E-Journal of Advanced Maintenance Vol.1 (2010) 99-108
Japan Society of Maintenology

Computational Methods in Nondestructive Evaluation:
A Revolution in Maintenance
Jeremy KNOPP1,*, John ALDRIN 2, Eric LINDGREN1, Enrique MEDINA1, and MarkBLODGETT1
1
2

United States Air Force Research Laboratory, WPAFB, Dayton, OH, United States
Computational Tools, Gurnee, IL, United States(Received; January 7th, 2010)
Abstract. The primary objective of this research program is to improve the characterization of small
discontinuities (cracks, corrosion) using eddy current and ultrasonic methods for complex structures using
computational methods in NDE. The research approach concerns the development and validation of efficient
3D models that accurately represent complex eddy current (EC) and ultrasonic (UT) inspection problems.
Simulated studies can then be used to gain a fundamental understanding of the NDE characterization problem
for differentiating and sizing small discontinuities in the presence of coherent noise features present in complex
structures. With this understanding and modeling capability, research on novel data analysis and classification
methods is conducted exploring multi-dimensional signal processing using data from scanning systems andarray sensors and model-based classifiers via inverse methods. The benefits of this program address
minimizing costs, minimizing disassembly, improving reliability, and maximizing availability of aircraft. A
probabilistic risk analysis method for assessing the value of NDE capabilities in maintenance strategies and theimpact of NDE characteristics on maintenance cost and reliability tradeoffs is also presented.

KEYWORDS: modeling, ultrasonic inspections, eddy current, nondestructive evaluation, model-assisted
probability of detection (MAPOD), economic service life management

1.

Introduction

The service life for several types of US Air Force aircraft is being extended beyond the design
life of these systems. Therefore, additional inspections are needed for complex, buried structure thatwas not anticipated during the design and development process. This will lead to an increased
maintenance burden by requiring additional inspections that can only be accomplished by disassemblyof structures when using the inspection processes currently available in production environments. As aresult, new inspection technologies and strategies are being investigated to mitigate the cost and timerequired for maintenance of aircraft structures. Currently the USAF uses Damage Tolerance
Assessment (DTA) to manage the structural integrity of aircraft and the US Navy uses the Safe-Lifeapproach. DTA requires time-phased inspections to detect damage before it can grow to a criticalsize. New concepts in maintenance include Condition-based Maintenance (CBM). CBM will
require the detection and characterization of flaws in aircraft [1] to identify when maintenance isrequired. This approach intends to minimize the number of inspections and the associateddisassembly and reassembly of aircraft required for these inspections. In the last several years,
research efforts at AFRL developed capabilities to detect cracks in locations with very limited access.
Other efforts are focusing on providing the science base necessary to achieve CBM.
A strategy to produce the science base necessary to achieve progress on aging aircraft*

Corresponding author, E-mail: Jeremy.knopp@wpafb.af.mil
US Air Force Research Laboratory., WPAFB, OH 45433, United States†

ISSN – 1883 – 9894/09 © 2009 – JSM and the authors. All rights reserved.

99

J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in Maintenancemaintenance problems is presented in Figure 1.

Specific areas of research include the following:

Forward model development for electromagnetic and ultrasonic methods
Rigorous benchmark experiments for model validation and discovery
Model-assisted probability of detection (MAPOD) methods for NDE validation
Model-based inversion for damage and material characterization
Probabilistic methods in probe design and optimization
Probabilistic methods for economic value analysis in NDE applications
Current research and development integrates these six areas. Forward modeling research
involves the development and improvement of models to accurately simulate the interaction of eddy
current and ultrasonic NDE methods with relevant materials properties, damage, degradation,
deformation, and failure mechanisms under laboratory or realistic conditions. Rigorous benchmark
experiments address the verification and validation of the accuracy and applicability of numericaland analytical models. In addition, this facilitates the discovery of new relationships between NDE
methods with different material and/or flaw states. Model-assisted probability of detection(MAPOD) research addresses the development of stochastic methods with NDE models to mitigate
the high cost and improve the quality of NDE technique validation studies. Model-based inversion
targets the primary objective of material and damage state characterization where model parameters
associated with the material and/or damage condition are solved in an iterative fashion until
agreement between the model and measured data for the sample under test is achieved.
Probabilistic methods research explores how to best address uncontrolled variability and uncertainty
in NDE design and optimization to improve reliability, minimize costs, and maximize availability of
the fleet. Finally, probabilistic risk analysis methods are used, together with NDE capability models,cost models, and multiobjective optimization techniques, to assess the effects of technology andhuman factors in NDE applications on figures of merit such as maintenance cost and system
reliability and availability. In this paper, three case studies are presented where computational
methods were used in the discovery, design and validation of NDE techniques. In addition, ademonstration case will be presented on probabilistic risk and value analysis tools for an NDE
application for optimal service life management.
Approach:
Model-based
Material State
Estimation

