configure inspection intervals for maintenance, and (4) establish criteria for design acceptance [7,12,22]. ...
... The results of the inspections in representative samples allow obtaining reliable parameters that relate the probability of detection of the defect with its size, and quantify the capacity of the nondestructive testing method (NDT) to detect discontinuities [12,[19][20][21][22]. This methodology allows to compare capabilities of inspection methods and techniques in order to (1) evaluate the performance of inspectors, (2) validate inspection procedures, (3) configure inspection intervals for maintenance, and (4) establish criteria for design acceptance [7,12,22]. Its usefulness has expanded to several techniques in different types of materials, such as those reported in ultrasonic tests [23], penetrant liquids [24][25][26], acoustic emission [27], and eddy currents [28]. ...
... The probability to detect POD discontinuities based on their size is a graphic relationship that is obtained by POD hit-or-miss statistical method [12,29]. To use the hit-or-miss method, test items must have at least 60 real defects of different sizes [12,22,29]. After the non-destructive test to process the data, categorical values of one and zero are assigned depending on whether the defect has been detected or not and it conforms to a binomial distribution. ...
... A POD is a function of the defect size; it evaluates the smallest flaw size and combines its quantitative and qualitative parameters [80]. The 90∕95 defect size information is used as a reference and detects defects with a probability of 90% at 95% of confidence level [81]. ...
Non-destructive evaluation of aircraft production is optimised and digitalised with Industry 4.0. The aircraft
structures produced using fibre metal laminate are traditionally inspected using water-coupled ultrasound
scans and manually evaluated. This article proposes Machine Learning models to examine the defects in
ultrasonic scans of A380 aircraft components. The proposed approach includes embedded image feature
extraction methods and classifiers to learn defects in the scan images. The proposed algorithm is evaluated
by benchmarking embedded classifiers and further promoted to research with an industry-based certification
process. The HoG-Linear SVM classifier has outperformed SURF-Decision Fine Tree in detecting potential
defects. The certification process uses the Probability of Detection function, substantiating that the HoG-Linear
SVM classifier detects minor defects. The experimental trials prove that the proposed method will be helpful to
examiners in the quality control and assurance of aircraft production, thus leading to significant contributions
to non-destructive evaluation 4.0.
... Non-invasive tests are widely used in the aeronautic industry, mainly for maintenance purposes, examples of which are visual inspection, microscopy, radiography, and penetrating dyes, among others [1]. Optical tests have been used as a non-invasive technique for measurement purposes, such as flow direction [2], particle image velocimetry [3], and Doppler anemometry [4], among others. ...
In this research, an impact reaction which was provoked far from its origins was studied. A metal box filled with sand was used to emulate a rigid body in which a steel bar was embedded; these conditions simulated the fuselage and wing, respectively, and the impact was applied to the rigid body and the measurement to the bar. For this, an optical technique was used to measure the relative displacement of the steel bar, and the measurements are obtained by applying digital image correlation; 2D images were obtained from the speckles generated as a reflection of the beam on the material. The results were studied through the modified Gauss–Newton analytical approach obtaining a maximum standard error deviation of 0.144 from the experimental results.
... Our review of the existing literature on NDE models shows that continuous/continuous probabilistic models are often learned in an ad-hoc manner. An example is the probability of (correct) sizing (POS), which describes the error in the measurement by an inspector of the continuous condition (e.g., a crack length) (Brennan, 2013;da Silva and de Padua, 2012;Granville and Charlton, 2016;Visser, 2002;Nath, 2021). Models for POS are continuous/continuous, but definitions vary and no application to reliability analysis is documented in the literature. ...
... devices is also typically represented through the PoD/PFA model (Swets, 1992;Sheils et al., 2010;da Silva and de Padua, 2012;Quirk et al., 2018). The transition between Model (3) to Model (4) corresponds to calibrating the NDE system to an operating point on an ROC curve, by fixing the threshold s th . ...
Non-destructive evaluation (NDE) inspections are an integral part of asset integrity management. The relationship between the condition of interest and the quantity measured by NDE is described with probabilistic models such as PoD or ROC curves. These models are used to assess the quality of the information provided by NDE systems, which is affected by factors such as the experience of the inspector, environmental conditions, ease of access, and the precision of the measurement device. In this paper, we review existing probabilistic models of NDE andshow how they are connected within a unifying framework. This frameworkprovides insights into how these models should be learned, calibrated, and applied. We investigate and highlighthow the choice of the model can affect the maintenance decisions taken on the basis of NDE results. In addition, we analyze the impact of experimental design on the performance of a given NDE system in a decision-making context.
