DOT/FRA/ORD-23/37 Final Report | September 2023 

Development of a Bayesian Network Based Accident 

Model for Hazmat Unit Trains

i 

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1. REPORT DATE

May 2022

2. REPORT TYPE

Technical Report

3. DATES COVERED (From - To)

August 2019 – May 2022

4. TITLE AND SUBTITLE

Development of a Bayesian Network-Based Accident Model for Hazardous Material Trains

5a. CONTRACT NUMBER

693JJ619C000016

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Peter Johnson – ORCID: 0000-0002-2586-6009

Mahesh Raju Bailakanavar – ORCID: 0000-0002-8537-1673

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Thornton Tomasetti

120 Broadway 15th Floor

New York

NY 10271

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REPORT NUMBER

NN19210-R01

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

U.S. Department of Transportation

Federal Railroad Administration

Office of Railroad Policy and Development

Office of Research, Development, and Technology

Washington, DC 20590

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NUMBER(S)

DOT/FRA/ORD-23/37

12. DISTRIBUTION/AVAILABILITY STATEMENT

This document is available to the public through the FRA website. 

13. SUPPLEMENTARY NOTES

COR: Francisco González, III 

14. ABSTRACT

The objective of this research project was to develop a predictive risk model for the release of hazardous material transported in unit trains using data 

science techniques for available rail accident and traffic data. This work builds upon previous research (Bing, et al., 2015) which examined the causal 

sequence of events which can lead to a rail accident and used historical accident record and rail traffic data to define conditional probabilities of occurrence 

and thereby predict the risk of a hazmat release. Three different Bayesian Networks (BNs) were implemented to study the causal relationships between 

weather, track, and train related risk factors and the primary causes leading to railroad accidents. The BN-based accident model has demonstrated 

potential to accurately predict the accident cause, given information about the train and track.

15. SUBJECT TERMS: Risk analysis, unit trains, hazmat

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 

ABSTRACT

18. NUMBER 

OF 

PAGES

48

19a. NAME OF RESPONSIBLE PERSON

Francisco González, III a. REPORT b. ABSTRACT c. THIS PAGE

19b. TELEPHONE NUMBER (Include area code)

202-493-6076

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=

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1 gallon (gal) = 3.8 liters (l)

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Centimeters 0 1 2 3 4 5 6 987 1110 1312

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iii

Contents

Executive Summary ........................................................................................................................ 1

1. Introduction ................................................................................................................. 3

1.1 Background ................................................................................................................. 3

1.2 Objectives .................................................................................................................... 5

1.3 Overall Approach ........................................................................................................ 5

1.4 Scope ........................................................................................................................... 5

1.5 Organization of the Report .......................................................................................... 5

2. Data Review ................................................................................................................ 6

2.1 RAIRS Accident Database .......................................................................................... 6

2.2 Traffic Data ................................................................................................................. 8

2.3 Data Review Discussion .............................................................................................. 9

3. Bayesian Network Based Rail Accident Model ........................................................ 11

3.1 Bayesian Networks .................................................................................................... 11

3.2 RAIRS Accident Data Sorting .................................................................................. 11

3.3 Railroad Accident Causes and Risk Factors Identification ....................................... 13

3.4 Risk Factors - Continuous to Categorical Data Conversion ...................................... 19

3.5 Bayesian Network-based Railroad Accident Risk Model Implementation ............... 24

3.6 Bayesian Network Validation ................................................................................... 32

4. Conclusions and Recommendations .......................................................................... 34

4.1 Conclusions ............................................................................................................... 34

4.2 Recommendations ..................................................................................................... 35

5. References ................................................................................................................. 36

Appendix A. Class I Unit Train Definitions ................................................................................. 38
iv

Illustrations

Figure 1. Timeline of Crude Oil and Ethanol Railroad Accidents in the U.S. 2009-2018 ............. 3

Figure 2. Trend of Accident Records from 1975 to 2018 Showing Primary Accident Cause 

Group ...................................................................................................................................... 6

Figure 3. RAIRS Freight Train Accidents and Hazmat Cars Releasing on Main Track, 2009-2018

............................................................................................................................................... 12

Figure 4. Distribution of Accidents by Railroad Type ................................................................. 12

Figure 5. Distribution of Accidents by FRA Track Class ............................................................. 12

Figure 6. Illustration of the Accident Cause Groups .................................................................... 14

Figure 7. Accident Counts for Categories Under T, M, & H Cause Groups ................................ 15

Figure 8. Consequence/Risk for Categories Under T, M, & H Cause Groups ............................. 16

Figure 9. Accident Count vs. Consequence for Categories Under T, M, & H Cause Groups ...... 16

Figure 10. Distribution of Sort-C Accidents Across Cause Groups (Bing, 2015) ........................ 17

Figure 11. Illustration of a Decision Tree (Source: https://www.diagrams.net/) .......................... 18

Figure 12. Distribution of Accidents Across Train Speed (TRNSPD) Categories ....................... 20

Figure 13. Distribution of Accident Categories Across Weather (WEATHER) Categories ........ 20

Figure 14. Distribution of Accidents Across Temperature (TEMP) Categories .......................... 21

Figure 15. Distribution of Accidents Across Visibility (VISIBLTY) Categories ........................ 22

Figure 16. Distribution of Accidents Across Number of Loaded Freight Cars (LOADF1) 

Categories ............................................................................................................................. 22

Figure 17. Distribution of Accidents Across Total Number of Cars (TOTALF1) Categories ..... 23

Figure 18. Distribution of Accidents Across Gross Tons (TONS) Categories ............................. 23

Figure 19. Distribution of Accidents Across Track Density in MGT (TRKDNSTY) Categories 24

Figure 20. BN for Weather and Climate Risk Factors .................................................................. 26

Figure 21. Marginal Probabilities for Weather and Climate Factors BN Fitted to the Sort C 

Accident Data (Derailment and Track Related Defects Only) ............................................. 26

Figure 22. Sensitivity Analysis for Temperature - Plot of Accident Cause Group Probabilities 

Across Temperature Categories ............................................................................................ 27

Figure 23. BN for Track Class and Track Annual Density........................................................... 28

Figure 24. Marginal Probabilities for Track Class and Track Density BN Fitted to the Sort C 

Accident Data (Derailment and Track Related Defects Only) ............................................. 28

Figure 25. Sensitivity Analysis for Track Class - Plot of Accident Cause Group Probabilities 

Across Track Classes ............................................................................................................ 29

Figure 26. BN for Gross Tonnage and Number of Freight Cars .................................................. 30
v 

Figure 27. Marginal Probabilities for Tonnage and Freight Cars BN Fitted to the Sort C Accident 

Data (Derailment and Track Related Defects Only) ............................................................. 30

Figure 28. Sensitivity Analysis for Railroad Companies - Plot of Accident Cause Group 

Probabilities Across Four Railroad Companies .................................................................... 31

Figure 29. Unified BN for Rail Operations, Tonnage, and Composition ..................................... 32
vi 

Tables

Table 1. List of Crude Oil and Ethanol Railroad Accidents in the U.S., 2009-2018 ...................... 4

Table 2. Entries in RAIRS Database for the Four Sorting Groups, 2009-2018.............................. 7

Table 3. Sort C Accidents Breakdown by Accident Type ............................................................ 13

Table 4. Accident Cause Groups .................................................................................................. 14

Table 5. Distribution of accident causes across the four accident data sorts ................................ 14

Table 6. Top-2 Categories for Track, Roadbed, and Structures (T) Cause Group ....................... 17

Table 7. Top-2 Categories for Mechanical and Electrical Failures (M) Cause Group ................. 17

Table 8. Top-2 Categories for Train Operations-Human Error (H) Cause Group ........................ 17

Table 9. Top Five Factors Affecting Track, Roadbed, and Structures (T) and Mechanical and 

Electrical Failures (M) .......................................................................................................... 19

Table 10. Top Five Factors Affecting Train Operations – Human Factors (H) ........................... 19

Table 11. Train Speed (TRNSPD) Categories .............................................................................. 19

Table 12. Weather Categories ....................................................................................................... 20

Table 13. Temperature (TEMP) Categories.................................................................................. 21

Table 14. Visibility Categories ..................................................................................................... 21

Table 15. Number of Loaded Freight Cars (LOADF1) Categories .............................................. 22

Table 16. Total Number Of Cars (TOTALF1) Categories ........................................................... 23

Table 17. Gross Tons (TONS) Categories .................................................................................... 23

Table 18. Track Density (TRKDNSTY) Categories..................................................................... 24

Table 19. Accident Cause Group Predictions for Specific Weather and Visibility Conditions ... 27

Table 20. Accident Cause Group Predictions for Railroad Company-A ...................................... 29

Table 21: Accident Cause Group Predictions for Railroad Company-A ...................................... 31

Table 22. Verification Results ...................................................................................................... 33

Table 23. Train Number Prefix Definitions – Unit Trains ............................................................ 38

Table 24. Class I Railroads and Subsidiary Company – Acronyms RAIRS ................................ 39

Table 25. Unit Train Definitions as Provided by Railroads.......................................................... 39
1 

Executive Summary

The Federal Railroad Administration (FRA) contracted with Thornton Tomasetti to develop a 

predictive risk model for the release of hazardous material (hazmat) transported in unit trains 

using data science techniques and available rail accident and traffic data. The research was 

coordinated by Thornton Tomasetti from their New York offices between August 2019 and May 

2022. This work builds upon previous research (Bing, et al., 2015) which examined the causal 

sequence of events that can lead to a rail accident. Researchers used historical accident record 

and rail traffic data to define conditional probabilities of occurrence and predict the risk of a 

hazmat release. 

