60. Alvarenga, A. V., C. E. R. Silva, and R. P. B.
Costa-Félix. 2016. “Monte Carlo uncertainty
assessment of ultrasonic beam parameters from
immersion transducers used to non-destructive
testing.” Ultrasonics 69: 144–51. https://doi.
org/10.1016/j.ultras.2016.04.009.
61. Kashif, M., M. Aslam, A. H. Al-Marshadi,
C.-H. Jun, and M. I. Khan. 2017. “Evaluation
of Modified Non-Normal Process Capability
Index and Its Bootstrap Confidence Inter-
vals.” IEEE Access: Practical Innovations, Open
Solutions 5:12135–42. https://doi.org/10.1109/
ACCESS.2017.2713884.
62. Rao, G. S., M. Albassam, and M. Aslam. 2019.
“Evaluation of Bootstrap Confidence Intervals
Using a New Non-Normal Process Capability
Index.” Symmetry 11 (4): 484. https://doi.
org/10.3390/sym11040484.
63. Nockemann, C., H. Heidt, and N.
Thomsen. 1991. “Reliability in NDT: ROC
study of radiographic weld inspections.” NDT
&E International 24 (5): 235–45. https://doi.
org/10.1016/0963-8695(91)90372-A.
64. Kybic, J. 2010. “Bootstrap Resampling for
Image Registration Uncertainty Estimation
Without Ground Truth.” IEEE Transactions on
Image Processing: A Publication of the IEEE
Signal Processing Society 19 (1): 64–73. https://
doi.org/10.1109/TIP.2009.2030955.
65. Gouvea, L. F., A. Ara, R. L. Gigante, R. A.
Spatti, and F. Louzada. 2020. “Bootstrap resa-
mpling as a tool for calculating uncertainty
measurement.” Brazilian Applied Science Review
4 (3): 901–12. https://doi.org/10.34115/basrv4n3-
013.
66. Białek, A., V. Vellucci, B. Gentil, D. Antoine,
J. Gorroño, N. Fox, and C. Underwood. 2020.
“Monte Carlo–Based Quantification of Uncer-
tainties in Determining Ocean Remote Sensing
Reflectance from Underwater Fixed-Depth Radi-
ometry Measurements.” Journal of Atmospheric
and Oceanic Technology 37 (2): 177–96. https://
doi.org/10.1175/JTECH-D-19-0049.1.
67. Wu, L., W. Ji, and S. M. AbouRizk. 2020.
“Bayesian Inference with Markov Chain Monte
Carlo–Based Numerical Approach for Input
Model Updating.” Journal of Computing in
Civil Engineering 34 (1): 04019043. https://doi.
org/10.1061/(ASCE)CP.1943-5487.0000862.
68. Cherry, M. R., J. S. Knopp, and M. P.
Blodgett. 2012. “Probabilistic collocation method
for NDE problems with uncertain parameters
with arbitrary distributions.” AIP Conference
Proceedings 1430: 1741–1748. https://doi.
org/10.1063/1.4716422.
69. Dobmann, G., A. Boulavinov, M. Kröning,
and J. H. Kurz. 2007. “New technologies for
detection, classification and sizing of defects
in combination with probabilistic FAD
approaches.” Presented at SMiRT Transactions,
19 Aug 2007, Toronto, ON, Canada. https://
publica.fraunhofer.de/entities/publication/
c41cfaf6-48b5-4fa9-a09b-a87a2eb8c38e.
70. Vereecken, E., W. Botte, G. Lombaert, and R.
Caspeele. 2022. “A Bayesian inference approach
for the updating of spatially distributed corro-
sion model parameters based on heterogeneous
measurement data.” Structure and Infrastructure
Engineering 18 (1): 30–46. https://doi.org/10.1080
/15732479.2020.1833046.
71. Nabiyan, M.-S., M. Sharifi, H. Ebrahimian,
and B. Moaveni. April 2023. “A variational
Bayesian inference technique for model
updating of structural systems with unknown
noise statistics.” Frontiers in Built Environ-
ment 9:1143597. https://doi.org/10.3389/
fbuil.2023.1143597.
