training, future studies will look at power spectral densities
generated numerically in addition to the exploration of a
physics informed network to help assist the training process.
ACKNOWLEDGMENTS
This work and the first author were supported by AAR/TTCI under the
program: Grand Challenge Research Topic: In-motion Track Stability
Assessment, agreement no. 20-0701-007537. Funding to perform the field
tests and to support the second author were provided by the US Federal
Railroad Administration under contract FR19RPD3100000022. The authors
acknowledge the logistic support of the host MxV Rail and Mr. Christopher
Johnson during the planning and execution of the field test. The authors
are also grateful to the host for sharing the ground truth RNT. Currently,
the second author is supported by the 2023 ASNT Fellowship Award.
Finally, the authors would like to acknowledge the contribution of Mr.
Charles (Scooter) Hager, at the University of Pittsburgh, for the technical
support provided during the preparation and execution of the experi-
ments.
DATA AVAILABILITY
Some or all data, models, or code that support the findings of this study
are available from the corresponding author upon reasonable request.
REFERENCES
Bagheri, A., E. La Malfa Ribolla, P. Rizzo, and L. Al-Nazer. 2016. “On the
coupling dynamics between thermally stressed beams and granular
chains.” Archive of Applied Mechanics 86 (3): 541–56. https://doi.
org/10.1007/s00419-015-1039-y.
Belding, M., A. Enshaeian, and P. Rizzo. 2022. “Vibration-Based Approach
to Measure Rail Stress: Modeling and First Field Test.” Sensors (Basel) 22
(19): 7447. https://doi.org/10.3390/s22197447.
Belding, M., A. Enshaeian, and P. Rizzo. 2023a. “A Machine Learning-Based
Approach to Determining Stress in Rails.” Structural Health Monitoring
22 (1): 639–56. https://doi.org/10.1177/14759217221085658.
Belding, M., A. Enshaeian, and P. Rizzo. 2023b. “Nondestructive Rail
Neutral Temperature Estimation based on Low-frequency Vibrations
and Machine Learning.” NDT&E International 137: 102840. https://doi.
org/10.1016/j.ndteint.2023.102840.
Belding, M., A. Enshaeian, C. Hager, and P. Rizzo. 2023c. “Machine
Learning for the Nondestructive Prediction of Neutral Temperature in
Continuous Welded Rails.” In print. Research in Nondestructive Evalua-
tion 34 (3-4): 121–35. https://doi.org/10.1080/09349847.2023.2237446.
Brincker, R., L. Zhang, and P. Andersen. 2001. “Modal identification of
output-only systems using frequency domain decomposition.” Smart
Materials and Structures 10 (3): 441–45. https://doi.org/10.1088/0964-
1726/10/3/303.
Devlin, J., M.-W. Chang, K. Lee, and K. Toutanova. 2018. “BERT:
Pre-training of Deep Bidirectional Transformers for Language Under-
standing.” Cornell University. https://doi.org/10.48550/arXiv.1810.04805.
Ding, C., and H. Peng. 2005. “Minimum redundancy feature selec-
tion from microarray gene expression data.” Journal of Bioinformatics
and Computational Biology 3 (2): 185–205. https://doi.org/10.1142/
S0219720005001004.
Enshaeian, A., and P. Rizzo. 2021. “Stability of Continuous Welded Rails:
A State-of-the-Art Review of Structural Modeling and Nondestructive
Evaluation.” Proceedings of the Institution of Mechanical Engineers.
Part F, Journal of Rail and Rapid Transit 235 (10): 1291–311. https://doi.
org/10.1177/0954409720986661.
Enshaeian, A., L. Luan, M. Belding, H. Sun, and P. Rizzo. 2021. “A Contact-
less Approach to Monitor Rail Vibrations.” Experimental Mechanics 61 (4):
705–18. https://doi.org/10.1007/s11340-021-00691-z.
He, K., X. Zhang, S. Ren, and J. Sun. 2015. “Deep Residual Learning
for Image Recognition.” Cornell University. https://doi.org/10.48550/
arXiv.1512.03385.
Huang, C. L., Y. Wu, X. He, M. Dersch, X. Zhu, and J. S. Popovics. 2023. “A
review of non-destructive evaluation techniques for axial thermal stress
and neutral temperature measurement in rail: Physical phenomena and
performance assessment.” NDT &E International 137:102832. https://doi.
org/10.1016/j.ndteint.2023.102832.
