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Probability of detection for surface-breaking holes with low-frequency eddy current testing - A non-linear multi-parametric approach
Abstract
The evaluation of non-destructive testing (NDT) methods in terms of reliability is an increasing demand in various industries and applications. The probability of detection (POD) is the most frequently used method for this task. In the testing of holes with low-frequency eddy current
testing, the frequently-used one-parametric POD approach cannot be used because the requirements, mainly the linearity, cannot be met. Therefore, the use of a multi-parametric non-linear regression approach to calculate the POD is proposed. Instead of numerical simulations, commonly used
in multi-parametric approaches, an analytical model is used. The goal of this work is to evaluate the reliability of the eddy current system for the testing of electron-beam welded copper canisters by calculating a POD with the help of different artificial hole-like defects. In this example,
the multi-parametric non-linear regression approach is shown to be successful, enabling the combination of depth and diameter in the POD calculation.
... The signal response and POD are also expressed as a function of flaw size [32][33][34]. Some recent studies have proposed a POD model considering multiple flaw parameters: the multivariate POD model [35][36][37][38][39][40]. Moreover, as preparing many experimental specimens for POD evaluation is very expensive and time consuming, model-assisted POD (MAPOD) [41][42][43][44] has been proposed to mitigate the cost and complexity of the work and to thus increase the efficiency of POD evaluation, with the help of the existing knowledge or numerical simulations. ...
This paper presents a multivariate probability of detection (POD) analysis method for long-range pipe inspection using microwave non-destructive testing (NDT). The proposed two-dimensional (2D) POD model considers both the size and location of pipe wall thinning (PWT) and is thus able to simultaneously characterize the detectability and detection range. First, the propagation of microwaves in a pipe with PWT was modeled through numerical simulation. The simulated S-parameters (S11) were converted into the time domain and were further processed to correlate the amplitude of the reflection signal with the corresponding PWT depth and location. The simulation results indicate that the logarithmic amplitude of the reflection signal is proportional to the PWT location and logarithmic PWT depth. Therefore, a prior multivariate regression model was established for the above three parameters. Second, an experiment was performed using a 14.5-m-long brass pipe. Twelve short pipes with six different inner diameters were used to emulate PWT and were deployed at eight different locations in the pipe. The experimental results suggest that each PWT can be detected with excellent repeatability, and show consistency with the simulation results. The processed experimental signals were subsequently employed for the regression model of the amplitude of the reflection signal, PWT depth, and location. Finally, a 2D POD model was constructed on the basis of the regression model and a dynamic-static threshold, combining in-pipe microwave signal attenuation with instrumental noises. The POD plot and contour give reasonable interpretations of the detection capability of this testing method against PWTs with different depths, considering the PWT locations.
... The reliability of finding the initial crack size using a non-destructive testing (NDT) technique is quantified through a parameter with statistical significance, called 'probability of detection (POD)' . POD is a function of the material used, the surface conditions, the type of cracks and the orientation of cracks, as well as length, width, etc [2][3][4][5][6] . ...
Assessing the reliability of non-destructive testing (NDT) techniques in detecting in-service fatigue cracks is vital for ensuring the structural integrity of aero engines. However, the requirement of a large number of in-service failed components with numerous initiating fatigue cracks makes it a cost-intensive methodology. Hence, laboratory samples with electrical discharge machined (EDM) notches representing fatigue cracks have also been used for NDT reliability studies. However, probability of detection (POD), a measure of NDT reliability, is usually a function of all crack dimensions rather than only length. This limits the applicability of EDM notches (minimum width of notch ~0.3 mm) as artificial fatigue cracks for POD studies. The current study demonstrates the methodology of generating cracks under laboratory conditions in nickel-based superalloy samples (representative aero engine material), mimicking in-service conditions such as crack tightness as low as 1 μm, crack tortuosity, transgranular nature, crack branching and multiple initiation sites of cracks. POD curves generated using these samples are demonstrated and the feasibility of this approach is discussed. © 2019 British Institute of Non-Destructive Testing. All Rights Reserved.
... More recently, more specific approaches such as multi-parameter PoD models have been proposed to account for the various intrinsic capability and parameters of NDT systems in applications such as inspection of thick walled components [23,29]. Extending the application of multi-parameter PoD, a non-linear model was proposed [12], but the data fit was not based on physical or experimental knowledge of the inspection process. In recent years, the advancements in PoD models discussed above are also increasingly sought to be supplemented with simulations which serve to reduce experimentation [6]. ...
Probability of detection (PoD) curves are a popular metric for the reliability assessment of Nondestructive Testing (NDT) procedures. However, the classical Berens method for signal response PoD analysis strongly relies on the hypothesis of Gaussian residuals which can be violated in practical conditions. In particular, data from sparse field trials can be scattered and or skewed. Hence, this paper studies the feasibility of assuming a Weibull distribution, which is known for versatility in representing several fundamental statistical states, for regression residuals without modifying the overall Berens framework for PoD curve determination. The proposed ‘Weibull-Berens’ PoD statistics is first shown to compare well with the classical Berens method for an ideal case of Gaussian residuals. The advantages of the method are further demonstrated using a synthesised dataset, as well as a practical case of non-Gaussian residuals arising from reduced number of experimental trials.
