A Framework for Track Geometry Defect Risk Prediction and Repair Optimization

1. A Framework for Track Geometry Defect Risk Prediction and Repair Optimization Qing He (SUNY Buffalo), Hongfei Li, DebarunBhattacharjya, Dhaivat Parikh, and Arun HampapurIBM T J Watson Research CenterINFORMS Annual Meeting, Phoenix, AZ October 15, 2012

2. Outline • Background and Motivations • Approaches • Data summary • Track deterioration model • Derailment risk model • Track repair optimization model • Case studies • Conclusions

3. Background – Track Defects • Two category of track defects: • Track structural defects • Structural conditions of the track, including the rail, sleeper, fastening systems, subgrade and drainage systems. • Track geometry defects (geo-defects) • Indicate severe ill-conditioned geometry parameters such as gage, profile, alignment, cant, wear, warp and so on.

4. Research Motivation • Consequence of track defects (Peng 2011): • leading cause of train accidents in the United States since 2009. • 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?

5. Research Approaches Track Geometry Car Inspection Class I Defects(Red) Class II Defects (Yellow) Existing Decision Model Inspect within 30 days Fix if required Fix Immediately Fix Immediately Inspect within 30 days Rank and Prioritize Class II based on 1 Proposed Decision Model 2 Track Deterioration Model Derailment Risk Model 3 Decision Analysis / Resource Optimization to prioritize the tracks and defects to be fixed

6. Data Summary • Data scope: 2000 mile main line track from January 2009 to December 2011 • Data sets: • Traffic data: Total Million Gross Tonnage (MGT), # of cars, # of trains • Derailment data (caused by geometry defects): derailment time, location and total costs • Geo-defect data: defect time&location, defect type, severity class (I or II), and severity amplitude • Data summary statistics: • ~ 4,000 Class I defects and 27,000 Class II defects • Top 5 most frequent geo-defects: • Gage, cross level, dip, wear, and cant

7. 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 7

8. Track Deterioration Modeling GAGE_W1 • Model the track deterioration rate of each defect type as follows Deterioration rate (inch/day) Traffic (MGT) GAGE_W2 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 Deterioration rate (inch/day) Traffic (# of cars)

9. Track Deterioration Model Results (Selected)

10. 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 Data sets Derailment risk model Derailments Survival Analysis • Cox proportional hazard model • Time to next inspection • # Class II defects by type • Amplitude of Class II defects Probability of derailment Track Properties Class I & II defects Derailment Inspection run: agg. geodefects Geo-defects case 1 case 2 Survival time T = L Survival time T > L

11. Track Derailment Risk Analysis – Results • Average derailment probability (3month): 0.95% • For some defect type the # of defects was significant predictor while for others it was amplitude (90 percentile) # of Class II defects Amplitude (90th per.) of Class II defects

12. Track Repair Optimization - Overview Track deterioration model Derailment risk model Defect Deterioration rate Probability of Class II converting to Class I Probability of derailment + Track Repair Optimization model Cost inputs Cost of: • Derailment • Class IIrepair • Class I repair Comparison of repair action Outputs (determined by minimizing total expected costs) Optimal type of Class II to repair

13. Track Repair Optimization - Objective Repair Cost Derailment Cost Class I $1000 Avg. $510K Cost to fix all the Class I defects, constant Low $10K Class II $500 Probability of a derailment in the time from this inspection run to the next, if action a is chosen for section i Decision variable: Indicator which is 1 if geo-defect repair action ais 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}

14. Track Repair Optimization – Constraints Only select 1 action Budget to repair Class II defects 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

15. Case Studies • Geo-Defect Data: • Time range: December 2011 • Track length: 1872 mile • Total number of Class II geo-defects: 3406 • Assumptions • derailment cost scenarios: $10k, $25k, $510k (true mean from derailment data) • Fix a Class II defect: $500 • Fix a Class IIwithin 5 mile of a same-type Class I: $250 • Fix a Class I: $1000 • 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 15

16. Scenario 1: Savings vs Budget for Derailment Cost = $10k Optimal # of Class II defects to fix = 571 (~18%)

17. Scenario 2: Savings vs Budget for Derailment Cost = $25k Optimal # of Class II defects to fix = 937 (~30%)

18. Scenario 3: Savings vs Budget for Derailment Cost = $510k Optimal # of Class II defects to fix = 3406 (100%) 80% of savings by fixing top 20% geo-defects

19. Compare with Heuristic Repair Strategy Heuristic I: Distance-based strategy (HEUI) Heuristic II: Severity-based strategy (HEUII) represents the distance to the nearest Class I defect represents severity measures Repair in ascending order of the distance index, until the budget is consumed. Repair in descending order of severity index, until the budget is consumed.

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

21. 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).

22. Thanks for your attention! • qinghe@buffalo.edu • {liho, debarunb, dhaivat.parikh, arunh}@us.ibm.com

23. Geo-Defect Types