Advanced
ModelsMulti-dimensional
Feature Extraction

damagecharacterization• material

Sensors(Arrays)

Payoff:• multiscale

Model-assisted
POD Assessment

properties
measurement

Improve NDE/SHM Sensitivity(Depth, Small Cracks, Sizing)

NDE/SHM
Validation

Integrated
Probabilistic Models• NDE/SHM• life prediction• risk assessment• cost-benefit analysis

Optimal Service
Life Management

Fig 1. Strategy for Computational Methods in Nondestructive Evaluation

2.

Modeling and Simulation

An NDT measurement model functions to predict the measurement response of a material under
test for an NDT technique using the appropriate physics. NDT simulation is defined as the operationof the NDT model across the measurement domain of interest, for example in the time, frequency
and/or spatial domains. A complete system model encompasses three major components: a source, asample, and a receiver. The source component of the model defines the incident field in the sample
through representation of the input signal, source hardware, electrical connection, source transducer,

100

J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in Maintenanceand the transducer interface condition with the sample. Given the incident field, the scattered field
can be calculated by the sample component model, given the material properties, sample geometry
and discontinuity (often cracks or corrosion) characteristics. Depending on the measurement
technique, significant material properties can include elastic properties, electrical conductivity,
magnetic permeability, dielectric permittivity, thermal conductivity, stress, and density. Sample
geometry including domain size (finite or infinite) guides the selection of the appropriate model.
Discontinuity characteristics include type (cracks, voids, porosity, corrosion, disbonds), geometry, andcondition (such as the interface condition between crack faces). The reception component
transforms the scattered field into measurement data through a relationship defined by the transducer
interface condition, receiver transducer, electrical connections and data acquisition hardware. The
model for each component is typically designed in order to provide the most accurate representationof a measurement technique while minimizing computational effort.
Models can produce significant benefits at several stages of the NDT technique development
process (see Figure 1). First, models can be used to aid in the interpretation of raw measurement
data. With this understanding, modeling can be beneficial in selecting the appropriate features of themeasurement for evaluation and classification. Probe design and optimization, whether it beultrasonic transducer characteristics or eddy current coil parameters, can greatly benefit fromparametric studies using accurate measurement models. For the development of automatedinspection techniques, models can augment the training data set, thus reducing sample costs. Models
can also be directly incorporated into automated signal classifiers through inverse methods. During
the validation process, models can be used to verify the robustness of the classification techniquewhile again reducing sample costs. MAPOD procedures have the potential to evaluate the reliabilityof an NDT technique at a lower cost with respect to conventional POD studies. Concerning thetransition of a new technique to a practical application, models can be quite beneficial in displaying afundamental understanding of the inspection problem to project sponsors and helpful during the
instruction of the inspectors. Lastly, NDE and structural health monitoring (SHM) reliability models
are crucial, together with system probability of failure models and inspection and maintenance costmodels, to achieve a capability to design and implement optimal service life management strategies
for structures.
3.

Case Study 1: Crack Detection in Vertical Riser Structures using UT

A significant challenge in NDE is the ability to discern signals originating from a crack and ageometric part feature when they are closely spaced or superimposed in time. An example problem
is the ultrasonic inspection of aircraft holes in vertical riser structures with limited accessibility for atransducer from an external wing surface. Figure 2 shows an example of the NDE problem.
Characteristics of the path of the ultrasonic signal and the contact condition between the fastener andhole can hinder the use of traditional amplitude dynamics for signal classification and crack detection[2]. To address this issue, models based on the boundary element method (BEM) were used todevelop a signal processing technique called the local correlation method to detect the relative shift ofsignals in time for adjacent transducer locations [3].
A simulation is shown in Figure 3 for the case of a hole with a notch with an incident shear
wave pulse. (Also, see Animation 1.) The hole contains an elastic insert representing the fastenerin fixed contact with the hole surface. First, there is primary reflection and transmission of
longitudinal and shear waves. The transmitted shear waves propagate within the elastic solid (i.e.
fastener), reflect from the boundary, and then produces a second transmission back into thesurrounding solid occurs. Signals due to the notch are observed when the transmitted shear signal
becomes incident at the notch. Both shear and longitudinal wave scattering occurs within the elastic
insert. These signals re-transmit into the elastic solid where they may be detected by transducers.
Interface waves are also generated and propagate about the cylindrical hole and are the criticalphenomena for this crack detection technique. Reflection of these interface waves by the notch isclearly observable. As the interface wave propagates back from the notch, circumferential shear
waves are generated that can be detected by the pitch transducer. Under certain conditions, it can bedifficult to separate the reradiated insert signals from the fastener with the scattered creeping wave
from a crack.

