Research Update on a Next Generation Rail Wear Model

Joseph W. Palese PE, MSCESenior Scientist

Railroad Engineering and Safety ProgramUniversity of Delaware

UNLV SymposiumRailroad Infrastructure Diagnosis and Prognosis

October 16-17, 2018

University of Delaware Newark, DE

Overview• Rail is a key component of the track structure• Rail replacement and maintenance of the order of

– $2-4 Billion in US alone– $8 to 10 Billion worldwide

• Essential for safe operations• Major failure modes

– Wear– Internal fatigue – Surface fatigue

• Long lead time item because of high cost of purchase and installation– Necessary for good planning of rail installation– Need for good forecasting model for planning of maintenance

Rail Wear Data

• Currently inspected using machine vision technology– Multiple times per year– Every 5’-15’– Cartesian coordinates of rail profile

• Generates terabytes of data Software to align measured profile to original profile

• Calculate wear parameters– A: Area of rail head remaining– A*: Area of rail head lost– h: Vertical wear (sometimes called head or top) taken at the center of the rail– g: Lateral wear (sometimes called gage or side), normally 5/8” below top of rail– l: Lip from plastic flow– Φ: Gage face angle

• Traditional modeling– Simple linear regression

• Single parameter

Curve Snapshot

• High rail head wear• 11 measurements in 6 years• Longitudinal misalignment• Easily see increase in wear

– Over time/MGT– Uniform in leading tangent– Non uniform in curve

• Note misalignment of data

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226.4 226.5 226.6 226.7 226.8 226.9 227 227.1

Hea

d W

ear

(inc

hes)

Milepost

Head wear on a high rail in a curve with leading and trailing tangents

3/14/2007 10/9/2007 5/22/2008 8/25/2008 1/26/2009 12/8/2009 8/9/2010 11/4/2010 10/26/2011 9/25/2012 1/8/2013

Variations in Data Sampling Intervals• Common milepost range• Each wear data point tagged with MP location• 123 to 174 samples per inspection• Min shows design sampling interval

– 15.84’ and 14.78’• Likely two separate inspection cars

• Max shows missed samples– Due to bad profile data

• Average varies from 15.1 to18.9’

Date Min Max Avg Count3/14/07 15.84 32.21 16.93 15510/9/07 15.84 32.21 16.30 1615/22/08 15.84 96.10 18.89 1398/25/08 14.78 44.88 15.72 1671/26/09 15.84 144.14 21.24 12312/8/09 14.78 45.94 15.36 169

8/9/10 15.84 48.05 18.47 13011/4/10 15.84 63.89 16.31 161

10/26/11 3.17 30.10 15.10 1749/25/12 15.84 49.10 17.16 153

1/8/13 14.78 29.57 15.10 170

New Longitudinal Alignment Process

• Utilize time series stochastic process– Requires uniform interval

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226.8 226.81 226.82 226.83 226.84 226.85

Head

Wea

r (in

ches

)

Milepost

Head wear on a high rail in a curve with leading and trailing tangents

3/14/07 - interpolated 3/14/07

Estimate a function for each inspection series using linear interpolation or spline

Up-sample each inspection series to common interval and milepost

Determine lag to reference series using cross-correlation

𝑝𝑝(𝑙𝑙) =∑ [(𝑥𝑥(𝑖𝑖) − �̅�𝑥) ∗ (𝑦𝑦(𝑖𝑖 − 𝑙𝑙) − 𝑦𝑦�)]𝑛𝑛𝑖𝑖=1

�∑ (𝑥𝑥(𝑖𝑖) − �̅�𝑥)2𝑛𝑛𝑖𝑖=1 �∑ (𝑦𝑦(𝑖𝑖 − 𝑙𝑙) − 𝑦𝑦�)2𝑛𝑛

𝑖𝑖=1

Shift each inspection series to reference according to lag

Aligned Data

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226.4 226.5 226.6 226.7 226.8 226.9 227 227.1

Hea

d W

ear

(inc

hes)

Milepost

Head wear on a high rail in a curve with leading and trailing tangents (aligned)

3/14/07 10/9/07 5/22/08 8/25/08 1/26/09 12/8/09 8/9/10 11/4/10 10/26/11 9/25/12 1/8/13

