discontinuity detectability in complex
materials [114]. In multi-sensor fusion,
Bayesian inference improves data inte-
gration by assigning weights to sensor
inputs based on their reliability and
confidence levels [87]. This allows NDE
systems to prioritize high-confidence
data sources, reducing the impact of
sensor noise, environmental variability,
and material inconsistencies. By contin-
uously updating probability estimates,
Bayesian inference supports adaptive
inspection strategies, allowing NDE
systems to dynamically adjust inspection
parameters based on real-time data. This
approach enhances multi-sensor reliabil-
ity and minimizes measurement incon-
sistencies. It also strengthens structural
health monitoring, ensuring long-term
asset integrity and operational safety.
Following are key multimodal
sensing strategies that leverage Bayesian
inference for uncertainty reduction.
THERMAL-ACOUSTIC HYBRID
DISCONTINUITY ANALYSIS:
ULTRASOUND +INFRARED
THERMOGRAPHY
The combination of ultrasonic testing
(UT) and infrared thermography (IRT)
significantly enhances delamination
detection in composites by enabling
multi-depth discontinuity character-
ization. UT enables deep subsurface
discontinuity detection through wave
reflection analysis, while IRT identi-
fies near-surface discontinuities via
thermal anomaly mapping. This synergy
addresses key limitations: UT’s reduced
sensitivity to surface discontinuities and
IRT’s diminished effectiveness in thicker
materials. Bayesian inference enhances
the thermal-acoustic hybrid approach by
quantifying uncertainties and improv-
ing discontinuity localization accuracy.
For example, Spaeth et al. [88] applied
Bayesian analysis to estimate bond line
thickness in composites, integrating
thermography data with Gaussian priors
for thermal diffusivity. Additionally, the
EVBTF-RPHF algorithm is applied to
optimize thermographic NDT, which
embeds pseudo-restored heat flux into a
low-rank decomposition framework [89].
These advancements demonstrate how
Bayesian methods refine multimodal
data fusion, enabling more reliable
discontinuity characterization. Future
research should prioritize computational
efficiency and broader applicability to
complex materials and discontinuity
types.
ELECTROMAGNETIC-BASED
STRUCTURAL INTEGRITY ASSESSMENT:
EDDY CURRENT +MAGNETIC FLUX
LEAKAGE
The combination of eddy current testing
(ECT) and magnetic flux leakage (MFL)
provides a powerful approach for crack
and corrosion detection in metallic
structures. ECT excels at detecting
surface and near-surface discontinuities,
while MFL enables deeper penetration
to identify subsurface corrosion and
material thinning. This fusion signifi-
cantly improves discontinuity depth
estimation, reducing false positives
in pipeline inspections and enhanc-
ing structural integrity assessments.
Applications of this hybrid approach are
demonstrated in discontinuity detec-
tion studies, where a dual-probe system
capable of capturing both eddy current
and MFL signals is applied to enhance
detection in carbon steel plates [90].
Bayesian techniques enhance the
reliability of electromagnetic-based
inspections by quantifying uncertainties
in discontinuity characterization. The
complementary nature of ECT and MFL
is highlighted in top-of-line corrosion
monitoring, where Bayesian methods
can refine depth sizing and discontinuity
clustering [91]. Adaptability to varying
inspection conditions, such as scanning
speed and material thickness, is further
explored by Piao et al. [92], which
examines motion-induced eddy currents
in high-speed MFL applications.
AI-Enhanced Signal Processing for
Real-Time Uncertainty Estimation
Traditional methods often struggle to
balance computational efficiency with
accurate uncertainty quantification,
prompting the adoption of advanced
techniques that offer principled uncer-
tainty estimates by leveraging probabilis-
tic frameworks. Real-time NDE requires
not only fast discontinuity detection
but also instant confidence estimates.
Modern AI-enhanced pipelines embed
probabilistic reasoning into raw sensor
data, producing uncertainty metrics
alongside each scan. Figure 6 highlights
advanced applications of UA and UQ in
support of industrial adoption.
BAYESIAN NEURAL NETWORKS FOR
CONFIDENCE-AWARE DISCONTINUITY
CLASSIFICATION
BNNs enhance discontinuity classifi-
cation by integrating multiple sensor
inputs and estimating probability dis-
tributions over model predictions.
Unlike traditional deep learning models,
adaptive Bayesian learning continuously
updates discontinuity probability esti-
mates as new inspection data becomes
available. This adaptive learning
increases confidence in discontinuity
detection and reduces false rejections,
particularly in aerospace and automo-
tive quality control. Variational inference
is commonly used to balance accuracy
and efficiency in industrial applications.
Dai et al. [93] demonstrated that ensem-
ble-based variational models improve
pseudo-label quality in semi-supervised
settings, offering a path to enhance
BNNs under limited labeled data con-
ditions. These developments high-
light the potential of BNNs for reliable,
confidence-aware discontinuity classifi-
cation in dynamic environments. Recent
hardware optimizations, such as Fast-
BCNN [94] and binary BNNs [95], have
further reduced computational costs,
supporting the practical deployment of
BNNs in real-time, uncertainty-aware
NDE systems. These innovations,
combined with theoretical foundations
and practical advancements, underscore
the growing role of BNNs in industrial
and real-time settings, bridging the gap
between uncertainty quantification and
operational efficiency.
