The increasing practical use of computer-aided inspection (CAI) methods requires assessment of their robustness in different contexts. This can be done by quantitatively comparing estimated CAI results with actual measurements. The objective is comparing the magnitude and dimensions of defects as estimated by CAI with those of the nominal defects. This assessment is referred to as setting up a validation metric. In this work, a new validation metric is proposed in the case of a fixtureless inspection method for nonrigid parts. It is based on using a nonparametric statistical hypothesis test, namely the Kolmogorov–Smirnov (K–S) test. This metric is applied to an automatic fixtureless CAI method for nonrigid parts developed by our team. This fixtureless CAI method is based on calculating and filtering sample points that are used in a finite element nonrigid registration (FENR). Robustness of our CAI method is validated for the assessment of maximum amplitude, area, and distance distribution of defects. Typical parts from the aerospace industry are used for this validation and various levels of synthetic measurement noise are added to the scanned point cloud of these parts to assess the effect of noise on inspection results.

References

References
1.
Abenhaim
,
G. N.
,
Desrochers
,
A.
, and
Tahan
,
A.
,
2012
, “
Nonrigid Parts' Specification and Inspection Methods: Notions, Challenges, and Recent Advancements
,”
Int. J. Adv. Manuf. Technol.
,
63
(5–8), pp.
741
752
.
2.
Abenhaim
,
G. N.
,
Tahan
,
S. A.
,
Desrochers
,
A.
, and
Lalonde
,
J.-F.
,
2013
, “
Aerospace Panels Fixtureless Inspection Methods With Restraining Force Requirements; A Technology Review
,”
SAE
Paper No. 2013-01-2172.
3.
Weckenmann
,
A.
, and
Weickmann
,
J.
,
2006
, “
Optical Inspection of Formed Sheet Metal Parts Applying Fringe Projection Systems and Virtual Fixation
,”
Metrol. Meas. Syst.
,
13
, pp.
321
330
.http://www.metrology.pg.gda.pl/full/2006/M&MS_2006_321.pdf
4.
Gentilini
,
I.
, and
Shimada
,
K.
,
2011
, “
Predicting and Evaluating the Post-Assembly Shape of Thin-Walled Components Via 3D Laser Digitization and FEA Simulation of the Assembly Process
,”
Comput. Aided Des.
,
43
(3), pp.
316
328
.
5.
Abenhaim
,
G. N.
,
Desrochers
,
A.
,
Tahan
,
A. S.
, and
Bigeon
,
J.
,
2015
, “
A Virtual Fixture Using a FE-Based Transformation Model Embedded Into a Constrained Optimization for the Dimensional Inspection of Nonrigid Parts
,”
CAD Comput. Aided Des.
,
62
, pp.
248
258
.
6.
Weckenmann
,
A.
,
Weickmann
,
J.
, and
Petrovic
,
N.
,
2007
, “
Shortening of Inspection Processes by Virtual Reverse Deformation
,”
Fourth International Conference and Exhibition on Design and Production of Machines and Dies/Molds
, Cesme, Turkey, June 21–23, pp. 391–398.
7.
Jaramillo
,
A.
,
Prieto
,
F.
, and
Boulanger
,
P.
,
2013
, “
Fixtureless Inspection of Deformable Parts Using Partial Captures
,”
Int. J. Precis. Eng. Manuf.
,
14
(1), pp.
77
83
.
8.
Abenhaim
,
G. N.
,
Tahan
,
A. S.
,
Desrochers
,
A.
, and
Maranzana
,
R.
,
2011
, “
A Novel Approach for the Inspection of Flexible Parts Without the Use of Special Fixtures
,”
ASME J. Manuf. Sci. Eng.
,
133
(1), p.
011009
.
9.
Aidibe
,
A.
,
Tahan
,
A. S.
, and
Abenhaim
,
G. N.
,
2012
, “
Distinguishing Profile Deviations From a Part's Deformation Using the Maximum Normed Residual Test
,”
WSEAS Trans. Appl. Theor. Mech.
,
7
(1), pp.
18
28
.http://www.wseas.org/multimedia/journals/mechanics/2012/54-077.pdf
10.
Radvar-Esfahlan
,
H.
, and
Tahan
,
S.-A.
,
2012
, “
Nonrigid Geometric Metrology Using Generalized Numerical Inspection Fixtures
,”
Precis. Eng.
,
36
(1), pp.
1
9
.
11.
Sabri
,
V.
,
Tahan
,
S. A.
,
Pham
,
X. T.
,
Moreau
,
D.