Insp Date Corr Coef Lag Miles Feet3/14/07 Reference 0 0 010/9/07 0.82 42 0.042 2225/22/08 0.86 37 0.037 1958/25/08 0.87 31 0.031 1641/26/09 0.78 45 0.045 23812/8/09 0.84 39 0.039 2068/9/10 0.69 80 0.080 42211/4/10 0.82 44 0.044 23210/26/11 0.83 44 0.044 2329/25/12 0.86 32 0.032 1691/8/13 0.80 49 0.049 259

Shift

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226.4 226.5 226.6 226.7 226.8 226.9 227 227.1

Head

Wea

r (in

ches

)

Milepost

Head wear on a high rail in a curve with leading and trailing tangents

3/14/2007 10/9/2007 5/22/2008 8/25/2008 1/26/2009 12/8/2009 8/9/2010 11/4/2010 10/26/2011 9/25/2012 1/8/2013

Results in 400 samples for each inspection at same milepost locations with consistent distance interval

3-D Plot: Head Wear, MP, Sum MGTCurve 226.5

226.65 226.70 226.75 226.80 226.85 226.90 226.95 227.00

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cdat$MP2cd

at$S

umM

GT

cdat

$Hav

g

Curve 226.5

226.65 226.70 226.75 226.80 226.85 226.90 226.95 227.00

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g

Curve 226.5

550 600 650 700 750 800 850 900 950

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226.65226.70

226.75226.80

226.85226.90

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cdat$SumMGT

cdat

$MP2

cdat

$Hav

g

Curve 226.5

550 600 650 700 750 800 850 900 950

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226.65226.70

226.75226.80

226.85226.90

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cdat$SumMGT

cdat

$MP2

cdat

$Hav

g

ARIMA – Auto Regressive Integrated Moving Average

Make data stationary –remove linear trend

Fit function – linear interpolation

Up-sample – Common MGT interval

Perform ARIMA modeling

Predict next MGT intervals

Transform to linear trend

Handles calibration and measurement errorsConverges to linear trend in most casesModel developed from 570-804 MGTForecast to 910 MGT to compare against next 3 measurements

ARIMA(p, d, q) = model for describing time seriesdata and for predicting future values

ARIMA Application Process• Perform ARIMA process for each milepost of up-sampled data• ARIMA factors (p, d, q) unique for each milepost• Linear trend unique for each milepost• Predict wear to defined MGT value

226.6 226.7 226.8 226.9

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MPW

ear (

in)

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Wea

r (in

)

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Wea

r (in

)

Subset of MPs in Spiral All MPs Resulting Forecast

ARIMA forecast not straight line

Last measurement variesRate varies

Forecast varies by Milepost

Validation – Entire curve• Model developed based

on 7 inspections from 3/14/07 to 11/4/10

• Predict for next inspection date; 10/26/2011

• ARIMA prediction shows very good agreement to actual

• Linear regression (LS) tends to overstate

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226.65 226.7 226.75 226.8 226.85 226.9 226.95 227

Head

Wea

r (in

ches

)

MP

Validation - 10/26/2011

11/4/2010 10/26/2011 ARIMA LS ARIMA Delta LS Delta

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226.65 226.7 226.75 226.8 226.85 226.9 226.95 227Wea

r Rat

e (in

/MGT

)

Nominal Wear Rates

ARIMA LS Min (in) -0.0586 -0.0331 Max (in) 0.0180 0.0564 Avg (In) -0.0080 0.0131 SD (in) 0.0159 0.0180

58 MGT (one year) produced 0.035” to 0.075” (average of 0.057”) of head wear in curve

ARIMA Forecast Example• Traditional forecast uses mean or mean+SD of full body of curve (or

segment) to determine rate of wear• Wear rate non-uniform through curve• Ability to forecast wear profile in curve• Take advantage of stochastic process to handle data uncertainty

Case Study• Two separate curves studied

• Forecast to:– First instance a point in the full body would reach the limit– 50% of full body reaches limit– 100% of full body reaches limit– Based on 11/16” wear limit (head and gage)

Rail Length Deg SE Rl Wt Speed Installed 1 634 5 1.5 141 25 2002 2 1795 7.25 1.75 141 25 2002