72. Chen, M., X. Zhang, K. Shen, and G. Pan.
2022. “Sparse Polynomial Chaos Expansion
for Uncertainty Quantification of Composite
Cylindrical Shell with Geometrical and Material
Uncertainty.” Journal of Marine Science and
Engineering 10 (5): 670. https://doi.org/10.3390/
jmse10050670.
73. Zou, M., L. Z. Fragonara, S. Qiu, and W.
Guo. 2023. “Uncertainty quantification of multi-
scale resilience in networked systems with
nonlinear dynamics using arbitrary polynomial
chaos.” Scientific Reports 13 (1): 488. https://doi.
org/10.1038/s41598-022-27025-w.
74. Papadopoulos, A. D., Y. Ma, Q. Luo, and G.
C. Alexandropoulos. 2024. “Adaptive Polynomial
Chaos Expansion for Uncertainty Quantification
and Optimization of Horn Antennas at SubTHz
Frequencies.” arXiv. https://doi.org/10.48550/
ARXIV.2404.04542.
75. Daxberger, E., A. Kristiadi, A. Immer, R.
Eschenhagen, M. Bauer, and P. Hennig. 2022.
“Laplace Redux – Effortless Bayesian Deep
Learning.” arXiv. https://doi.org/10.48550/
arXiv.2106.14806.
76. Galapon Jr., A. V., A. Thummerer, J. A.
Langendijk, D. Wagenaar, and S. Both. 2024.
“Feasibility of Monte Carlo dropout-based
uncertainty maps to evaluate deep learning‐
based synthetic CTs for adaptive proton
therapy.” Medical Physics 51 (4): 2499–509.
https://doi.org/10.1002/mp.16838.
77. Sahay, R., G. C. Birch, J. J. Stubbs, and C.
G. Brinton. 2022. “Uncertainty Quantifica-
tion-Based Unmanned Aircraft System Detection
using Deep Ensembles.” 2022 IEEE 95th Vehic-
ular Technology Conference: (VTC2022-Spring),
Helsinki, Finland: 1–5. https://doi.org/10.1109/
VTC2022-Spring54318.2022.9860853.
78. Li, L., J. Chang, A. Vakanski, Y. Wang, T. Yao,
and M. Xian. 2024. “Uncertainty quantification
in multivariable regression for material property
prediction with Bayesian neural networks.”
Scientific Reports 14 (1): 10543. https://doi.
org/10.1038/s41598-024-61189-x.
79. Jiang, G., J. Yang, T. Cheng, and H. Sun.
2023. “Remaining useful life prediction of rolling
bearings based on Bayesian neural network and
uncertainty quantification.” Quality and Reli-
ability Engineering International 39 (5): 1756–74.
https://doi.org/10.1002/qre.3308.
80. Mosser, L., and E. Zabihi Naeini. 2022. “A
comprehensive study of calibration and uncer-
tainty quantification for Bayesian convolutional
neural networks – An application to seismic
data.” Geophysics 87 (4): IM157–76. https://doi.
org/10.1190/geo2021-0318.1.
81. Choubineh, A., J. Chen, F. Coenen, and
F. Ma. 2023. “Applying Monte Carlo Dropout
to Quantify the Uncertainty of Skip Connec-
tion-Based Convolutional Neural Networks
Optimized by Big Data.” Electronics (Basel)
12 (6): 1453. https://doi.org/10.3390/
electronics12061453.
82. Klanecek, Z., T. Wagner, Y.-K. Wang, L.
Cockmartin, N. Marshall, B. Schott, A. Deatsch,
A. Studen, K. Hertl, K. Jarm, M. Krajc, M.
Vrhovec, H. Bosmans, and R. Jeraj. 2023.
“Uncertainty estimation for deep learning-based
pectoral muscle segmentation via Monte Carlo
dropout.” Physics in Medicine and Biology 68
(11): 115007. https://doi.org/10.1088/1361-6560/
acd221.
