Model Assisted Probability Of Detection Research Articles

Uncertainty propagation for MAPoD in eddy current NDT by polynomial chaos–kriging

ABSTRACT In this article, the Polynomial Chaos–Kriging (PCK) metamodel is proposed to surrogate the physical model for model-assisted probability of detection (MAPoD) analysis in eddy current non-destructive testing (ECNDT). Two popular non-intrusive metamodels, the Polynomial Chaos Expansion (PCE) and Kriging, are combined properly to replace the time-consuming boundary element method-based ECNDT forward solver for accelerating the uncertainty propagation within MAPoD analysis in NDT. In PCK, the global behaviour of the model is estimated by the trend function of PCE, and the remaining local changes of it are captured by Kriging. Both the accuracy and efficiency of the proposed PCK metamodel are demonstrated on 3D ECNDT MAPoD cases involving surface flaws on the conducting thick plate using the detecting coil with rectangular cross section. Numerical results show improved performance of PCK metamodel over PCE and Kriging metamodels, respectively, while maintaining at least two digits of accuracy of the PoD metrics.

Robustness of Structural Health Monitoring Systems for Offshore Energy Structures based on Damage Characteristics

Offshore energy structures such as fixed/floating wind turbines, tidal turbines and wave energy converters are exposed to loads coming from different sources. Recent advances in SHM offer many unique opportunities to assess the structural integrity of offshore energy infrastructure. The process of SHM generally involves the use of a system of sensors mounted on a structure; the processing of signals received from the sensors to attain damage sensitive features; and the detection of damage in the structure. Over the past decades, most of the research in SHM has been focused on improving and developing new sensor technology, signal processing, and damage detection algorithms. However, there are very few studies assessing the performance of SHM systems with respect to damage detection, localization, and quantification. Moreover, most of the performance analysis models for SHM systems rely only on 'probability of detection (POD)', that is an assessment index used in NDT to evaluate the probability of detecting a damage as a function of its size. For SHM systems, the replicability of POD is influenced by the environment, measurement noise, and the deterioration of sensors and instruments. Therefore, the distribution of POD is often determined by performing an extensive number of test sets with existing damage of varying magnitude. This paper aims to reduce the volume of experimental data required, as well as the uncertainties associated with POD prediction by using a model-assisted probability of detection (MAPOD) approach. We develop a Bayesian network (BN) method to evaluate the performance of SHM systems in terms of damage detection, localization, and assessment. In addition to POD, the probability of accurate localization (POAL) and probability of accurate assessment (POAA) are also incorporated into the analysis. The BN and limit state functions are applied to a fixed offshore energy structure equipped with a vibration based SHM system.

Efficient MAPoD via Least Angle Regression based Polynomial Chaos Expansion Metamodel for Eddy Current NDT

In this article, a metamodeling approach based on non-intrusive polynomial chaos expansion (PCE) with least angle regression (LAR) method is used in boundary element analysis for a model-assisted probability of detection (MAPoD) study of eddy current nondestructive testing (NDT) systems. The LAR-PCE metamodel represents the NDT system model responses by a set of coefficients with the polynomial basis functions in lieu of pure kernel degeneration accelerated boundary element method (KD-BEM) based physical model. Both the computational accuracy and efficiency of the LAR-PCE metamodel over the ordinary least squares (OLS) based PCE metamodel are demonstrated by testing the 3D eddy current NDT benchmarks with different system setups, flaw lengths and widths. The simulation results show two digits accuracy of the PoD metrics compared with the ones achieved by the KD-BEM based physical model as the benchmark. The LAR-PCE metamodel has remarkable improvements in computational efficiency over the OLS-PCE metamodel and accelerates the MAPoD study.

Modeling of Eddy Current NDT Simulations by Kriging Surrogate Model

ABSTRACT In this article, the Kriging surrogate model is proposed to accelerate the model-assisted probability of detection (MAPoD) analysis for eddy current nondestructive testing (NDT). The Kriging surrogate model is the key for enabling the efficient MAPoD analysis, considering huge number of uncertainties propagate in the eddy current NDT system, by replacing the time-consuming physical model. To generate the model responses of NDT system, a precise physical model based on the adaptive cross approximation algorithm accelerated boundary element method (BEM) is applied. In the numerical case, the MAPoD study of eddy current for detecting surface flaws in the conducting plate is analyzed. By comparing the PoD metrics achieved by the pure physical model and by the Kriging surrogate model, the accuracy and efficiency of the proposed surrogate model are demonstrated.

