SpatialAnalyzer Advanced Uncertainty Analysis

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SpatialAnalyzer Advanced Uncertainty Analysis

• USMN

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Agenda

• Review of USMN
• Open Questions
• New USMN Features/Additions

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Presentation Outline

• Background and Motivation
• Instrument Uncertainty Characterization
• Discrete Point Cloud Uncertainty Fields
• Combining CASs Traditional Approach
• Unified Spatial Metrology Network (USMN)
• Case Studies

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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

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

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Combined Results
Software A
Software B
Software C
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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.)

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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 Im fitting a cylinder. What is the
  uncertainty of my fit?
• What about my hidden point bar?

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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)

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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.

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Instrument Example Laser Tracker
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Measurement Process

• Establish a field of unknown fixed points.

56 feet
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Measurement Process

• Measure the points from the first instrument
  location.

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Measurement Process

• Measure the points from the second instrument
  location.

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Measurement Process

• Measure the points from the third instrument
  location.

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Measurement Process

• Measure the points from the fourth instrument
  location.

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Solve for Instrument Transformations

• Instrument Transform Computation

• Point Computation
• Find
• Minimize

Find
Minimize
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Extract Uncertainty from Residual Errors

• Group residuals by component

• Type A uncertainty evaluation

• Result

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Coordinate Acquisition System Outputwith
Realistic Uncertainty Statement
Uncertainties including all measurable effects
operator, environment, target, mechanical
backlash, etc.
Coordinate Acquisition System
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Instrument Performance Comparison
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Uncertainty Characterization as an Operational
Check
Component 1 Sigma Uncertainty Before Compensation 1 Sigma Uncertainty 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 1.3 arcseconds
Distance 0.0087 inches 0.000598 inches 0.0006 inches
Total measurements 32 32
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Coordinate Uncertainty Fields
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Uncertainty Field Density
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Field Density How many field points are needed?
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Combining 2 CASs Traditional Approach

• Match common points by minimizing residuals.
• Apply transformation to all points and the
  instrument.

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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

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Unified Spatial Metrology NetworkA 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.

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Relative Uncertainty Weighting in Point
Computation

• Different instrument types
• Different uncertainty characteristics
• Weight measurement components based on relative
  uncertainty.

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Weighting Example
U
m
D
W
e
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Weighting Example 4 Measurements
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USMN Uncertainty Analysis
2 Instruments Before Combination
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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
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USMN Uncertainty Propagation
Fixed Reference
2 Instruments After Combination
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USMN Uncertainty Propagation
Add a 3rd Instrument to the Measurement Chain
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USMN Uncertainty Propagation
Fixed Reference
Add a 3rd Instrument to the Measurement Chain
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USMN Uncertainty Propagation
Fixed Reference
Close the Measurement Loop to Reduce Uncertainty
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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 its a GO?

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USMN Task-Specific Uncertainty

• Given coordinate uncertainty fields.
• What is the uncertainty of the sphere fit in part
  coordinates?

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USMN Task-Specific Uncertainty

• What is the uncertainty of the measured cylinder
  axis and diameter?

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Analysis Hidden Point Bar Uncertainty

• Uncertainty Fields Interact
• End-Point is extrapolated
• And so is the uncertainty!
• Yikes!

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USMN Software Integration
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USMN Advanced Settings
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Case Studies

• Aircraft Carrier Catapult Alignment
• (CVN-76)
• Disney Concert Hall Panel Positioning
• Submarine Fabrication (SSN 774)
• Nuclear Power Steam Generator Replacement

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Aircraft Carrier Catapult Alignment (CVN-76)

• Long narrow structure
• 350 x 6 trough
• 4 laser trackers chained together

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Catapult
1,797 Measured Points 300 field samples 15 minute
run time P-4 1.8 gigahertz
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Disney Concert Hall (LA)
285 measured points 300 field points 11 minute
run time P-4 1.8 gigahertz
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Submarine Fabrication (SSN-774)
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296 points 1.6 sec. for single solution 300 field
points 28 minutes run time P-4 1.3 gigahertz
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Steam Generator Replacement
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Uncertainty Chain
106 points 300 field points 9 minute run time P-4
1.8 gigahertz
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Uncertainty Reduced by Closing the Measurement
Chain
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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 GDT FDT analysis
  process decision uncertainty.

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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.

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Questions?
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Mersenne Twister Random Number Generator
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Attempts at Mapping Numerical Uncertainty