... POD data generation is usually carried out either using HIT (detected)/MISS (undetected) approach or â (signal response) vs. a (flaw size) approach as per MIL-HDBK 1823A (2009) standard [4] which describes the procedure to be adopted along with the various parameters such as sample shape, size and defect classification to be considered. In addition, MIL-HDBK [4] also specifies that if the NDT technique reliability is influenced by several parameters, POD calculations should be considered by incorporating multi-parameter POD approaches [5][6][7][8][9][10][11][12][13][14][15]. However in the current study, only crack length as the parameter was considered and hence the conventional/standard POD approaches are only followed. ...
In order to successfully implement Damage Tolerance (DT) methodology for aero-engines, Non-Destructive Testing (NDT) techniques are vital for assessing the remaining life of the component. Probability of Detection (POD), a standard measure of NDT reliability, is usually estimated as per MIL-HDBK-1823A standard. Estimation of POD of any NDT technique can be obtained by both experimental and model assisted methods. POD depends on many factors such as material, geometry, defect characteristics, inspection technique, etc. These requirements put enormous limitations on generating experimental POD curves and hence, Model Assisted Probability of Detection (MAPOD) curves are currently in vogue. In this study, MAPOD approaches were demonstrated by addressing various issues related to selection of crack sizes distribution, challenges involved in censoring and regression, estimation of distribution parameters, etc. Ultrasonic testing on volumetric defects has been identified as a platform to discuss the challenges involved. A COMSOL Multiphysics based FEM numerical model developed to simulate ultrasonic response from a Ti-6Al-4V cylindrical block has been validated experimentally. Further, the individual ultrasonic response from various Flat Bottom Hole (FBH) defects following lognormal distribution has been generated using the numerical model. a90/95(detecting a flaw with 90% probability and 95% confidence) value obtained from POD curve showed that the POD value increased with an increase in decision threshold.
... In contrast, various flaws would appear in various components in nuclear power plants, which indicates the difficulty in characterizing a flaw using a single parameter. To address this issue, earlier studies of the authors have proposed how to construct POD with multiple flaw parameters [5,6] without postulating a closed-form of signal response or a constant variance [7,8]. The studies demonstrated its effectiveness by evaluating the POD from eddy current signals. ...
This study proposes a probability of detection (POD) model to discuss the capability of non-destructive testing methods for the detection of stress corrosion cracks appearing in the steam generator tubes of pressurized water reactors. Three-dimensional finite element simulations were conducted to evaluate eddy current signals due to stress corrosion cracks. The simulations consider an absolute type pancake probe and model a stress corrosion crack as a region with a certain electrical conductivity inside to account for eddy currents flowing across a flaw. The probabilistic nature of a non-destructive test is simulated by varying the electrical conductivity of the modelled stress corrosion cracking. A two-dimensional POD model, which provides the POD as a function of the depth and length of a flaw, is presented together with a conventional POD model characterizing a flaw using a single parameter. The effect of the number of the samples on the PODs is also discussed.
Reliability evaluations of modern test systems under the Industry 4.0 technologies, play a vital role in the successful transformation to NDE 4.0. This is due to the fact that NDE 4.0 is mainly based on the interconnection between the cyber-physical systems. When the individual reliability of the various important technologies from the Industry 4.0 such as the digital twin, digital thread, Industrial Internet of Things (IIoT), artificial intelligence (AI), data fusion, digitization, etc. is high, then it is possible to obtain the reliability beyond the intrinsic capability of the test system. In this paper, the significance of the reliability evaluation is reviewed under the vision of NDE 4.0, including examples of data fusion concepts as well as the importance of algorithms (like explainable artificial intelligence), the practical use is discussed and elaborated accordingly.
This study proposes the construction of the probability of detection (POD) as a function of both the depth and length of a flaw. In addition, this study discusses how to censor signals in constructing the POD. The general effects of the flaw parameters on signals are evaluated by numerical simulations, and the scattering of signals, which is critical to the POD, is estimated by signals obtained in experiments. A new likelihood function is introduced, and the proposed method is demonstrated using eddy current signals caused by various artificial flaws on a flat type 316 L stainless steel plate obtained in a laboratory test. The demonstration confirms that the proposed method can provide a reasonable POD with a small amount of experimental signals, and reveals that proper censoring significantly decreases the detrimental effect of noise on the POD.
The assessment of the Probability of Detection (POD) is used to evaluate the reliability of the non-destructive testing (NDT) system. The POD is required in industries, where a missed flaw might cause grave consequences. If only the artificial defects are evaluated, the POD could lead to wrong conclusion or even be invalid. The POD based on real flaws is needed. A small amount of real flaws can lead to a not statistically significant result or even to incorrect results. This work presents an approach to obtain to a significant result for the POD of the current dataset, despite the small amount of real defects. Two steps are necessary to assess a NDT system based on real flaws. First we evaluated the correlation between the NDT signal and the real size of the flaw. Second we use a statistical approach based on the Bayesian statistics to assess a POD in spite of the small amount of data. The approach allows including information of the POD evaluation of artificial defects in the assessment of the POD of real flaws.
