1. SpatialAnalyzer Advanced Uncertainty Analysis
USMN
SpatialAnalyzer Advanced Uncertainty Analysis

2. Agenda
Review of USMN
Open Questions
New USMN Features/Additions

3. Presentation Outline Background and Motivation
Instrument Uncertainty Characterization
Discrete Point Cloud Uncertainty Fields
Combining CASs – Traditional Approach
Unified Spatial Metrology Network (USMN)
Case Studies

4. 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

5. Measurement Tools Portable CMMs Theodolites & Total Stations
Digital Photogrammetry
Laser Trackers
Digital Levels
Laser Scanners

6. Background ? Need: General Software
Common User Interface
Unify Metrology Processes
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. ?
Combined
Results
Software A
Software B
Software C

7. 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.)

8. 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?

9. Unified Spatial Metrology Network Answers… 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)

10. 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.

11. Instrument Example: Laser Tracker

12. Measurement Process
Establish a field of unknown fixed points.
56 feet

13. Measurement Process
Measure the points from the first instrument location.

14. Measurement Process
Measure the points from the second instrument location.

15. Measurement Process
Measure the points from the third instrument location.

16. Measurement Process
Measure the points from the fourth instrument location.

17. Solve for Instrument Transformations
Instrument Transform Computation:
Point Computation:
Find
Minimize
Find
Minimize

18. Extract Uncertainty from Residual Errors
Group residuals by component
“Type A” uncertainty evaluation
Result:

19. Coordinate Acquisition System Output with Realistic Uncertainty Statement
Uncertainties including all measurable effects: operator, environment, target, mechanical backlash, etc.
Coordinate Acquisition System

20. Instrument Performance Comparison

21. Uncertainty Characterization as an Operational Check
Component
1 Sigma Uncertainty
Before Compensation
After 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
Distance
inches
inches
inches
Total
measurements 32

22. Coordinate Uncertainty Fields

23. Uncertainty Field Density

24. Field Density: How many field points are needed?

25. Combining 2 CASs – Traditional Approach
Match common points by minimizing residuals.
Apply transformation to all points and the instrument.

26. 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

27. 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.

28. Relative Uncertainty Weighting in Point Computation
Different instrument types
Different uncertainty characteristics
Weight measurement components based on relative uncertainty.

29. Weighting Example U m D W e

30. Weighting Example: 4 Measurements

31. USMN Uncertainty Analysis
2 Instruments Before Combination

32. USMN Uncertainty Field Analysis
Network Solution
with Actual
Measured Values
Inject U into
all measurements
Network Solution
with Measured + U
Values
Composite
Coordinate Set +
Uncertainty
Field

33. USMN Uncertainty Propagation
Fixed Reference
2 Instruments After Combination

34. USMN Uncertainty Propagation
Add a 3rd Instrument to the Measurement Chain

35. USMN Uncertainty Propagation
Fixed Reference
Add a 3rd Instrument to the Measurement Chain

36. USMN Uncertainty Propagation
Fixed Reference
Close the Measurement Loop to Reduce Uncertainty

37. 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?

38. USMN Task-Specific Uncertainty
Given coordinate uncertainty fields….
What is the uncertainty of the sphere fit in part coordinates?

39. USMN Task-Specific Uncertainty
What is the uncertainty of the measured cylinder axis and diameter?

40. Analysis: Hidden Point Bar Uncertainty
Uncertainty Fields Interact
End-Point is extrapolated…
And so is the uncertainty!
Yikes!

41. USMN Software Integration

43. USMN Advanced Settings

44. Case Studies Aircraft Carrier Catapult Alignment (CVN-76)
Disney Concert Hall Panel Positioning
Submarine Fabrication (SSN 774)
Nuclear Power: Steam Generator Replacement

45. Aircraft Carrier Catapult Alignment (CVN-76)
Long narrow structure
350’ x 6’ trough
4 laser trackers chained together

46. Catapult 1,797 Measured Points 300 field samples 15 minute run time
P gigahertz

48. Disney Concert Hall (LA)
285 measured points
300 field points
11 minute run time
P gigahertz

49. Submarine Fabrication (SSN-774)

50. 296 points
1.6 sec. for single solution
300 field points
28 minutes run time
P gigahertz

51. Steam Generator Replacement

52. Uncertainty Chain 106 points 300 field points 9 minute run time
P gigahertz

53. Uncertainty Reduced by Closing the Measurement Chain

54. 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.

55. 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.

56. Questions?

57. Mersenne Twister Random Number Generator

58. Attempts at Mapping Numerical Uncertainty
Instrument reference frame
Ux = ± 1
Uy = ± 2
Part reference frame
Point in Part frame:
X = -3, Y = 6
Ux = ?, Uy = ?
Point in Instrument frame:
X = 2.5, Y = 4
Ux = ± 1, Uy = ± 2