a framework for track geometry defect risk prediction and repair optimization

© Copyright IBM Corporation 2012

Qing He (SUNY Buffalo), Hongfei Li, Debarun Bhattacharjya, Dhaivat Parikh, and Arun Hampapur

IBM T J Watson Research Center

INFORMS Annual Meeting, Phoenix, AZ October 15, 2012

A Framework for Track Geometry Defect Risk Prediction and Repair Optimization

© 2012 IBM Corporation

Outline

Background and Motivations

Approacheso Data summaryo Track deterioration modelo Derailment risk modelo Track repair optimization model

Case studies

Conclusions


Background – Track Defects Two category of track defects:

o Track structural defects• Structural conditions of the track, including the rail, sleeper, fastening systems,

subgrade and drainage systems.o Track geometry defects (geo-defects)

• Indicate severe ill-conditioned geometry parameters such as gage, profile, alignment, cant, wear, warp and so on.


Research Motivation

Consequence of track defects (Peng 2011):o leading cause of train accidents in the United States since 2009. o 658 of 1,890 (34.8%) train accidents were caused by track defects in

2009, incurring a $108.7 million loss

Limited literature to predict train derailment risk according to geo-defects.

Limited literature to optimize defect repair activities, considering both defect fix costs and derailment costs

Research Problem

After each track geometry inspection, how to prioritize and repair geo-defects, in order to minimize total expected cost?


Research ApproachesTrack Geometry Car Inspection

Class II Defects (Yellow)Class I Defects(Red)

Fix ImmediatelyInspect within 30 daysFix if required

Fix Immediately Inspect within 30 daysRank and Prioritize Class II based on

Decision Analysis / Resource Optimization to prioritizethe tracks and defects to be fixed

Existing Decision

Model

Proposed Decision

Model1 2

3

Track Deterioration Model Derailment Risk Model


Data Summary

Data scope: 2000 mile main line track from January 2009 to December 2011

Data sets:o Traffic data: Total Million Gross Tonnage (MGT), # of cars, # of trainso Derailment data (caused by geometry defects): derailment time, location

and total costs o Geo-defect data: defect time&location, defect type, severity class (I or

II), and severity amplitude

Data summary statistics:o ~ 4,000 Class I defects and 27,000 Class II defectso Top 5 most frequent geo-defects:

• Gage, cross level, dip, wear, and cant

© 2012 IBM Corporation7

Track Deterioration Model Regression Model

– Track is divided into 0.02mile(~100ft), in order to monitor defect deterioration in a small range.

– Regression was used to model the relationship between track deterioration and predictor variables

– The track deterioration is modeled as exponential component of predictor variables because for most predictors the deterioration accelerates at higher level of predictor variable

Predictor of track deterioration– Elapsed time, current amplitude, traffic (MGT, # of cars, # of

trains), # of inspection runs since last Class I defects, track class/speed,

– All variables do not have equal weight or explanatory power for different defects


Model the track deterioration rate of each defect type as follows

8

Track Deterioration Modeling

log(amplitude increase / (time lag * current amplitude)) = a0 + a1*traffic (MGT) + a2*traffic (# of cars) + a3*traffic (# of trains) + a4*time duration since last red tag + a5*traffic speed

Xetyt

tytty *)()()(

X

tyttytty

)(*)()(log

Traffic (MGT)

Det

erio

ratio

n ra

te (i

nch/

day)

GAGE_W1

Traffic (# of cars)

GAGE_W2

Det

erio

ratio

n ra

te (i

nch/

day)


Track Deterioration Model Results (Selected)

Defect Type Intercept Traffic (MGT)

Traffic (# of cars)

Traffic (# of trains)

Sequence # MSE

CANT -7.66E+00 -7.01E-02 6.05E-06 6.52E-04 6.71E-02 0.242

DIP -7.58E+00 7.21E-02 -- -- -- 0.099GAGE_C -8.53E+00 8.62E-02 -- -- 1.13E-01 0.042GAGE_W1 -7.42E+00 3.58E-02 4.64E-06 -- 7.02E-02 0.021GAGE_W2 -8.08E+00 1.90E-02 -- 2.05E-04 7.98E-02 0.061OVERELEV -7.58E+00 2.45E-01 -- -- 6.99E-02 0.102

