optimize inspection timing, reducing
unnecessary interventions while improv-
ing asset longevity. They are extensively
applied in aircraft fleet maintenance,
offshore wind turbine monitoring, and
nuclear plant condition tracking, sup-
porting data-driven decision-making for
critical infrastructure. For instance, the
benefits of UA in CBM are highlighted by
Bott et al. [102], where Bayesian frame-
works and cloud-ready pipelines are
applied for remaining useful life (RUL)
prediction in bearings and ball screws,
improving accuracy while quantifying
predictive uncertainty. Yardimci and
Cavus [103] introduced the Rashomon
perspective to address model multiplicity
in survival analysis, revealing how cen-
soring levels impact uncertainty in RUL
predictions. By embedding UA&UQ into
CBM, industries achieve smarter, cost-ef-
fective, and data-driven maintenance,
improving long-term structural integrity
and operational efficiency.
ROBOTICS AND AUTONOMOUS NDE
INSPECTION SYSTEMS
Robotics and autonomous systems are
transforming NDE by integrating UQ
into advanced perception and planning
algorithms, enabling them to navigate
complex and uncertain environments.
UAV-based structural health monitor-
ing is increasingly used in large-scale
inspections, where drones equipped
with thermographic, ultrasonic, and lidar
sensors provide real-time discontinuity
probability distributions [104]. Pairet et
al. [105] demonstrated how probabilistic
safety and online mapping allow auton-
omous underwater vehicles to perform
inspections in unpredictable conditions.
Innovations like the EELS robot illus-
trate how autonomous systems adapt to
unknown terrains, such as icy moons, by
quantifying risks and planning motions
under uncertainty [106]. Additionally, a
semantic-aware framework is introduced
for inspection in unknown environ-
ments, emphasizing active uncertainty
reduction. These advancements demon-
strate how robotics and autonomous
systems, empowered by UA, are revolu-
tionizing NDE inspections.
Outlook: Digital Twins,
AI-Enhanced UA&UQ, and
Automation
The next phase of UA&UQ in NDE will
be defined by advanced AI modeling,
digital twin integration, and fully auton-
omous robotic inspection systems.
These advancements will enhance real-
time discontinuity detection, predictive
maintenance, and adaptive inspection
planning—improving safety, efficiency,
and cost-effectiveness across industries
such as aviation, nuclear energy, and
offshore drilling.
DIGITAL TWIN–BASED PREDICTIVE
MAINTENANCE AND SELF-ADAPTIVE
INSPECTION
Digital twins will integrate multi-source
sensor data with AI-driven probabilistic
models, providing real-time updates on
structural health and optimizing inspec-
tion schedules based on failure risk
predictions. These self-adaptive mainte-
nance systems will reduce unnecessary
inspections, extend asset lifespan, and
improve failure risk forecasting [107].
Industries such as aerospace, energy,
and offshore operations will benefit
from dynamic, risk-informed inspection
strategies, minimizing downtime while
ensuring greater structural reliability.
AI-ENABLED EDGE COMPUTING FOR
INSTANTANEOUS UNCERTAINTY
ESTIMATION IN AUTONOMOUS NDE
AI-enabled edge computing, combined
with uncertainty-aware models, is revolu-
tionizing autonomous NDE by enabling
real-time discontinuity detection, risk
assessment, and adaptive inspection
without dependence on cloud infra-
structure [108]. Through local processing,
these systems minimize latency, reduce
bandwidth demands, and enable imme-
diate decision-making—essential for
predictive maintenance in safety-critical
environments. Self-learning AI and
quantum-enhanced sensors further
optimize inspections in complex, noisy,
or remote settings such as aerospace
composites, buried pipelines, and harsh
industrial facilities. IoT-connected smart
sensors enhance system adaptability by
forming probabilistic networks that adjust
inspection parameters based on real-time
risk modeling. Together, these edge-AI
and IoT innovations deliver scalable, resil-
ient, and uncertainty-aware NDE systems,
improving operational efficiency, safety,
and lifecycle reliability [109].