A Model-Assisted Probability of Detection Framework for Optical Fiber Sensors

Optical fiber sensors (OFSs) represent an efficient sensing solution in various structural health monitoring (SHM) applications. However, a well-defined methodology is still missing to quantify their damage detection performance, preventing their certification and full deployment in SHM. In a recent study, the authors proposed an experimental methodology to qualify distributed OFSs using the concept of probability of detection (POD). Nevertheless, POD curves require considerable testing, which is often not feasible. This study takes a step forward, presenting a model-assisted POD (MAPOD) approach for the first time applied to distributed OFSs (DOFSs). The new MAPOD framework applied to DOFSs is validated through previous experimental results, considering the mode I delamination monitoring of a double-cantilever beam (DCB) specimen under quasi-static loading conditions. The results show how strain transfer, loading conditions, human factors, interrogator resolution, and noise can alter the damage detection capabilities of DOFSs. This MAPOD approach represents a tool to study the effects of varying environmental and operational conditions on SHM systems based on DOFSs and for the design optimization of the monitoring system.

Efficient Model Assisted Probability of Detection Estimations in Eddy Current NDT with ACA-SVD Based Forward Solver.

Model assisted probability of detection (MAPoD) is crucial for quantifying the inspection capability of a nondestructive testing (NDT) system which uses the coil or probe to sense the size and location of the cracks. Unfortunately, it may be computationally intensive for the simulation models. To improve the efficiency of the MAPoD, in this article, an efficient 3D eddy current nondestructive evaluation (ECNDE) forward solver is proposed to make estimations for PoD study. It is the first time that singular value decomposition (SVD) is used as the recompression technique to improve the overall performance of the adaptive cross approximation (ACA) algorithm-based boundary element method (BEM) ECNDE forward solver for implementation of PoD. Both the robustness and efficiency of the proposed solver are demonstrated and testified by comparing the predicted impedance variations of the coil with analytical, semi-analytical and experimental benchmarks. Calculation of PoD curves assisted by the proposed simulation model is performed on a finite thickness plate with a rectangular surface flaw. The features, which are the maximum impedance variations of the coil for various flaw lengths, are obtained entirely by the proposed model with selection of the liftoff distance as the uncertain parameter in a Gaussian distribution. The results show that the proposed ACA-SVD based BEM fast ECNDE forward solver is an excellent simulation model to make estimations for MAPoD study.

Real-Time Nondestructive Evaluation of Additive Manufacturing Using a Laser Vibrometer and Shock Tube

Abstract Additive manufacturing (AM) parts retain a certain degree of individuality and could suffer from a combination of different defect types, and therefore the nondestructive evaluation on AM parts remains a challenging task. Engineering non-contact and nondestructive real-time inspection and in situ quality assurance of AM parts would be a net improvement compared to current quality control methods that are conducted post-production. Here, the authors propose to combine the use of a laser vibrometer with a compression-driven shock tube to assess the quality of AM parts through the evaluation of the vibration spectra of the part. An AM of a cylindrical part was selected for the study, along with different defect types and sizes. These defects include internal voids of different sizes at different locations, local changes in thickness (infill), and local changes in melting temperatures. A numerical model was created and validated using experimental data to conduct model-assisted probability of detection (MAPOD). Results were analyzed by evaluating correlation matrices between different models. Results showed that vibration spectra induced by a shock wave were sensitive to different types and sizes of defects under the studied geometry. The defect index yielded an approximately linear relationship with respect to defect void severity. MAPOD curve studies revealed a minimum detectable void defect of 0.039% of the AM part’s volume.

Simulation-Based Investigation of a Probability of Detection (POD) Model Using Phased Array Ultrasonic Testing (PAUT) Technique

Probability of detection (POD) as a metric for quantifying the capability of inspection procedures in nondestructive evaluation (NDE), has been applied and evolved in industries since 1970s. Progress had been noted when certain statistical functions were brought up to model POD behavior, including log-normal model (also referred as Probit model). This model had been concluded to be the best fit and therefore has been widely used in many studies, while the involved assumptions and conditions were not carefully addressed and explored. To make flexible POD datasets available for specific inspection procedures and reduce the number of expensive experiments needed, model-assisted POD (MAPOD) is an alternative. This paper addresses a pure simulation-based POD procedure of an inspection scenario involving phased array ultrasonic testing (PAUT) on lack-of-fusion defects in additive manufactured (AM) components. The mathematical simulations are performed by an ultrasonic testing (UT) simulation software, simSUNDT, developed at Chalmers University of Technology in Sweden. Resulted inspection datasets with the proposed data processing steps are evaluated in terms of the assumptions and conditions of log-normal POD model, with the purpose of discussing the POD model validity under different circumstances. Simulation-based POD curves are finally compared with several discrete POD values at some defect sizes, calculated through massive computations from physics-model based metamodel. Comparisons and observations confirm satisfactory application of log-normal POD model despite some violations in model hypotheses.