5 Degree Curve

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8.3600 8.3800 8.4000 8.4200 8.4400 8.4600 8.4800 8.5000

Gage

Wea

r (in

ches

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Milepost

5 deg High Rail - Gage Wear

3/16/2007 10/22/2007 5/27/2008 8/27/2008 1/28/2009

12/3/2009 8/4/2010 11/10/2010 10/31/2011 9/20/2012

13

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8.30 8.32 8.34 8.36 8.38 8.40 8.42 8.44 8.46 8.48 8.50

Heas

e W

ear (

inch

es)

Milepost

5 deg High Rail - Head Wear

3/16/2007 10/22/2007 5/27/2008 8/27/2008 1/28/2009

12/3/2009 8/4/2010 11/10/2010 10/31/2011 9/20/2012

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8.3 8.32 8.34 8.36 8.38 8.4 8.42 8.44 8.46 8.48 8.5

Head

Wea

r (in

ches

)

Milepost

5 deg Low Rail - Head Wear

3/16/2007 10/22/2007 5/27/2008 8/27/2008 1/28/2009 12/3/2009

8/4/2010 11/10/2010 10/31/2011 9/20/2012 1/3/2013

5 Degree Curve – High Rail Forecast

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8.36 8.38 8.40 8.42 8.44 8.46 8.48 8.50

Gag

e W

ear (

inch

es)

Milepost

5 deg High Rail - Gage Wear

3/16/2007 9/20/2012 1257 MGT 1347 MGT 1577 MGT

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0.0015

8.36 8.38 8.40 8.42 8.44 8.46 8.48 8.50

Gag

e W

ear R

ate

(in/

MG

T)

Milepost

5 deg High Rail - Gage Wear Rates

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8.36 8.38 8.40 8.42 8.44 8.46 8.48 8.50

Hea

d W

ear

(inc

hes)

Milepost

5 deg High Rail - Head Wear

3/16/2007 9/20/2012 1257 MGT 1347 MGT 1577 MGT

0.0000

0.0005

0.0010

0.0015

8.36 8.38 8.40 8.42 8.44 8.46 8.48 8.50

Hea

d W

ear

Rate

(in

/MG

T)

Milepost

5 deg High Rail - Head Wear Rates

5 Degree Curve – Low Rail Forecast

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8.30 8.32 8.34 8.36 8.38 8.40 8.42 8.44 8.46 8.48 8.50

Head

Wea

r (in

ches

)

Milepost

5 deg Low Rail - Head Wear

3/16/2007 1/3/2013 1346 MGT 1416 MGT 1486 MGT

0.0000

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8.30 8.32 8.34 8.36 8.38 8.40 8.42 8.44 8.46 8.48 8.50

Head

Wea

r Rat

e (in

/MGT

)

Milepost

5 deg Low Rail - Head Wear Rates

5 Degree Curve Summary

• High rail head wear has most severe rate• Out paces gage face wear• Similar to low rail head wear rate• Head wear controls replacement• Replace rail in year 2038 – 2045

– Based on railroads determination of “failure”

• Both rails due between 2041-2045– Savings associated with replacing both

rails at same time

16

Wear Rates (in/100MGT)

Low RailHead Gage Head

Minimum 0.0427 0.0003 0.0448Maximum 0.0574 0.0137 0.0499Average 0.0515 0.0081 0.0479Std Dev 0.0036 0.0028 0.0011

Cumulative MGT to Head Wear LimiHigh Rail Low Rail

First Hit 1257 134650% 1347 1416100% 1577 1486

Replacement Date (30 MGT/Yr)High Rail Low Rail

First Hit 4/21/2038 4/4/204150% 4/20/2041 8/4/2043100% 12/17/2048 12/2/2045

High Rail5 Deg Curve

7.25 Degree Curve

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Head

Wea

r (in

ches

)

Milepost

7.25 deg High Rail - Head Wear

3/16/2007 10/22/2007 5/27/2008 8/27/2008 1/28/2009

12/3/2009 8/4/2010 11/10/2010 9/20/2012 1/3/2013

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Gage

Wea

r (in

ches

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Milepost

7.25 deg High Rail - Gage Wear

3/16/2007 10/22/2007 5/27/2008 8/27/2008 1/28/2009

12/3/2009 8/4/2010 11/10/2010 9/20/2012 1/3/2013

0.00

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Head

Wea

r (in

ches

)