ENHANCED MONTE CARLO SENSOR
FUSION FOR REAL-TIME UNCERTAINTY
ESTIMATION
Monte Carlo methods, integrated with
AI-driven signal processing, enhance
sensor data fusion by providing
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 33
materials [114]. In multi-sensor fusion,
Bayesian inference improves data inte-
gration by assigning weights to sensor
inputs based on their reliability and
confidence levels [87]. This allows NDE
systems to prioritize high-confidence
data sources, reducing the impact of
sensor noise, environmental variability,
and material inconsistencies. By contin-
uously updating probability estimates,
Bayesian inference supports adaptive
inspection strategies, allowing NDE
systems to dynamically adjust inspection
parameters based on real-time data. This
approach enhances multi-sensor reliabil-
ity and minimizes measurement incon-
sistencies. It also strengthens structural
health monitoring, ensuring long-term
asset integrity and operational safety.
Following are key multimodal
sensing strategies that leverage Bayesian
inference for uncertainty reduction.
THERMAL-ACOUSTIC HYBRID
DISCONTINUITY ANALYSIS:
ULTRASOUND +INFRARED
THERMOGRAPHY
The combination of ultrasonic testing
(UT) and infrared thermography (IRT)
significantly enhances delamination
detection in composites by enabling
multi-depth discontinuity character-
ization. UT enables deep subsurface
discontinuity detection through wave
reflection analysis, while IRT identi-
fies near-surface discontinuities via
thermal anomaly mapping. This synergy
addresses key limitations: UT’s reduced
sensitivity to surface discontinuities and
IRT’s diminished effectiveness in thicker
materials. Bayesian inference enhances
the thermal-acoustic hybrid approach by
quantifying uncertainties and improv-
ing discontinuity localization accuracy.
For example, Spaeth et al. [88] applied
Bayesian analysis to estimate bond line
thickness in composites, integrating
thermography data with Gaussian priors
for thermal diffusivity. Additionally, the
EVBTF-RPHF algorithm is applied to
optimize thermographic NDT, which
embeds pseudo-restored heat flux into a
low-rank decomposition framework [89].
These advancements demonstrate how
Bayesian methods refine multimodal
data fusion, enabling more reliable
discontinuity characterization. Future
research should prioritize computational
efficiency and broader applicability to
complex materials and discontinuity
types.
ELECTROMAGNETIC-BASED
STRUCTURAL INTEGRITY ASSESSMENT:
EDDY CURRENT +MAGNETIC FLUX
LEAKAGE
The combination of eddy current testing
(ECT) and magnetic flux leakage (MFL)
provides a powerful approach for crack
and corrosion detection in metallic
structures. ECT excels at detecting
surface and near-surface discontinuities,
while MFL enables deeper penetration
to identify subsurface corrosion and
material thinning. This fusion signifi-
cantly improves discontinuity depth
estimation, reducing false positives
in pipeline inspections and enhanc-
ing structural integrity assessments.
Applications of this hybrid approach are
demonstrated in discontinuity detec-
tion studies, where a dual-probe system
capable of capturing both eddy current
and MFL signals is applied to enhance
detection in carbon steel plates [90].
Bayesian techniques enhance the
reliability of electromagnetic-based
inspections by quantifying uncertainties
in discontinuity characterization. The
complementary nature of ECT and MFL
is highlighted in top-of-line corrosion
monitoring, where Bayesian methods
can refine depth sizing and discontinuity
clustering [91]. Adaptability to varying
inspection conditions, such as scanning
speed and material thickness, is further
explored by Piao et al. [92], which
examines motion-induced eddy currents
in high-speed MFL applications.
AI-Enhanced Signal Processing for
Real-Time Uncertainty Estimation
Traditional methods often struggle to
balance computational efficiency with
accurate uncertainty quantification,
prompting the adoption of advanced
techniques that offer principled uncer-
tainty estimates by leveraging probabilis-
tic frameworks. Real-time NDE requires
not only fast discontinuity detection
but also instant confidence estimates.
Modern AI-enhanced pipelines embed
probabilistic reasoning into raw sensor
data, producing uncertainty metrics
alongside each scan. Figure 6 highlights
advanced applications of UA and UQ in
support of industrial adoption.
BAYESIAN NEURAL NETWORKS FOR
CONFIDENCE-AWARE DISCONTINUITY
CLASSIFICATION
BNNs enhance discontinuity classifi-
cation by integrating multiple sensor
inputs and estimating probability dis-
tributions over model predictions.
Unlike traditional deep learning models,
adaptive Bayesian learning continuously
updates discontinuity probability esti-
mates as new inspection data becomes
available. This adaptive learning
increases confidence in discontinuity
detection and reduces false rejections,
particularly in aerospace and automo-
tive quality control. Variational inference
is commonly used to balance accuracy
and efficiency in industrial applications.
Dai et al. [93] demonstrated that ensem-
ble-based variational models improve
pseudo-label quality in semi-supervised
settings, offering a path to enhance
BNNs under limited labeled data con-
ditions. These developments high-
light the potential of BNNs for reliable,
confidence-aware discontinuity classifi-
cation in dynamic environments. Recent
hardware optimizations, such as Fast-
BCNN [94] and binary BNNs [95], have
further reduced computational costs,
supporting the practical deployment of
BNNs in real-time, uncertainty-aware
NDE systems. These innovations,
combined with theoretical foundations
and practical advancements, underscore
the growing role of BNNs in industrial
and real-time settings, bridging the gap
between uncertainty quantification and
operational efficiency.
ENHANCED MONTE CARLO SENSOR
FUSION FOR REAL-TIME UNCERTAINTY
ESTIMATION
Monte Carlo methods, integrated with
AI-driven signal processing, enhance
sensor data fusion by providing
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 33