Demonstration of model-assisted probability of detection framework for ultrasonic inspection of cracks in compressor blades

The fatigue crack detection capability of nondestructive testing was quantitatively evaluated using the model-assisted probability of detection (MAPOD) process. A framework based on conventional MAPOD with dimension reduction was studied. By conducting a metamodel-assisted sensitivity analysis, the dimension of the physics-based model was reduced. The factors selected based on the sensitivity analysis were partitioned for both computational and physical experiments. Subsequently a transfer function was constructed. Additionally, a linear model of the relationship between the ultrasonic signal and crack size was obtained and calibrated by the transfer function by conducting physical experiments. The probability of detection curve and the corresponding detectable crack size were evaluated using the calibrated model. Furthermore, the improved MAPOD process was demonstrated by the fatigue crack detection in a J85 engine compressor first-stage blade tang hole.

Digital clone testing platform for the assessment of SHM systems under uncertainty

The performance of a Structural Health Monitoring (SHM) system can be assessed using Probability of Detection (PoD) curves, which is a common tool for the evaluation of Non-Destructive Testing (NDT) methods. This study presents a novel digital clone platform to quantify and account for uncertainties that can be detrimental to the reliability of a SHM system. Uncertainties relating to experimental measurement noise and Environmental and Operational Conditions (EOC) are considered during the definition of a threshold value that aims at reliably distinguishing between pristine and damaged signals. At the same time, the variability of impact damage characteristics and uncertainties associated with Lamb waves interaction in composites are captured though the Bayesian calibration of a Finite Element (FE) model using experimental observations. The FE model is integrated within the digital clone testing platform to substitute the experimental testing and generate a statistical sample of distributed impact events at different locations on a composite plate and compute the Model Assisted Probability of Detection (MAPOD). This approach allows the estimation of the system’s performance under different EOC that can be used during the selection and operation of a specific SHM configuration.

Multifidelity Modeling by Polynomial Chaos-Based Cokriging to Enable Efficient Model-Based Reliability Analysis of NDT Systems

This work proposes a novel multifidelity metamodeling approach, the polynomial chaos-based Cokriging (PC-Cokriging). The proposed approach is used for fast uncertainty propagation in a reliability analysis of nondestructive testing systems using model-assisted probability of detection (MAPOD). In particular, PC-Cokriging is a multivariate version of polynomial chaos-based Kriging (PC-Kriging), which aims at combining the advantages of the regression-based polynomial chaos expansions and the interpolation-based Kriging metamodeling methods. Following a similar process as Cokriging, the PC-Cokriging advances PC-Kriging by enabling the incorporation of multifidelity physics information. The proposed PC-Cokriging is demonstrated on two analytical functions and three ultrasonic testing MAPOD cases. The results show that PC-Cokriging outperforms the state-of-the-art metamodeling approaches when providing the same number of training points. Specifically, PC-Cokriging reduces the high-fidelity training sample cost of the Kriging and PCE metamodels by over one order of magnitude, and the PC-Kriging and conventional Cokriging multifidelity metamodeling by up to $$50\%$$ to reach the same accuracy level (defined by the root mean squared error being no greater than $$1\%$$ of the standard deviation of the testing points). The accuracy and robustness of the proposed method of the key MAPOD metrics versus various detection thresholds are investigated and satisfactory results are obtained.

Comparison of \xe2 Versus a and Hit/Miss POD-Estimation Methods: A European Viewpoint

For estimating the probability of detection (POD) in non-destructive evaluation (NDE), there are two standard methods, the so-called â versus a approach and the hit/miss approach. The two approaches have different requirements for the quality and quantity of input data as well as for the underlying NDE method. There is considerable overlap between the methods, and they have different limitations, so it is of interest to study the differences arising from using each methodology. In particular, if the dataset is not ideal, the methodologies may exhibit different problems dealing with various limitations in the data. In this paper, a comparison between â versus a and hit/miss analysis was completed for two different data sets, a manual aerospace eddy-current inspection and a nuclear industry phased array ultrasonic weld inspection using a simplified online tool. It was found that the two standard methods (â vs. a and hit/miss) may give significantly different results, if the true hit/miss decision is based on inspector judgement and not automated signal threshold. The true inspector hit/miss performance shows significant variance that is not attributable to signal amplitude. Model-assisted POD was not able to model the inspector performance due to lack of representative amplitude threshold and difficulties in capturing true signal variance. The paper presents experience from practical cases and may be considered a European viewpoint.