Knopf, K., D. C. Rizos, Y. Qian, and M. Sutton. 2021. “A non-contacting
system for rail neutral temperature and stress measurements: Concept
development.” Structural Health Monitoring 20 (1): 84–100. https://doi.
org/10.1177/1475921720923116.
Krizhevsky, A., I. Sutskever, and G. E. Hinton. 2012. “ImageNet Classifica-
tion with Deep Convolutional Neural Networks.” Advances in Neural Infor-
mation Processing Systems: 25.
Lanza di Scalea, F. and C. Nucera. 2014. Nonlinear ultrasonic testing for
non-destructive measurement of longitudinal thermal stresses in solids.
US Patent US20150377836A1. Filed 5 February 2014, and issued 5 June 2018.
Nasrollahi, A., and P. Rizzo. 2018. “Axial stress determination using highly
nonlinear solitary waves.” Journal of the Acoustical Society of America 144
(4): 2201–12. https://doi.org/10.1121/1.5056172.
Nasrollahi, A., and P. Rizzo. 2019. “Numerical analysis and experimental
validation of an nondestructive evaluation method to measure stress in
rails.” Journal of Nondestructive Evaluation, Diagnostics and Prognostics of
Engineering Systems 2: 031002. https://doi.org/10.1115/1.4043949.
Niu, X., Zhu, Z. Yu, X. Xu, and H. Shen. 2023. “Detection method of
the neutral temperature in continuous welded rails based on nonlinear
ultrasonic guided waves.” Nondestructive Testing and Evaluation 38 (5):
798–826. https://doi.org/10.1080/10589759.2023.2170373.
Nucera, C., and F. Lanza di Scalea. 2014a. “Nondestructive measurement
of neutral temperature in continuous welded rails by nonlinear ultra-
sonic guided waves.” Journal of the Acoustical Society of America 136 (5):
2561–74. https://doi.org/10.1121/1.4896463.
Nucera, C., and F. Lanza di Scalea. 2014b. “Nonlinear wave propagation
in constrained solids subjected to thermal loads.” Journal of Sound and
Vibration 333 (2): 541–54. https://doi.org/10.1016/j.jsv.2013.09.018.
Nucera, C., R. Phillips, F. Lanza di Scalea, M. Fateh, and G. Carr.
2013. “System for the in situ measurement of neutral tempera-
ture in continuous-welded rail: Results from laboratory and field
tests.” Transportation Research Record: Journal of the Transportation
Research Board (2374): 154–61. https://doi.org/10.3141/2374-18.
Pandrol. 2019. VERSE® technical information pack. Accessed 29 October
2022. https://railway-news.com/wp-content/uploads/2020/02/
VERSE-Technical-Information-Pack.pdf.
Szela˛z˙ek, J. 1992. “Ultrasonic measurement of thermal stresses in contin-
uously welded rails.” NDT &E International 25 (2): 77–85. https://doi.
org/10.1016/0963-8695(92)90497-5.
Thoppilan, R., et al. 2022. “LaMDA: Language Models for Dialog Applica-
tions.” Cornell University. https://doi.org/10.48550/arXiv.2201.08239
Wang, P., K. Xie, L. Shao, L. Yan, J. Xu, and R. Chen. 2016. “Longitudinal
force measurement in continuous welded rail with bi-directional FBG
strain sensors.” Smart Materials and Structures 25 (1): 015019. https://doi.
org/10.1088/0964-1726/25/1/015019.
Yang, W., K. Wang, and W. Zuo. 2012. “Neighborhood Component Feature
Selection for High-Dimensional Data.” Journal of Computers 7 (1): 161–68.
http://www.jcomputers.us/vol7/jcp0701-19.pdf.
Zhu, X., and F. Lanza di Scalea. 2017. “Thermal Stress Measurement in
Continuous Welded Rails Using the Hole-Drilling Method.” Experimental
Mechanics 57 (1): 165–78. https://doi.org/10.1007/s11340-016-0204-8.
ME
|
RAILROADS
78
M A T E R I A L S E V A L U A T I O N • J A N U A R Y 2 0 2 4
2401 ME January.indd 78 12/20/23 8:01 AM
generated numerically in addition to the exploration of a
physics informed network to help assist the training process.