SURF -6.99E+00 2.00E-01 -- -1.33E-03 4.36E-02 0.174

WEAR -8.22E+00 2.95E-02 -- 4.73E-04 7.49E-02 0.051XLEVEL -7.66E+00 -- 2.64E-06 3.23E-04 9.18E-02 0.112


Track Derailment Risk Analysis – Data Input and Methodology

Mainline portion of the track network is divided into ~ 2-mile sections

Traffic and geo-defect data are aggregated at section and inspection level form 2009-2011

Derailments

Track Properties

Class I & II defects

Data sets Derailment risk model

Survival Analysis• Cox proportional hazard model• Time to next inspection• # Class II defects by type• Amplitude of Class II defects

Probability of

derailment

Survival time T = L Survival time T > L

Inspection run: agg. geodefects Derailment

case 1 case 2

Geo-defects


• Average derailment probability (3month): 0.95%• For some defect type the # of defects was significant predictor while for others it was

amplitude (90 percentile)

Track Derailment Risk Analysis – Results

covariates coef exp(coef) (hazard ratio)

se(coef) z Pr(>|z|)

numCII_GAGE_W1 1.01E-01 1.11E+00 1.96E-02 5.165 2.40E-07

numCII_GAGE_W2 2.28E-01 1.26E+00 1.17E-01 1.948 0.05139

numCII_REV_X 6.66E-01 1.95E+00 3.21E-01 2.077 0.03782

amp90_SUPER_X 5.10E-01 1.67E+00 1.68E-01 3.028 0.00246

amp90_GAGE_C 6.33E-01 1.88E+00 2.10E-01 3.013 0.00259

amp90_DIP 9.58E-01 2.61E+00 4.67E-01 2.052 0.04016

amp90_WARP 7.44E-01 2.10E+00 3.69E-01 2.014 0.04404

amp90_HARM_X 5.43E+00 2.29E+02 2.78E+00 1.958 0.05028

amp90_WEAR 1.54E+00 4.65E+00 8.34E-01 1.843 0.06533

amp90_ALIGN 4.17E+00 6.45E+01 2.40E+00 1.736 0.08261

# of Class II defects

Amplitude (90th per.) of Class II defects


Optimal type of Class II to repair

Track Repair Optimization - Overview

Outputs (determined by minimizing total expected costs)

Derailment risk model

Probability of derailment+

Track deterioration model

Defect Deterioration

rate

Probability of Class II

converting to Class I

Cost inputs

Cost of:•Derailment•Class II repair•Class I repair

Track Repair Optimization model

Comparison of repair action


Track Repair Optimization - Objective

Class I

Repair Cost

Class II

$1000

$500

Avg.

Derailment Cost

$510K

Low $10KCost to fix all the Class I defects,

constant

Decision variable: Indicator which is 1 if geo-defect repair action a is chosen for section i , otherwise 0

Suppose the geo-defect types in section i are GAGE_W1 and XLEVEL. The total repair action set contains four actions: {NULL},{GAGE_W1},{XLEVEL}, {GAGE_W1, XLEVEL}

Probability of a derailment in the time from this inspection run to the next, if action a is chosen for section i


Track Repair Optimization – Constraints

OUTPUTS• Type of Class II defects to repair:

for given track segments/inspection run

• Avg. cost: The avg. expected cost from optimal repair (for a track segment/inspection run) over a 3 month period

Only select 1 action

Budget to repair Class II defects

© 2012 IBM Corporation15

Case Studies

Geo-Defect Data: o Time range: December 2011o Track length: 1872 mileo Total number of Class II geo-defects: 3406

Assumptionso derailment cost scenarios: $10k, $25k, $510k (true mean from

derailment data)o Fix a Class II defect: $500o Fix a Class II within 5 mile of a same-type Class I: $250o Fix a Class I: $1000o Total cost to fix all yellow tags: $1,538,250

Savings = Total cost of repairing nothing – Total cost of repairing some percentage of yellow tags


Scenario 1: Savings vs Budget for Derailment Cost = $10k

16

Optimal # of Class II defects to fix = 571 (~18%)



