1. Validating Transfer Line Fit University of Wisconsin-Madison
James N. Bellinger
University of Wisconsin-Madison
7-Oct-2011
James N Bellinger UW Madison

2. Validation Exercise Stage 1
Fix Transfer Lines using positions at MAB3
Predict DCOPS centers all along the lines
Compare my prediction with Barrel MAB1 DCOPS centers
Two possible sources for MAB3 positions
Barrel fit (more likely to be self-consistent w/ MAB1?)
Link fit (use z-bar fit)
Fit fixing Barrel MAB1 and MAB3 positions
Look at residuals
2 January 2019
James N Bellinger UW Madison

3. Validation Exercise Stage 2
From estimated errors in Link or Barrel predict estimated errors at ME stations
Project anchored lines to ME stations
Using Rphi only, fit for best agreement with Photogrammetry, letting disk X,Y,and RotZ vary
Find the residuals and compare with estimated errors
Look for strangeness
1/2/2019
James N Bellinger UW Madison

4. Description of Stage 1
Study “radial” direction for DCOPS: insensitive to MAB rotations, and “tangential=RPhi” directions which are
Given PG MAB calibration, find DCOPS center wrt MAB center
Use the Barrel fit for MAB center and orientation to calculate the DCOPS center position for all MABs
Anchor my laser line fits using the Barrel MAB3 DCOPS Centers from 3
Calculate “radial” positions for all other DCOPS
Compare MAB1 Barrel fit position w/ my prediction
My fit does not include MAB1 Barrel information: independent
2 January 2019
James N Bellinger UW Madison

5. Schematic of my fit using MAB3
Calculate relative offsets for each DCOPS
and add to the anchor line
Compare w/ Barrel fit for MAB1
Fit fixes relative offset=0
Barrel or Link fit position used
to define an anchor line
Calculation uses
average profile
position at center
of DCOPS—no tilt
of laser fan
MAB+3
MAB-3
Given profile centers for both lasers, fit for laser lines and DCOPS offsets
2 January 2019
James N Bellinger UW Madison

6. Schematic of my fit using all MAB
Line fit holding MAB radial offsets
to Barrel-fit values, creates anchor line
Look at residuals
1) Residuals within MAB
2) Residuals for fit to disk
position (stage 2)
Calculation uses
average profile
position at center
of DCOPS—no tilt
of laser fan
MAB+3
MAB+1
MAB-1
MAB-3
Given profile centers for both lasers, fit for laser lines and DCOPS offsets
2 January 2019
James N Bellinger UW Madison

7. Fit for Disk Position, global
Stage 2
1/2/2019
James N Bellinger UW Madison

8. Fit for Disk Position, local
Stage 2 Y
PG shift
from
nominal
Fit shift
from nominal X
Fit Shift
Difference in shifts from nominal.
Combination of disk shift, disk
rotation, and measurement error
Use all 6 stations to fit for disk shift
and rotation. Only RPhi used
-PG Shift
1/2/2019
James N Bellinger UW Madison

9. Barrel MAB3, look at MAB1 Predicted radius - Barrel radius
0.56mm systematic shift
RMS=0.27mm!
Very tight distribution
Why the offset?
2 January 2019
James N Bellinger UW Madison

10. Barrel MAB3, look at MAB1 Predicted RPhi – Barrel RPhi
Again an offset;
1.2mm= 2x the radial
RMS is better than
earlier analyses, but
not as good as radial
Rotation about CMS-Z?
2 January 2019
James N Bellinger UW Madison

11. Barrel MAB3, look at MAB1 RPhi Predicted – Barrel; Fit details
Difference of
differences is
almost the same
at each line,
(modulo sign
change)!
Strongly suggests
calculation
artifact somewhere
Precision better
than accuracy
2 January 2019
James N Bellinger UW Madison

12. Barrel MAB3; look at MAB1 Predicted radius - Barrel radius
MAB+1 and
MAB-1 have
consistent
mean and RMS
(MAB+1/Line5
MAB did not
read out)
MAB-1
2 January 2019
James N Bellinger UW Madison

13. Repeat Using Link for MAB3
Still use barrel for MAB1
Some MAB rotations are default values
The fit is exactly the same—the only thing that changes are the points I use to anchor the DCOPS line. This uses the Link fit to MAB3 instead of the Barrel fit.
2 January 2019
James N Bellinger UW Madison

14. Link MAB3: look at MAB1 Radial Differences
Line 4 looks bad.
If I omit it, the
mean =0.47
RMS =0.71
Compare w/slide 9
mean =0.56
RMS =0.27
Consistent
Nota bene: I use
defaults for some
Link MAB params
1/2/2019
James N Bellinger UW Madison

15. Link MAB3, looking at MAB1 Predicted RPhi – Barrel RPhi
Looks
worse:
See Slide 10
Here:
mean=-1.80
RMS=1.27
Before:
mean=-1.22
RMS=0.71
Consistent
2 January 2019
James N Bellinger UW Madison

