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UNCERTAINTY ANALYSIS AND
QUANTIFICATION FOR NONDESTRUCTIVE
EVALUATION
BY ZI LI AND YIMING DENG
Uncertainty analysis and quantification (UA&UQ) are redefining NDE—
enhancing reliability, enabling predictive maintenance, and advancing
automation through AI, digital twins, and real-time data for smarter,
safer, and more informed inspections.
Introduction
Nondestructive evaluation (NDE) is
widely used in aerospace, nuclear
energy, transportation, and civil infra-
structure, and is essential for structural
health monitoring, quality assurance,
and predictive maintenance [1, 2], while
ensuring and improving the safety, reli-
ability, and cost efficiency of complex
systems, materials, and infrastructure.
However, no NDE inspection is perfect.
Factors such as sensor imperfections,
simplified models, and uncontrolled
inspection conditions introduce devi-
ations between the ideal and the
measured response, which is called
uncertainty [3]. Generally, uncertainty
encompasses all known/unknown errors
and variations in the inspection process,
from data collection through final inter-
pretation. Since NDE is safety-critical, if
uncertainty is not properly addressed, it
can produce false positives (overestimat-
ing damage) or false negatives (missing
critical discontinuities), potentially
leading to unnecessary repairs or unde-
tected damage that must be repaired
later [4, 5].
Every NDE inspection performance
will be affected by many uncertainty
factors. For example, poor surface con-
ditions—such as rust, paint, or machin-
ing marks—can scatter or weaken the
inspection signal, hiding shallow discon-
tinuities or producing false indications
[6]. In addition, the choices of signal
processing methods may further amplify
noise or suppress weak echoes, dis-
torting the discontinuity response and
affecting decision-making [7]. Additional
uncertainty may arise from such factors
as equipment aging, probe geometry,
operator expertise, discontinuity mor-
phology, material properties, and envi-
ronmental variability these factors can
distort signals, reducing confidence
in inspection results and collectively
increasing operational risks [3, 8].
Uncertainty analysis and quantifi-
cation (UA&UQ) provide a systematic
approach to identifying and managing
these uncertainties. Traditional UQ
methods for NDE rely on statistical tech-
niques such as probability-of-detection
(POD) curves, sizing-uncertainty
bounds, and risk-informed inspection
criteria. These are applied to yield con-
fidence bounds or intervals for reliable
discontinuity detectability and sizing
accuracy across diverse NDE applica-
tions [9]. Recent advancements have
extended beyond these conventional
approaches, improving the robustness,
interpretability, and applicability of UQ
in more complex inspection scenarios.
Aldrin et al. [10] developed and
validated a model-based inversion
method to estimate crack length and
depth at multilayer fastener sites using
bolt-hole eddy current (BHEC) testing,
along with guidance on calculating the
95% lower uncertainty bound (LUS) to
support safety assessments. Knott et al.
[11] expanded traditional POD analysis
by creating a structured framework that
accounts for added uncertainties such
as material type, discontinuity shape,
gain settings, and inspector variability,
offering a clearer, step-by-step alterna-
tive to the standard transfer function
method. Additionally, statistical methods
are being applied to uncertainty quanti-
fication for example, one approach uses
a numerical inversion algorithm to prob-
abilistically estimate fatigue crack size
from eddy current signals, incorporating
both the estimated value and its uncer-
tainty [12].
Recent AI-enabled NDE systems
have boosted automation but also
introduced new uncertainty sources,
such as data-driven uncertainty from
limited or biased training sets and model
uncertainty stemming from the opaque
decision boundaries of deep networks
[13]. To mitigate these challenges, hybrid
UQ approaches are proposed, which
integrate classical probabilistic and
statistical tools with physics-informed
constraints to improve uncertainty
management in NDE applications and
provide more reliable discontinuity-
sizing metrics [14].
With the adoption and prevalence
of digital transformation in NDE—also
known as NDE 4.0—AI-driven automa-
tion, real-time sensor networks, and
digital twin technologies are transform-
ing inspection processes. However,
these advancements also create a need
for standardized UA&UQ frameworks.
This tutorial presents a comprehen-
sive review of UA&UQ methodologies,
including probabilistic, statistical, simu-
lation-based, and AI-driven approaches.
FEATURE
|
NDTTUTORIAL
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