28. Lei, C. L., S. Ghosh, D. G. Whittaker, Y.
Aboelkassem, K. A. Beattie, C. D. Cantwell,
T. Delhaas, C. Houston, G. M. Novaes, A. V.
Panfilov, P. Pathmanathan, M. Riabiz, R. W. dos
Santos, J. Walmsley, K. Worden, G. R. Mirams,
and R. D. Wilkinson. 2020. “Considering
discrepancy when calibrating a mechanistic
electrophysiology model.” Philosophical Trans-
actions of the Royal Society A: Mathematical,
Physical, and Engineering Sciences 378 (2173):
20190349. https://doi.org/10.1098/rsta.2019.0349.
29. Xie, W., C. Li, Y. Wu, and P. Zhang. 2021.
“A Nonparametric Bayesian Framework for
Uncertainty Quantification in Stochastic Simu-
lation.” SIAM/ASA Journal on Uncertainty
Quantification 9 (4): 1527–52. https://doi.
org/10.1137/20M1345517.
30. Kontolati, K., D. Loukrezis, K. R. M. Dos
Santos, D. G. Giovanis, and M. D. Shields. 2022.
“Manifold Learning-based Polynomial Chaos
Expansions for High-dimensional Surrogate
Models.” International Journal for Uncertainty
Quantification 12 (4): 39–64. https://doi.
org/10.1615/Int.J.UncertaintyQuantification
.2022039936.
31. Zhang, B., Q. Guo, Y. Wang, and M. Zhan.
2019. “Model-Form and Parameter Uncertainty
Quantification in Structural Vibration Simula-
tion Using Fractional Derivatives.” Journal of
Computational and Nonlinear Dynamics 14 (5):
051006. https://doi.org/10.1115/1.4042689.
32. Nasir, V., and F. Sassani. 2021. “A review on
deep learning in machining and tool moni-
toring: Methods, opportunities, and challenges.”
International Journal of Advanced Manufac-
turing Technology 115 (9–10): 2683–709. https://
doi.org/10.1007/s00170-021-07325-7.
33. Ochella, S., F. Dinmohammadi, and M.
Shafiee. 2024. “Bayesian neural networks
for uncertainty quantification in remaining
useful life prediction of systems with sensor
monitoring.” Advances in Mechanical Engi-
neering 16 (7): 16878132241239802. https://doi.
org/10.1177/16878132241239802.
34. Xiong, Y., S. Liu, L. Hou, and T. Zhou. 2024.
“Magnetic flux leakage defect size estimation
method based on physics-informed neural
network.” Philosophical Transactions. Series
A, Mathematical, Physical, and Engineering
Sciences 382 (2264): 20220387. https://doi.
org/10.1098/rsta.2022.0387.
35. Sandhu, H. K., S. S. Bodda, and A. Gupta.
2023. “A Future with Machine Learning: Review
of Condition Assessment of Structures and
Mechanical Systems in Nuclear Facilities.”
Energies 16 (6): 2628. https://doi.org/10.3390/
en16062628.
36. Xu, C., W. Zhao, J. Zhao, Z. Guan, X. Song,
and J. Li. 2023. “Uncertainty-Aware Multiview
Deep Learning for Internet of Things Applica-
tions.” IEEE Transactions on Industrial Infor-
matics 19 (2): 1456–66. https://doi.org/10.1109/
TII.2022.3206343.
37. Li, Z., Y. Yang, L. Li, H. Ma, and X. Chen.
2022. “Model-Free Fault Detection Based on
Performance Residual for Feedback Control
Systems.” IEEE Transactions on Circuits and
Systems II, Express Briefs 69 (11): 4453–57.
https://doi.org/10.1109/TCSII.2022.3182655.
38. Liang, Z., X. Wang, Y. Cui, W. Xu, Y. Zhang,
and Y. He. 2023. “A new data-driven probabi-
listic fatigue life prediction framework informed
by experiments and multiscale simulation.”
International Journal of Fatigue 174: 107731.
https://doi.org/10.1016/j.ijfatigue.2023.107731.
39. Shi, H., M. Ebrahimi, P. Zhou, K. Shao,
and J. Li. 2023. “Ultrasonic and phased-array
inspection in titanium-based alloys: A review.”
Proceedings of the Institution of Mechanical
Engineers: Part E, Journal of Process Mechan-
ical Engineering 237 (2): 511–30. https://doi.
org/10.1177/09544089221114253.
