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Statistical Modeling of Passenger Train Derailment Likelihood
at Level Crossings in the United States
Photo by Eric E. Johnson, used with permission
Samantha G. Chadwick
M. Rapik Saat
Christopher P. L. Barkan
Rail Transportation and Engineering Center
University of Illinois at Urbana-Champaign, USA
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Outline
•  Introduction
•  Objectives
•  Derailment Likelihood Factors
•  Passenger Train Model Development
•  Future Work
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Introduction
•  From 1991 to 2010, approximately 70,000 collisions occurred at highway-rail level
crossings in the United States
–  5,000 involved passenger trains
•  Such collisions have the potential to cause passenger casualties, in addition to train
crew casualties and property damage
•  A number of serious collisions have
occurred in recent years:
–  Valhalla, NY (6 fatalities)
–  Oxnard, CA (1 fatality)
–  Halifax, NC (no fatalities)
•  Interest from members of the
railway industry, government
officials, and academic researchers
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Level Crossing Safety
•  Research has focused on predicting collision likelihood in order to improve safety from
perspective of highway users
•  Little work has focused on the likelihood of train derailments occurring due to level
crossing incidents
–  Incidents resulting in derailment potentially more severe
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Project Objectives
•  Develop a modeling tool to predict the likelihood of a level crossing collision resulting in a
derailment
–  Both freight and passenger trains
–  Capable of combining with any collision likelihood model
•  Prioritize level crossing improvements based on hazards to both rail and highway users
–  Resources for highway-rail level crossing improvements are finite so it is desirable to
identify which crossings pose the greatest risk
–  Relative likelihood of catastrophic level-crossing-collision-caused derailments
compared to other sources of railroad and highway risk
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Data Sources
•  Data from three Federal Railroad Administration (FRA) databases
–  Rail Equipment Accident (REA) database
–  Highway Rail Accident (HRA) database
–  U.S. DOT Level Crossing Inventory History File (GCI)
•  Each provides different information needed for analysis
•  Model development: all U.S. railroads, 1991 through 2010
•  Validation: all U.S. railroads, 2011 through 2014
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Derailment Likelihood Factors
What factors affect
derailment likelihood?
vV: Highway vehicle speed
mV: Mass of highway vehicle
vT: Train speed
mT: Mass of train
α: Angle of collision
Incident type*
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Derailment Likelihood Factors
What factors affect
derailment likelihood?
vV: Highway vehicle speed
mV: Mass of highway vehicle
vT: Train speed
mT: Mass of train
α: Angle of collision
Incident type*
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Derailment Likelihood Factors
What factors affect
derailment likelihood?
vV: Highway vehicle speed
mV: Mass of highway vehicle
vT: Train speed
mT: Mass of train
α: Angle of collision
Incident type*
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Incident Type
Train Strikes
Vehicle
(TSV)
Vehicle Strikes
Train
(VST)
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Derailment Likelihood Factors
What factors affect
derailment likelihood?
vV: Highway vehicle speed
mV: Mass of highway vehicle
vT: Train speed
mT: Mass of train
α: Angle of collision
Incident type*
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Freight Analysis Conclusions
•  Critical factors
–  Highway vehicle size
•  Large vehicles more likely to cause derailments
–  Incident type
•  Different distributions for TSV vs. VST
–  Highway vehicle speed
•  Derailments more likely at higher speeds
–  Train speed
•  Derailments more likely at higher speeds
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Passenger Train Model Development
•  Likelihood of passenger train derailment is 70% greater than that of freight trains (1.2%
vs. 0.7% of incidents result in derailment)
–  Ironic since passenger safety often given greater consideration than freight
•  Despite the higher rate, level crossing-caused derailments involving passenger trains are
much less common
–  Fewer than 100 derailments in the past 30 years
•  Not possible to fit a good model using only passenger train data since some
combinations of factor levels only occurred in one or two incidents
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Passenger Train Model Development
•  What makes passenger trains different than freight trains that might be contributing to
increased rate?