The research team reviewed accident and traffic data sources to inform the development of a risk 

model for hazmat transportation by rail. Due to the limitations of the available traffic data, the 

team decided to focus research on building a Bayesian-based accident model using data from 

FRA’s Railroad Accident/Incident Reporting System (RAIRS). 

The most detailed traffic data, the Surface Transportation Board (STB) Confidential Carload 

Waybill Samples (CCWS), provides information about car and commodity movements, but does 

not provide information about the train in which the car was transported, limiting its use in the 

research. Other traffic data reviewed, such as Class I railroad R-1 reports (Surface Transportation 

Board, 2021a) and the Association of American Railroads (AAR)’s Ten-Year Trends

(Association of American Railroads, 2020), provide annual statistics on freight transport, 

including unit train miles, but do not distinguish hazmat unit trains from non-hazmat unit trains. 

Consequently, the research team was unable to calculate risk, even in simple terms of accident 

likelihood per unit distance travelled by hazmat unit train versus hazmat manifest train. 

Therefore, researchers focused on building a predictive model based solely on the RAIRS 

accident data. The objective of the model was to predict the cause of an accident from

information about the accident, based on trends and associations derived from 10 years of 

historical accident records. The trends and associations derived from the accident data may then 

indicate differences in unit train accidents compared to manifest trains and provide information 

about the relative risk of hazmat transportation. 

The research team implemented three different Bayesian Networks (BNs) to study the causal 

relationships between weather, track, and train related risk factors and the primary causes leading 

to railroad accidents. These primary causes were selected based on the risk/consequences they 

posed and were then categorized in groups developed by Bing et al. (Bing et al., 2015). The team 

used a random forest algorithm to select the risk factors in continuous data form and then convert

them into discrete categories by studying their distributions. Researchers demonstrated the 

capabilities of the BN-based accident risk model (e.g., predictive analytics, sensitivity analysis, 

and estimation of marginal and joint probability distributions) by implementing of the three 

separate BNs for weather, track, and train related factors. The final network integrated the train 

and track networks into one single network and included a variable for train type (i.e., unit train). 

The team identified hazmat unit trains in the RAIRS database based on the number of hazmat 

cars (≥70) and the number of buffer cars (≤5). 

After reviewing the model predictions, the team found that train type did not have significant 

influence on the predicted accident cause, likely due to the limited scope of the current model. 

This model is built upon a subset of data comprising hazmat freight trains travelling on main 
2 

track where a derailment occurred and the cause was one of four specific cause groups: Wide 

Gauge (03T), Track Geometry (04T), Buckled Track (05T), Broken Rail, or Welds (08T). This 

limits the number of unit train accidents in the data set, which consequently limits the ability to 

identify differences in accident properties. 

Researchers used accident data from the year 2019 and 2020 to validate the integrated BN and

applied data filters used for developing the Sort-C1 on this data; in total, 24 accidents were 

selected. An important aspect of the validation is that the BN had not seen this data previously. 

The risk factors from the 24 accidents were provided as inputs to the BN and the network was 

tasked to make blind predictions on the cause for these accidents. The integrated network 

predicted with 100 percent accuracy for accident cause groups 03T and 08T and 79 percent

accuracy for 04T. The lower accuracy for cause group 05T is attributed to the small amount of 

training data in Sort-C1. However, the overall accuracy of the network predictions was about 79 

percent, which appears promising. Increasing the training data pool (i.e., Sort C1) is expected to 

improve this accuracy of the network. 

Improvements in accident and traffic data collection are required to aid future research on the 

risk of hazmat transportation by unit train. The team recommends a new field be added to the 

FRA RAIRS database, indicating whether the train is a unit train. However, since researchers 

observed significant variation in how a unit train is defined, such a change would require 

adoption of a standard definition of a unit train. 

It may not be feasible to collect the level of information required to fully incorporate traffic data 

into the architecture of the Bayesian-based accident model, even in a geographically limited 

model. This would require that all successful train journeys over a given period be added into the 

database alongside those which ended in an accident. However, for more traditional statistical 

methods, improvements could be made to identifying hazmat unit train traffic. Schedule 755 of 

the R-1 reports (i.e., Railroad Operating Statistics) submitted annually to the STB (Surface 

Transportation Board, 2021a) includes data on total train-miles and car-miles by train type, 

including unit trains. Therefore, the team recommends that the collection of railroad operating 

statistics be expanded to provide total train-miles and car-miles by train type transporting 

hazmat.

The BN-based accident model has demonstrated potential to accurately predict accident cause

when provided with information about the train and track. The team recommends further 

development of the model’s capabilities by the incorporation of additional cause groups (e.g., 

mechanical, electrical, and human causes) and the inclusion of track maintenance inspection and 

repair data, which could enhance causal relationship learning. 
3 

1. Introduction

The Federal Railroad Administration (FRA) contracted with Thornton Tomasetti to develop a 

predictive risk model for the release of hazardous material (hazmat) transported in unit trains 

using data science techniques and available rail accident and traffic data. The research was 

coordinated by Thornton Tomasetti from their New York offices between August 2019 and May 

2022. 

1.1 Background

Freight railroads continually strive to increase their productivity by transporting greater amounts 

of goods in the shortest amount of time. Consequently, average axle loads and train speeds have 

tended to increase over time. Freight railroads also boost their productivity by operating unit 

trains. A unit train is a train transporting the same commodity from the same origin to the same 

destination. Railroads operate unit trains to increase efficiency and productivity by reducing 

costs, employing bulk loading, improving asset utilization, and reducing transit time. The use of 

unit trains began to be prevalent in the 1950s to transport large shipments of coal. By the end of 

the 1960s, approximately 90 percent of all coal traffic on U.S. railroads was transported via unit 

trains (Starr, 1976). Railroads now operate unit trains for bulk shipments of commodities such as 

iron ore; corn, wheat, and grain; sand and gravel; garbage and liquid sludge; automobiles; steel 

billets; citrus fruits and vegetables; and hazardous materials. However, the risk of using unit 

trains to transport hazmat has come under scrutiny after several recent railroad hazmat accidents. 

Figure 1 shows a timeline of railroad accidents in the U.S. involving the release of crude oil and 

ethanol between 2009 and 2018.1

Table 1 lists the accident date, accident location, commodity released, and whether a unit train 

was involved. The table links to National Transportation Safety Board (NTSB) accident reports. 

Figure 1. Timeline of Crude Oil and Ethanol Railroad Accidents in the U.S. 2009-2018 

1 This ten-year period was the targeted timeframe for the current project. It should be noted that several accidents 

involving the release of crude oil occurred in Canada during this timeframe, including one of the deadliest in 

Canadian railroad history (Lac-Mégantic, Quebec on July 6, 2013). 
4 

Table 1. List of Crude Oil and Ethanol Railroad Accidents in the U.S., 2009-2018 

Date Location Hazmat Unit Train 

(Y/N)

NTSB Report 

No.