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J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in MaintenanceTo address this problem, the signal processing approach is based on the varying echo dynamics
from crack and part geometries. This approach analyzes a series of signals from a moving
transducer by accurately aligning the signals to the primary part signal using a correlation method andsubsequently measuring the shift of secondary signals of interest within multiple time windows.
This novel methodology detects the relative shift of signals in time for adjacent transducer locations
resulting from differing echo dynamics from cracks and part geometries. To generally address suchclasses of problems, amplitude dynamic measures were supplemented with both change in timemeasures and signal variation measures to generate robust signal classification methods. Thisapproach was successfully implemented to assist in the analysis of data for a very complex aerospacecomponent and the technique was validated via a probability of detection study [4].
x = -0.080"

amplitude (normalized)

x = -0.100"

near
crack

x = -0.120"
x = -0.140"

y’hole withfastenerx’

x = -0.160"
x = -0.180"
x = -0.200"
x = -0.220"

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

y

x

far
crack

7.0

transducer

time (μs)

Fig. 2. Diagram of inspection problem and associated plot of a series of experimental pulse-echo signals
from a moving transducer (far crack case presented in plot.)

τ=0

τ=1

τ=2

τ=3

τ=4

τ=5

τ=6

τ=7

τ=8

Fig. 3. Contour plots of the total displacement field generated by an incident in-plane shear pulse on a
3/16" diameter rib clip hole with a 0.070” notch and containing an aluminum insert – elastic contact
between insert and hole (smooth contact) - for nine time steps, τ = 0,1,2,3,4,5,6,7,8. [3]102J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in Maintenancehttp://www.jsm.or.jp/ejam/Vol.1.No.4/AA/Animation1.
html

Animation 1

4.

2D creeping wave with reradiated insert signals

Case Study 2: 3D Spiral Creeping Wave Discovery

Another general problem for the USAF is the inspection of fastener sites in multilayer
horizontal joints in aircraft structures. For some cases such as the one shown in Figure 4, 360 degree
coverage is necessary. To achieve 360 degree coverage without mechanically rotating the transducer
around the hole, the concept of generating and detecting “spiral” creeping waves at a fastener site wasinvestigated. Both analytical and 2D BEM models have been developed to approximate the behaviorof spiral creeping waves as they propagate around a cylindrical hole [5], but 3D models are essential
to fully study this complex ultrasonic scattering problem when fatigue cracks are present [6].
Figure 2 presents the transient finite element response of an ultrasonic wave scattering around afastener site with a radial notch (in the shadow region of the hole) in 3D. (Also, see Animation 2.)
Three select times-of-flight are displayed: (a) the main shear wave incident at the hole surface, (b)the propagating spiral creeping wave reflecting from the hole bottom edge and (c) the reflected spiral
creeping wave propagating upward from the far surface. Of particular interest, in Figure 2 (a), theincident shear wave on the hole surface not only simulates the specular reflection from the hole but as
generates a surface wave that both propagates around and leaks away from the hole. As shown here,
numerical methods such as the finite element method can accurately represent the complex scatteringand propagation of ultrasonic waves at 3D geometries. The insight from this model has provided agreater understanding of both the potential benefits and inherent limitations of the technique. Further
modeling studies are under investigation to optimize incident angle, transducer location, andtransducer focusing for subsurface crack detection applications.
z

z

x

y

layers[spiral creeping waveytransducerθ

fastener sitex

corner crack

Fig. 4.

Schematic diagram of the ultrasonic inspection of fastener sites for corner cracks in multilayer
structures using spiral creeping waves to detect cracks in the shadow region of the hole.