FULLY AUTONOMOUS INSPECTION
WITH SELF-OPTIMIZING UA&UQ
MODELS
The next generation of autonomous
NDE systems will feature self-optimizing
UA&UQ models, allowing robots to
perform real-time discontinuity assess-
ments with minimal human inter-
vention [110]. Bayesian-driven sensor
networks will enable proactive inspec-
tion scheduling, improving discontinu-
ity detection accuracy while reducing
maintenance costs. These self-learning,
real-time adaptive inspection workflows
will minimize unexpected failures and
enhance operational efficiency, setting
new standards for automated NDE and
structural health monitoring.
Conclusions
Uncertainty analysis and quantification
(UA&UQ) are essential for enhancing the
reliability and decision-making of NDE
applications across aerospace, nuclear
energy, transportation, and infrastruc-
ture sectors. This tutorial reviewed key
UA&UQ methodologies, addressing
factors such as measurement noise,
material variability, environmental
influences, and model uncertainties.
By examining probabilistic, statisti-
cal, simulation-based, and AI-driven
approaches, UQ contributes to improved
discontinuity detection, greater con-
fidence in inspection outcomes, and
more effective predictive maintenance
planning.
Advances in sensor technology
enable real-time uncertainty assess-
ment and failure probability estimation,
paving the way for adaptive inspections
and proactive maintenance. NDE 4.0,
with real-time sensor networks, digital
twins, and AI automation, is revolu-
tionizing discontinuity detection, while
UQ in advanced manufacturing miti-
gates process-induced uncertainties to
enhance discontinuity classification,
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 35

structural reliability, and process
control.
Nonetheless, challenges remain
in standardizing UA&UQ methods,
improving AI model interpretability,
and integrating hybrid physics and AI
uncertainty models. Future research
should focus on scalable real-time UQ,
uncertainty-aware autonomous NDE,
and digital twin–driven predictive main-
tenance. These innovations will set new
benchmarks for automation, reliabil-
ity, and safety, ultimately enabling fully
automated, uncertainty-aware inspec-
tions for cost-effective and risk-informed
decision-making.
AUTHORS
Zi Li: Assistant Professor, Department of Physics
and Engineering, Alma College, Alma, MI
Department of Electrical and Computer Engi-
neering, Michigan State University, MI liz@
alma.edu lizi4@msu.edu
Yiming Deng: Professor, Nondestructive Evalu-
ation Laboratory, Department of Electrical and
Computer Engineering, Michigan State Univer-
sity, East Lansing, MI dengyimi@egr.msu.edu
Materials Evaluation 83 (8): 24–39
https://doi.org/10.32548/2025.me-04541
©2025 American Society for Nondestructive Testing
REFERENCES
1. Taheri, H., and A. S. Beni. First online
6 January 2025. “Artificial Intelligence, Machine
Learning, and Smart Technologies for Nonde-
structive Evaluation.” In Handbook of Nonde-
structive Evaluation 4.0, pp. 1–29. Meyendorf,
N., N. Ida, R. Singh, and J. Vrana (eds.). Springer
Cham. https://doi.org/10.1007/978-3-030-48200-
8_70-1.
2. Meyendorf, N., N. Ida, R. Singh, and J.
Vrana (eds.). 2021. Handbook of Nondestructive
Evaluation 4.0. Springer Cham. https://doi.
org/10.1007/978-3-030-73206-6.
3. Jaber, A., S. S. Karganroudi, M. S. Meiabadi,
A. Aminzadeh, H. Ibrahim, M. Adda, and
H. Taheri. 2022. “On Smart Geometric
Non-Destructive Evaluation: Inspection
Methods, Overview, and Challenges.” Materials
(Basel) 15 (20): 7187. https://doi.org/10.3390/
ma15207187.