ACKNOWLEDGMENTS
This work and the first author were supported by AAR/TTCI under the
program: Grand Challenge Research Topic: In-motion Track Stability
Assessment, agreement no. 20-0701-007537. Funding to perform the field
tests and to support the second author were provided by the US Federal
Railroad Administration under contract FR19RPD3100000022. The authors
acknowledge the logistic support of the host MxV Rail and Mr. Christopher
Johnson during the planning and execution of the field test. The authors
are also grateful to the host for sharing the ground truth RNT. Currently,
the second author is supported by the 2023 ASNT Fellowship Award.
Finally, the authors would like to acknowledge the contribution of Mr.
Charles (Scooter) Hager, at the University of Pittsburgh, for the technical
support provided during the preparation and execution of the experi-
ments.
DATA AVAILABILITY
Some or all data, models, or code that support the findings of this study
are available from the corresponding author upon reasonable request.
REFERENCES
Bagheri, A., E. La Malfa Ribolla, P. Rizzo, and L. Al-Nazer. 2016. “On the
coupling dynamics between thermally stressed beams and granular
chains.” Archive of Applied Mechanics 86 (3): 541–56. https://doi.
org/10.1007/s00419-015-1039-y.
Belding, M., A. Enshaeian, and P. Rizzo. 2022. “Vibration-Based Approach
to Measure Rail Stress: Modeling and First Field Test.” Sensors (Basel) 22
(19): 7447. https://doi.org/10.3390/s22197447.
Belding, M., A. Enshaeian, and P. Rizzo. 2023a. “A Machine Learning-Based
Approach to Determining Stress in Rails.” Structural Health Monitoring
22 (1): 639–56. https://doi.org/10.1177/14759217221085658.
Belding, M., A. Enshaeian, and P. Rizzo. 2023b. “Nondestructive Rail
Neutral Temperature Estimation based on Low-frequency Vibrations
and Machine Learning.” NDT&E International 137: 102840. https://doi.
org/10.1016/j.ndteint.2023.102840.
Belding, M., A. Enshaeian, C. Hager, and P. Rizzo. 2023c. “Machine
Learning for the Nondestructive Prediction of Neutral Temperature in
Continuous Welded Rails.” In print. Research in Nondestructive Evalua-
tion 34 (3-4): 121–35. https://doi.org/10.1080/09349847.2023.2237446.
Brincker, R., L. Zhang, and P. Andersen. 2001. “Modal identification of
output-only systems using frequency domain decomposition.” Smart
Materials and Structures 10 (3): 441–45. https://doi.org/10.1088/0964-
1726/10/3/303.
Devlin, J., M.-W. Chang, K. Lee, and K. Toutanova. 2018. “BERT:
Pre-training of Deep Bidirectional Transformers for Language Under-
standing.” Cornell University. https://doi.org/10.48550/arXiv.1810.04805.
Ding, C., and H. Peng. 2005. “Minimum redundancy feature selec-
tion from microarray gene expression data.” Journal of Bioinformatics
and Computational Biology 3 (2): 185–205. https://doi.org/10.1142/
S0219720005001004.
Enshaeian, A., and P. Rizzo. 2021. “Stability of Continuous Welded Rails:
A State-of-the-Art Review of Structural Modeling and Nondestructive
Evaluation.” Proceedings of the Institution of Mechanical Engineers.
Part F, Journal of Rail and Rapid Transit 235 (10): 1291–311. https://doi.
org/10.1177/0954409720986661.
Enshaeian, A., L. Luan, M. Belding, H. Sun, and P. Rizzo. 2021. “A Contact-
less Approach to Monitor Rail Vibrations.” Experimental Mechanics 61 (4):
705–18. https://doi.org/10.1007/s11340-021-00691-z.
He, K., X. Zhang, S. Ren, and J. Sun. 2015. “Deep Residual Learning
for Image Recognition.” Cornell University. https://doi.org/10.48550/
arXiv.1512.03385.
Huang, C. L., Y. Wu, X. He, M. Dersch, X. Zhu, and J. S. Popovics. 2023. “A
review of non-destructive evaluation techniques for axial thermal stress
and neutral temperature measurement in rail: Physical phenomena and
performance assessment.” NDT &E International 137:102832. https://doi.
org/10.1016/j.ndteint.2023.102832.
