Show By Example How Evaluation of Data Performance in General Will Be Carried out

1. Evaluation of Geometry Data Error Performance on A Geometry Car Using Geometry Data Alignment Techniques H. James Rome Rome Navigation Innovations,Inc 27 Old County Rd, Gloucester , MA 978-281-5623 James_Rome@uml.edu • Show By Example How Evaluation of Data Performance in General Will Be Carried out • Showcase Geometry Data Alignment Techniques as A Solution to Many Problems. Purpose of the Presentation

2. Presentation Concentrates on a case Study: Comparison of “Alternate” and Standard Gage • Example of Performance Analysis • Investigate Repeatability and stability of two measures of gage.

3. What’s This Geometry Data Alignment Package? • Lines up data from several runs to data on Reference Run. Can align data to an Accuracy ~ 1 ft • Used For: • Trend Analysis • Repeatability and Error Analysis • Example Follows

4. Example …Before Data Alignment: Plot .vs.time at ft location37825 0.1 -2 0 0 2 -0.1 Profile, Inch,-> -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -12 -10 -8 -6 -4 -2 0 time back from reference run, months 0.6 Left Profile Lined up with GPS to about 2 meters 1 2 3 0.4 4 5 6 0.2 7 8 9 Profile, Inch,-> 0 10 11 12 -0.2 13 14 15 -0.4 16 17 18 -0.6 Distance along track, ftX104 -> 19 20 21 -0.8 22 3.78 3.781 3.782 3.783 3.784 3.785 3.786 3.787 3.788 3.789 3.79 23 4 x 10 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

5. Plots after Data Alignment up with With Package, 0.6 1 2 3 0.4 4 5 6 0.2 7 8 9 0 Profile, Inch,-> 10 11 12 -0.2 13 14 15 -0.4 16 17 18 -0.6 19 Distance along track, ftX104 -> 20 21 -0.8 22 3.78 3.781 3.782 3.783 3.784 3.785 3.786 3.787 3.788 3.789 3.79 23 4 x 10 Plot .vs.time at ft location37825 24 -0.1 -2 0 2 -0.2 Trend Apparent -0.3 Profile, Inch,-> -0.4 -0.5 -0.6 -0.7 25 -0.8 -12 -10 -8 -6 -4 -2 0 26 time back from reference run, months

6. Use of Alignment for Error Analysis • Approach can be used to Evaluate Repeatability Errors. • If Data is Taken Close Enough in time, Differences in Aligned Data imply the sum of the errors in Both measurements .. examples follow

7. NOTE! • This alignment can be carried out over 10’s or even 100’s of miles with the click of a mouse. • Thus no need to constrain evaluations to a several thousand ft “Test Track”. • Occasional rare events, long term error error trends, and Data Reliability can be evaluated.

8. Example Comparison of Alternate and Standard Gage • Both Measures were available on the Same Car • Two Runs over the same 70 mi of track were used for the Study • Each Is Analyzed as if the other did not exist From an FRA Car ~ 2006

9. Snippet Aligned Alternate Gage, and Standard Gage Alternate Gage “Standard” Gage Is Noisier! 1000 Pt mean subracted Standard Gage

10. What We Do Next X+1000 x Take Difference of Two Curves Find Root Mean Square of Difference,RMS Plot RMS vs. X

11. Plot of Running 1000 Pt. RMS differences vs. Distance for Both Gages plot of 1000 pt rms alt gage differences 0.2 standard gage differences 0.18 0.16 0.14 0.12 0.1 0.08 RMS (Units) 0.06 0.04 Record # along track  0.02 0 0.5 1 1.5 2 2.5 3 3.5 5 x 10 RMS’s ~ 40 % Less for Alternate Gage

12. Note There is usually a Calibration Error in Gage Measurement • Is the Calibration Stable During the Run?

13. Sample of Gage Aligned with ( 1000 pt) Bias Removed the Bias Gage, Inches Distance along track,ft

14. Sample of Gage Aligned gage ..NOTE here Bias is not removed! Gage, Inches Distance along track,ft Is this “Bias” stable?

15. Plot of 1000 pt Mean difference of same Paramter: for Alternate and Standard Gages Vs. Distance plot of 1000 pt mean vs distance 0.35 alt gage standard gage 0.3 0.25 0.2 0.15 0.1 Record # along track  0.05 0.5 1 1.5 2 2.5 3 3.5 5 x 10 Typical Max Shift… Standard, .1” Alternative: .06”

16. From Histogram of All Differences, Find Cumulative Distribution FRACTION ACTUAL DIFFERENCES LESS THAN X, mean subtrated 1 0.9 alt gage standard gage 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.05 0.1 0.15 0.2 0.25 Error Limits, (Units) X Alternative Gage: 70% of error<.05’’ Standard Gage: ~ 70% of errors <.08’’

17. Histogram of 1000 pt RMS errors For Both Gages. Most Likely Value Standard ~.075 Noise Floor Most Likely Value Alternative ~.055 Noise Floor hisotragm of 1000 pt. RMS differences, mean subtrated 0.35 alt gage standard gage 0.3 0.25 0.2 Fraction in Bin Less than ½ # Outliers! 0.15 0.1 0.05 0 0 0.05 0.1 0.15 0.2 0.25 Bin Value , Linear Units

18. Power Spectra, vs Frquency from Both Gages 0.12 Standard Gage Alternative Gage 0.1 0.2 Note error power is about Double for Standard Gage 0.08 0.15 0.06 0.1 Period ~39 units 0.04 Lots of High Frequency Noise. 0.05 0.02 0 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 Frequency, 1/( Unit record)  Frequency, 1/ (Unit Record) 

19. Conclusions Comparing Standard and Alternative Gages • Alternative Gage has significantly: • Lower RMS errors • Fewer large Errors • More Bias Stability • Less high Frequency Noise • Bottom Line: From the Point of View of Repeatability,Alternative Gage is Just Better!

21. NOTE! • Most of this Quality Information could not be obtained from a short stretch of Data • With Automated Data Alignment, No test track required. Track of Opportunity can be used • Simply Run over same ( say 20-50 mile) length of track twice within a few days or weeks.

22. Other Uses • Compare Results of GRMS Vehicles without having them Coordinate their Runs..and over a long distance. • Compare Geometry measurement Equipment • Find Fraction of time when there are data outages

23. What About Other Parameters • The Key is the the ability to Align Massive amounts of Geometry car Data. It puts an Entirely new spin on how extensive and how inexpensive Quality Evaluation can be! • Similar studies can be carried out on Any measurement taken on the Geometry car • And That includes GPS