June 19, 2009 Cherry Valley, IL Ethanol Y RAR1201

February 6, 2011 Arcadia, OH Ethanol Y - 

October 7, 2011 Tiskilwa, IL Ethanol N - 

July 11, 2012 Columbus, OH Ethanol N RAB1302

August 5, 2012 Plevna, MT Ethanol N 

March 27, 2013 Parkers Prairie, MN Crude Oil N RAB1408

May 20, 2013 Bassett, IA Ethanol Y - 

November 7, 2013 Aliceville, AL Crude Oil Y - 

December 30, 2013 Casselton, ND Crude Oil Y - 

January 31, 2014 New Augusta, MS Crude Oil N - 

February 23, 2014 Vandergrift, PA Crude Oil N - 

April 30, 2014 Lynchburg, VA Crude Oil Y RAB1701

May 9, 2014 LaSalle, CO Crude Oil Y - 

February 4, 2015 Sherrill, IA Ethanol Y - 

February 16, 2015 Mount Carbon, WV Crude Oil Y - 

March 5, 2015 Galena, IL Crude Oil Y RAB1601

May 6, 2015 Heimdal, ND Crude Oil Y - 

July 11, 2015 Alma, WI Ethanol N - 

July 16, 2015 Culbertson, MT Crude Oil Y - 

September 19, 2015 Lesterville, SD Ethanol Y - 

November 7, 2015 Watertown, WI Crude Oil Y - 

June 3, 2016 Mosier, OR Crude Oil Y RAB1712

March 10, 2017 Graettinger, IA Ethanol Y - 

April 20, 2017 Money, MS Crude Oil N - 

June 30, 2017 Plainfield, IL Crude Oil Y - 

June 22, 2018 Doon, IA Crude Oil Y RAB1707
5 

Bing et al. (2015) examined Railroad Accident/Incident Reporting System (RAIRS) data for a 

five-year period between 2004 and 2008 (inclusive) to study the causes of freight train accidents 

and derailed freight cars. The use of unit trains to transport hazmat was not included in this study 

but was recommended for future research.

Since this time, research has been conducted to examine the risk of operating unit trains (Liu, 

2017) (Li et al., 2018). Li et al. (2018) studied the 15-year period between 2001 and 2015. 

However, the focus of this study was to characterize the common modes of derailment for empty 

and fully loaded unit tank cars. 

1.2 Objectives

The objective of this research project was to develop a predictive risk model for the release of 

hazardous material transported in unit trains using data science techniques for available rail 

accident and traffic data.

1.3 Overall Approach

This work builds upon previous research (Bing et al., 2015) which examined the causal sequence 

of events which can lead to a rail accident. Researchers used historical accident record and rail 

traffic data to define conditional probabilities of occurrence and thereby predict the risk of a 

hazmat release. The team used available data collected by FRA, railroads, and track inspection 

service providers on accidents, rail traffic, and track condition. Researchers used artificial neural 

networks and data science approaches to identify predictable patterns, with a particular focus on

unit train accidents. These patterns and the process of their identification provided a foundation 

for accident prediction and were incorporated into a predictive model for hazmat release. 

1.4 Scope

The scope of the research was limited to transportation of hazardous goods via freight train in the 

United States, excluding all other train traffic, analyzed using artificial neural networks and data 

science approaches. The team used accident data from FRA's RAIRS and obtained detailed 

traffic data from the Surface Transportation Bureau (STB)’s Confidential Carload Waybill 

Samples (CCWS) (Surface Transportation Board, 2021b), summary data from STB R-1 annual 

reports (Surface Transportation Board, 2021a), and the Association of American Railroads 

(AAR) Ten-Year Trends report (Association of American Railroads, 2020). 

1.5 Organization of the Report

Section 2 describes the data reviewed for the research. Section 3 describes the development and 

verification of the Bayesian-based accident model. Section 4 presents conclusions and 

recommendations. 
6 

2. Data Review

The objective of the research was to understand the relative risk of transporting hazmat by unit 

train versus manifest train. In the context of train accidents, risk is expressed as a likelihood of 

an accident per unit distance travelled by a train, typically expressed in miles. This requires 

information on accidents (i.e., the numerator) and rail traffic (i.e., the denominator). A method is 

required to identify hazmat unit trains and hazmat manifest trains in both accident data and rail 

traffic data.

The following section provides an overview of the data reviewed for this research and how it was

used to meet the central objective of the study. 

2.1 RAIRS Accident Database

2.1.1 Overview

FRA's RAIRS includes a database of accident records comprising 200,000 accidents between 

1975 and 2018. For the development of a predicative model, a date range must be selected, and 

recent data was considered preferable since it is representative of current standards.

The team performed an initial review of the accident data and found a significant variation in 

accident number and cause group since 1975, showing an overall trend of a decrease in the 

number of accidents per year (Figure 2). In the years 2009-2018 (inclusive), the number and 

causes of accidents has been relatively consistent; therefore, this date range was chosen for the 

model. 

Figure 2. Trend of Accident Records from 1975 to 2018 Showing Primary Accident Cause 

Group
7 

2.1.2 Accident Data Filtering 

The RAIRS database was sorted into several subsets for use in the analysis, filtered down to the 

group containing those in which hazmat unit trains were found. 

• Sort-A = All accident entries from 2009-2018 

• Sort-B = Sort-A and the train must contain a hazmat car (i.e., CARS > 0)

• Sort-C = Sort-B and must comprise a freight train on main track (i.e., TYPEQ = 1 and 

TYPTRK = 1)

• Sort-D = Sort-C and a hazmat car released product (i.e., CARSHZD > 0) 

The number of accident entries in RAIRS for each sorting group is listed in Table 2, where each 

entry refers to a train involved in an accident. For multiple trains involved in a single accident, 

there is an entry for each train.

For comparison of unit trains versus manifest trains carrying hazmat, Sort-C is the most relevant. 

Sort-C filters out trains that are not carrying hazmat and accidents on track types that are not 

typically used by unit trains of any type. 

Table 2. Entries in RAIRS Database for the Four Sorting Groups, 2009-2018 

Year Sort-A Sort-B Sort-C Sort-D

2009 2,597 609 180 12

2010 2,641 621 192 13

2011 2,748 662 216 8 

2012 2,429 599 167 22

2013 2,497 603 202 14

2014 2,280 539 179 12

2015 2,553 553 154 14

2016 2,309 477 159 7

2017 2,403 526 184 9

2018 2,563 522 183 8

Total 25,020 5,711 1,816 119

It should be noted that the statistical methods proposed for this research are best suited to 

datasets several orders of magnitude larger than the Sort C group (i.e., the 2009-2018 date range, 

or 1,816). While this limitation was noted, the team decided to proceed with this date range for 

initial research and then once the model was completed, conduct a model validation exercise to 

show the accuracy of the model and determine whether there was justification to increase the 

date range.

2.1.3 Identification of Unit Trains

The RAIRS data fields do not include an indicator for accidents involving a hazmat unit train, 

nor does it include fields from which one can directly infer whether the train is carrying a single 

commodity or whether all cars are transported from a single origin to a single destination. 

Furthermore, while a general definition of a unit train is well understood, several different 
8 

hazmat unit train definitions were identified. A combination of these were ultimately used to 

arrive at working definition of a hazmat unit train and this was applied to the RAIRS Sort C data. 

The initial approach taken to identify hazmat unit trains in the RAIRS database included review 

of each of the accident narratives in the Sort D dataset (i.e., 119 entries) to identify those where 

hazmat unit trains were recorded as involved in the accident event, relying primarily on 

information provided in NTSB accident reports and news reports. This review identified a total 

of 23 hazmat unit trains in the Sort D dataset. A review of the trains’ common characteristics 

showed that they were typically comprised of many cars, ranging between 61 and 116 cars in 

total. Also, all 23 trains were almost entirely comprised of loaded hazmat freight cars, and the 

number of buffer cars (i.e., cars which were recorded as not carrying hazmat) ranged between 1 

and 3. Consequently, review indicated that both train length and number of buffer cars could be 

used to identify unit trains in the RAIRS database. 

Researchers ultimately used the unit train definition provided in Title 49 (Transportation) of the 

Code of Federal Regulations (CFR)2

 to identify unit trains. This describes a High-Hazard 

Flammable Unit Train (HHFUT) as “a single train transporting 70 or more loaded tank cars 

containing Class 3 flammable liquid.” Using this description to analyze the Sort D dataset, “≥70 

cars” was determined to be an appropriate ruleset for identifying a unit train in the RAIRS 

database.

NTSB safety recommendation report R-17-01 (National Transportation Safety Board, 2020)

recommended “positioning placarded railcars in a train and require that all trains have a 

minimum of five non-placarded cars between any locomotive or occupied equipment and the 

nearest placarded car transporting hazardous materials, regardless of train length and consist.”

Therefore, trains ≥70 cars in length and containing ≤5 buffer cars were flagged as unit trains in 

the RAIRS database. 