It is not always only the size of the flaw that determines the severity of the flaw for the structure. In such cases, it is important to express the capability of the non-destructive testing (NDT) system to detect a flaw with respect to exactly those parameters that determine flaw severity.
The multi-parameter reliability model presented in this article shows a way of calculating and expressing the probability of detection (POD) as a function of different influencing parameters, using numerically simulated NDT system responses and experimentally measured responses. A successful
application of the model is demonstrated on the data from a transmit-receive longitudinal (TRL) ultrasonic inspection of a cast iron component. The POD of the surface-breaking semi-elliptical crack-like flaw is expressed as a function of its depth and length. In a direct comparison with the
conventional signal response analysis, where the POD is expressed as a function of only the flaw size, the method provides a more comprehensive estimation of the reliability of the NDT system.
Eddy current inspection is widely used in nondestructive evaluation to detect cracks in metal structures. The impedance plane measurement response collected using our motion controlled eddy current inspection system, are used in the analysis. A scalar reduction from the impedance plane response is used to minimize human-factor variation. We apply a noise interference model to the data from a large-scale experiment taking measurements on fastener rivet holes in multi-layer structures with fatigue cracks, and estimate the probability of detection (POD). The estimates of POD as a function of crack size will be valuable for future model-assisted POD study.
Previously suggested methods for constructing confidence bands for cumulative distribution functions have been based on the classical Kolmogorov-Smirnov test for an empirical distribution function. This paper gives a method based on maximum likelihood estimation of the parameters. The method is described for a general continuous distribution. Detailed results are given for a location-scale parameter model, which includes the normal and extreme-value distributions as special cases. Results are also given for the related lognormal and Weibull distributions. The formulas derived for these distributions give a band with exact confidence coefftcient. A chi-squared approximation, which avoids the use of special tables, is also described. An example is used to compare the resulting bands with those obtained by previously published methods.
Recent advances are presented to model discontinuities in random anisotropies that arise in certain materials, such as titanium alloys. A numerical model is developed to provide a full anisotropic representation of each crystalline in a gridded region of the material. Several simulated and experimental demonstrations are presented highlighting the effect of grain noise on eddy current measurements. Agreement between VIC-3D (c) model calculations and experimental data in titanium alloy specimens with known flaws is demonstrated.
Fatigue cracks are prone to develop around fasteners found in multi-layer aluminum structures on ageing aircraft such as the
CC-130 Hercules and CP-140 Aurora (P-3 Orion). Probability of Detection (POD) studies using eddy current techniques within
the bolt holes contribute to risk assessments used in evaluating the serviceability of these aircraft. Improving POD by optimizing
the inspection system can reduce the required frequency of inspections, since assurance of detection of smaller crack sizes
extends the interval for which growth of cracks to a critical size may occur. In this work signal analysis and POD of laboratory
grown fatigue cracks in the corners of bolt holes of 7075-T6 aluminum is examined. A number of parameters that enhance crack
detection are identified, including the use of intimate contact probes versus steel sheath (non-contact), higher frequencies
and the use of C-Scan display. Results demonstrate better detectability at 1600 kHz, than at the normally used 400 kHz, and
enhanced recognition and assurance of identification of peak crack signal for data recorded and displayed in a C-Scan format.
Results are compared with a previous POD study, which used current field techniques for detection.
Probability of detection (PoD) studies are broadly used to determine the reliability of specific nondestructive inspection procedures, as well as to provide data for damage tolerance life estimations and calculation of inspection intervals for critical components. They require inspections on a large set of samples, a fact that makes these statistical assessments time- and cost-consuming. Physics-based numerical simulations of nondestructive testing inspections could be used as a cost-effective alternative to empirical investigations. They realistically predict the inspection outputs as functions of the input characteristics related to the test piece, transducer and instrument settings, which are subsequently used to partially substitute and/or complement inspection data in PoD analysis. This work focuses on the numerical modelling aspects of eddy current testing for the bolt hole inspections of wing box structures typical of the Lockheed Martin C-130 Hercules and P-3 Orion aircraft, found in the air force inventory of many countries. Boundary element-based numerical modelling software was employed to predict the eddy current signal responses when varying inspection parameters related to probe characteristics, crack geometry and test piece properties. Two demonstrator exercises were used for eddy current signal prediction when lowering the driver probe frequency and changing the material's electrical conductivity, followed by subsequent discussions and examination of the implications on using simulated data in the PoD analysis. Despite some simplifying assumptions, the modelled eddy current signals were found to provide similar results to the actual inspections. It is concluded that physics-based numerical simulations have the potential to partially substitute or complement inspection data required for PoD studies, reducing the cost, time, effort and resources necessary for a full empirical PoD assessment.