40. Li, Z., X. Huang, O. Elshafiey, S. Mukherjee,
and Y. Deng, 2021. “FEM of magnetic flux
leakage signal for uncertainty estimation in
crack depth classification using Bayesian convo-
lutional neural network and deep ensemble.”
2021 International Applied Computational Elec-
tromagnetics Society Symposium (ACES): 1–4.
41. Virkkunen, I., T. Koskinen, S. Papula, T.
Sarikka, and H. Hänninen. 2019. “Comparison
of â Versus a and Hit/Miss POD-Estimation
Methods: A European Viewpoint.” Journal of
Nondestructive Evaluation 38 (4): 89. https://doi.
org/10.1007/s10921-019-0628-z.
42. Knopp, J., R. Grandhi, L. Zeng, and J. Aldrin.
2012. “Considerations for Statistical Analysis
of Nondestructive Evaluation Data: Hit/Miss
Analysis.” E-Journal of Advanced Maintenance
4 (3): 105–115. https://www.jsm.or.jp/ejam/
Vol.4No.3/AA/AA45/AA45.pdf.
43. Jiang, F., Z. Guan, Z. Li, and X. Wang. 2021.
“A method of predicting visual detectability
of low-velocity impact damage in composite
structures based on logistic regression model.”
Chinese Journal of Aeronautics 34 (1): 296–308.
https://doi.org/10.1016/j.cja.2020.10.006.
44. Lampman, S., M. Mulherin, and R. Shipley.
2022. “Nondestructive Testing in Failure
Analysis.” Journal of Failure Analysis and
Prevention 22 (1): 66–97. https://doi.org/10.1007/
s11668-021-01325-1.
45. Sarkar, S., P. Wahi, and P. Munshi.
2019. “An empirical correction method for
beam-hardening artifact in Computerized
Tomography (CT) images.” NDT &E Interna-
tional 102: 104–13. https://doi.org/10.1016/j.
ndteint.2018.11.009.
46. Kurz, J. H., A. Jüngert, S. Dugan, G.
Dobmann, and C. Boller. 2013. “Reliability
considerations of NDT by probability of
detection (POD) determination using ultra-
sound phased array.” Engineering Failure
Analysis 35: 609–17. https://doi.org/10.1016/j.
engfailanal.2013.06.008.
47. Zhu, J., Q. Min, J. Wu, and G. Y. Tian. 2018.
“Probability of Detection for Eddy Current
Pulsed Thermography of Angular Defect Quan-
tification.” IEEE Transactions on Industrial Infor-
matics 14 (12): 5658–66. https://doi.org/10.1109/
TII.2018.2866443.
48. Yosifov, M., M. Reiter, S. Heupl, C. Gusen-
bauer, B. Fröhler, R. Fernández-Gutiérrez, J. De
Beenhouwer, J. Sijbers, J. Kastner, and C. Heinzl.
2022. “Probability of detection applied to X-ray
inspection using numerical simulations.” Nonde-
structive Testing and Evaluation 37 (5): 536–51.
https://doi.org/10.1080/10589759.2022.2071892.
49. Suwanasri, C., I. Yongyee, and T. Suwanasri.
2022. “Lifetime Estimation of Transmission Line
Based on Health Index and Normal Distribution
Technique.” 2022 9th International Confer-
ence on Condition Monitoring and Diagnosis
(CMD), Kitakyushu, Japan: 309–313. https://doi.
org/10.23919/CMD54214.2022.9991508.
50. Feng, M., L.-J. Deng, F. Chen, M. Perc, and
J. Kurths. 2020. “The accumulative law and its
probability model: an extension of the Pareto
distribution and the log-normal distribution.”
Proceedings of the Royal Society A: Mathe-
matical, Physical, and Engineering Sciences
476 (2237): 20200019. https://doi.org/10.1098/
rspa.2020.0019.
51. Kadir, D. H., and A. R. K. Rahi. 2023.
“Applying the Bayesian Technique in Designing
a Single Sampling Plan.” Cihan University-Erbil
Scientific Journal 7 (2): 17–25. https://doi.
org/10.24086/cuesj.v7n2y2023.pp17-25.
52. Haldar, A., and S. Mahadevan. 1995. “First-
Order and Second-Order Reliability Methods.”
In Probabilistic Structural Mechanics Handbook,
pp. 27–52. Sundararajan, C. (ed.). Boston, MA:
Springer US. https://doi.org/10.1007/978-1-4615-
1771-9_3.