In summary, for the Sort C RAIRS dataset, which comprises freight trains on main track 

transporting hazmat, the following filters were applied to the RAIRS database to identify unit 

trains: 

• (Total number of cars) – (Loaded hazmat cars + empty hazmat cars) <= 5 

• (Total number of cars) >= 70 

Further information on train type was obtained for Class I railroads and their subsidiaries. Of the 

1,816 records in the Sort C dataset, 1,594 (88 percent) included trains operated by Class I 

railroads or their subsidiaries. These definitions were not used as a general ruleset, serving 

instead as a verification of the adopted ruleset. A summary of unit train definitions obtained for 

Class I railroads is provided in Appendix A. 

2.2 Traffic Data

2.2.1 STB Confidential Carload Waybill Samples (CCWS)

The CCWS is collated by STB. It is a stratified sample of carload waybills for all U.S. rail traffic 

submitted by those rail carriers terminating 4,500 or more revenue carloads annually (Surface 

2 Code of Federal Regulations (CFR), Title 49 (Transportation), Subtitle B, Chapter I, Subchapter C, Part 171, 

Subpart A, Section 171.8 – Definitions and abbreviations
9 

Transportation Board, 2021b). Upon request, STB provided confidential carload waybill samples 

from 2009-2018 (inclusive), in line with the range of accident data considered, to assist with the 

research. 

Each line of the database describes the movement of a carload, including details on origin, 

destination, material transported, and date transported. However, the data is limited in that it does 

not provide any information on the train with which any individual car was transported. This 

information cannot be determined by using common dates, origins, and destinations to try to 

reconstruct a theoretical train; because the dates are from accounting data and not operational 

data, the carload may not have moved on the same day. Therefore, there is no means of 

identifying historical traffic by train type using the CCWS data, and no means of discerning 

relative risk for transporting hazmat by unit train or manifest train. 

2.2.2 Summary Reports

All Class I railroads are required to submit annual R-1 reports to the STB, which are made 

available to the public via the STB website (Surface Transportation Board, 2021a). These reports 

provide data on total train miles and car miles for unit trains and manifest trains (Subsection 

“Schedule 755 – Railroad Operating Statistics”). Similarly, AAR’s Ten-Year Trends 

(Association of American Railroads, 2020) provides annual statistical summaries of rail 

transportation derived from various STB annual reports. However, neither of these sources 

provide a breakdown of hazmat transportation by unit train or manifest train. 

2.3 Data Review Discussion

The team reviewed both accident data and traffic data sources to assist in the development of a 

risk model for hazmat transportation by rail. However, due to the limitations of the available 

traffic data, researchers decided to build a model using only RAIRS accident data. 

One of the constraints of the research was determining how to apply a consistent analytical 

method to accident and traffic datasets, which necessarily contain different information. For 

example, each row of the RAIRS database contains information about a train which was 

involved in an accident, with each column describing some feature of the train or the accident. 

Using this information, the team proposed a model which could predict the cause of an accident 

given information about the accident, based on trends and associations derived from 10 years of 

historical accident records. The trends and associations derived from the accident data may then 

indicate differences in unit train accidents compared to manifest trains when analyzing the 

relative risk of hazmat transportation.

Using only the RAIRS database, this model would not be able to calculate risk (i.e., the 

likelihood of an accident per unit distance travelled by unit train or manifest train). This requires 

information on overall traffic to contextualize the number of accidents for hazmat unit trains and 

hazmat manifest trains. To include traffic data, the RAIRS data would have to be supplemented 

with additional entries as rows in the dataset, where each entry describes a successful journey 

with equivalent data regarding the train and journey (e.g., train makeup, origin, destination, etc.) 

in each column. The STB CCWS data is the most detailed traffic information available, but it is 

limited in that it represents only a sample of journeys and does not provide information about the 

train in which the car travelled in. The former issue could be addressed by scaling the number of 

entries in the augmented RAIRS database based on the sampling rate used in the STB CCWS. 

However, the latter cannot be surmounted, as each entry in the augmented RAIRS database 
10 

would represent a train, and there is no way to link the cars recorded in the STB CCWS to a train 

or determine whether it was transported by unit train or a manifest train.

Other traffic data sources covering 2009-2018, such as R-1 reports and AAR’s Ten-Year Trends 

(Association of American Railroads, 2020), provide only annual statistical summaries of Class I

railroad train traffic and could not be incorporated into the RAIRS-based model due to a lack of 

detail on individual train movements. These data sources provide annual traffic statistics in terms 

of train miles and car miles for all freight train traffic and unit train traffic, so the team 

investigated whether a simple statistical risk calculation could be conducted to determine the 

accident frequency per mile travelled by the average hazmat unit train and compare this with the 

accident frequency for the average hazmat manifest train. However, neither the R-1 reports nor 

AAR’s Ten-Year Trends (Association of American Railroads, 2020) provide information on 

whether the unit trains are hazmat unit trains.

In summary, after a review of available data, the team concluded that the central objective of the 

research could not be met because it required more detailed information, particularly on hazmat 

unit train traffic. Therefore, the primary focus of the research became the development of a 

Bayesian-based accident model, based on RAIRS data between 2009-2018, as described in the 

following section. 
11 

3. Bayesian Network Based Rail Accident Model

3.1 Bayesian Networks

Bayesian Networks (BNs) are directed acyclic graphs (DAGs) consisting of nodes representing 

random variables and arrows that correspond to the probabilistic cause-effect (i.e., parent-child) 

relationship between the random variables. BNs are versatile; the lines between boxes are 

agnostic to the method of characterization and robust enough to handle small and incomplete 

data sets. Statistical or computational methods are used to estimate the conditional dependencies 

between the random variables. BNs are powerful tools for knowledge representation, reasoning, 

and modeling the causal relationships of a given effect. BNs allow for integrating historical data 

with a subject matter expert (SME)’s knowledge to visually show the probabilistic relationships 

among a set of random variables. 

BNs have been used extensively for casual relationship modeling, risk assessment, decision 

making, and uncertainty quantification across industry sectors. They have been used in medical 

diagnostics (Heckerman et al., 1995), environmental modeling (Uusitalo, 2007), civil 

engineering and construction management risk analysis (Fan & Yu, 2004; Luu et al., 2009) 

(Zhang et al., 2014), structural health monitoring (Zhang et al., 2016), and accident risk analysis 

(Cheng et al., 2010; Hänninen, 2014; Camino López et al., 2008; Martín et al., 2009). 

In this research, the BN model was implemented to establish the probabilistic cause and effect 

relationship between railroad accidents and various contributing factors, and to model any 

interdependencies that exist between the causal factors themselves. It is important to note that the 

accident cause descriptor used in the RAIRS database (i.e., CAUSE and CAUSE2 columns) is

the end effect and the rest of the 143 parameters recorded post-accident are considered causal

factors. There are five key stages to the implementation of the BN-based accident model as set 

out below: 

1. RAIRS Accident Data Sorting 

2. Railroad Accident Causes and Risk Factors Identification 

3. Risk Factors – Continuous to Categorical Data Conversion 

4. BN-based Railroad Accident Risk Model Implementation 

5. Railroad Accident Risk Model Validation 

3.2 RAIRS Accident Data Sorting

3.2.1 Accident Statistics

This section discusses the accident statistics derived from the Sort-C and Sort-D data and the 

trends observed. 

Figure 3 shows the number of train accidents and the number of hazmat cars releasing hazmat for 

each year between 2009 and 2018. Over this period, a total of 388 cars released hazmat in 119 

freight train accidents. While the total number of hazmat cars releasing each year fluctuated over 

this time span, the number of accidents per year was relatively constant except for a spike in 

2012. The breakdown of the accidents by railroad type and track class for Sort-C and Sort-D is 
12 

shown in Figure 4 and Figure 5, respectively. The figures show that most of the Class I railroad 

accidents occurred on Class-4 track, followed by Class-3 and Class-2 track. 

Figure 3. RAIRS Freight Train Accidents and Hazmat Cars Releasing on Main Track, 

2009-2018 

Figure 4. Distribution of Accidents by Railroad Type 

Figure 5. Distribution of Accidents by FRA Track Class 
13 

A breakdown of the Sort-C accident data by accident type is shown in Table 3. Approximately 

60 percent of the accidents in Sort-C are derailment type accidents followed by highway rail 

crossing at 26 percent. 