Multifidelity model-assisted probability of detection via Cokriging

This work introduces multifidelity metamodeling for reliability analysis of nondestructive testing (NDT) systems. Specifically, the Cokriging metamodel is utilized to accelerate the uncertainty propagation within model-assisted probability of detection (MAPOD) analysis of ultrasonic testing (UT) systems. The Cokriging multifidelity metamodel fuses a limited amount of data obtained from high-fidelity (HF) physics-based UT models, which are accurate but time-consuming to evaluate, with a conservative to large amount of data from low-fidelity (LF) physics-based UT models, which are less accurate but faster to evaluate. The resulting Cokriging metamodel is fast to evaluate and yields an accurate estimate of the output of the HF model. The proposed approach is demonstrated on three benchmark UT MAPOD cases involving spherically-void and pill-box shaped defects in flat aluminum plates using planar and focused transducers. The results show that a two-level Cokriging metamodel is capable of yielding estimations of the HF model that are globally accurate within 1% of the standard deviation of the testing points. Furthermore, the result show that the Cokriging metamodeling approach needs around one order of magnitude fewer training data points when compared to the current state-of-the-art approaches that rely on metamodels constructed with Kriging.

Simulation Tools for a Fiber-Optic Based Structural Health Monitoring System

Probability of detection (POD) graphics allow for a change from qualitative to quantitative assessment for every damage detection system, and as such it is a main request for conventional non-destructive testing (NDT) techniques. Its availability can greatly help towards the industrialization of the corresponding Structural health monitoring (SHM) system. But having in mind that for SHM systems the sensors are at fixed positions, and the location of a potential damage would change its detectability. Consequently robust simulation tools are required to obtain the model assisted probability of detection (MAPOD) which is needed to validate the SHM system. This tool may also help for the optimization of the sensor distribution, and finally will allow a probabilistic risk management. INDEUS, simulation of ultrasonic waves SHM system, was a main milestone in this direction. This article deals with the simulation tools for a strain based SHM system, using fiber optic sensors (FOS). FOS are essentially strain/temperature sensors, either with multi-point or with distributed sensing. The simulation tool includes the finite element model (FEM) for the original and damaged structure, and algorithms to compare the strain data at the pre-established sensors locations, and from this comparison to extract information about damage occurrence and location. The study has been applied to the structure of an all-composite unmanned aircraft vehicle (UAV) now under construction, designed at Universidad Politecnica de Madrid for the inspection of electrical utilities networks. Distributed sensing optical fibers were internally bonded at the fuselage and wing. Routine inspection is planned to be done with the aircraft at the test bench by imposing known loads. From the acquired strain data, damage occurrence may be calculated as slight deviations from the baselines. This is a fast inspection procedure without requiring trained specialists, and it would allow for detection of hidden damages. Simulation indicates that stringer partial debondings are detected before they become critical, while small delaminations as those produced by barely visible impact damages would require a prohibited number of sensing lines. These simulation tools may easily be applied to any other complex structure, just by changing the FEM models. From these results it is shown how a fiber optic based SHM system may be used as a reliable damage detection procedure.

Model-Assisted Approach for Probability of Detection (POD) in High-Temperature Ultrasonic NDE Using Low-Temperature Signals

Advanced piezoelectric-based ultrasonic transducers offer the potential for in-coolant nondestructive testing (NDT) measurements at high temperatures (HTs), including during hot standby (~260°C) for liquid-sodium–cooled advanced small modular reactors. The reliability of the NDT measurements is typically quantified by the probability of detection (POD) measured at the corresponding temperature. Obtaining such data in liquid sodium is challenging. Using a model-assisted POD approach, a transfer function is reported that enables data obtained on low carbon steel specimens at room temperature to give an estimated POD at an HT. A primary source of the difference in POD between room temperature and HT is due to the transducer material temperature-dependent performance. This paper demonstrates the transfer function approach using data for modified lead zirconium titanate (PZT-5A). A physics-based model was developed using a finite element method and used to quantify reduction in the scattering amplitude for standard reflectors, side drilled holes (SDHs), for a range of sizes, from 15°C to 195°C. Scattering amplitudes for the room-temperature–simulated data are compared with the experimental data measured at 2.25 MHz. A temperature correction and transfer functions were developed to transform the simulated temperature effect in the physics-based model to compare with the experimental data. The model-based approach was validated with experimental data. It was seen and validated for a PZT-5A ultrasonic transducer operating at 2.25 MHz that the 95% POD at 15°C was 0.58 λ, and due to variation in temperature-dependent properties of PZT-5A, the 95% POD was achieved only for a 1.41 λ SDH diameter.

