A Framework for Track Geometry Defect Risk Prediction and Repair Optimization. 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. Outline. - PowerPoint PPT Presentation
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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?
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:
– 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
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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
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
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
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).
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.