53. El-Reedy, M. A. Reinforced Concrete Struc-
tural Reliability. 2012. Boca Raton, FL: CRC
Press. https://doi.org/10.1201/b12978.
54. Zhu, S., and T. Xiang. 2021. “Dynamic Reli-
ability Evaluation by First-Order Reliability
Method Integrated with Stochastic Pseudo Exci-
tation Method.” International Journal of Struc-
tural Stability and Dynamics 21 (2): 2150024.
https://doi.org/10.1142/S0219455421500243.
55. Gonzalez, O., S. Rodriguez, R. Perez-Jimenez,
B. R. Mendoza, and A. Ayala. 2005. “Error
Analysis of the Simulated Impulse Response on
Indoor Wireless Optical Channels Using a Monte
Carlo-Based Ray-Tracing Algorithm.” IEEE
Transactions on Communications 53 (1): 124–30.
https://doi.org/10.1109/TCOMM.2004.840625.
56. Yang, S., D. Meng, H. Yang, C. Luo, and
X. Su. 2025. “Enhanced soft Monte Carlo simu-
lation coupled with support vector regression
for structural reliability analysis.” Proceedings of
the Institution of Civil Engineers: Transport (Jan):
1–16. https://doi.org/10.1680/jtran.24.00128.
57. Faraji, J., M. Aslani, H. Hashemi-Dezaki,
A. Ketabi, Z. De Grève, and F. Vallée. 2024.
“Reliability Analysis of Cyber–Physical Energy
Hubs: A Monte Carlo Approach.” IEEE Transac-
tions on Smart Grid 15 (1): 848–62. https://doi.
org/10.1109/TSG.2023.3270821.
58. Liu, X.-X., J.-J. Xiao, and K. Lu. May 2024.
“Reliability and sensitivity analysis of delam-
ination growth of composite laminate struc-
tures using two efficient sampling methods.”
AIP Advances 14 (5): 055020. https://doi.
org/10.1063/5.0210827.
59. Kirkup, L., and R. B. Frenkel. 2006. An intro-
duction to uncertainty in measurement: using
the GUM (guide to the expression of uncertainty
in measurement). Cambridge University Press.
https://doi.org/10.1017/CBO9780511755538.
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 37
Aboelkassem, K. A. Beattie, C. D. Cantwell,
T. Delhaas, C. Houston, G. M. Novaes, A. V.
Panfilov, P. Pathmanathan, M. Riabiz, R. W. dos
Santos, J. Walmsley, K. Worden, G. R. Mirams,
and R. D. Wilkinson. 2020. “Considering
discrepancy when calibrating a mechanistic
electrophysiology model.” Philosophical Trans-
actions of the Royal Society A: Mathematical,
Physical, and Engineering Sciences 378 (2173):
20190349. https://doi.org/10.1098/rsta.2019.0349.
29. Xie, W., C. Li, Y. Wu, and P. Zhang. 2021.
“A Nonparametric Bayesian Framework for
Uncertainty Quantification in Stochastic Simu-
lation.” SIAM/ASA Journal on Uncertainty
Quantification 9 (4): 1527–52. https://doi.
org/10.1137/20M1345517.
30. Kontolati, K., D. Loukrezis, K. R. M. Dos
Santos, D. G. Giovanis, and M. D. Shields. 2022.
“Manifold Learning-based Polynomial Chaos
Expansions for High-dimensional Surrogate
Models.” International Journal for Uncertainty
Quantification 12 (4): 39–64. https://doi.
org/10.1615/Int.J.UncertaintyQuantification
.2022039936.
31. Zhang, B., Q. Guo, Y. Wang, and M. Zhan.
2019. “Model-Form and Parameter Uncertainty
Quantification in Structural Vibration Simula-
tion Using Fractional Derivatives.” Journal of
Computational and Nonlinear Dynamics 14 (5):
051006. https://doi.org/10.1115/1.4042689.
32. Nasir, V., and F. Sassani. 2021. “A review on
deep learning in machining and tool moni-
toring: Methods, opportunities, and challenges.”
International Journal of Advanced Manufac-
turing Technology 115 (9–10): 2683–709. https://
doi.org/10.1007/s00170-021-07325-7.
33. Ochella, S., F. Dinmohammadi, and M.
Shafiee. 2024. “Bayesian neural networks
for uncertainty quantification in remaining
useful life prediction of systems with sensor
monitoring.” Advances in Mechanical Engi-
neering 16 (7): 16878132241239802. https://doi.
org/10.1177/16878132241239802.