... For example, the ASM Handbook of Non-destructive Evaluation and Quality Control recommends using at least 30 target flaws for hit/ miss POD data [16]. Another issue with this approach is that the fabrication of artificial weld defects with dimensions, locations and characteristics that can simulate real weld defects is very difficult to achieve [17]. ...
... Recently, methods based on computer simulation have become popular [17,20]. In Ultrasonic Testing, POD is related to the likelihood of an overlap between the ultrasonic beam and the defect. ...
... A Monte Carlo Simulation (MCS) can be used to calculate these probabilities. The estimation of POD with MCS may be achieved by solving the equation below [17]: ...
Estimation of probability detection curves for non-destructive evaluation (NDE) typically involves the manufacturing of a high number of defect specimens followed by trial NDE and statistical analysis of the data based on the hit/miss approach. This is a time-consuming and costly procedure. Besides, probability of detection (POD) depends on a number of variables, such as human factors (operator), and the testing environment, resulting in a significant mismatch between those POD curves generated in the lab and those in practice.
One application of POD curves is in the quality control of welded joints [1]. Weld quality is often characterised by the number of defects found and their size which is, inevitably, dependent on the POD of the employed NDE. Therefore, a predefined generic POD curve has certain limitations.
In this paper, a method of estimating POD curves based on the Bayesian theorem of conditional probability is presented and its applicability is validated by studying an existing database under both Bayesian and the hit/miss methods. Overall, the POD predicted by the Bayesian theorem is found to be consistent with the commonly used hit/miss model. Finally, the Bayesian model is used to estimate the POD, and the true weld defect size and frequency in two ship manufacturing yards. The estimated weld defect size and frequency models provide valuable information to estimate the fatigue and fracture reliability of ship and offshore structures. It is shown that one of the yards has both better weld quality production and superior NDE detection. This will have a valuable benefit for weld quality control (QC) programmes through saving the testing resources.
... A POD is a function of the defect size; it evaluates the smallest flaw size and combines its quantitative and qualitative parameters [80]. The 90∕95 defect size information is used as a reference and detects defects with a probability of 90% at 95% of confidence level [81]. ...
Non-destructive evaluation of aircraft production is optimised and digitalised with Industry 4.0. The aircraft
structures produced using fibre metal laminate are traditionally inspected using water-coupled ultrasound
scans and manually evaluated. This article proposes Machine Learning models to examine the defects in
ultrasonic scans of A380 aircraft components. The proposed approach includes embedded image feature
extraction methods and classifiers to learn defects in the scan images. The proposed algorithm is evaluated
by benchmarking embedded classifiers and further promoted to research with an industry-based certification
process. The HoG-Linear SVM classifier has outperformed SURF-Decision Fine Tree in detecting potential
defects. The certification process uses the Probability of Detection function, substantiating that the HoG-Linear
SVM classifier detects minor defects. The experimental trials prove that the proposed method will be helpful to
examiners in the quality control and assurance of aircraft production, thus leading to significant contributions
to non-destructive evaluation 4.0.
... 2. In all the six major industrial projects, PoD is empirically derived from the data produced experimentally by employing the method known as 'round-robin testing' (RRT) [8]. This experimental method is time consuming and expensive due to high specimen fabrication cost and inspection cost. ...
... For signal-response data the parameters of the PoD (a) function are estimated from the scatter in â values about the median response to crack size a [8]. It has been noticed in numerous studies [2,19] that an approximately linear relationship occurs amid ln(â) and ln(a) for signal-response data, and the relationship is written as: Furthermore, for signal-response data, a flaw is regarded as 'detected' if â exceeds some pre-defined threshold â th . ...
... POD a a a th ( ) ln(ˆ) ln(ˆ) = > Probability (8) In other words, it is the area contained between the pdf of ln(â) and above the flaw evaluation threshold ln(â th ) as shown in Fig.5. ...
VARIOUS NON-DESTRUCTIVE EVALUATION (NDE) methods are used in the offshore industry during in-service inspections to detect the cracks in the structures and mechanical items. The metric generally used to quantify the capability of the NDE method is probability of detection (PoD), which is expressed as a function of crack size through a PoD curve. Human skills play a major role in determining the overall reliability of the NDE method used for crack detection. Thus, a brief discussion relating to human factors in NDE reliability is presented. Thereafter, based on a literature review, the history and development of PoD curves is provided. The statistics of the PoD curve, along with the statistical models of the curve for different NDE methods is also presented. Furthermore, the limitations of PoD curves are discussed in the paper and, finally, a brief discussion about model-assisted PoD is presented.
