minor variations leading to significant
measurement variabilities [20]. Sensor-
related errors, such as calibration drift,
noise, or environmental interference,
further exacerbate uncertainty, partic-
ularly in challenging or extreme oper-
ational conditions. These factors often
interact, creating compounded uncer-
tainties that complicate data interpreta-
tion. For example, sensor inaccuracies
may obscure true material variations,
while geometric uncertainties can com-
plicate signal analysis [21].
Such challenges highlight the need
for robust methodologies, includ-
ing statistical analysis and advanced
signal processing, to mitigate uncer-
tainty and enhance NDE reliability.
Statistical analysis methods, such as
high-dimensional data analytics, are
widely used to manage large datasets
and reduce measurement variability
in structural health monitoring [22].
Sensor calibration and fusion tech-
niques, including multi-view ultrasonic
data integration, improve discontinuity
detection reliability by combining com-
plementary information from multiple
sources [23]. Stochastic simulations
and Bayesian inference methods are
powerful tools for addressing these
uncertainties, enabling more precise
discontinuity parameter estimation.
For instance, Li and Deng [24] demon-
strated how Bayesian approximation and
deep learning can quantify predictive
uncertainty in damage classification,
particularly in magnetic flux leakage
(MFL) inspections, where discontinuity
geometry plays a critical role.
Signal processing and adaptive filter-
ing also play a critical role in reducing
electronic noise and operator-induced
variability. Machine learning (ML)
approaches, like those described by
Huang et al. [25], can be used to decouple
material parameters and reduce errors in
property estimation to within 3.5%. Spatial
domain linearization, explored by Wang
et al. [26], transforms liftoff effects into
predictable linear relationships, enhanc-
ing measurement accuracy.
Model uncertainties arise during
the forward modeling process in NDE,
where simplified physical and math-
ematical models are used to simulate
inspection scenarios and predict system
responses. As there will always be sim-
plifications, assumptions, and approx-
imations in forward mathematical and
physics models to simulate the NDE
inspection and data generation, discrep-
ancies arise between model-predicted
and experimentally measured responses.
Specifically, two types of uncertainty
are introduced: parametric uncertainty,
which stems from uncertain input values
like material properties or discontinuity
dimensions and structural uncertainty,
which results from model assumptions,
unmodeled physics, and numerical
errors. The distinction between paramet-
ric and structural uncertainties is critical,
as their interplay can complicate model
calibration and validation. For instance,
nonlinear interactions in complex
systems can introduce biases during
parameter tuning [27], while divergence
between simplified models and real-
world behavior—known as model dis-
crepancy—poses additional challenges
[28].
For parametric uncertainty, several
methods have been proposed to address
these uncertainties. Bayesian calibration
provides a robust framework by incor-
porating prior knowledge and updating
beliefs with observed data, effectively
quantifying input parameter uncertainty
[29]. Stochastic finite element methods
help propagate these uncertainties, espe-
cially when dealing with spatial variabil-
ity. Global sensitivity analysis, such as
that using polynomial chaos expansions,
identifies the most influential parameters
and helps focus modeling efforts [30].
Other techniques, including perturba-
tion methods and fractional derivative
models, offer localized assessments and
help address model-form uncertainty
[31]. Ultimately, advancing UQ in NDE
requires integrating both parametric
and structural uncertainty into calibra-
tion workflows, balancing model fidelity,
computational efficiency, and predictive
accuracy for real-world applications.
Inverse characterization and learning
uncertainty arise during the inverse NDE
process, where discontinuity parame-
ters such as size, shape, and depth are
inferred from either model-generated or
experimentally/field-obtained NDE data.
Limited training data, sensor noise, and
indirect measurements all contribute
to challenges in discontinuity classifi-
cation and sizing [32]. In recent years,
as AI models are increasingly used for
damage prediction, learning model–
related uncertainty has become a major
concern. Overfitting, often caused by
insufficient data, can lead to false detec-
tions and misclassifications of damage.
Bayesian neural networks (BNNs)
provide a robust framework for address-
ing model uncertainty in AI-based
damage prediction by treating network
parameters as probabilistic distributions
rather than fixed values [33]. Hybrid
model calibration issues occur when ML
predictions conflict with physics-based
models, reducing predictive accuracy.
For example, Xiong et al. [34] embedded
MFL governing equations into a
neural-network loss function the result-
ing physics-informed model achieved
high-precision discontinuity quantifi-
cation, illustrating the value of integrat-
ing domain knowledge with learning
algorithms.
Data assimilation challenges occur
when combining noisy, incomplete, or
inconsistent data, which further impacts
AI-based NDE and makes discontinuity
signature interpretation unreliable [35].
To enhance discontinuity estimation reli-
ability and classification accuracy, robust
data augmentation, physics-informed AI
models, and adaptive learning frame-
works are essential and have been
investigated.
Uncertainty-aware deep learning
approaches address noise interfer-
ence, data heterogeneity, and nonlin-
ear correlations by explicitly account-
ing for uncertainties in both data and
models. For instance, Xu et al. [36]
proposed an evidential multi-view deep
learning method that dynamically fuses
view-specific evidence, improving deci-
sion-making in industrial IoT scenarios.