Table 3. Sort C Accidents Breakdown by Accident Type

Accident Type Code Accident Type Description Sort C Count Sort C %

1 Derailment 1073 59%

7 Highway Rail Crossing 470 26%

13 Other 64 4%

9 Obstruction 58 3%

3 Rear End Collision 42 2%

11 Fire/Violent Eruption 39 2%

4 Side Collision 21 1%

12 Other Impacts 18 1%

5 Raking Collision 12 1%

2 Head On Collision 10 1%

6 Broken Train Collision 5 0%

8 Railroad Grade Crossing 3 0%

10 Explosive Detonation 1 0%

Total 1816

3.3 Railroad Accident Causes and Risk Factors Identification

The following terminologies are used in the discussion of the implementation of the BN for rail 

accident risk analysis. 

Risk Factors, also referred to as Causal Factors, are the parameters that are recorded in the 

RAIRS accident database (~146 parameters) following a railroad accident. For the BN 

implementation these factors are grouped into the following categories: 

• Weather and climate factors

• Track factors (e.g., track density, track class) 

• Rail factors (e.g., gross tons, number of loaded freight cars, total number of cars) 

• Tonnage and Train Composition 

Accident Causes (Effect) are the causes that lead to a railroad accident that are considered to be 

the end effect. In this context, a broken joint bar (cause code T214) or a roller type journal 

bearing failure due to overheating (cause code E53C) are the end effects that can lead to an 

accident. 

3.3.1 Data Culling - Accident Cause Categories 

The RAIRS accident database contains more than 400 unique cause codes to identify the primary 

reason for train accidents and derailments. These codes are categorized under five major cause 

groups as shown in Table 4 and Figure 6. 
14 

Table 4. Accident Cause Groups

Cause Group Description Cause Group Code

Track, Roadbed and Structures T

Signal and Communication S

Train Operation – Human Factor H 

Mechanical and Electrical Failures E 

Miscellaneous Causes M 

Figure 6. Illustration of the Accident Cause Groups

Table 5 shows the distribution of accidents across the cause groups over the period 2009 to 2018. 

The track, roadbed, and structure group is the leading cause for railroad accidents where a 

hazmat car released product. 

Table 5. Distribution of accident causes across the four accident data sorts

Cause Group Sort A Sort B Sort C Sort D

Track, Roadbed, and Structures 6,525 1,496 416 64

Mechanical and Electrical Failures 2,776 711 408 19

Train Operation – Human Factor 9,260 2,178 294 14

Miscellaneous Causes 5,758 1,143 688 22

Signal and Communication 701 183 10 0

Total 25,020 5,711 1,816 119

The Sort C accident data pertaining to Track, Roadbed, and Structures (T), Mechanical and 

Electrical Failures (M), and Train Operations – Human Factor (H) was analyzed to identify cause 

categories with high accident counts and/or high consequence (i.e., risk). The consequence/risk is 

the monetary loss incurred due to a train accident or derailment. The total reportable damage 

(ACCDMG) data available in the RAIRS database was used to calculate the consequence/risk: 
15 

where the average loss for an accident category is given by 

The plot of accident count and consequence for each of the cause categories under T, M, and H 

cause groups is shown in Figure 7 and Figure 8, respectively. The plot of accident count versus 

consequence for the same categories is shown in Figure 9. 

Figure 7. Accident Counts for Categories Under T, M, & H Cause Groups 
16 

Figure 8. Consequence/Risk for Categories Under T, M, & H Cause Groups

Figure 9. Accident Count vs. Consequence for Categories Under T, M, & H Cause Groups
17 

Based on the analysis, the top-2 high-count, high-risk categories for the T, M, and H cause 

groups are shown in Table 6, Table 7, and Table 8, respectively. Since track, roadbed, and 

structure related issues pose the greatest risk/consequence, the BN-based accident risk model 

will only consider the causes pertaining to this group, specifically cause categories T1 and T2. In 

addition, the current study only considers derailments since this is the leading type of accident by 

counts. The implementation of BNs to study causal relationships for the other cause groups and 

accident types is outside the scope for this research. After the derailment accident type and track, 

roadbed, and structure (T) cause groups filter is applied, the total number of accidents in Sort-C 

is reduced to 409 accidents. For ease of reference, the reduced Sort-C database with 409 

accidents is referred to as Sort-C1. 

Table 6. Top-2 Categories for Track, Roadbed, and Structures (T) Cause Group

Category Description Category Code

Track Geometry T1

Rail, Joint Bar, and Rail Anchoring T2

Table 7. Top-2 Categories for Mechanical and Electrical Failures (M) Cause Group

Category Description Category Code

Axles and Journal Bearings E5

Wheels E6

Table 8. Top-2 Categories for Train Operations-Human Error (H) Cause Group

Category Description Category Code

General Switching Rules H3

Switches, Use of H7

To simplify the implementation of the Bayesian-based accident model, the team used the 

grouping of accident causes by Alan Bing and others (Bing et al., 2015). The distribution of 

accidents related to track, roadbed, and structures in Sort C as per this grouping is presented in 

Figure 10. The top-four accident groups (i.e., 08T, 04T, 05T, and 03T) comprise approximately 

75 percent of the accidents in Sort-C1. The number of accidents in the remainder of the groups is 

too small to fit the accident model and therefore removed in the implementation of the BN. 

Figure 10. Distribution of Sort-C Accidents Across Cause Groups (Bing, 2015) 
18 

3.3.2 Feature Selection – Rail Operations, Weather and Climate, Tonnage, and 

Train Composition

The RAIRS accident database consists of approximately 146 parameters that are recorded in the 

event of an accident or a derailment. For data-driven risk analysis, it is important to identify the 

most important factors contributing to rail accidents and derailments and discard the insignificant 

parameters, a process called Feature Selection in Machine Learning (ML). Feature Selection 

helps reduce the number of input variables (i.e., reduce curse of dimensionality), reduce the 

computational cost, and in some cases improve the performance of the ML model. The terms 

features, parameters, or factors will be interchangeably used throughout this report to refer to the 

146 recorded parameters. 

The team used the Random Forest model to identify the important factors affecting the Track, 

Roadbed, and Structures (T), Mechanical and Electrical Failures (M), and Human Factor (H) 

accident causes. The concept of decision trees is central to the implementation of random forests 

for feature selection. A decision tree consists of a root node, intermediary nodes, and leaf nodes 

all connected by branches through which information flows down the tree (see Figure 11). The 

decision tree is built recursively by splitting the data to make use of the features. For the rail 

accident data, this is akin to splitting (i.e., bagging) the accident data into different accident 

cause categories by making use of the 146 recorded parameters. At each node the feature that 

best splits the data is evaluated by using metrics like Gini impurity or entropy for categorical 

data and residual or mean squared error (MSE) for continuous data. Splitting the data at a node 

results in the creation of two intermediary nodes, the first node that contains data split by the 

selected feature and the second node where the data is yet to be split or bagged. The process of 

splitting the data at the second node is then repeated. This data splitting process is recursively 

done until there is no data left to be split or bagged. 

Figure 11. Illustration of a Decision Tree (Source: https://www.diagrams.net/) 

The Random Forest method involves building several hundred such decision trees, each built by 

the random extraction of features and accident data pertaining to those features. This ensures that 

not every tree sees all the features or all the observations, thereby reducing overfitting. The 

significance of each feature based on how well it can split the data (Gini impurity or entropy for 

categorical data and residual or MSE for continuous data) is averaged over all the trees to 

determine the overall significance of the feature. 

The top five parameters identified for each of the three cause groups are shown in Table 9 and 

Table 10. The factors affecting the Track, Roadbed, and Structures (T) and Mechanical and 

Electrical Failures (M) are identical and in the same order of priority. For Human Factors (H), 

the type of track takes precedence over the month during which the accident occurred. The 

remaining four factors are identical to the T & M cause groups but not in the same order. 
19 

Table 9. Top Five Factors Affecting Track, Roadbed, and Structures (T) and Mechanical 

and Electrical Failures (M) 

Parameter Description Parameter Code

Train speed TRNSPD

Temperature in degrees Fahrenheit TEMP

Number of loaded freight cars LOADF1

Gross tonnage excluding power units TONS

Month of incident MONTH

Table 10. Top Five Factors Affecting Train Operations – Human Factors (H)

Parameter Description Parameter Code

Train Speed TRNSPD

Number of loaded freight cars LOADF1

Type of track TYPTRK

Temperature in degrees Fahrenheit TEMP

Gross tonnage excluding power units TONS

3.4 Risk Factors - Continuous to Categorical Data Conversion

The BN for rail derailment risk analysis in this study was implemented in the open-source 

software pomegranate3 (Schreiber, 2018). Since pomegranate currently supports discrete data

only, the continuous data fields (i.e., accident factors) in the Sort C dataset were converted to 

discrete variables. Histograms were used to visualize the data for each field, while grouping of 

the continuous data into categorical data was performed iteratively to ensure that the number of 

bins (i.e., categories) captured the distribution of the data. The bins were named with appropriate 

labels to match the distribution of the data. 