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J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in Maintenancebottom surface

around hole (near side)around hole (far side)transducer (on top)

(a)
notch

notch

(b)

(c)

Fig. 5. Simulated response of ultrasonic wave scattering around a hole with a notch in 3D from several
views (left column: bottom surface; center and right column; hole surface) and at select times (a) main
shear wave incident at hole, (b) spiral creeping wave reflecting from hole bottom edge and (c) spiral
creeping wave propagating upward with corner surface wave at scattering at notch. [6]http://www.jsm.or.jp/ejam/Vol.1.No.4/AA/Animation2.html

Animation 2

3D spiral creeping wave104

J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in Maintenance

5.

Case Study 3: Model-Assisted Probability of Detection (MAPOD) via Eddy Current NDE

Probability of detection (POD) studies are used to evaluate the reliability of detecting cracks
across a distribution of sizes. Recently the USAF standard for conducting POD studies was revised
to incorporate modern statistical techniques [7]-[8]. Software using the R statistical language has beendeveloped to calculate POD [9]. Due to the cost of manufacturing the number of samples required fora traditional study, empirical POD evaluation is often prohibitive. A new strategy for the design andexecution of POD studies has been proposed using a model-assisted POD (MAPOD) approach [10].
Demonstration studies have been presented for a class of aerospace structural inspection problems andconsider the use of models in the POD evaluation [11]. Eddy current measurements for varying
crack length around fastener holes in a two-layer aluminum structure were studied using bothexperimental and simulated data. General agreement was achieved between experimental andfull-model assisted (FMA) results for cracks located at both the first and second layers. However,sensitivity of the POD results was found to be dependent upon the NDE technique design andassumptions used in the model-assisted POD analysis. Parametric sensitivity studies were performed
exploring the role of crack feature measures in the image data, model design, the model fit withexperimental data and the presence of coherent noise in measurement data on the full-model assisted
evaluation. Key insight is presented for improving the quality of future MAPOD evaluation studies.
Future work will address uncertainty analysis in MAPOD evaluation, in particular using mixed(experimental and simulated) data sets, and ascertain the precise aspect ratio of the grown cracks [11].
Future work is also planned to explore applying model-assisted probabilistic reliability assessment
methods to validate structural health monitoring systems, which will be critical for justifying the valueof SHM systems for USAF fleet service life management [12].
6.

Model-based Inversion and Estimation Theoretic Metrics

Significant advances have been made by the research community on inverse problems in NDE.
However, transitions of this research to practical applications have been limited in part due to poor
representation or uncertainty of the critical parameters in the forward model and sensitivity of theinverse method performance to noise and test sample variations. First, there is a need in thedevelopment and validation of an inverse method for an NDE inspection problem to demonstratecapability using quantitative performance metrics. An overview of metrics has recently beenpresented addressing the condition of the ill-posed problem, the quality of feature extraction
algorithms, and performance of inversion algorithms. In particular, the relationship between metrics
found in estimation theory, linear algebra and statistics are presented including Fisher Information,
covariance, and Cramer-Rao-Lower-Bound (CRLB). These performance metrics can be used toquantify sensitivity, multi-collinearity, noise invariance, and the general robustness of inversion.
Optimization of system parameters using singular value decomposition was compared with the
optimal parameters selected by the inversion metrics. The connections and utility of these metrics
were illustrated through a series of basic examples of estimating material loss (thickness),
conductivity, and liftoff [13]. Another key objective for model-based inverse methods isdemonstrating its robustness to the vast array of inspection variables and specimen conditions present
for a typical NDE inspection problem. A process for validating inversion sensitivity was developed
and applied to a case study problem pit characterization to quantify the impact of potential sources forvariation on the performance of NDE procedures [14]-[15]. In particular, the impact of changes to
the NDE model, the inversion algorithm design, and experiment conditions are explored with respect
to the quality of the inversion results. The long-term goals of this work are to initiate development ofa framework for inverse method reliability assessment and demonstrate its practical value to the larger
NDE community.

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J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in Maintenance7.

