Future work will continue to search for other resonances
that exhibit high correlation to strain regardless of rail tem-
perature and stress condition (RNT). Additionally, the relative
changes among resonances will be investigated to explore res-
onance combinations that can lead to a unique relationship
with strain for different and arbitrary locations. Different rail
structure types and deployment of machine learning tech-
niques will also be considered in this effort.
ACKNOWLEDGMENTS
This work was made possible by financial support from the US National
Academy of Sciences Rail Safety IDEA program, project RS-41, and the
Federal Railroad Administration through contract 693JJ621C000025. The
authors are also grateful to BNSF Railway for providing access to the test
site, the rail-cutting procedure, and on-site assistance and monitoring for
personnel safety.
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tion: theory, safety concepts, and applications.” Technical Report. US
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Kish, A., G. Samavedam, and D. Jeong. 1987. “The neutral temperature
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ABSTR ACT
This paper presents the latest findings of a
nondestructive evaluation technique currently
under development at the University of Pittsburgh
to determine the rail neutral temperature (RNT) in
continuous welded rails. The technique is based
on the extraction of relevant features from rail
vibrations and the use of machine learning (ML) to
associate these features to the longitudinal stress of
the rail of interest. The features contain the spectral
information of the vibrations and are pooled together
by frequency domain decomposition for input to
ML algorithms. Minimum redundancy–maximum
relevance and neighboring component analysis are
used to identify relevant features to reduce the size of
the input vector. In addition, seven algorithms were
considered to identify the most accurate model for
neutral temperature with respect to the ground truth
RNT measured with a strain-gage rosette. The data
used in this study were collected from a 5° curved rail
on concrete ties. The vibrations were triggered with a
hammer and recorded with a few wireless and wired
accelerometers attached on the railhead. The results
showed that the Gaussian process regressor performs
best, and as few as 20 frequencies can be used to
predict the RNT with sufficient accuracy.
KEYWORDS: machine learning, nondestructive evaluation,
continuous welded rails, feature extraction, rail neutral
temperature
Introduction
Continuous welded rail (CWR) refers to an uninterrupted
rail that is formed by many rails welded together to form one
continuous rail that may be several miles long. Structurally
speaking, CWR can be simplified as very long beams that
are in tension when the temperature of the rail is below the
so-called rail neutral temperature (RNT), and in compression
otherwise. On or above the RNT, the metal dilation induced by
a rise in temperature is counteracted by a compressive force
that may be significantly increased by an approaching train.
This scenario may lead to a buckle (called a sun kink in the
US), one of the most expensive causes of damage in the North
American rail network. When considered equivalent to an ideal
column, CWR buckles when the temperature TR of the rail
reaches the critical temperature Tcr, calculated as: ​ ​
(1)​ ​ ​ σ​cr​​
Eα ​
+​ TN​​ ​ =​ Tcr​​​​
where ​ ​
T​N​​​ is the RNT, ​ ​
σ​cr​​​ is the critical (Euler) stress of the rail, and
E and ​ ​ are the Young’s modulus and the coefficient of
thermal expansion of the steel, respectively.
As ​​ ​ cr​​​ E, and ​ ​ are known by design, the determination of
TN becomes relevant and can be obtained at any temperature
TR from the formula: ​ ​
(2)​ ​ TN​​ ​ =​ TR​​ ​ − ​ ​ σ​R​​
Eα ​ ​
where​​
σ​R​​​ is the longitudinal stress and is considered positive when
the rail is under compression.
In common practice, pretension is applied before welding
to compensate thermal expansion when a new rail segment
is laid. The level of prestress, and therefore the value of the
RNT, depends upon the geographic location of the site (i.e., by
the local climate history). However, operational maintenance
and stress relaxation decrease the designed RNT to unknown
values over time, increasing the risk of buckling. This calls for
nondestructive methods to measure ​​ ​ R​​​ and thus TN such that
slow orders or track closures can be issued properly. In current
practice, the desired accuracy for the estimation of the RNT is
±2.78 °C (or ±5 °F) (Zhu and Lanza di Scalea 2017).
NONDESTRUCTIVE ESTIMATION OF NEUTRAL
TEMPERATURE IN RAILS: A COMPARATIVE
STUDY OF MACHINE LEARNING STRATEGIES
MATTHEW BELDING*, ALIREZA ENSHAEIAN†, AND PIERVINCENZO RIZZO†‡
*Department of Electrical and Computer Engineering, University of Pittsburgh,
Pittsburgh, PA 15261
† Department of Civil and Environmental Engineering, University of Pittsburgh,
Pittsburgh, PA 15261
‡ pir3@pitt.edu 1-412-624-9575
Materials Evaluation 82 (1): 67–78
https://doi.org/10.32548/2024.me-04384
©2024 American Society for Nondestructive Testing
NDTTECHPAPER
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