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SpatialAnalyzer Advanced Uncertainty Analysis. USMN. Agenda. Review of USMN Open Questions New USMN Features/Additions. Presentation Outline. Background and Motivation Instrument Uncertainty Characterization Discrete Point Cloud Uncertainty Fields Combining CASs – Traditional Approach - PowerPoint PPT Presentation
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SpatialAnalyzer Advanced Uncertainty Analysis
USMN
Agenda
• Review of USMN• Open Questions• New USMN Features/Additions
Presentation Outline
• Background and Motivation• Instrument Uncertainty Characterization• Discrete Point Cloud Uncertainty Fields• Combining CASs – Traditional Approach• Unified Spatial Metrology Network
(USMN)• Case Studies
Open Question
• What is Ranking … how does it relate to measurement confidence?
• Statistics Review… Predicting local fit error on a daily basis (point RMS, uncertainty)
• Instrument uncertainty why should we use average
• explain usmn with nominal point groups when we can use it
• can I get summary stats out after I have shut down USMN
• some questions on instrument uncertainty
Measurement Tools
Theodolites & Total Stations
Digital Photogrammetry Laser Trackers
Portable CMMs
Digital LevelsLaser Scanners
Background
• Many instrument types and models in use.
• Each manufacturer has individual, incompatible, software applications.
• Users need to apply several devices to a single measurement task.
• Operators need to re-train on each software package. Software
ASoftware
BSoftware
C
Need: General SoftwareCommon User Interface
Unify Metrology Processes
CombinedResults
Motivation• Uncertainty statements must accompany
measurements. (NIST TN/1297, ISO Guide, ANSI GUM, NCSL RP-12)
• Coordinate measurements used to make important (and expensive) decisions
• Multiple systems are often used to perform a single measurement job.
• Current industry practice is to make guesses at (or ignore) overall combined uncertainty based on instrument manufacturer specifications.
• Needed:– Instrument performance in the “real-world” – Geometric representation of uncertainty– Combination of measurements and uncertainty– Task-Specific Uncertainty (geometrical fits, etc.)
Questions… Questions… Questions…
• What is the uncertainty of my instruments in the “real-world”?
• What is the effect of uncertainty propagation on the quality of my measurements?
• How can I make optimal use of my measurements to minimize uncertainty?
• Ok, its nice to know the uncertainty of a point, but I’m fitting a cylinder. What is the uncertainty of my fit?
• What about my hidden point bar?
Unified Spatial Metrology NetworkAnswers… Answers… Answers…
• Combine measurement systems• Characterize instrument uncertainty• Verify instrument performance• Determine uncertainty fields• Take advantage of the relative
uncertainty of the measurement components.
• Geometric fitting uncertainty (sphere, line, plane, cylinder, etc)
Coordinate Acquisition System (CAS) Uncertainty Characterization
• Measure the performance of the entire system under the conditions of interest.
• Include instrument, operator, environment, etc.
• Determine uncertainty of compensated instrument output values.
• Determine effect of these uncertainties on the measured coordinates.
Instrument Example: Laser Tracker
,,
m
kkiik mfp ,
Measurement Process
• Establish a field of unknown fixed points.
56 feet
Measurement Process• Measure the points from the first
instrument location.
Measurement Process• Measure the points from the second
instrument location.
Measurement Process• Measure the points from the third
instrument location.
Measurement Process• Measure the points from the fourth
instrument location.
Solve for Instrument TransformationsPoint Computation:• Find • Minimize
Instrument Transform Computation:
p
1
2
31
kkiik mfp , ,,
m
*ip
n
in
2
1000
),,(
z
y
x
Worldk B
BR
B
T
R
R
R
B
B
B
t z
y
x
k
Find
...
3
2
1
t
t
t
T
Minimize
m
mE2
...
2
1
0
Extract Uncertainty from Residual Errors
• Group residuals by component
fromallr
fromallr
fromallr
• “Type A” uncertainty evaluation
componentcomponent rU
J
jjcomponent r
JU
1
2)(1
1
UUU ,,• Result:
Coordinate Acquisition System Outputwith Realistic Uncertainty Statement
UUU ,,
,,
m
Uncertainties including all measurable effects: operator,
environment, target, mechanical backlash, etc.