83. Pyle, R. J., R. R. Hughes, A. A. S. Ali, and P.
D. Wilcox. 2022. “Uncertainty Quantification for
Deep Learning in Ultrasonic Crack Characteri-
zation.” IEEE Transactions on Ultrasonics, Ferro-
electrics, and Frequency Control 69 (7): 2339–51.
https://doi.org/10.1109/TUFFC.2022.3176926.
84. Chen, G., and Y. Liu. 2024. “Combining
unsupervised deep learning and Monte Carlo
dropout for seismic data reconstruction and
its uncertainty quantification.” Geophysics 89
(1): WA53–65. https://doi.org/10.1190/geo2022-
0632.1.
85. Yonekura, K., Aoki, R., &Suzuki, K. 2025.
“Quantification and reduction of uncertainty in
aerodynamic performance of GAN-generated
airfoil shapes using MC dropouts.” Theoretical
and Applied Mechanics Letters 15 (4): 100504.
https://doi.org/10.1016/j.taml.2024.100504.
86. Pyle, R. J., R. L. T. Bevan, R. R. Hughes,
R. K. Rachev, A. A. S. Ali, and P. D. Wilcox.
2021. “Deep Learning for Ultrasonic Crack
Characterization in NDE.” IEEE Transactions
on Ultrasonics, Ferroelectrics, and Frequency
Control 68 (5): 1854–65. https://doi.org/10.1109/
TUFFC.2020.3045847.
87. De Paola, A., S. Gaglio, G. Lo Re, and M.
Ortolani. 2011. “Multi-sensor Fusion through
Adaptive Bayesian Networks.” In AI*IA 2011:
Artificial Intelligence Around Man and Beyond,
Lecture Notes in Computer Science series, Vol.
6934: 360–371. Pirrone, R., and F. Sorbello
(eds.). Springer Berlin Heidelberg. https://doi.
org/10.1007/978-3-642-23954-0_33.
88. Spaeth, P. W., J. N. Zalameda, J. Bisgard, T. B.
Hudson, R. I. Ledesma, and R. A. Huertas. 2023.
“Composite bond line measurements based on
a Bayesian analysis of flash thermography data.”
In Thermosense: Thermal Infrared Applications
XLV, Vol. 12536. Avdelidis, N. P. (ed.). Orlando,
FL: SPIE. https://doi.org/10.1117/12.2662824.
NDT TUTORIAL
|
UA&UQ
38
M AT E R I A L S E V A L U AT I O N • A U G U S T 2 0 2 5

89. Wang, H., Y. Hou, Y. He, C. Wen, B.
Giron-Palomares, Y. Duan, B. Gao, V. P. Vavilov,
and Y. Wang. 2024. “A Physical-Constrained
Decomposition Method of Infrared Thermog-
raphy: Pseudo Restored Heat Flux Approach
Based on Ensemble Bayesian Variance Tensor
Fraction.” IEEE Transactions on Industrial Infor-
matics 20 (3): 3413–24. https://doi.org/10.1109/
TII.2023.3293863.
90. Zaini, M. A. H. P., M. M. Saari, N. A. Nadzri,
Z. Aziz, N. H. Ramlan, and K. Tsukada. 2021.
“Extraction of Flux Leakage and Eddy Current
Signals Induced by Submillimeter Backside Slits
on Carbon Steel Plate Using a Low-Field AMR
Differential Magnetic Probe.” IEEE Access: Prac-
tical Innovations, Open Solutions 9: 146755–70.
https://doi.org/10.1109/ACCESS.2021.3123421.
91. Khan, T., and P. Ramuhalli. 2008. “A
Recursive Bayesian Estimation Method for
Solving Electromagnetic Nondestructive Eval-
uation Inverse Problems.” IEEE Transactions
on Magnetics 44 (7): 1845–55. https://doi.
org/10.1109/TMAG.2008.921842.
92. Piao, G., J. Guo, T. Hu, and H. Leung. 2020.
“The Effect of Motion-Induced Eddy Current
on High-Speed Magnetic Flux Leakage (MFL)
Inspection for Thick-Wall Steel Pipe.” Research
in Nondestructive Evaluation 31 (1): 48–67.
https://doi.org/10.1080/09349847.2019.1595987.