Knopf, K., D. C. Rizos, Y. Qian, and M. Sutton. 2021. “A non-contacting
system for rail neutral temperature and stress measurements: Concept
development.” Structural Health Monitoring 20 (1): 84–100. https://doi.
org/10.1177/1475921720923116.
Krizhevsky, A., I. Sutskever, and G. E. Hinton. 2012. “ImageNet Classifica-
tion with Deep Convolutional Neural Networks.” Advances in Neural Infor-
mation Processing Systems: 25.
Lanza di Scalea, F. and C. Nucera. 2014. Nonlinear ultrasonic testing for
non-destructive measurement of longitudinal thermal stresses in solids.
US Patent US20150377836A1. Filed 5 February 2014, and issued 5 June 2018.
Nasrollahi, A., and P. Rizzo. 2018. “Axial stress determination using highly
nonlinear solitary waves.” Journal of the Acoustical Society of America 144
(4): 2201–12. https://doi.org/10.1121/1.5056172.
Nasrollahi, A., and P. Rizzo. 2019. “Numerical analysis and experimental
validation of an nondestructive evaluation method to measure stress in
rails.” Journal of Nondestructive Evaluation, Diagnostics and Prognostics of
Engineering Systems 2: 031002. https://doi.org/10.1115/1.4043949.
Niu, X., Zhu, Z. Yu, X. Xu, and H. Shen. 2023. “Detection method of
the neutral temperature in continuous welded rails based on nonlinear
ultrasonic guided waves.” Nondestructive Testing and Evaluation 38 (5):
798–826. https://doi.org/10.1080/10589759.2023.2170373.
Nucera, C., and F. Lanza di Scalea. 2014a. “Nondestructive measurement
of neutral temperature in continuous welded rails by nonlinear ultra-
sonic guided waves.” Journal of the Acoustical Society of America 136 (5):
2561–74. https://doi.org/10.1121/1.4896463.
Nucera, C., and F. Lanza di Scalea. 2014b. “Nonlinear wave propagation
in constrained solids subjected to thermal loads.” Journal of Sound and
Vibration 333 (2): 541–54. https://doi.org/10.1016/j.jsv.2013.09.018.
Nucera, C., R. Phillips, F. Lanza di Scalea, M. Fateh, and G. Carr.
2013. “System for the in situ measurement of neutral tempera-
ture in continuous-welded rail: Results from laboratory and field
tests.” Transportation Research Record: Journal of the Transportation
Research Board (2374): 154–61. https://doi.org/10.3141/2374-18.
Pandrol. 2019. VERSE® technical information pack. Accessed 29 October
2022. https://railway-news.com/wp-content/uploads/2020/02/
VERSE-Technical-Information-Pack.pdf.
Szela˛z˙ek, J. 1992. “Ultrasonic measurement of thermal stresses in contin-
uously welded rails.” NDT &E International 25 (2): 77–85. https://doi.
org/10.1016/0963-8695(92)90497-5.
Thoppilan, R., et al. 2022. “LaMDA: Language Models for Dialog Applica-
tions.” Cornell University. https://doi.org/10.48550/arXiv.2201.08239
Wang, P., K. Xie, L. Shao, L. Yan, J. Xu, and R. Chen. 2016. “Longitudinal
force measurement in continuous welded rail with bi-directional FBG
strain sensors.” Smart Materials and Structures 25 (1): 015019. https://doi.
org/10.1088/0964-1726/25/1/015019.
Yang, W., K. Wang, and W. Zuo. 2012. “Neighborhood Component Feature
Selection for High-Dimensional Data.” Journal of Computers 7 (1): 161–68.
http://www.jcomputers.us/vol7/jcp0701-19.pdf.
Zhu, X., and F. Lanza di Scalea. 2017. “Thermal Stress Measurement in
Continuous Welded Rails Using the Hole-Drilling Method.” Experimental
Mechanics 57 (1): 165–78. https://doi.org/10.1007/s11340-016-0204-8.
ME
|
RAILROADS
78
M A T E R I A L S E V A L U A T I O N • J A N U A R Y 2 0 2 4
2401 ME January.indd 78 12/20/23 8:01 AM