16. Link MAB3, lookng at Barrel MAB1 Looking for Artifacts in Rphi
Line 6 is
out of line
with the rest.
Most show
about 1mm
between
residuals, as
before—but
with a new
sign pattern.
See slide 7
2 January 2019
James N Bellinger UW Madison

17. Link MAB3, looking at MAB1 Predicted – Barrel RPhi w/o Line 6
Without 6,
distribution
tighter, offset
smaller.
Compare
w/ Slide 15, 10
Here (Link cut):
-1.26±0.58
Link uncut (15)
-1.8±1.27
Slide 6 (barrel):
-1.22±0.71
2 January 2019
James N Bellinger UW Madison

18. Repeat MAB1 and MAB3 Use Barrel MAB1 and MAB3 to anchor the fit.
Look at residuals for smoking guns
Compare with Link MAB3
2 January 2019
James N Bellinger UW Madison

19. Comparing MAB3 Barrel and Link
RPhi R
Either I’ve made some
blunder or there’s a lot
of variation between what
the Barrel fit finds and what
Link finds for the MAB3
DCOPS centers.
I’m not sure I can usefully
compare a Barrel-anchored
fit to the Link MAB3 values.
Plus
Minus
1/2/2019
James N Bellinger UW Madison

20. Stage 1 Conclusions
Using MAB3 as fixed points validates the precision of the Transfer Line fit at the MAB1 positions at the .7mm RMS level in RPhi and .27mm in radius.
The accuracy of the fit there I estimate from the offsets: 1.2mm in RPhi and .6 in R.
Link-based MAB3 gives precisions about as good as Barrel-based MAB3, but bad measurements can throw the accuracy off
2 January 2019
James N Bellinger UW Madison

21. Barrel Error estimates
Quoted numbers are 1mm and 1μrad
I find an offset of 1.2mm in RPhi, but with an rms of 0.7mm—Barrel precision is potentially better than quoted, especially in radial (rms=0.27mm)
We see systematic offsets from the Transfer Line prediction to the Barrel measurements, whether we fix the MAB using the Barrel or Link
THIS SHOULD BE FED INTO THE BARREL FIT, IF AT ALL POSSIBLE
1/2/2019
James N Bellinger UW Madison

22. Stage 2 Fit to Barrel MAB1 and MAB3
Project to ME stations using default Z
ASSUME Transfer Plates are precise
Transform PG values to Transfer Plate coordinate frame position of Transfer Line DCOPS
Take difference of projection and PG estimate
Fit for disk shift in X/Y and rotation by Z
Examine residuals
1/2/2019
James N Bellinger UW Madison

23. Estimated Error in Projection 4-MAB fit
Given the precision seen in the MAB1 study, dominated by uncertainties in MAB DCOPS position
If uncertainties are the same in a given direction (σ quoted as 1mm)
Station
Approx error
ME1
0.7σ
ME2
0.8σ
ME3
1.0σ
ME4
1.1σ
1/2/2019
James N Bellinger UW Madison

24. Estimated Error in RPhi Projection: Link anchored
There are “good” and “fair” uncertainties
RPhi has contributions from position and Phi_Z
Position: good=0.22μ , fair=210μ
Rotation: good=0.014μrad , fair=230μrad
Station
RPhi err
from angle
Overall err
ME+4
0.3mm
0.33mm
ME+3
0.2mm
0.25mm
ME+2
0.1mm
0.18mm
ME+1
0.01mm
0.15mm
ME-1
1.0mm
ME-2
1.1mm
ME-3
1.2mm
ME-4
1.3mm
1/2/2019
James N Bellinger UW Madison

25. Fits to disk position and rotation All MAB Anchor
Stations ME+2 and ME+3 are on the same disk, likewise ME-2 and ME-3
I’d hope the fits would give the same results for the disk positions
Station
dX (mm)
dY (mm)
dZ (mrad)
ME+4
.37
2.20
0.16
ME+3
1.97
8.23
0.24
ME+2
1.13
6.65
ME+1
0.48
2.62
0.77
ME-1
4.60
1.38
0.79
ME-2
4.45
4.61
-0.004
ME-3
7.09
3.94
0.65
ME-4
4.57
3.51
0.67
1.9mm
Poor agreement: >5mm
1/2/2019
James N Bellinger UW Madison

26. Raw Residuals All MAB Anchor
RMS=1.8mm
not as good
as hoped
1/2/2019
James N Bellinger UW Madison

27. Residuals vs Station All MAB Anchor
Curiosities:
Line 1 (black)
and 4 (blue)
drive most of
the RMS.
ME+4 and -4
have much
tighter
distributions!
I expect a
butterfly shape!
1/2/2019
James N Bellinger UW Madison

28. Station by Station All MAB Anchor
RMS (mm)
ME+4
0.84
ME+3
2.56
ME+2
1.91
ME+1
1.95
ME-1
2.23
ME-2
1.23
ME-3
1.74
ME-4
0.67
I expect the distribution to be tighter near
the anchored region and grow as you get
farther away.
We don’t see that.
The photogrammetry cannot be that bad,
because it was used to reconstruct chamber
positions with better precision than this.
Even potato-chipping bending of the disk
won’t give RPhi shifts of this magnitude
1/2/2019
James N Bellinger UW Madison