Models for Probabilistic Risk Assessment and Economic Service Life Management

The aircraft fleet management problem involves unavoidable tradeoffs between aircraft
availability, reliability, and total ownership cost goals. It is often impossible to change one of thesevariables without affecting one or both of the other two. The success of maintenance approaches
currently including NDE and of those expected to complementarily use NDE and SHM in the future
depends on the ability to evaluate and establish the optimal tradeoffs between these factors. Value
analysis tools including probabilistic risk assessment, cost-benefit analysis and multicriteria
optimization can provide the framework for this evaluation. The remainder of this section briefly
describes a software approach for applying such tools for (a) evaluating the effects of human factors
on the cost and reliability effects of an NDE application, and (b) studying the effects of varying themean detectable flaw size of a damage-detection SHM system and a secondary NDE system so that an
optimal maintenance program can be achieved.
Details of the methodology and software can be found in [16] and the references therein. The
general class of problem discussed here is the inspection of fatigue cracks at fastener sites in
multilayer aircraft wing structures as found in such aircraft as the C-130 [17]. The life of thecomponent is divided into a number of service intervals separated by inspection and repair events.
Precise data on specific cases for the equivalent initial flaw size distribution, the flaw growth model,
the POD capability, and cost were difficult to obtain, and therefore values were set based upon a
combination of information acquired from maintenance personnel and values cited in the literature forrelated aircraft components. The POD model for these demonstrations consists of four parameters: a50
is the median detectable flaw size, σ controls the slope of the POD curve, FC is the false call rate, and
RMC is the rate of random missed flaws.
The first hypothetical maintenance study was performed by varying each of the four POD model
parameters between two levels: a baseline and a degraded performance level. Three service intervals
with two inspection and repair events were considered, and the same POD model was used for bothinspections. The probability of failure (POF) model included both probability of fracture andprobability of a crack growing to a critical size of 19.05 mm (0.75 in). The results from the parametricstudy are displayed as a function of total life-cycle cost and maximum probability of failure in Figure
6.
Degraded performance associated with the experience level of the NDE technician, modeled as
an increase in median detectable flaw size, resulted in a higher POF and lower total cost. A reductionin the slope of the POD curve, associated with differences in operator skill and experience, resulted invery small increases in POF and total cost. An increase of 1% in the false call rate, associated withdegraded concentration and over-sensitivity to noise, increased the total cost and had little impact on
POF. Lastly, an increase in the percentage of random missed calls by 10%, associated with a lack ofintegrity, poor focus, or a bias concerning the expected frequency of detected cracks, was found to
significantly increase the probability of failure with a slight decrease in total cost. Interesting results
were also obtained by studying the relative sensitivities of the total cost and POF with respect tovarying changes in the POD parameters. It is also important to note that the changes observed should
not be construed as absolute trends, but rather they depend on the particular inputs given to the model.
The second hypothetical study explores variations in the detectable flaw size for both an SHM
system and a secondary NDE inspection technique. Specifically, the 50% detectable flaw size for the
SHM and NDE inspection models were both varied from 0.51 mm (0.02 in) to 2.54 mm (0.10 in) as afull-factorial study. Figure 7 shows the design solution space resulting from the study in terms of
maximum probability of failure and total cost, and allows the user to select the Pareto solutions
providing the desired optimal tradeoff between the two objectives. Moreover, for this case it ispossible to select from this reduced solution set a design that minimizes cost while maintaining an
acceptable probability of failure, typically set at 10-6. Using these criteria, the optimal SHM system
50% detectable flaw size was found to be 1.52 mm (0.06 in), with the secondary NDE system 50%
detectable flaw size set to any value greater than 1.27 mm (0.05 in).
While simplified in nature, these examples show the capability of the method and software tofacilitate analysis of sensitivities and tradeoffs of the various factors involved in designing andimplementing NDE and SHM technologies as part of system life cycle management. Finally, it isimportant to recognize the need for improved data to enable successful application of these powerful106

J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in Maintenancemethods to optimal economic service life management strategies.

Fig. 6. Effects of varying each of the four POD parameters on the total cost and maximum probability of
failure, showing with vectors the main trends with respect to the baseline case.

Fig. 7. Design solution space for varying SHM and secondary NDE sensitivity in terms of maximum
probability of failure and total cost.

8.

Conclusion

Advances in computational methods for NDE are now having an impact on maintenance in manyindustries. Two case studies of crack detection problems using ultrasonic NDE and one case study
using eddy current NDE were presented. For these examples, modeling played a significant role inthe development and validation of the inspection techniques. MAPOD and model-based inversion
schemes were also discussed and these concepts will surely have a greater impact on maintenance inthe future once rigorous demonstrations are fully achieved. Finally, a probabilistic model was
introduced to assess the impact of NDE and SHM POD capability on maintenance cost and in-service
risk. This is a tool that brings everything together and can be used to manage the risk and107

J. Knopp et al./Computational Methods in Nondestructive
Evaluation: A Revolution in Maintenancemaintenance of assets, and also provide guidance in the development of NDE or health monitoring
systems.