4. Fong, J. T., N. A. Heckert, J. J. Filliben, and S.
R. Doctor. 2018. “Three Approaches to Quan-
tification of NDE Uncertainty and a Detailed
Exposition of the Expert Panel Approach Using
the Sheffield Elicitation Framework.” in Volume
1A: Codes and Standards: V01AT01A007. ASME
2018 Pressure Vessels and Piping Conference,
Prague, Czech Republic, 15–20 July 2018. https://
doi.org/10.1115/PVP2018-84771.
5. Potukuchi, S., V. Chinthapenta, and G. Raju.
2023. “A review of NDE techniques for hydro-
gels.” Nondestructive Testing and Evaluation 38
(1): 1–33. https://doi.org/10.1080/10589759
.2022.2144304.
6. Bøving, K. G. 1989. NDE handbook:
non-destructive examination methods for
condition monitoring. London, Boston:
Butterworths.
7. Vejdannik, M., A. Sadr, V. H. C. de Albu-
querque, and J. M. R. S. Tavares. First online
28 June 2018. “Signal Processing for NDE.” In
Handbook of Advanced Non-Destructive Evalua-
tion, pp. 1–19. Ida, N., and N. Meyendorf (eds.).
Springer Cham. https://doi.org/10.1007/978-3-
319-30050-4_53-1.
8. Bertovic, M. 2015. “Human factors in
non-destructive testing (NDT): risks and chal-
lenges of mechanised NDT.” Doctoral thesis.
Technische Universität Berlin. https://doi
.org/10.14279/depositonce-4685.
9. Dann, M. R., and L. Huyse. 2018. “The
effect of inspection sizing uncertainty on the
maximum corrosion growth in pipelines.” Struc-
tural Safety 70: 71–81. https://doi.org/10.1016/j.
strusafe.2017.10.005.
10. Aldrin, J., D. Motes, M. Hughes, D. Forsyth,
E. Sabbagh, H. A. Sabbagh, R. K. Murphy, G.
Nuxoll, C. Knott, and E. A. Lindgren. 2025.
“Uncertainty Evaluation of Crack Sizing Capa-
bility Incorporating Model-Based Inversion
Applied to Bolt-Hole Eddy Current Inspections.”
Materials Evaluation 83 (8): 42–56.
11. Knott, C., C. S. Kabban, and J. Aldrin.
2025. “Multivariate Probability of Detection
Modeling Including Categorical Variables and
Higher-Order Response Models.” Materials Eval-
uation 83 (8): 57–72.
12. Tomizawa, T., and N. Yusa. 2025. “Proba-
bilistic Sizing of a Fatigue Crack on Type 304
Austenitic Stainless Steel from Eddy Current
Signals.” Materials Evaluation 83 (8): 73–80.
13. Chiachío, M., M. Megía, J. Chiachío, J.
Fernandez, and M. L. Jalón. 2022. “Structural
digital twin framework: Formulation and tech-
nology integration.” Automation in Construc-
tion 140: 104333. https://doi.org/10.1016/j.
autcon.2022.104333.
14. Li, Z. 2023. Uncertainty Quantification
Framework with Interdependent Dynamics of
Data, Modeling, and Learning in Nondestructive
Evaluation. Doctoral thesis. Michigan State
University. https://doi.org/10.25335/34mn-bn95.
15. Ceberio, J., J.-C. Cortés, F. Fernández de
Vega, O. Garnica, J. I. Hidalgo, J. M. Velasco, and
R.-J. Villanueva. 2022. “Approaching epistemic
and aleatoric uncertainty with evolutionary opti-
mization: examples and challenges.” Proceedings
of the 2022 Genetic and Evolutionary Computa-
tion Conference Companion: 1909–1915. https://
doi.org/10.1145/3520304.3533978.
16. Depeweg, S., J. M. Hernández-Lobato, F.
Doshi-Velez, and S. Udluft. 2018. “Decomposi-
tion of Uncertainty in Bayesian Deep Learning
for Efficient and Risk-sensitive Learning.” arXiv.
https://doi.org/10.48550/arXiv.1710.07283.