Milepost

7.25 deg Low Rail - Head Wear

3/16/2007 10/22/2007 5/27/2008 8/27/2008

1/28/2009 12/3/2009 8/4/2010 11/10/2010

• Note average wear of 0.60” is close to limit of 0.69” as of last measurement (Nov. 2010)

7.25 Degree Curve – High Rail Forecast

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Hea

d W

ear

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hes)

Milepost

7.25 deg High Rail - Head Wear

3/16/2007 1/3/2013 706 MGT 796 MGT 866 MGT

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Hea

d W

ear

Rate

(in

/MG

T)

Milepost

7.25 deg High Rail- Head Wear Rates

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Gag

e W

ear (

inch

es)

Milepost

7.25 deg High Rail - Gage Wear

3/16/2007 1/3/2013 706 MGT 796 MGT 866 MGT

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Gag

e W

ear R

ate

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MG

T)

Milepost

7.25 deg High Rail - Gage Wear Rates

7.25 Degree Curve – Low Rail Forecast

• ARIMA forecast model has some inconsistencies at several locations

• These are currently being investigated

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Head

Wea

r (in

ches

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Milepost

7.25 deg Low Rail - Head Wear

3/16/2007 11/10/2010 434 MGT 484 MGT 534 MGT

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4.7112 4.7612 4.8112 4.8612 4.9112 4.9612

Head

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r Rat

e (in

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)

Milepost

7.25 deg Low Rail- Head Wear Rates

7.25 Degree Curve Summary

• High rail head wear out paces gage face wear

• Low rail head wear has most severe rate• Head wear controls replacement• Replace high rail in year 2019 – 2025

– Based on railroads determination of “failure”

• Replace low rail in year 2011 – 2014– Last measurement in 2010– Rail actually replaced prior to

September 2012 where next two inspections show minimal wear

20

Wear Rates (in/100MGT)

Low RailHead Gage Head

Minimum 0.0823 0.0092 0.1133Maximum 0.1074 0.0311 0.1390Average 0.0932 0.0211 0.1273Std Dev 0.0069 0.0053 0.0060

Cumulative MGT to Head Wear LimitHigh Rail Low Rail

First Hit 706 43450% 796 484100% 866 534

Replacement Date (30 MGT/Yr)High Rail Low Rail

First Hit 12/9/2019 6/20/201150% 12/8/2022 2/17/2013100% 4/8/2025 10/19/2014

High Rail7.25 Deg Curve

Rail Lives

• Sharp curve low rail exhibiting very low life (< 500 MGT)

• Sharp curve high rail exhibiting reasonable life (800 MGT)

– Due to head wear– Gage face wear being controlled

• Moderate Curve high/low rails exhibiting good lives (1350 – 1400 MGT)

– Due to head wear

21

High Rail Low Rail High Rail Low RailCumulative MGT at time of last measurement 489 498 498 416MGT Remaining (50% Limit) 858 918 298 68Life (MGT) 1347 1416 796 484

5 Deg Curve 7.25 Deg Curve

• 7.25 degree curve high rail wears faster than 5 degree curve

– 2x for head– 3x for gage

• Head wear outpaces gage wear on high rail

• Low rail head wear dominant on severe curves

• Significant time (MGT) difference to replacement based on first hit, 50% of curve, 100% of curve

– 3 to 10 year difference in remaining “life”

Conclusions• Good longitudinal alignment of wear data allows for better understanding of wear rate

distribution• ARIMA stochastic process allows for refinement of wear forecasting

– More accurate than Least Squares Linear Regression• Approach allows for defining wear renewal forecast based on wear distribution in

curve– 1st point, 50%, 100% past wear limit

• Process validated and case study presented

• Determine applicability to combined wear parameters– Head and Gage– Head area loss

• Extend approach to transverse rail profile forecasting– Allow for forecasting of rail profile grinding

• Develop comprehensive wear equation• Develop wear rate distribution analysis

– Highlight geometry, unbalance issues– Identify lubrication effectiveness/implementation

Future Research

Acknowledgements

• Research funded by US Department of Transportation, University Transportation Center program, (RailTeam UTC)