34. Xiong, Y., S. Liu, L. Hou, and T. Zhou. 2024.
“Magnetic flux leakage defect size estimation
method based on physics-informed neural
network.” Philosophical Transactions. Series
A, Mathematical, Physical, and Engineering
Sciences 382 (2264): 20220387. https://doi.
org/10.1098/rsta.2022.0387.
35. Sandhu, H. K., S. S. Bodda, and A. Gupta.
2023. “A Future with Machine Learning: Review
of Condition Assessment of Structures and
Mechanical Systems in Nuclear Facilities.”
Energies 16 (6): 2628. https://doi.org/10.3390/
en16062628.
36. Xu, C., W. Zhao, J. Zhao, Z. Guan, X. Song,
and J. Li. 2023. “Uncertainty-Aware Multiview
Deep Learning for Internet of Things Applica-
tions.” IEEE Transactions on Industrial Infor-
matics 19 (2): 1456–66. https://doi.org/10.1109/
TII.2022.3206343.
37. Li, Z., Y. Yang, L. Li, H. Ma, and X. Chen.
2022. “Model-Free Fault Detection Based on
Performance Residual for Feedback Control
Systems.” IEEE Transactions on Circuits and
Systems II, Express Briefs 69 (11): 4453–57.
https://doi.org/10.1109/TCSII.2022.3182655.
38. Liang, Z., X. Wang, Y. Cui, W. Xu, Y. Zhang,
and Y. He. 2023. “A new data-driven probabi-
listic fatigue life prediction framework informed
by experiments and multiscale simulation.”
International Journal of Fatigue 174: 107731.
https://doi.org/10.1016/j.ijfatigue.2023.107731.
39. Shi, H., M. Ebrahimi, P. Zhou, K. Shao,
and J. Li. 2023. “Ultrasonic and phased-array
inspection in titanium-based alloys: A review.”
Proceedings of the Institution of Mechanical
Engineers: Part E, Journal of Process Mechan-
ical Engineering 237 (2): 511–30. https://doi.
org/10.1177/09544089221114253.
40. Li, Z., X. Huang, O. Elshafiey, S. Mukherjee,
and Y. Deng, 2021. “FEM of magnetic flux
leakage signal for uncertainty estimation in
crack depth classification using Bayesian convo-
lutional neural network and deep ensemble.”
2021 International Applied Computational Elec-
tromagnetics Society Symposium (ACES): 1–4.
41. Virkkunen, I., T. Koskinen, S. Papula, T.
Sarikka, and H. Hänninen. 2019. “Comparison
of â Versus a and Hit/Miss POD-Estimation
Methods: A European Viewpoint.” Journal of
Nondestructive Evaluation 38 (4): 89. https://doi.
org/10.1007/s10921-019-0628-z.
42. Knopp, J., R. Grandhi, L. Zeng, and J. Aldrin.
2012. “Considerations for Statistical Analysis
of Nondestructive Evaluation Data: Hit/Miss
Analysis.” E-Journal of Advanced Maintenance
4 (3): 105–115. https://www.jsm.or.jp/ejam/
Vol.4No.3/AA/AA45/AA45.pdf.
43. Jiang, F., Z. Guan, Z. Li, and X. Wang. 2021.
“A method of predicting visual detectability
of low-velocity impact damage in composite
structures based on logistic regression model.”
Chinese Journal of Aeronautics 34 (1): 296–308.
https://doi.org/10.1016/j.cja.2020.10.006.
44. Lampman, S., M. Mulherin, and R. Shipley.
2022. “Nondestructive Testing in Failure
Analysis.” Journal of Failure Analysis and
Prevention 22 (1): 66–97. https://doi.org/10.1007/
s11668-021-01325-1.
45. Sarkar, S., P. Wahi, and P. Munshi.
2019. “An empirical correction method for
beam-hardening artifact in Computerized
Tomography (CT) images.” NDT &E Interna-
tional 102: 104–13. https://doi.org/10.1016/j.
ndteint.2018.11.009.
46. Kurz, J. H., A. Jüngert, S. Dugan, G.
Dobmann, and C. Boller. 2013. “Reliability
considerations of NDT by probability of
detection (POD) determination using ultra-
sound phased array.” Engineering Failure
Analysis 35: 609–17. https://doi.org/10.1016/j.
engfailanal.2013.06.008.
47. Zhu, J., Q. Min, J. Wu, and G. Y. Tian. 2018.
“Probability of Detection for Eddy Current
Pulsed Thermography of Angular Defect Quan-
tification.” IEEE Transactions on Industrial Infor-
matics 14 (12): 5658–66. https://doi.org/10.1109/
TII.2018.2866443.