Coordinate Acquisition System
Instrument Performance ComparisonManufacturer Measurement Horizontal Vertical Distance
Location (arcseconds) (arcseconds) (1,000th inch)
A 1 0.6 0.4 0.2
1 0.6 0.4 0.2
2 1.1 1.5 0.5
3 1.4 1.5 0.7
4 1.3 1.7 0.3
Average 1.0 1.1 0.4
B 1 1.8 2.9 1.5
1 0.9 0.8 0.1
2 1.0 1.4 0.7
2 1.1 0.5 0.4
3 2.2 1.3 0.5
3 1.8 1.0 1.0
3 1.8 1.0 1.0
Average 1.5 1.3 0.7
C 1 1.8 1.9 1.0
1 1.9 1.8 0.4
2 1.0 0.9 0.4
3 1.4 1.3 1.3
4 1.2 1.3 0.7
5 1.3 1.4 0.6
6 1.7 1.5 1.4
Average 1.5 1.5 0.8
A, B, C Average 1.3 1.3 0.6
Horizontal
Vertical
Distance
A
B
C
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Arc
sec.
or
1/10
00th
inch
Average Uncertainty Results by Manufacturer
A
B
C
Uncertainty Characterization as an Operational Check
Parameter Before Compensation After Compensation Delta
Vertical index (arcseconds) 17.820 20.736 2.916Axis tilt (arcseconds) 27.864 25.272 -2.592
Mirror tilt (arcseconds) -10.692 -10.692 0.000Home distance (inches) 6.09528 6.09661 0.00134
Component 1 Sigma UncertaintyBefore Compensation
1 Sigma UncertaintyAfter Compensation
Typical Performance(from Table 4.2)
Horizontal Angle
3.47 arcseconds 0.91 arcseconds 1.3 arcseconds
Vertical Angle 11.45 arcseconds 1.18 arcseconds 1.3 arcseconds
Distance 0.0087 inches 0.000598 inches 0.0006 inches
Totalmeasurements
32 32
Coordinate Uncertainty Fields
**** ,,
jm
U
U
U
U
randf
randf
randf
R j
jj RU
jj mm
,ijij mfp
X
Y
)(14
00220.00012.26
00145.09224.88
00077.09085.304
inchesip
)(
)(
)(
zz
yy
xx
CMZ
CMY
CMX
Uncertainty Field Density
Laser Tracker
Uncertainty Field with 100,000 Samples
X
Y
Uncertainty Field Component Standard Deviation:Percent Deviation from 100,000 Sample Result
0%
5%
10%
15%
20%
25%
30%
35%
40%
Sample Size
% D
ev
iati
on
fro
m 1
00
,00
0 S
am
ple
R
es
ult X
Y
Z
Mag
Field Density: How many field points are needed?
Combining 2 CASs – Traditional Approach
• Match common points by minimizing residuals.
• Apply transformation to all points and the instrument.
Measured Points (Moving)
Nominal Points (Fixed)
ii
ii
ii
zzi
yyi
xxi
MFe
MFe
MFe
)23(
)13(
)3(
1000
000
000
000
1000
),,(
s
s
s
B
BR
B
Tz
y
x
iMF
MiF PTP
*
Chain of CASs - Traditional Best-Fit• Transform tracker to
CAD• Transform Arm to
Tracker• Transform Scanner to
Arm• All transformations
based on XYZ coordinate residuals
• Usually performed using multiple software packages
TTTT CMMPScanner
TracCMMP
CADTrac
CADScanner
ker
ker
Unified Spatial Metrology Network:A Method for CAS Combination
• Simultaneous combination of CASs• Relative uncertainty weighting for
measurements• Determine uncertainty fields based
on CAS combination.• Task-Specific: Apply uncertainty
fields to downstream analysis.
Laser Tracker
Total Station
• Different instrument types
• Different uncertainty characteristics
• Weight measurement components based on relative uncertainty.
Laser Tracker
Total Station
L = 518 inches
L = 376 inches
Relative Uncertainty Weighting in Point Computation
Weighting Example
,,
m
PPMUUD
UD
UD
)sin(
)sin(
D
DW
D
DW
D
DW
U
U
U
U
Total Station Laser TrackerHorizontal Angle (arcseconds) 0.5 1.3Vertical Angle (arcseconds) 0.5 1.3Distance (inches) 0.03937 0.0006
(parts per million) 2 0
Total Station Laser TrackerHorizontal Angle (degrees) 306.418 54.737Vertical Angle (degrees) 100.192 123.621Distance (inches) 376.2864 518.2100
Total Station Laser TrackerHorizontal Angle (inches) 0.00091 0.00330Vertical Angle (inches) 0.00091 0.00330Distance (inches) 0.04012 0.00060
Total Station Laser TrackerHorizontal Angle Weight 10.77 2.97Vertical Angle Weight 10.77 2.97Distance Weight 0.24 16.33
Total StationResidual (inches) Weight Objective Contribution
Horizontal Angle -0.00055 10.77 -0.00592Vertical Angle -0.00061 10.77 -0.00657Distance 0.00825 0.24 0.00198
Laser TrackerResidual (inches) Weight Objective Contribution
Horizontal Angle 0.00409 2.97 0.01215Vertical Angle 0.00970 2.97 0.02881Distance 0.00003 16.33 0.00049
U
m
D
W
e
M500 Optimal Point Laser Tracker #5
Total Station #0
Total Station #4
Total Station #2
Horizontal Error Vertical Error Distance Error Magnitude
Total Station #0 -0.0017 0.0042 0.0032 0.0056Weights 11.2 11.2 0.24
Total Station #2 -0.0052 0.0036 -0.0784 0.0786Weights 5.0 5.0 0.24
Total Station #4 -0.0008 -0.0088 -0.0403 0.0413Weights 8.2 8.2 0.24
Laser Tracker #5 0.0072 -0.0094 0.0005 0.0118Weights 2.9 2.9 16.4
Weighting Example: 4 Measurements
USMN Uncertainty Analysis
Laser Tracker
Total Station
Common Targets
2 Instruments Before Combination
USMN Uncertainty Field Analysis
Network Solutionwith Actual
Measured Values
Inject U intoall measurements
Network Solutionwith Measured + U
Values
UncertaintyField
CompositeCoordinate Set
+
USMN Uncertainty Propagation
T1
T2
T3
A
B
C
Total Station
Laser Tracker
Composite Point, T1, and Uncertainty Field
2 Instruments After Combination
Fixed Reference
USMN Uncertainty Propagation
Add a 3rd Instrument to the Measurement Chain
Add a 3rd Instrument to the Measurement Chain
USMN Uncertainty Propagation
Fixed Reference
Close the Measurement Loop to Reduce Uncertainty
Fixed Reference
USMN Uncertainty Propagation
Task-Specific Measurement Uncertainty• Given point uncertainties, how is my
actual measurement job result affected?