–  Higher speed
–  Shorter train length
–  Rail vehicles (cars and sometimes locomotives) typically of lower mass
–  Differences in energy absorption due to equipment design, especially
crashworthiness standards
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Research Approach
•  Higher speed
–  Combining model solely on speed does not predict passenger derailments as well
as freight derailments
–  Explains some of the difference
•  Train length
–  May influence TSV incidents, does not appear to influence VST incidents
•  Lower rail vehicle mass
–  Actual mass (more difficult to test – requires new data)
–  “Weight class” based on rolling stock type
•  Energy absorption/structural behavior
–  FEM modeling (outside scope)
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Rail Vehicle Mass
•  Rail vehicle mass is not directly reported in any of the three FRA databases used so far
•  Reporting mark is recorded
–  Reporting mark: a unique number that identifies the rail vehicle and can be used to
find characteristic details from other sources
•  Rail vehicle weights are being sourced from locomotive registers, the Official Railway
Equipment Register (ORER), and the Universal Machine Language Equipment Register
(UMLER)
–  Process is time-consuming and may not provide better results
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Weight Class
•  Divide rail vehicles into weight classes based on type
–  Freight vs. passenger
–  Locomotive vs. rail car
•  Hypotheses:
–  Freight rail vehicles typically heavier than passenger
–  Locomotives typically heavier than rail cars
–  Would expect heavier rail vehicles to be less likely to derail
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SAS LOGISTIC Procedure and Rare Events
Logistic Regression (RELR)
•  Uses the method of maximum likelihood to fit a linear logistic regression model to
binary response data
•  However, if data has many more non-events than events, regression will produce poor
fit despite strong statistical relationships in the data
–  To obtain low overall error rate, model predicts non-events more correctly at the
expense of predicting events
•  To avoid this, RELR uses a random subset of non-events equal to 1-5 times the
number of events to develop the model
–  My model: 67% non-events, 33% events
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Model Adjustment
•  Produces a model that identifies the probability of a derailment having occurred as the
result of the subset of crossing collisions
•  Calibrate the model to accurately represent the probability of a derailment occurring in
the overall population, as derailment likelihood is overrepresented by the RELR model
–  “Retrospective” vs. “prospective” model (Dick et al., 2001)
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Regression Model Variables
Variable
Definition
VS
Highway Vehicle Speed
(mph)
Continuous
Range: 0-105 mph (0-169 kph)
Average: 10.50 mph (16.90 kph)
Standard Deviation: 13.57 (21.84 kph)
TS
Train Speed
(mph)
Continuous
LV
Large Highway Vehicle
Involved?
Binary
(Yes or No)
Range: 0-80 mph (0-129 kph)
Average: 31.45 mph (50.61 kph)
Standard Deviation*: 15.58 (25.07 kph)
Y if yes; N if no
EC
Equipment Class:
Freight or Passenger,
Rail Car or Locomotive
Categorical
Freight Rail Car (FC); Freight Locomotive (FL);
Passenger Rail Car (PC); Passenger
Locomotive (PL)
Binary
TSV if train struck highway user; VST if
highway user struck train
TRNSTK Incident Type:
Train Struck Vehicle or
Vehicle Struck Train
Variable
Type
Range of Values
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Combined Freight-Passenger Train Model – VST
•  Where VS is highway vehicle speed, LV indicates the highway vehicle was a truck, and
EC is equipment class
•  The probability of derailment given an incident, 𝑝(𝐷|𝐼) increases:
•  As vehicle speed increases
•  If a large highway vehicle is involved
•  𝑝(𝐷|𝐼) varies with equipment class
•  Passenger car
More likely to derail
•  Freight car
•  Passenger locomotive
•  Freight locomotive
Less likely to derail
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Future Work
•  Develop the freight-passenger model for TSV incidents
•  Combine VST and TSV models using prior probabilities of incident type to give an
overall level crossing derailment model
•  Integrate into a single derailment calculator to evaluate risk of level crossing-caused
derailment at any crossing
–  Consider the ratio of freight to passenger train traffic
•  Typical distribution of train types and rail vehicle weights at a crossing can be used to
combine derailment models
•  Ratios may depend on variance in speed and length of passenger and freight trains
–  Passenger trains are shorter and faster than freight trains so occupy the crossing
for a shorter period of time
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Expected Impact
–  Serve as a ranking tool for transportation agencies trying
to determine which level crossings to upgrade warning
systems or eliminate using available funds
•  Crossings may have similar incident likelihoods, but
prioritization could be further refined using derailment
consequence
•  For high-risk crossings, justification for crossing
closure
–  Put in perspective the relative likelihood of catastrophic
grade-crossing-collision-caused derailments compared to
other sources of railroad and highway risk
•  Expected number of lives lost in level-crossing-caused
derailments vs. level crossing collisions generally
•  Cost-benefit analysis of safety programs
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Acknowledgements
•  Eisenhower Transportation Fellowship Program
•  CN Graduate Research Fellowship in Railroad Engineering
•  RailTEC: Tyler Dick, Sam Sogin, Xiang Liu, Laura Ghosh,
Jesus Aguilar Serrano, Lijun Zhang
•  Illinois Commerce Commission: Steve Laffey
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Thank you!
Questions?
Samantha G. Chadwick, EIT
Graduate Research Assistant, RailTEC
University of Illinois at Urbana-Champaign
[email protected]