48. Yosifov, M., M. Reiter, S. Heupl, C. Gusen-
bauer, B. Fröhler, R. Fernández-Gutiérrez, J. De
Beenhouwer, J. Sijbers, J. Kastner, and C. Heinzl.
2022. “Probability of detection applied to X-ray
inspection using numerical simulations.” Nonde-
structive Testing and Evaluation 37 (5): 536–51.
https://doi.org/10.1080/10589759.2022.2071892.
49. Suwanasri, C., I. Yongyee, and T. Suwanasri.
2022. “Lifetime Estimation of Transmission Line
Based on Health Index and Normal Distribution
Technique.” 2022 9th International Confer-
ence on Condition Monitoring and Diagnosis
(CMD), Kitakyushu, Japan: 309–313. https://doi.
org/10.23919/CMD54214.2022.9991508.
50. Feng, M., L.-J. Deng, F. Chen, M. Perc, and
J. Kurths. 2020. “The accumulative law and its
probability model: an extension of the Pareto
distribution and the log-normal distribution.”
Proceedings of the Royal Society A: Mathe-
matical, Physical, and Engineering Sciences
476 (2237): 20200019. https://doi.org/10.1098/
rspa.2020.0019.
51. Kadir, D. H., and A. R. K. Rahi. 2023.
“Applying the Bayesian Technique in Designing
a Single Sampling Plan.” Cihan University-Erbil
Scientific Journal 7 (2): 17–25. https://doi.
org/10.24086/cuesj.v7n2y2023.pp17-25.
52. Haldar, A., and S. Mahadevan. 1995. “First-
Order and Second-Order Reliability Methods.”
In Probabilistic Structural Mechanics Handbook,
pp. 27–52. Sundararajan, C. (ed.). Boston, MA:
Springer US. https://doi.org/10.1007/978-1-4615-
1771-9_3.
53. El-Reedy, M. A. Reinforced Concrete Struc-
tural Reliability. 2012. Boca Raton, FL: CRC
Press. https://doi.org/10.1201/b12978.
54. Zhu, S., and T. Xiang. 2021. “Dynamic Reli-
ability Evaluation by First-Order Reliability
Method Integrated with Stochastic Pseudo Exci-
tation Method.” International Journal of Struc-
tural Stability and Dynamics 21 (2): 2150024.
https://doi.org/10.1142/S0219455421500243.
55. Gonzalez, O., S. Rodriguez, R. Perez-Jimenez,
B. R. Mendoza, and A. Ayala. 2005. “Error
Analysis of the Simulated Impulse Response on
Indoor Wireless Optical Channels Using a Monte
Carlo-Based Ray-Tracing Algorithm.” IEEE
Transactions on Communications 53 (1): 124–30.
https://doi.org/10.1109/TCOMM.2004.840625.
56. Yang, S., D. Meng, H. Yang, C. Luo, and
X. Su. 2025. “Enhanced soft Monte Carlo simu-
lation coupled with support vector regression
for structural reliability analysis.” Proceedings of
the Institution of Civil Engineers: Transport (Jan):
1–16. https://doi.org/10.1680/jtran.24.00128.
57. Faraji, J., M. Aslani, H. Hashemi-Dezaki,
A. Ketabi, Z. De Grève, and F. Vallée. 2024.
“Reliability Analysis of Cyber–Physical Energy
Hubs: A Monte Carlo Approach.” IEEE Transac-
tions on Smart Grid 15 (1): 848–62. https://doi.
org/10.1109/TSG.2023.3270821.
58. Liu, X.-X., J.-J. Xiao, and K. Lu. May 2024.
“Reliability and sensitivity analysis of delam-
ination growth of composite laminate struc-
tures using two efficient sampling methods.”
AIP Advances 14 (5): 055020. https://doi.
org/10.1063/5.0210827.
59. Kirkup, L., and R. B. Frenkel. 2006. An intro-
duction to uncertainty in measurement: using
the GUM (guide to the expression of uncertainty
in measurement). Cambridge University Press.
https://doi.org/10.1017/CBO9780511755538.
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 37















































































