Issues in estimating probability of detection of NDT techniques – A model assisted approach

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.

Performance evaluation of a magnetic field measurement NDE technique using a model assisted Probability of Detection framework

Receiver Operating Characteristics (ROC) are a powerful tool used to evaluate the performance of NDE methods; however, the need to manufacture and scan many test pieces with realistic defects means that they are expensive and time-consuming to produce. Advances in computational power now mean that it is possible to use numerical models to greatly increase the efficiency of producing ROC for practical applications. A Model Assisted Probability of Detection (MAPOD) framework has been developed to predict the performance of magnetic field measurement NDE techniques. The MAPOD method is used to predict the performance of a promising new technique relying on the deflection of a current injected into a pipe at remote locations, and measurement of the resulting magnetic field perturbations due to defects. A significant proportion of pipes cannot be inspected by pigging methods, and external inspection often requires complete coating removal; therefore, an NDE method that functions outside pipe coatings and cladding is attractive. In this method, changes in the radial and axial components of the field are measured and attributed to defects, but a strong azimuthal component means that misalignment can give significant apparent radial and axial signals due to the azimuthal field apparently having a component in these directions. This requires that the second-order gradient of the magnetic field be measured to maximise sensitivity. Fluctuations in the sensitivity and orientation of the gradiometer during the scan are expected to determine the maximum sensitivity of the technique in most practical applications; however, the flexibility of the framework allows performance to be rapidly predicted and quantified for many test scenarios. Results suggest good detection performance for defects greater than 15% of the wall thickness (T = 7.1 mm) in a 6″ pipe with 2 A (200 A/m2) current injected when measuring above typical insulation thickness (25–50 mm).

Model Assisted Probability of Detection Curves: New Statistical Tools and Progressive Methodology

The probability of detection curve is a standard tool in several industries to evaluate the performance of non destructive testing (NDT) procedures for the detection of harmful defects for the inspected structure. Due to new capabilities of NDT process numerical simulation, model assisted probability of detection (MAPOD) approaches have also been recently developed. In this paper, a generic and progressive MAPOD methodology is proposed. Limits and assumptions of the classical methods are enlightened, while new metamodel-based methods are proposed. They allow to access to relevant information based on sensitivity analysis of MAPOD inputs. Applications are performed on eddy current non destructive examination numerical data.

Surrogate Modeling of Ultrasonic Nondestructive Evaluation Simulations

Ultrasonic testing (UT) is used to detect internal flaws in materials or to characterize material properties. Computational simulations are an important part of the UT process. Fast models are essential for UT applications such as inverse design or model-assisted probability of detection. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to use data-driven surrogate modeling techniques (kriging interpolation), and physics-based surrogate modeling techniques (space mapping), as well a mixture of the two approaches. These techniques are investigated for two cases involving UT simulations of metal components immersed in a water bath during the inspection process.

Physical Model-Assisted Probability of Detection of Flaws in Titanium Forgings Using Ultrasonic Nondestructive Evaluation

Nondestructive evaluation is used widely in many engineering and industrial areas to detect defects or flaws such as cracks inside parts or structures during manufacturing or for products that need to be inspected while in service. The commonly used standard statistical model for such data is a simple empirical linear regression between the (possibly transformed) signal response variables and the (possibly transformed) explanatory variable(s) such as defect size. For some applications, such a simple empirical approach is inadequate. An important alternative approach is to use knowledge of the physics of the inspection process to provide information about the underlying relationship between the response and the explanatory variable or variables. Use of such knowledge can greatly increase the power and accuracy of the statistical analysis and enable, when needed, limited extrapolation outside the range of the observed explanatory variables. This article describes a set of physical model-assisted analyses to study the capability of two different ultrasonic testing inspection methods to detect synthetic hard alpha inclusion defects in titanium forging disks. Supplementary materials for this article are available online.