Distributional Analysis of Track Inspection Data

Background

A method of projecting degradation of track geometry

Stephen Wilk, Ph.D.Principal Investigator I MxV Rail, Pueblo, CO

MxV Rail (formerly TTCI) has developed an alternative method of projecting the degradation of track geometry and track components using foot-by-foot track inspection data. By using the 95th percentile of a track segment instead of a median or maximum, this method may be better-suited to identify when larger-scale track maintenance is required. e median value of a track segment o entimes does not represent problematic locations (e.g., if only 20 percent of locations are degrading) while the maximum number of degradation locations is o en addressed with spot maintenance. e 95th percentile (or some percentile between 75 and 99 depending on the situation) balances the two typical approaches and may better identify locations requiring production work. An example of the application of this method may be the prioritization of production tamping or determining when 10 percent of track components are nearing a maintenance threshold.

On North American railroads, regular track inspection is required to ensure both track geometry and component conditions meet railroad and regulatory standards. Technological innovations over the past few decades have allowed railroads to consolidate di erent types of track inspections into a single inspection vehicle with regular inspection intervals. Track-based inspection data generally provides the current track condition and typically identi es locations that exceed railroad and regulatory thresholds so they can be maintained. However, with frequent inspections and improved data analytics, railroads will have the ability to calculate degradation trends and project future track conditions, thereby creating the possibility for systematic proactive maintenance planning and the prioritization of track regions at risk of exceeding railroad internal and regulatory thresholds in the near future.

Several methods can be used to calculate track degradation trends, and each method emphasizes certain aspects of track health. For example, a median (50th percentile) may indicate average track roughness but may not be able to identify locations that surpass internal track geometry maintenance limits. Alternatively, track geometry exceptions may indicate a few locations that require frequent maintenance but may not be representative of the majority of track. Appropriate balancing between general track roughness (majority of track) and the number of track geometry exceptions makes ballast maintenance planning challenging because, among other reasons, while there is a correlation between the roughness of the majority of the track and the number of high-degradation locations, the relationship is not always predictable.

Degradation Analysis Challenges

Track degradation is typically calculated using trending analyses that use various statistical methods to “ t” historical data and project future degradation. (1) e track degradation method is well-suited for identifying locations that will require spot maintenance in the near future if problematic regions are isolated in the analysis and calculating the maximum. However, largerscale track maintenance typically involves larger track sections where the majority of track in that section (i.e., median) is performing well with multiple problematic locations within that section. Representing the degradation in these situations presents two challenges.

e rst challenge is to determine the length of track needed to represent as a single data point. Existing track geometry degradation analysis methods include footby-foot, 250-foot windows, and aggregated speci ed track distances (100 feet to 1 mile or even larger). Aggregating into 0.1- to 1-mile segments is a common practice because it balances the need for high-enough resolution data with identifying localized high-degradation regions while keeping data quantities at a manageable level. High resolution methods are becoming more common with more powerful computing abilities, but a higher resolution requires a more accurate data location alignment and a better means of storing, analyzing, and making decisions with large amounts of data. e second challenge is to select an appropriate metric to represent the desired parameter (e.g., surface pro le of the aggregated section). is metric may range from simple statistical values (e.g., maximum or median) to proprietary Track Quality Indices (TQIs). e metric selection also presents a tradeo regarding whether to emphasize a representation of the entire track segment (percentile) or focus on the degraded locations (maximum surface pro le). e “distributional analysis” method uses percentiles (e.g., 95th percentile) of larger track segments (e.g., mainline turnout to mainline turnout or single curve) to calculate degradation. is method is therefore less dependent on data alignment, and the analyzed segment, typically, has similar track structure, loading conditions, and production maintenance histories, allowing this method to reduce the in uence of the above factors. Percentiles can be a bit more di cult to calculate than the median or maximum in some so ware products, but there are available codes for these calculations.

Statistical Distribution Visualization

e statistical distribution can be visualized by plotting the desired parameter (e.g., the absolute value of foot-by-foot, 62-foot surface pro le data) as an inverse cumulative distribution function. e y-axis is in logarithmic form ( ipped to match percentiles) because the statistical distribution of the track geometry/components tends to be exponential.

is visualization is an important rst step in exploring how the data is distributed and selecting appropriate percentiles. Figure 1 visualizes the distribution of (a) multiple track geometry runs and (b) a more generic track index.

