Abstract
Optimal mass transport (OMT) is an optimization problem that determines a method of moving mass or value from one function to another in the most efficiently and optimally. Using the ideas of OMT, this technical note aims to formulate and solve an OMT model for railway track safety. The inputs for the analysis include (a) geometry data, (b) rail defect, (c) subsurface condition, and (d) tonnage. The technical note only presents the steps in achieving a complete OMT analysis. Therefore, the idea of the note is to serve as an illustration of the effectiveness of OMT in railway engineering applications.
References
1.
Zhang
,
J.
,
Zhang
,
W.
, and
Ma
,
P.
, 2021
, “
A Review on Modern Computational Optimal Transport Methods and Applications in Biomedical Research
,” arXiv:2008.0299V3.2.
Métivier
,
L.
,
Brossier
,
R.
,
Mérigot
,
Q.
,
Oudet
,
E.
, and
Virieux
,
J.
, 2016
, “
An Optimal Transport Approach for Seismic Tomography: Application to 3D Full Waveform Inversion
,” Inverse Probl.
,
32
(11
), p. 115008
.10.1088/0266-5611/32/11/1150083.
Kolouri
,
S.
,
Park
,
S. R.
,
Thorpe
,
M.
,
Slepcev
,
D.
, and
Rohde
,
G. K.
, 2017
, “
Optimal Mass Transport: Signal Processing and Machine Learning Applications
,” IEEE Signal Process. Mag.
,
34
(4
), pp. 43
–59
.10.1109/MSP.2017.26958014.
Palese
,
J. W.
,
Zarembski
,
A. M.
, and
Attoh-Okine
,
N. O.
, 2020
, “
Methods for Aligning Near Continuous Railway Track Inspection Data
,” Proc. Inst. Mech. Eng., Part F
,
234
, pp. 709
–721
.10.1177/09544097198607185.
Ndiaye
,
L.
,
Ndiaye
,
B. M.
,
Mendy
,
P.
, and
Seck
,
D.
, 2012
, “
Numerical Approach of Network Problems in Optimal Mass Transportation
,” Appl. Math.
,
3
(5
), pp. 457
–466
.10.4236/am.2012.350696.
Thingstad
,
S. W.
, 2020
, “
Interpolating Between Images Using Optimal Transport
,” Degree Project
,
KTH
,
Sweden
.https://www.diva-portal.org/smash/get/diva2:1441536/FULLTEXT01.pdf7.
Husic
,
A.
,
Fox
,
J.
,
Mahoney
,
T.
,
Gerlitz
,
M.
,
Pollock
,
E.
, and
Backus
,
J.
, 2020
, “
Optimal Transport for Assessing Nitrate Source Pathways Connectivity
,” Water Resour. Res.
,
15
(10
), p. 22
.10.1029/2020WR0274468.
Zarembski
,
A.
,
Einbinder
,
D.
, and
Attoh-Okine
,
N.
, 2016
, “
Using Multiple Adaptive Regression to Address the Impact Track Geometry on Development of Rail Defects
,” Constr. Build. Mater.
,
127
(30
), pp. 546
–555
.10.1016/j.conbuildmat.2016.10.0129.
Liu
,
X.
,
Lovett
,
A.
,
Dick
,
T.
,
Rapik Saat
,
M.
, and
Barkan
,
C. P. L.
, 2014
, “
Optimization of Ultrasonic Rail Defect Inspection for Improving Railway Transportation Safety and Efficiency
,” J. Transp. Eng.
,
140
(10
), p. 04014048
.10.1061/(ASCE)TE.1943-5436.000069710.
He
,
Q.
,
Li
,
H.
,
Bhattacharjya
,
D.
,
Parikh
,
D. P.
, and
Hampapur
,
A.
, 2015
, “
Track Geometry Defect Rectification Based on Track Deterioration Modeling and Derailment Risk Assessment
,” J. Oper. Res. Soc.
,
66
(3
), pp. 392
–404
.10.1057/jors.2014.711.
Silvast
,
M.
, 2010
, “
An Inspection of Railway Ballast Quality Using Ground Penetrating Radar in Finland
,” Proc. Inst. Mech. Eng., Part F
,
224
(5
), pp. 345
–351
.10.1243/09544097JRRT36712.
Lasisi
,
A.
, and
Attoh-Okine
,
N.
, 2018
, “
Principal Components Analysis and Track Quality Index: A Machine Learning Approach
,” Transp. Res. Part C: Emerg. Technol.
,
91
, pp. 230
–248
.10.1016/j.trc.2018.04.00113.
Zarembski
,
A.
, and
Palese
,
J.
, 2005
, “
Characterization of Broken Rail Risk for Freight and Passenger Railway Operations
,” AREMA Annual Conference
,
Chicago, IL
.14.
Stock
,
M.
,
Poisot
,
T.
, and
De Baets
,
B.
, 2021
, “
Optimal Transportation Theory for Species Interaction Networks
,” Ecol. Evol.
,
11
(9
), pp. 3841
–3855
.10.1002/ece3.725415.
Bonneel
,
N.
, 2015
, “
Optimal Transport for Computer Graphics and Temporal Coherence of Image Processing Algorithms
,” Habilitation dissertation
,
University of Lyon
,
France
.https://hal.science/tel-01935678