Factors such as railroad company, track class, weather, and visibility are recorded as categories 

in the RAIRS database. Only the distribution of these variables across each of the categories is 

presented for these factors. For train speed, the categories were based on the speed limits for 

each track class. For each of the risk factors used in the implementation of the BN, their 

categories and the distribution of accidents across the categories is shown in Table 11 to Table 

18 and Figure 12 to Figure 19. 

Table 11. Train Speed (TRNSPD) Categories 

Track Class Speed Range Train Speed Category

Class 1 Min to 10 mph LT10

Class 2 10 to 25 mph 10TO25

Class 3 25 to 40 mph 25TO40

Class 4 40 to 60 mph 40TO60

Class 5 60 to 80 mph 60TO80

3 pomegranate is a Python package that implements fast and flexible probabilistic models ranging from individual 

probability distributions to compositional models such as Bayesian networks and hidden Markov models. 
20 

Figure 12. Distribution of Accidents Across Train Speed (TRNSPD) Categories 

Table 12. Weather Categories 

Weather Code Weather Category

1 Clear

2 Cloudy

3 Rain

4 Fog

5 Sleet

6 Snow

Figure 13. Distribution of Accident Categories Across Weather (WEATHER) Categories 
21 

Table 13. Temperature (TEMP) Categories

Temperature Category Temperature Range

Very Cold Min to 0F

Cold 0F to 40F

Moderate 40F to 60F

Warm 60F to 80F

Hot 80F to 100F

Very Hot 100F to Max

Figure 14. Distribution of Accidents Across Temperature (TEMP) Categories

Table 14. Visibility Categories

Visibility Code Visibility Category

1 Dawn

2 Day

3 Dusk

4 Dark
22 

Figure 15. Distribution of Accidents Across Visibility (VISIBLTY) Categories

Table 15. Number of Loaded Freight Cars (LOADF1) Categories

Categories # Loaded Freight Cars

LT35 Min to 35 cars

35TO70 35 to 70 cars

70TO100 70 to 100 cars

GT100 100 to Max cars

Figure 16. Distribution of Accidents Across Number of Loaded Freight Cars (LOADF1) 

Categories 
23 

Table 16. Total Number Of Cars (TOTALF1) Categories

Categories # Loaded Freight Cars

LT50 Min to 50 total cars

50TO100 50 to 100 total cars

100TO150 100 to 150 total cars

GT150 Greater than 150 total cars

Figure 17. Distribution of Accidents Across Total Number of Cars (TOTALF1) Categories

Table 17. Gross Tons (TONS) Categories

Tonnage Category Gross Tonnage (excluding power units) 

LT5K Min to 5000 tons

5TO10K 5000 to 10,000 tons

10TO15K 10,000 to 15,000 tons

GT15K 15,000 to Max tons

Figure 18. Distribution of Accidents Across Gross Tons (TONS) Categories
24 

Table 18. Track Density (TRKDNSTY) Categories

Track Density Category Track density in MGT

LT40 Min to 40 MGT track density

40TO80 40 to 80 MGT track density

80TO120 80 to 120 MGT track density

GT120 Greater than 120 MGT track density

Figure 19. Distribution of Accidents Across Track Density in MGT (TRKDNSTY) 

Categories

3.5 Bayesian Network-based Railroad Accident Risk Model Implementation 

The important features, assumptions, and limitations of the BN-based accident model are listed 

below. 

1. The BN-based accident model is a tool that provides insight into the degree to which the 

causal factors influence railroad accidents, specifically derailments. This information will 

enable railroad companies to implement measures to monitor these factors to improve 

overall railroad safety and mitigate the risk of derailments.

2. RAIRS accident data between 2009 to 2018 is used to fit the BN-based accident model. 

Further, the Sort-C1 accident data considers freight trains operating on main tracks and 

carrying hazmat, with derailment type of accident attributed to track, roadbed, and 

structure-related causes for groups 03T, 04T, 05T, and 08T (Bing, et al., 2015). 

The implementation of a BN consists of two components, structure learning and parameter 

learning. 

Structure Learning – Structure learning involves the process of establishing the structure of the 

directed acyclic graph, which comprises nodes representing random variables and edges that 

establish the probabilistic causal relationship between the nodes. In this project, the parameters 

(i.e., risk factors) for constructing the BN were identified using the Random Forests method 

discussed in Section 3.3.2. Additionally, subject matter experts’ recommendations were 

incorporated when finalizing the structures of the BNs implemented in this project. 
25 

Parameter Learning – This part of the BN implementation involves fitting the data to the Bayes 

model to learn the distributions for each of the nodes (i.e., parameters) in the network. 

Pomegranate uses the maximum likelihood estimate (MLE) method to develop either univariate 

or multivariate distributions for each of the nodes in the BN structure. 

Bayesian Inferencing – Bayesian inferencing is the process of unearthing information once the 

data has been fit to an established network. Bayesian inferencing consists of calculating joint 

probabilities, performing predictive analytics, and using sensitivity analysis. 

Joint Probability Estimation – This involves evaluating the total probability for each variable 

in a network or a subset of a network. The joint distribution for a BN is equal to the product of 

probabilities of the node given its parents: 

Predictive Analytics – An important feature of BNs is their ability to calculate the probability 

distribution over the unobserved variables (i.e., unknown parameters) given the evidence (i.e., 

known parameters). The more the observed variables, the higher is the confidence in the 

predicted values for the unobserved variables. Pomegranate uses the loopy belief algorithm to 

perform Bayesian inferencing. 

Sensitivity Analysis – The likelihood of a railroad accident depends on all the contributing risk 

factors in the BN. However, different factors may have distinctive levels of influence on the 

railroad accident. Sensitivity analysis allows understanding the influence of the individual risk 

factors on the accident. These analyses help railroad companies and regulatory authorities 

develop safety policies that mitigate risk and reduce the number of accidents. 

As mentioned earlier, the BN for probabilistic risk analysis of train derailments was implemented 

using pomegranate (Schreiber, 2018). The networks capture the causal as well as the statistical 

correlations between the risk factors and the primary accident causes. The following four 

networks were initially established by integrating the causal relationship learnt from the feature 

selection exercise in Section 3.3.2 and subject matter experts’ knowledge. 

3.5.1 Weather and Climate Factors

The accident data was fit to the BN for weather and climate related risk factors shown in Figure 

20. The calculated marginal probabilities for the four track-related accident cause groups are

shown in Figure 21. For the given data, none of the accident cause groups have a probability of 

more than 50 percent. 
26 

Figure 20. BN for Weather and Climate Risk Factors

Figure 21. Marginal Probabilities for Weather and Climate Factors BN Fitted to the Sort C 

Accident Data (Derailment and Track Related Defects Only) 

The predictive capabilities of the BN are illustrated through three observations listed in Table 19. 

In the first observation, the weather and the visibility are known, while temperature and the 

cause group are the unknown factors. With only two out of the four factors known, the BN 

cannot attribute the accident to one specific cause group. In the second observation, when 

information on temperature (TEMPERATURE=COLD) is added, the BN predicts the probable 

cause of an accident to broken rails and welds (08T). Likewise, when the temperature factor is 
27 

set to very-hot (TEMPERATURE=VERY HOT) in the third observation, the BN network 

attributes the cause of the accident to buckled track (05T) with a 100 percent certainty. An 

important aspect to be noted here is that the BN has learned the underlying physics between cold 

temperatures causing material embrittlement and fracture (i.e., broken rails and welds) and hot 

temperatures causing track buckling through statistical correlations existing in the data. 

Table 19. Accident Cause Group Predictions for Specific Weather and Visibility Conditions

Observations Temperature Weather Visibility Cause Group

03T 04T 05T 08T

#1 UNKNOWN Clear Day 18% 16% 18% 48%

#2 COLD Clear Day 21% 0% 0% 79%

#3 VERY HOT Clear Day 0% 0% 100% 0%

A sensitivity analysis for temperature was performed to understand the effect of varying 

temperature on accident causes. From the temperature sensitivity analysis plot in Figure 22, it is 

evident that cold temperatures lead to broken rails and welds (08T) and hot weather conditions 

cause track buckling (05T). 