Additionally, adaptive feedback loops
dynamically adjust models based on
NDT TUTORIAL
|
UA&UQ
26
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
measurement variabilities [20]. Sensor-
related errors, such as calibration drift,
noise, or environmental interference,
further exacerbate uncertainty, partic-
ularly in challenging or extreme oper-
ational conditions. These factors often
interact, creating compounded uncer-
tainties that complicate data interpreta-
tion. For example, sensor inaccuracies
may obscure true material variations,
while geometric uncertainties can com-
plicate signal analysis [21].
Such challenges highlight the need
for robust methodologies, includ-
ing statistical analysis and advanced
signal processing, to mitigate uncer-
tainty and enhance NDE reliability.
Statistical analysis methods, such as
high-dimensional data analytics, are
widely used to manage large datasets
and reduce measurement variability
in structural health monitoring [22].
Sensor calibration and fusion tech-
niques, including multi-view ultrasonic
data integration, improve discontinuity
detection reliability by combining com-
plementary information from multiple
sources [23]. Stochastic simulations
and Bayesian inference methods are
powerful tools for addressing these
uncertainties, enabling more precise
discontinuity parameter estimation.
For instance, Li and Deng [24] demon-
strated how Bayesian approximation and
deep learning can quantify predictive
uncertainty in damage classification,
particularly in magnetic flux leakage
(MFL) inspections, where discontinuity
geometry plays a critical role.
Signal processing and adaptive filter-
ing also play a critical role in reducing
electronic noise and operator-induced
variability. Machine learning (ML)
approaches, like those described by
Huang et al. [25], can be used to decouple
material parameters and reduce errors in
property estimation to within 3.5%. Spatial
domain linearization, explored by Wang
et al. [26], transforms liftoff effects into
predictable linear relationships, enhanc-
ing measurement accuracy.
Model uncertainties arise during
the forward modeling process in NDE,
where simplified physical and math-
ematical models are used to simulate
inspection scenarios and predict system
responses. As there will always be sim-
plifications, assumptions, and approx-
imations in forward mathematical and
physics models to simulate the NDE
inspection and data generation, discrep-
ancies arise between model-predicted
and experimentally measured responses.
Specifically, two types of uncertainty
are introduced: parametric uncertainty,
which stems from uncertain input values
like material properties or discontinuity
dimensions and structural uncertainty,
which results from model assumptions,
unmodeled physics, and numerical
errors. The distinction between paramet-
ric and structural uncertainties is critical,
as their interplay can complicate model
calibration and validation. For instance,
nonlinear interactions in complex
systems can introduce biases during
parameter tuning [27], while divergence
between simplified models and real-
world behavior—known as model dis-
crepancy—poses additional challenges
[28].
For parametric uncertainty, several
methods have been proposed to address
these uncertainties. Bayesian calibration
provides a robust framework by incor-
porating prior knowledge and updating
beliefs with observed data, effectively
quantifying input parameter uncertainty
[29]. Stochastic finite element methods
help propagate these uncertainties, espe-
cially when dealing with spatial variabil-
ity. Global sensitivity analysis, such as
that using polynomial chaos expansions,
identifies the most influential parameters
and helps focus modeling efforts [30].
Other techniques, including perturba-
tion methods and fractional derivative
models, offer localized assessments and
help address model-form uncertainty
[31]. Ultimately, advancing UQ in NDE
requires integrating both parametric
and structural uncertainty into calibra-
tion workflows, balancing model fidelity,
computational efficiency, and predictive
accuracy for real-world applications.
Inverse characterization and learning
uncertainty arise during the inverse NDE
process, where discontinuity parame-
ters such as size, shape, and depth are
inferred from either model-generated or
experimentally/field-obtained NDE data.
Limited training data, sensor noise, and
indirect measurements all contribute
to challenges in discontinuity classifi-
cation and sizing [32]. In recent years,
as AI models are increasingly used for
damage prediction, learning model–
related uncertainty has become a major
concern. Overfitting, often caused by
insufficient data, can lead to false detec-
tions and misclassifications of damage.
Bayesian neural networks (BNNs)
provide a robust framework for address-
ing model uncertainty in AI-based
damage prediction by treating network
parameters as probabilistic distributions
rather than fixed values [33]. Hybrid
model calibration issues occur when ML
predictions conflict with physics-based
models, reducing predictive accuracy.
For example, Xiong et al. [34] embedded
MFL governing equations into a
neural-network loss function the result-
ing physics-informed model achieved
high-precision discontinuity quantifi-
cation, illustrating the value of integrat-
ing domain knowledge with learning
algorithms.
Data assimilation challenges occur
when combining noisy, incomplete, or
inconsistent data, which further impacts
AI-based NDE and makes discontinuity
signature interpretation unreliable [35].
To enhance discontinuity estimation reli-
ability and classification accuracy, robust
data augmentation, physics-informed AI
models, and adaptive learning frame-
works are essential and have been
investigated.
Uncertainty-aware deep learning
approaches address noise interfer-
ence, data heterogeneity, and nonlin-
ear correlations by explicitly account-
ing for uncertainties in both data and
models. For instance, Xu et al. [36]
proposed an evidential multi-view deep
learning method that dynamically fuses
view-specific evidence, improving deci-
sion-making in industrial IoT scenarios.
Additionally, adaptive feedback loops
dynamically adjust models based on
NDT TUTORIAL
|
UA&UQ
26
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