93. Dai, W., X. Li, and K.-T. Cheng, 2023.
“Semi-Supervised Deep Regression with
Uncertainty Consistency and Variational Model
Ensembling via Bayesian Neural Networks.”
arXiv. https://doi.org/10.48550/arXiv.2302.07579.
94. Wan, Q., and X. Fu. 2020. “Fast-BCNN:
Massive Neuron Skipping in Bayesian Convo-
lutional Neural Networks.” In 2020 53rd
Annual IEEE/ACM International Symposium
on Microarchitecture (MICRO): 229–240.
Athens, Greece: IEEE. https://doi.org/10.1109/
MICRO50266.2020.00030.
95. Ahmed, S. T., K. Danouchi, M. Hefenbrock,
G. Prenat, L. Anghel, and M. B. Tahoori. 2024.
“Spatial-SpinDrop: Spatial Dropout-Based
Binary Bayesian Neural Network with Spin-
tronics Implementation.” IEEE Transactions
on Nanotechnology 23: 636–43. https://doi.
org/10.1109/TNANO.2024.3445455.
96. Xue, H., M. Zhang, P. Yu, H. Zhang, G.
Wu, Y. Li, and X. Zheng. 2021. “A Novel Multi-
Sensor Fusion Algorithm Based on Uncertainty
Analysis.” Sensors (Basel) 21 (8): 2713. https://
doi.org/10.3390/s21082713.
97. Ernst, D., S. Vogel, H. Alkhatib, and I.
Neumann. 2024. “Monte Carlo variance prop-
agation for the uncertainty modeling of a
kinematic LiDAR-based multi-sensor system.”
Journal of Applied Geodesy 18 (2): 237–52.
https://doi.org/10.1515/jag-2022-0033.
98. W. Chen, T. Huang, and A. Maalla,
“Research on Adaptive Monte Carlo Location
Method Based on Fusion Posture Estimation,” in
2019 IEEE 3rd Advanced Information Manage-
ment, Communicates, Electronic and Automa-
tion Control Conference (IMCEC), Chongqing,
China: IEEE, Oct. 2019, pp. 1209–1213. https://
doi.org/10.1109/IMCEC46724.2019.8983808.
99. Thin, A., N. Kotelevskii, A. Doucet, A.
Durmus, E. Moulines, and M. Panov. 2021.
“Monte Carlo Variational Auto-Encoders.” arXiv.
https://doi.org/10.48550/ARXIV.2106.15921.
100. Şahin, T., D. Wolff, M. Von Danwitz, and
A. Popp. 2024. “Towards a Hybrid Digital Twin:
Fusing Sensor Information and Physics in Surro-
gate Modeling of a Reinforced Concrete Beam.”
In 2024 Sensor Data Fusion: Trends, Solutions,
Applications (SDF): 1–8. Bonn, Germany: IEEE.
https://doi.org/10.1109/SDF63218.2024.10773885.
101. Land, W. H., and J. D. Schaffer. 2020.
“Bayesian Probabilistic Neural Network
(BPNN).” In The Art and Science of Machine
Intelligence: 187–210. Springer Cham. https://doi.
org/10.1007/978-3-030-18496-4_7.
102. Bott, A., B. Liu, A. Puchta, and J. Fleischer.
2024. “Machine Learning-Driven RUL Prediction
and Uncertainty Quantification for Ball Screw
Drives in a Cloud-Ready Maintenance Frame-
work.” Journal of Machine Engineering 24 (3):
17–31. https://doi.org/10.36897/jme/192681.
103. Yardimci, Y., and M. Cavus. 2025.
“Rashomon perspective for measuring uncer-
tainty in the survival predictive maintenance
models.” arXiv. https://doi.org/10.48550./
arXiv.2502.15772.
104. Akbar, M. A., U. Qidwai, and M. R. Jahan-
shahi. 2019. “An evaluation of image-based
structural health monitoring using integrated
unmanned aerial vehicle platform.” Structural
Control and Health Monitoring 26 (1): e2276.
https://doi.org/10.1002/stc.2276.