Acknowledgement
Funding for work on computational methods in NDE has been provided by the Air Force Officeof Scientific Research and the Air Force Research Laboratory – NDE Branch.

References[1] E.A. Lindgren, J.S. Knopp, J.C. Aldrin, G.J. Steffes, and C.F. Buynak, Aging aircraft NDE:
capabilities, challenges, and opportunities, Review of Progress in Quantitative Nondestructive
Evaluation: 26B (2007), 1731-1738.
[2] J.C. Aldrin, C.V. Kropas-Hughes, J.S Knopp, J. Mandeville, D. Judd, E. Lindgren, Advanced
echo-dynamic measures for the characterization of multiple ultrasonic signals in aircraft
structures. Insight 48 (2006), 144–148.
[3] J. C. Aldrin, and J. D., Achenbach, Model and methodology for crack detection on a cylindricalhole containing an elastic insert, Review of Progress in Quantitative Nondestructive Evaluation:
21, (2002), 181-188.
[4] E. Lindgren, et al., “Probability of detection results and deployment of the inspection of thevertical leg of the C-130 center wing beam/spar cap”, Aging Aircraft Conf., Palm Springs,
California, Jan 31 – Feb. 3, 2005.
[5] J.C. Aldrin, J.R. Mandeville, D. Judd, J.R. Mandeville, and E. Lindgren, Spiral creeping waves inultrasonic angled-beam shear wave inspection of fastener holes in multilayer structures, Review
of Progress in Quantitative Nondestructive Evaluation: 25A (2006), 187-194.
[6] J.C. Aldrin, and J.S. Knopp, Modeling and Simulation for Nondestructive Testing with
Applications to Aerospace Structures, Materials Evaluation: 66 (2008), 53-59.
[7] C. Annis and J. S. Knopp, Comparing the Effectiveness of a90/95 Calculations, Review ofProgress in Quantitative Nondestructive Evaluation 26B (2007), 1767-1774.
[8] MIL-HDBK-1823A, Nondestructive Evaluation System Reliability Assessment (2009):
https://assist.daps.dla.mil/quicksearch/basic_profile.cfm?ident_number=206122.
[9] C. Annis, (2009). web site: http://www.statisticalengineering.com/.
[10] R.B. Thompson, A unified approach to the model-assisted determination of probability ofdetection, Materials Evaluation: 66 (2008), 667-673.
[11] J.C. Aldrin, J.S. Knopp, E. Lindgren, H.A. Sabbagh, E.H. Sabbagh, and R.K. Murphy,
Model-assisted evaluation of the reliability of an eddy current nondestructive evaluation
technique, 25th Annual Review of Progress in Applied Computational Electromagnetics (2009),
598-605.
[12] J.C. Aldrin, E.A. Medina, E.A. Lindgren, C.F. Buynak, G. Steffes, M. Derriso, Model-assisted
probabilistic reliability assessment for structural health monitoring systems, Review of Progress
in QNDE: 29, (submitted for publication, 2010).
[13] J.S. Knopp, J.C. Aldrin, H.A. Sabbagh, and K.V. Jata., Estimation theory metrics inelectromagnetic NDE, Electromagnetic Nondestructive Evaluation Workshop Proceedings, 12,(2009), 321-328.
[14] H.A. Sabbagh, R.K. Murphy, E.H. Sabbagh, J.C. Aldrin, Application of model-based inversion to
eddy-current NDE of heat-exchanger tubing, Materials Evaluation: 66 (2008) 764-774.
[15] J.C. Aldrin, H.A. Sabbagh, R.K. Murphy, E.H. Sabbagh, and J.S. Knopp, Sensitivity analysis of
inverse methods in eddy current pit characterization, Review of Progress in Quantitative
Nondestructive Evaluation: 29, (submitted for publication, 2010).
[16] E.A. Medina, J.C. Aldrin, Value assessment approaches for structural life management through
SHM, in: Encyclopedia of Structural Health Monitoring, C. Boller, F-K Chang, and Y. Fujino(Editors), John Wiley & Sons, 2009[17] E. Lindgren et al, Validation and deployment of automated ultrasonic inspections for the C-130
center wing, ASIP Conference, Savannah, GA, USA, 2–4 December 2004.

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