17. Charpentier, B., R. Senanayake, M. Kochen-
derfer, and S. Günnemann. 2022. “Disentan-
gling Epistemic and Aleatoric Uncertainty in
Reinforcement Learning.” arXiv. https://doi.
org/10.48550/arXiv.2206.01558.
18. Zschocke, S., W. Graf, and M. Kaliske. 2023.
“Incorporating uncertainty in stress-strain data
acquisition: Extended model-free data-driven
identification.” Proceedings in Applied Math-
ematics and Mechanics 23 (2): e202300008.
https://doi.org/10.1002/pamm.202300008.
19. Li, A., A. D. Parsekian, D. Grana, and B. J.
Carr. May 2025. “Quantification of measurement
uncertainty in electrical resistivity tomography
data and its effect on the inverted resistivity
model.” Geophysics 90 (3): WA275–91. https://
doi.org/10.1190/geo2024-0466.1.
20. Abebe, M., Y. Cho, S. C. Han, and B. Koo.
2024. “Mitigating Measurement Inaccuracies
in Digital Twins of Construction Machinery
through Multi-Objective Optimization.” Sensors
(Basel) 24 (11): 3347. https://doi.org/10.3390/
s24113347.
21. Herrera, P., C. Goyne, and R. Rockwell. 2024.
“Propagation of uncertainty in experimental
dynamic coefficients of fluid film journal
bearings.” Journal of Tribology 146 (7): 074501.
https://doi.org/10.1115/1.4065002.
22. Momeni, H., and A. Ebrahimkhanlou. 2022.
“High-dimensional data analytics in struc-
tural health monitoring and non-destructive
evaluation: A review paper.” Smart Materials
and Structures 31 (4): 043001. https://doi.
org/10.1088/1361-665X/ac50f4.
23. Jasiūnienė, E., B. Yilmaz, D. Smagulova,
G. A. Bhat, V. Cicėnas, E. Žukauskas, and L.
Mažeika. 2022. “Non-Destructive Evaluation of
the Quality of Adhesive Joints Using Ultrasound,
X-ray, and Feature-Based Data Fusion.” Applied
Sciences (Basel, Switzerland) 12 (24): 12930.
https://doi.org/10.3390/app122412930.
24. Li, Z., and Y. Deng. 2024. “Quantifying
predictive uncertainty in damage classifi-
cation for nondestructive evaluation using
Bayesian approximation and deep learning.”
Inverse Problems 40 (4): 045031. https://doi.
org/10.1088/1361-6420/ad2f63.
25. Huang, P., Z. Bao, R. Huang, J. Jia, K. Liu,
X. Yu, W. Yin, and Y. Xie. 2023. “Decoupling
Permeability, Conductivity, Thickness, Lift-Off
for Eddy Current Testing Using Machine
Learning.” IEEE Transactions on Instrumenta-
tion and Measurement 72: 1–10. https://doi.
org/10.1109/TIM.2023.3293565.
26. Wang, J., E. Li, J. Wu, and X. Xu. 2021.
“Linearization of the lift-off effect for magnetic
flux leakage based on Fourier transform.”
Measurement Science &Technology 32 (6):
065012. https://doi.org/10.1088/1361-6501/
abe89e.
27. Qian, Y., H. Wan, B. Yang, J.-C. Golaz, B.
Harrop, Z. Hou, V. E. Larson, L. R. Leung, G. Lin,
W. Lin, P.-L. Ma, H.-Y. Ma, P. Rasch, B. Singh, H.
Wang, S. Xie, and K. Zhang. 2018. “Parametric
Sensitivity and Uncertainty Quantification
in the Version 1 of E3SM Atmosphere Model
Based on Short Perturbed Parameter Ensemble
Simulations.” Journal of Geophysical Research:
Atmospheres 123 (23): 13046–13073. https://doi.
org/10.1029/2018JD028927.
NDT TUTORIAL
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UA&UQ
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