Figure 22. Sensitivity Analysis for Temperature - Plot of Accident Cause Group 

Probabilities Across Temperature Categories

3.5.2 Track Factors - Track Class and Track Annual Density 

The BN for track-related risk factors is shown in Figure 23. The marginal probabilities for the 

four accident cause groups following fitting of the network to the accident data is shown in 

Figure 24. For the given data, none of the accident cause groups have a probability of more than 

50 percent. 

An example of the predictive capability of the network is presented in Table 20. In the first 

observation, the railroad company (Company-A) and the track density (TRK_DNSTY=LT40) 
28 

are the observed variables, while the track class is the unobserved variable (unknown). With two 

out of the four variables known, the BN cannot attribute the accident to one specific cause group. 

In the second observation, in addition to the railroad company and the track density, the track 

class is also known (TRACK_CLASS = CLASS 1). After knowing the value for the track class, 

the BN increases the accident probability due to track geometry (04T) from 40 to 72 percent. The

knowledge of increased accident risk on CLASS 1 tracks due to geometry issues (04T) can help 

railroad companies prioritize maintenance activities accordingly. 

Figure 23. BN for Track Class and Track Annual Density

Figure 24. Marginal Probabilities for Track Class and Track Density BN Fitted to the Sort 

C Accident Data (Derailment and Track Related Defects Only) 
29 

Table 20. Accident Cause Group Predictions for Railroad Company-A 

Observations Track Class Track 

Density

Cause Group

03T 04T 05T 08T

#1 UNOBSERVED LT40 7% 40% 28% 25%

#2 CLASS 1 LT40 14% 72% 14% 0%

The plot of the sensitivity analysis for track class for railroad Company-A, operating on tracks 

with track density less than 40 MGT (TRK_DNSTY = LT40), is shown in Figure 25. This figure 

shows that accidents due to track geometry issues (04T) are more likely to occur on CLASS-1 

and CLASS-2 tracks, whereas accidents due to broken rails and welds (08T) are more likely to 

occur on CLASS-3 and CLASS-4 tracks. 

Figure 25. Sensitivity Analysis for Track Class - Plot of Accident Cause Group 

Probabilities Across Track Classes

3.5.3 Train Factors - Gross Tonnage and Freight Cars 

The BN for gross tonnage and number of freight cars is shown in Figure 26. The marginal 

probabilities for the four accident cause groups following fitting of the network to the accident 

data is shown in Figure 27. For the given data, none of the accident cause groups have a 

probability of more than 50 percent. 

Two examples illustrating the predictive capability of the network are presented in Table 21. In 

Observation #1 the railroad company (Company-A) and the number of loaded freight cars 

(LOADF1=LT35) are the observed (i.e., known) variables, and the total number of freight cars 

(TOTALF1) and the cause group are the unobserved (i.e., unknown) variables. The BN cannot 

attribute the cause of the accident to any specific cause group as only information about two out 

of the four variables is available. In the second observation the total number of cars is also 

known (TOTALF1=LT50) and the cause group is the only unknown variable. With three out of 
30 

the four variables known, the BN attributes the cause of the accident to broken rails and welds 

(08T) with an 80 percent certainty. Likewise, in the second example (Observations #3 and #4), 

when information about three out of the four variables is available, the BN attributes the cause of 

the accident to track geometry (04T) with an 84 percent chance.

Figure 26. BN for Gross Tonnage and Number of Freight Cars

Figure 27. Marginal Probabilities for Tonnage and Freight Cars BN Fitted to the Sort C 

Accident Data (Derailment and Track Related Defects Only) 
31 

Table 21: Accident Cause Group Predictions for Railroad Company-A 

Observations

Number of 

Loaded Cars

LOADF1

Total Number of 

Cars TOTALF1

Cause Group

03T 04T 05T 08T

#1 LT35 UNOBSERVED 10% 33% 36% 21%

#2 LT35 LT50 0% 20% 0% 80%

#3 35TO70 UNOBSERVED 11% 49% 17% 23%

#4 35TO70 100 TO150 0% 84% 16% 0%

The plot of the sensitivity analysis for four railroad companies, with the total number of loaded 

cars less than thirty-five (LOADF1 = LT35) and the total number of cars less than fifty 

(TOTALF1=LT50) is shown in Figure 28. For the given number of loaded cars and total number 

of freight cars, the cause of an accident is attributed to broken rails and welds (08T) for three out 

of the four railroads. For railroad Company-B the BN attributes the cause to track geometry 

issues (04T) and broken welds and rails (08T) with equal probability of 50 percent. 

Figure 28. Sensitivity Analysis for Railroad Companies - Plot of Accident Cause Group 

Probabilities Across Four Railroad Companies 

3.5.4 Unified Bayesian Network – Track and Train Factors 

Next the rail operations, train composition, and tonnage networks are grouped into a unified 

network. Whereas the weather and climate parameters provide a good understanding of the 

causal relationship, these factors are beyond the control of railroad companies and therefore were 

not incorporated into the unified network. The unified BN for derailment risk analysis is 

presented in Figure 29. 
32 

Figure 29. Unified BN for Rail Operations, Tonnage, and Composition 

In the unified BN a term has been introduced for train type, which identifies the train as either 

unit train or manifest train. Unit trains were identified using the ruleset described in Section 

2.1.3. Review of the model predictions found that train type did not have significant influence on 

the predicted accident cause. This is suspected to be due to the limited scope of the current 

model, which is built upon a subset of Sort C data comprising train derailment accidents caused 

by four specific cause groups: Wide Gauge (03T), Track Geometry (04T), Buckled Track (05T), 

and Broken Rail or Welds (08T). This limits the number of unit train accidents in this data set 

and the ability to identify differences in accident properties. To address this limitation, the team 

recommends further development of the model to include additional accident cause code groups, 

other accident types outside of train derailment, and a larger time period.

3.6 Bayesian Network Validation 

This section discusses the details of the validation of the unified BN discussed in Section 3.5. 

Researchers used RAIRS accident data for the years 2019 and 2020 to validate the BN. A total of 

2750 accidents were recorded in 2019 and another 2214 accidents were recorded in 2020. The 

following three filters were applied to align the data with the 2008-2019 data set used for training 

the BN. 

1. Sort C filter (freight train on main track consisting of hazmat cars) 

2. Derailment type of accident 
33 

3. Accident cause code groups (03T, 04T, 05T, and 08T) 

After application of the above filters, the data was reduced to 4 accidents from 2019 and 20 

accidents from the year 2020. The data from these 24 accidents was input to the unified BN to 

predict the accident cause group for each of the accidents. Table 22 lists a summary of the 

accuracy of the predictions from the unified BN. The derailment risk model achieves a good 

accuracy for the 03T, 04T, and 08T groups. The lower accuracy for the 05T group is attributed to 

the small number of accidents belonging to that group in Sort C (i.e., the sort used to train the 

BN). However, for a training dataset comprising 296 accidents, an overall accuracy of 79 percent

is reasonably good. The accuracy of the model can be improved by augmenting the Sort C 

accident data. 

Table 22. Verification Results

Cause Group

Number of 

Accidents

Accidents

Accurately 

Predicted

Accuracy

Sort-C1 

Accidents by 

Cause Group

Wide Gauge (03T) 1 1 100% 39

Track Geometry (04T) 11 8 73% 66

Buckled Track (05T) 3 1 33% 49

Broken Rail or Welds (08T) 9 9 100% 142

Overall 24 19 79% 296
34 

4. Conclusions and Recommendations

4.1 Conclusions

The objective of this research project was to develop a predictive risk model for the release of 

hazardous material transported in unit trains using data science techniques for available rail 

accident and traffic data. This work builds upon previous research (Bing, et al., 2015) which 

examined the causal sequence of events that can lead to a rail accident and used historical 

accident record and rail traffic data to define conditional probabilities of occurrence and thereby 

predict the risk of a hazmat release.

The research team reviewed sources of accident data and traffic data to inform the development 

of a risk model for hazmat transportation by rail. The team concluded that due to the limitations 

of the available traffic data, the research would focus on building a Bayesian-based accident 

model using RAIRS accident data. 

The most detailed traffic data, the STB CCWS, provides information about car and commodity 

movements, but does not provide information about the train in which the car was transported, 

limiting its ability to address the central question of the research. Other traffic data reviewed, 

including Class I railroad R-1 reports (Surface Transportation Board, 2021a) and AAR’s TenYear Trends (Association of American Railroads, 2020), provide annual statistics on freight 

transport, including unit train miles, but do not distinguish hazmat unit trains from non-hazmat 

unit trains. 