17

Optimal # of Class II defects to fix = 937 (~30%)



18

Optimal # of Class II defects to fix = 3406 (100%)

80% of savings by fixing top 20% geo-defects


Compare with Heuristic Repair Strategy

Heuristic I: Distance-based strategy (HEUI)

jidD ikj

ij ,)min(

Repair in ascending order of the distance index, until the budget is consumed.

represents the distance to the nearest Class I defect

Heuristic II: Severity-based strategy (HEUII)

Repair in descending order of severity index, until the budget is consumed.

represents severity measures

jinS ij

j

ikji

j ,)(ln))max(

exp( max

Name Length (mile)

Num. of sections

Num. of Class II defects

Num. of Class I defects

Budget (USD)

Geo-defect types observed

A 50 13 60 4 12,000 GAGE_C, GAGE_W1, XLEVELB 100 21 77 2 25,000 GAGE_C, GAGE_W1, HARM_X,

OVERELEV, TWIST, XLEVELC 300 49 122 37 45,000 GAGE_C, GAGE_W1, GAGE_W2,

HARM_X, OVERELEV, REV_X, TWIST, XLEVEL

D 500 94 343 38 65,000 ALIGN, GAGE_C, GAGE_W1, GAGE_W2, OVERELEV, REV_X, TWIST, XLEVEL


Comparison of average total costs from BIP (proposed), HEUI and HEUII


Conclusions

Derailment costs determine how many Class II defects to fix. The higher the derailment cost is, the larger the number of Class II defects should be repaired.

Fix even only a small fraction (1%~10% )of Class II defects will generate a large amount of savings, compared with fix nothing.

Saving curve looks like a log(x) function. The saving increasing speed will start to slow down above a turn point, specially above 20%.

Our proposed framework generates large amount of savings compared with traditional heuristic methods, especially for long track segments (33% reduced costs).


Thanks for your attention!

[email protected]

{liho, debarunb, dhaivat.parikh, arunh}@us.ibm.com


Defect Type DescriptionALIGN ALIGN is the average of the left and right a certain chord alignment.

CANT Rail cant (angle) measure the amount of vertical deviation between two flat rails from their designed value. (1 degree = 1/8” for all Rail Weights, approximation)

DIP DIP is the largest change in elevation of the centerline of the track within a certain distance moving window. Dip may represent either a depression or a hump in the track and approximates the profile of the centerline of the track.

GAGE_C Gage Change is the difference in two gage readings up to a certain distance.GAGE_TGHT GAGE_TGHT measures how much tighter from standard gage (56-1/2”).GAGE_W1 Gage is the distance between right and left rail measured 5/8” below the railhead. GAGE_WIDE measures

how much wider from standard gage (56-1/2”). The amplitude of GAGE_WIDE plus 56-1/2” is equal to the actual track gage reading.

GAGE_W2 Same as GAGE_W1 for concrete

HARM_X Harmonic cross-level defect is two cross-level deviations a certain distance apart in a curve.

OVERELEV Over-elevation occurs when there is an excessive amount of elevation in a curve (overbalance) based on the degree of curvature and the board track speed.

REV_X Reverse cross-level occurs when the right rail is low in a left-hand curve or the left rail is low in a right-hand curve.

SUPER_X Super cross-level is cross-level, elevation or super-elevation measured at a single point in a curve.

SURF Uniformity of rail surface measured in short distances along the tread of the rails. Rail surface is measured over a 62-foot chord, the same chord length as the FRA specification

TWIST Twist is the difference between two cross-level measurements a certain distance apart.

WARP Warp is the difference between two cross-level or elevation measurements up to a certain distance apart.

WEAR The Automated Rail Weight Identification System (ARWIS) identifies the rail weight while the car is testing and measures the amount of head loss. The system measures for vertical head wear (VHW) and gage face wear (GFW) per rail.

XLEVEL Cross-level is the difference in elevation between the top surfaces of the rails at a single point in a tangent track segment.

Geo-Defect Types

a framework for track geometry defect risk prediction and repair optimization

Documents

defect data

defects yellowclass

track geometry inspection

defect deterioration

defect repair activities

defect timelocation

ibm corporation1

defect type