29. Why are the farthest away best?
Spread is less
than half the
average RMS
Means are 0
because of
fit
1/2/2019
James N Bellinger UW Madison

30. Repeat Anchoring w/ Link MAB3
1/2/2019
James N Bellinger UW Madison

31. Fit to Disk Position and Rotation Anchor to the Link
Station
dX(mm)
dY(mm)
dRotZ(mrad)
ME+4
0.37
2.20
0.16
ME+3
3.39
10.01
0.36
ME+2
2.54
8.43
0.28
ME+1
1.10
4.24
0.78
ME-1
0.72
2.11
0.21
ME-2
-0.94
5.74
-0.69
ME-3
2.77
4.60
0.02
ME-4
-0.25
4.05
-0.02
1.9mm
Poor agreement: >6mm
Like Slide 25.
1/2/2019
James N Bellinger UW Madison

32. Difference Between Disk Fit using MAB Anchor and Link Anchor
ME+4 is the same?!
Plus side much better agreement
Minus side systematic shifts
Some bias at work
Station
dX(mm)
dY(mm)
dRotZ(mrad)
ME+4 0.
ME+3
1.42
1.87
0.12
ME+2
1.41
1.78
ME+1
0.62
1.62
0.01
ME-1
-3.88
0.73
-0.58
ME-2
-5.39
1.13
-0.69
ME-3
-4.32
0.66
-0.63
ME-4
-4.82
0.54
1/2/2019
James N Bellinger UW Madison

33. Raw Residuals Link MAB3 Anchor
RMS=2.3mm
worse than
Barrel fit in
Slide 26
1/2/2019
James N Bellinger UW Madison

34. Residuals vs Station Link MAB3 Anchor
Compare Slide 27
All but ME+4
have large rms
No smoking gun
Does not look
like predictions
in Slide 24
1/2/2019
James N Bellinger UW Madison

35. Something odd The ME+4 looks the same again Line fit fixes MAB3!
Station
RMS (mm)
4-MAB
Link
ME+4
0.84
ME+3
2.56
3.39
ME+2
1.91
2.87
ME+1
1.95
2.73
ME-1
2.23
1.41
ME-2
1.23
1.99
ME-3
1.74
1.62
ME-4
0.67
2.70
The ME+4 looks the same again
Line fit fixes MAB3!
Repeat dropping bad line?
1/2/2019
James N Bellinger UW Madison

36. Status
Either there has been a substantial blunder in my fit for the disk position, or the projections are not as accurate as they could be.
The Link MAB anchor is potentially very accurate, but something, possibly the Minus side measurements, prevents it.
The Transfer Line is precise at the .5-.7mm level.
Even ME+4, as far as you can get, has RMS of .84mm
I cannot demonstrate the accuracy of the predictions to better than a sigma of 1.8mm overall
Varies by station
Driven by problems in anchoring the lines
1/2/2019
James N Bellinger UW Madison

37. BACKUP
2 January 2019
James N Bellinger UW Madison

38. ME+4 – ME-4 Coords VS Phi ME+4 – ME-4 Vertical (radius) and Horizontal
(tangent)
Clear pattern:
YE+3 is shifted
wrt YE-3 by
O(5.5mm)
(Transfer Plate
mounting
corrections NOT
included)
2 January 2019
James N Bellinger UW Madison

39. YE+3 vs YE+2 ME+4 vs ME+2 Very clearly YE+3 is shifted wrt YE+2 by
O(5.1mm)
2 January 2019
James N Bellinger UW Madison

40. Consistency at/between YE+2 YE-2
Fair agreement
YE2 bending: Expect
ME3-ME2 radius O(-4): OK
variation in horiz O(.2): not
dR=-5.7±1.3
dRPhi=-1.2±.9
dR=-3.9±.6
dRPhi=-1.5±.4
PG variation in mounting O(1.5)
2 January 2019
James N Bellinger UW Madison

41. Calculation
I use a Pari/gp script, interpreted by the gp program. Not COCOA
I know what it is doing
Chi-squared calculation rather than fit
Arbitrary precision in matrix inversions
Generates relative offsets
Fast.
I used this for producing the position vs time plots to determine if a MAB fall had caused blockage or whether the floor was sagging. Processing a thousand events took hours—Cocoa would have spent days at it.
2 January 2019
James N Bellinger UW Madison

42. Data Event from 10-June Barrel event 3981
Almost all Transfer Line stations reproducible!
Barrel event 3981
MAB+1/9 does not read out; no position fit
Calculations done using tools shown in
2 January 2019
James N Bellinger UW Madison

43. Notes
Difference between DCOPS center radius and the local “Vertical” coordinate is at most 12 microns, so I don’t worry about it
The local DCOPS coordinate center is taken at the ideal position
Positive “Horizontal” coordinate is in the direction of positive phi
2 January 2019
James N Bellinger UW Madison