Consequently, there was no means of calculating risk, even in the simple terms of accident 

likelihood per unit distance travelled by hazmat unit train versus hazmat manifest train. 

Therefore, the research focused on building a predictive model based solely on the RAIRS 

accident data. The aim of the model was to predict the cause of an accident, given information 

about the accident, based on trends and associations derived from 10 years of historical accident 

records. The trends and associations derived from the accident data could then indicate 

differences in unit train accidents compared to manifest trains and speak to the central question 

regarding relative risk of hazmat transportation. 

Three different BNs were implemented to study the causal relationships between weather, track, 

and train related risk factors and the primary causes leading to railroad accidents. The primary 

causes were selected based on the risks/consequences they posed. These causes were then 

categorized according to the grouping suggested in the work by Bing et. al (2015). A Random 

Forest algorithm was used to select the risk factors. The risk factors in continuous data form 

were then converted into discrete categories by studying their distributions. The capabilities of 

the BN-based accident risk model, such as predictive analytics, sensitivity analysis, and 

estimation of marginal and joint probability distributions, were demonstrated through the 

implementation of three separate BNs for weather, track, and train related factors. The final 

network integrated the train and track networks into one single network, and included a variable 

for train type (i.e., unit train). Hazmat unit trains were identified in the RAIRS database based on 

the number of hazmat cars (≥70) and the number of buffer cars (≤5). 

Review of the model predictions found that train type did not have significant influence on the 

predicted accident cause. This is suspected to be due to the limited scope of the current model, 

which is built upon a subset of data comprising hazmat freight trains travelling on main track, 
35 

where a derailment occurred, and the cause was one of four specific cause groups: Wide Gauge 

(03T), Track Geometry (04T), Buckled Track (05T), and Broken Rail or Welds (08T). This 

limits the number of unit train accidents in this data set and the ability to identify differences in 

accident properties.

Accidents from 2019 and 2020 were used to validate the integrated BN and data filters used for 

developing the Sort-C1 were applied on this accident database. In total, 24 accidents were 

selected. An important aspect of the validation is that the BN has not seen this data previously. 

The risk factors from the 24 accidents were provided as inputs to the BN and the network was 

tasked to make blind predictions on the cause for these accidents. The integrated network 

predicted with 100 percent accuracy for accident cause groups 03T and 08T and 79 percent

accuracy for 04T. The lower accuracy for cause group 05T is attributed to the small amount of 

training data in the Sort-C1. However, the overall accuracy of the network predictions was about 

79 percent, which is promising. Increasing the training data pool (Sort C1) is expected to 

improve the accuracy of the network. 

4.2 Recommendations

To aid future research on the risk of hazmat transportation by unit train, improvements in 

accident and traffic data collection are needed. 

In terms of accident data, the research team recommends that a new field be added to the FRA 

RAIRS database, indicating whether the train is a unit train. During the research, significant 

variation was observed in how a unit train is defined. Therefore, such a change would require 

adoption of a standard definition of a unit train. 

It may not be feasible to collect the level of information required to fully incorporate traffic data 

into the architecture of the Bayesian-based accident model, even in a geographically limited 

model. This would require that all successful train journeys over a given time-period are added 

into the database alongside those which ended in an accident. However, for more traditional 

statistical methods, improvements could be made to identifying hazmat unit train traffic. 

Schedule 755 of the R-1 reports (Railroad Operating Statistics) submitted annually to the STB 

(Surface Transportation Board, 2021a) includes data on total train-miles and car-miles by train 

type, which includes unit trains. Therefore, the team recommends that the collection of railroad 

operating statistics be expanded to provide total train-miles and car-miles by train type 

transporting hazmat. 

The BN-based accident model has demonstrated potential to accurately predict accident cause, 

given information about the train and track. The team recommends that consideration is given to 

further developing the capabilities of the BN-based accident risk model by incorporating 

additional causes groups (e.g., mechanical and electrical, and human causes). In addition, 

inclusion of track maintenance inspection and repair data could enhance causal relationship 

learning. 
36 

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Camino López, M. A., Ritzel, D. O., Fontaneda, I., & Gonzalez Alcantara, O. J. (2008). 

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(Investigation No. RRD19FR007/ RRD20FR002). Washington, DC: NTSB. 
37 

Norfolk Southern (2019). Freight Tariff NS 6004-D. Pricing Services, Norfolk Southern Railway 

Company and Consolidated Subsidiaries.

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PyMC3. PeerJ Computer Science, 2:e55. 

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38 

Appendix A. 

Class I Unit Train Definitions

A Trains magazine article provides insight on the meaning behind the train number assigned to 

Class I railroad operators and their subsidiaries (Schmidt, 2015). The train number is 

documented in the RAIRS database system (under the field title “TRNNBR”), which provides an 

alternate approach to identifying unit trains. However, as it is limited to Class I railroads and 

their subsidiaries, it was not adopted for the purposes of this research, which instead used a 

consistent rule for train length and number of buffer cars to identify unit trains. The train number 

is prefix dependent on the material being transported, and those which describe unit trains are 

summarized in Table 23. 

Table 23. Train Number Prefix Definitions – Unit Trains 

Class I Railroad Operator Train Number Prefix Description

BNSF C Loaded coal trains

E Empty coal trains

G Unit grain trains

U Unit trains

X Empty grain trains

CN B3 Unit potash trains

B7 Unit potash trains

C7 Coal trains

G8 Grain trains

S7 Unit sulphur trains

U7 Other unit trains

CP 300 Grain trains

600 Unit trains

800 Coal trains

KCS C Unit coal

G Unit grain

L Coal

O Unit aggregate

U Other unit

CSX E Empty unit trains

G Grain trains

K Various unit trains

N Loaded coal trains

T Loaded coal trains

U Loaded coal trains

V Grain trains

NS 400 or X Coal and coke trains

500 or Y Coal and grain trains

600 or Z Coal and unit trains

700 or Q Coal trains

800 or S Coal trains

UP C Coal trains

G Grain trains

O Ore, crude oil trains

U Other unit trains
39 

Table 24. Class I Railroads and Subsidiary Company – Acronyms RAIRS

Railroad Unit Train Definition

BNSF BN, LAJ, BNSF

CSX CSX, BOCT, CARR, AWRY, DMRR, RFP, SIRT and TTIS

NS NS, SOU, CNTP, AGS, CGA, CRSH

CPRS CPRS, CP, SOO, DH, DME

CN CN, GTW, IC, CEDR, CC, WC, EJE, DWP.

KCS KCS, GWWR, GWWE, TM

UP UP, ALS, CCT, CWI, SJ&GI, TCT, PTO

Further definitions were obtained from websites and reports published by Class I railroads, as 

shown in Table 25. The variations illustrate the lack of a consistent definition across the rail 

industry. In some cases, total number of cars is provided and ranges between 50 and 90. 

Table 25. Unit Train Definitions as Provided by Railroads 

Railroad Unit Train Definition Reference

BNSF Non-stop service between a single origin and destination (BNSF, 2022)

CSX

A train operating generally intact between point of origin and final 

destination, normally hauling a single bulk commodity, composed of like cars, 

equipped with high-tensile couplers

(CSX, 2022)

NS

A railway train with a minimum of 50 cars that is permitted and approved by 

NS to move in Merchandise Unit Train service and where all of the 

customer’s railcars are moving from a single origin to a single destination

(NS, 2019)

CPRS

Unit Train or Solid Train means a physically consecutive and connected set of 

at least 80 cars tendered for movement together, unless otherwise stated in 

your contract

(CP, 2019)

CN

A train with a fixed, coupled consist of cars operated continuously in shuttle 

service under load from origin and delivered intact at destination and returning 

usually for reloading at the same origin

(CN, 2001)

KCS Train that carries the same cargo (opposite of Manifest train); a train whose 

cars all carry the same commodity, such as grain or oil (KCS, 2022)

UP Unit trains transport more than 90 rail cars of one type of freight in one car 

type for one destination (UP, 2022)
40 

Abbreviations and Acronyms

ACRONYM DEFINITION

AAR Association of American Railroads

BN Bayesian Network

CCWS Confidential Carload Waybill Samples 

DAG Directed Acyclic Graph

FRA Federal Railroad Administration

hazmat hazardous material

HHFUT High-Hazard Flammable Unit Train 

ML Machine Learning

MLE Maximum Likelihood Estimate

MSE Mean Squared Error

NTSB National Transportation Safety Board

RAIRS Railroad Accident/Incident Reporting System 

SME Subject Matter Expert

STB Surface Transportation Board