105. Pairet, E., J. D. Hernandez, M. Lahijanian,
and M. Carreras. 2018. “Uncertainty-based
Online Mapping and Motion Planning for
Marine Robotics Guidance.” In 2018 IEEE/RSJ
International Conference on Intelligent Robots
and Systems (IROS): 2367–2374. Madrid: IEEE.
https://doi.org/10.1109/IROS.2018.8593394.
106. Ginting, M. F., D. D. Fan, S.-K. Kim, M. J.
Kochenderfer, and A.-A. Agha-Mohammadi.
2024. “Semantic Belief Behavior Graph: Enabling
Autonomous Robot Inspection in Unknown
Environments.” In 2024 IEEE/RSJ Interna-
tional Conference on Intelligent Robots and
Systems (IROS): 7604–7610. Abu Dhabi, United
Arab Emirates: IEEE. https://doi.org/10.1109/
IROS58592.2024.10802336.
107. Gupta, R., B. Tian, Y. Wang, and K.
Nahrstedt. 2024. “TWIN-ADAPT: Continuous
Learning for Digital Twin-Enabled Online
Anomaly Classification in IoT-Driven Smart
Labs.” Future Internet 16 (7): 239. https://doi.
org/10.3390/fi16070239.
108. Pérez, E., C. E. Ardic, O. Çakıroğlu, K.
Jacob, S. Kodera, L. Pompa, M. Rachid, H.
Wang, Y. Zhou, C. Zimmer, F. Römer, and A.
Osman. 2024. “Integrating AI in NDE: Tech-
niques, Trends, and Further Directions.” arXiv.
https://doi.org/10.48550/arXiv.2404.03449.
109. Jamil, M. N., O. Schelén, A. Afif Monrat,
and K. Andersson. 2024. “Enabling Industrial
Internet of Things by Leveraging Distributed
Edge-to-Cloud Computing: Challenges and
Opportunities.” IEEE Access: Practical Innova-
tions, Open Solutions 12: 127294–308. https://
doi.org/10.1109/ACCESS.2024.3454812.
110. Aghaei, M., M. Kolahi, A. Nedaei, N. S.
Venkatesh, S. M. Esmailifar, A. M. Moradi
Sizkouhi, A. Aghamohammadi, A. K. V. Oliveira,
A. Eskandari, P. Parvin, J. Milimonfared, V.
Sugumaran, and R. Rüther. 2025. “Autonomous
Intelligent Monitoring of Photovoltaic Systems:
An In‐Depth Multidisciplinary Review.” Progress
in Photovoltaics: Research and Applications 33
(3): 381–409. https://doi.org/10.1002/pip.3859.
111. Knopp, J. S., J. C. Aldrin, and M. P. Blodgett.
2011. “Efficient Propagation of Uncertainty in
Simulations Via the Probabilistic Collocation
Method.” Electromagnetic Nondestructive Eval-
uation: 141–148. Szczecin, Poland: XIV. https://
doi.org/10.3233/978-1-60750-750-5-141.
112. Knopp, J. S., R. Grandhi, J. C. Aldrin, and I.
Park. 2013. “Statistical Analysis of Eddy Current
Data from Fastener Site Inspections.” Journal of
Nondestructive Evaluation 32 (1): 44–50. https://
doi.org/10.1007/s10921-012-0157-5.
113. Knopp, J. S. 2014. “Modern statistical
methods and uncertainty quantification for
evaluating reliability of nondestructive evalua-
tion systems.” Dissertation. Wright State Univer-
sity. https://corescholar.libraries.wright.edu/
etd_all/1178/.
114. Cheng, Y., Y. Deng, J. Cao, X. Xiong,
L. Bai, and Z. Li. 2013. “Multi-Wave and Hybrid
Imaging Techniques: A New Direction for
Nondestructive Testing and Structural Health
Monitoring.” Sensors, 13 (12): 16146–16190.
https://doi.org/10.3390/s131216146.
A U G U S T 2 0 2 5 • M AT E R I A L S E V A L U AT I O N 39