• What is the uncertainty of a sphere fit?
• Hidden Point Bar?• Go/No Go Decision? How certain are
you it’s a GO?
USMN Task-Specific Uncertainty
Small Coverage Large CoverageSphere Center:Ux 0.0018 0.0003Uy 0.0027 0.0004Uz 0.0012 0.0002Umag 0.0035 0.0005
Udia 0.0067 0.0008
Analysis time 3.3 sec. 3.7 sec.Points in Fit 186 222Field Points 1000 1000
• Given coordinate uncertainty fields….
• What is the uncertainty of the sphere fit in part coordinates?
• What is the uncertainty of the measured cylinder axis and diameter?
Small Coverage Large CoverageCylinder:
U Axis (deg) 0.0021 0.0009U Diameter (inches) 0.0027 0.0005
Analysis time (P-4 1.3 GHz) 14.7 sec. 32.3 sec.Points in Fit 217 495Field Points 1000 1000
USMN Task-Specific Uncertainty
Analysis: Hidden Point Bar Uncertainty
• Uncertainty Fields Interact
• End-Point is extrapolated…
• And so is the uncertainty!
• Yikes!
USMN Software Integration
USMN Advanced Settings
Case Studies
• Aircraft Carrier Catapult Alignment (CVN-76)
• Disney Concert Hall Panel Positioning• Submarine Fabrication (SSN 774)• Nuclear Power: Steam Generator
Replacement
Tracker #0
Tracker #1
Tracker #2
Tracker #3
Aircraft Carrier Catapult Alignment (CVN-76)
• Long narrow structure
• 350’ x 6’ trough
• 4 laser trackers chained together
Catapult
1,797 Measured Points300 field samples15 minute run timeP-4 1.8 gigahertz
Disney Concert Hall (LA)
285 measured points300 field points11 minute run timeP-4 1.8 gigahertz
Submarine Fabrication (SSN-774)
296 points1.6 sec. for single solution300 field points28 minutes run timeP-4 1.3 gigahertz
Steam Generator Replacement
Uncertainty Chain
106 points300 field points9 minute run timeP-4 1.8 gigahertz
Additional Point Measured by #0 & #5
Uncertainty Reduced by Closing the Measurement Chain
Future Applications
• Wrap optimization around USMN to determine instrument type and placement.
• Expand instrument models to include the multitude of internal parameters.
• Extend Task-Specific analysis to point to surface fitting and other analyses.
• Extend Uncertainty to entire GD&T & FD&T analysis process – decision uncertainty.
Conclusions• It is now possible to obtain realistic
geometrical uncertainty statements for combined measurement systems.
• It is also possible to obtain these results on the shop floor at the technician level.
• Realistic uncertainty statements provide ISO / ANSI compliant measurements. Replaces uncertain uncertainty guesses.
• This information will help to educate measurement technicians and designers so they may reduce measurement uncertainty in the future.
X
Y
M500 Optimal Point Laser Tracker #5
Total Station #0
Total Station #4
Total Station #2
Questions?
Mersenne Twister Random Number Generator
Gaussian Random Number Generator:Percent Deviation from 100,000 Sample Result for 6 Data Sets
0%
5%
10%
15%
20%
25%
30%
35%
40%
Sample Size
% D
ev
iati
on
fro
m 1
00
,00
0 S
am
ple
Re
su
lt
1
2
3
4
5
6
Attempts at Mapping Numerical Uncertainty
Instrument reference frame
Ux = ± 1
Uy = ± 2
Part reference frame
Point in Part frame:X = -3, Y = 6Ux = ?, Uy = ?
Point in Instrument frame:X = 2.5, Y = 4Ux = ± 1, Uy = ± 2