These plots show the 50th percentile (median), the 75th percentile, and the 90th percentile with the plot separated between a majority of track (up to and including the 99th percentile) and the outliers (>99th percentile). The use of “outlier” is meant as “extreme” in a colloquial sense, not in the statistical sense of a data point that should be removed from a dataset. The left plot shows that the surface profile appears generally linear in this representation (“exponentially distributed”), and the range in values increases significantly with increasing percentiles. The right plot shows a different trend where the distribution is more non-linear in this representation but is linear if the y-axis is in a linear scale.

Degradation Anlaysis

e second step is to take the calculated percentile value over multiple runs, plot the degradation, and project future behavior. Two track segments (A, B) are presented as examples in this article. Both segments

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are from the same subdivision of a western railroad. During the analysis time period, multiple track inspections and at least one surfacing event were conducted on each segment. Two considerations for this analysis are discussed.

Percentile Consideration

e rst consideration is the percentile used to represent degradation. In the rst example, Segment A is used because it has low degradation and high inspection frequencies (due to being recently undercut and a single mainline track). Figure 2 shows the distribution and degradation trends for this segment. More speci cally, Figure 2a shows the overall distributional analysis and the general rightward movement with increasing accumulated tonnage measured in units of million gross tons (MGT) (green is low accumulated MGT a er surfacing; red is high accumulated MGT). A careful look shows this consistently rightward trend changes at about 99.5% with the red lines moving to the le of the orange lines, which suggests spot maintenance between those time intervals.

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WhatitisWhatitdoes $46.95 e appropriate percentile will vary by situation (analysis goal, output, output distribution). For this situation (Segment A, Surfacing Cycle 1), the 95th percentile would be recommended because spot maintenance was only performed in about 0.5 percent of track. In other situations, the appropriate percentile may be much lower (75 to 95th percentile) and the data should be explored in manner presented in Figure 2a.

Figure 2b indicates the 95th percentile degradation is generally linear with an obvious reset from the scheduled surfacing. is consistent increase in degradation matches the general rightward trend in Figure 2a (only rst surfacing cycle is shown). Figure 2c displays the 99.9th percentile where the initial trend is similar, but the value levels o around 50 MGT and uctuates in a small range until the reset from the scheduled surfacing. is small uctuation characteristic likely represents unscheduled spot maintenance, and, since the magnitude of the surface pro le is relatively low, it may be a non-track-geometry issue such as a rail break or a tie replacement. ese results show how spot maintenance is more common late in a surfacing cycle to maintain the degraded locations before scheduled maintenance resets the entire segment.

Inspection Frequency

A second consideration for trending analyses is the inspection frequency required to capture an accurate trending t. is consideration is important because highdegradation locations require a higher inspection frequency to capture a trend due to high rates of degradation and unscheduled spot maintenance. Knowing the degradation rate will help forwardly project degradation and identify appropriate inspection intervals. e appropriate inspection interval will depend on multiple factors. However, since degradation occurs at di erent rates in di erent track segments, there is potential in optimizing track-based inspections in complicated networks and double mainline territories if the inspection frequency of these various segments can be reliably calculated.

Figure 3 shows the 95th percentile of Segment B. Segment B is a good example of how a gap in inspection intervals can produce multiple interpretations of degradation trends. is phenomenon is known as “aliasing.” e 95th percentile can be interpreted with a non-linear stabilizing trend or an unknown production surfacing event. ese two situations are shown by the blue and red lines.

Final Remarks

Finding simple representations of track conditions is a di cult task because the conditions of track components are sometimes distributed in very non-linear manners. Appropriate representation in one situation may not be appropriate in another. Visualizing the distribution and then selecting an appropriate percentile to calculate the degradation may be a bene cial task in certain situations, such as planning largescale track maintenance.

References

1. Wilk, S. Y. Paudel, R. Alishio, and D. Li. 2022. “Distributional Analysis of Track Geometry.” Technology Digest TD22015. AAR/MxV Rail, Pueblo, CO.

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