, and
Galibois
,
S.
,
2016
, “
Fixtureless Profile Inspection of Non-Rigid Parts Using the Numerical Inspection Fixture With Improved Definition of Displacement Boundary Conditions
,”
Int. J. Adv. Manuf. Technol.
,
82
(5–8), pp.
1343
1352
.
12.
Sattarpanah Karganroudi
,
S.
,
Cuillière
,
J.-C.
,
Francois
,
V.
, and
Tahan
,
S.-A.
,
2016
, “
Automatic Fixtureless Inspection of Non-Rigid Parts Based on Filtering Registration Points
,”
Int. J. Adv. Manuf. Technol.
,
87
(
1–4
), pp.
687
712
.
13.
Weckenmann
,
A.
,
Gall
,
P.
, and
Hoffmann
,
J.
,
2004
, “
Inspection of Holes in Sheet Metal Using Optical Measuring Systems
,”
Sixth International Science Conference on Coordinate Measuring Technique
, Bielsko-Biala, Poland, Apr. 21–24, pp.
339
346
.
14.
Schwer
,
L.
,
Mair
,
H.
, and
Crane
,
R.
,
2012
, “
Guide for Verification and Validation in Computational Solid Mechanics
,” American Society of Mechanical Engineers, New York, Standard No. ASME V&V10-2006.
15.
Besl
,
P. J.
, and
Mckay
,
N. D.
,
1992
, “
A Method for Registration of 3-D Shapes
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
14
(2), pp.
239
256
.
16.
Bronstein
,
A. M.
,
Bronstein
,
M. M.
, and
Kimmel
,
R.
,
2006
, “
Generalized Multidimensional Scaling: A Framework for Isometry-Invariant Partial Matching
,”
Proc. Natl. Acad. Sci. U.S.A.
,
103
(5), pp.
1168
1172
.
17.
Kimmel
,
R.
, and
Sethian
,
J. A.
,
1998
, “
Computing Geodesic Paths on Manifolds
,”
Proc. Natl. Acad. Sci.
,
95
(15), pp.
8431
8435
.
18.
Borouchaki
,
H.
,
George
,
P. L.
, and
Lo
,
S. H.
,
1996
, “
Optimal Delaunay Point Insertion
,”
Int. J. Numer. Methods Eng.
,
39
(20), pp.
3407
3437
.
19.
AIAG
,
2010
, “
Measurement Systems Analysis (MSA)
,”
Reference Manual
,
4th ed.
,
the Automotive Industries Action Group
,
Troy, Turkey
.
20.
Oberkampf
,
W. L.
,
Trucano
,
T. G.
, and
Hirsch
,
C.
,
2004
, “
Verification, Validation, and Predictive Capability in Computational Engineering and Physics
,”
ASME Appl. Mech. Rev.
,
57
(5), pp.
345
384
.
21.
Sornette
,
D.
,
Davis
,
A.
,
Ide
,
K.
,
Vixie
,
K.
,
Pisarenko
,
V.
, and
Kamm
,
J.
,
2007
, “
Algorithm for Model Validation: Theory and Applications
,”
Proc. Natl. Acad. Sci. U.S.A.
,
104
(16), pp.
6562
6567
.
22.
Oberkampf
,
W. L.
, and
Barone
,
M. F.
,
2006
, “
Measures of Agreement Between Computation and Experiment: Validation Metrics
,”
J. Comput. Phys.
,
217
(1), pp.
5
36
.
23.
Hills
,
R. G.
, and
Trucano
,
T. G.
,
1999
, “
Statistical Validation of Engineering and Scientific Models: Background
,” Sandia National Laboratories, Albuquerque, NM, Report No.
SAND99-1256
.http://www4.ncsu.edu/~rsmith/Hills-1.pdf
24.
Committee
,
A. S.
,
1998
,
Guide: Guide for the Verification and Validation of Computational Fluid Dynamics Simuations
, American Institute of Aeronautics and Astronautics, Reston, VA, Standard No. G-077-1998.
25.
ASME,
2009
, “
Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer
,” American Society of Mechanical Engineers, New York, Standard No.
ASME V&V 20-2009
.https://www.asme.org/products/codes-standards/v-v-20-2009-standard-verification-validation
26.
Cowles
,
B.
,
Backman
,
D.
, and
Dutton
,
R.
,
2012
, “
Verification and Validation of ICME Methods and Models for Aerospace Applications
,”
Integr. Mater. Manuf. Innovation
,
1
, p. 2.
27.
Liu
,
Y.
,
Chen
,
W.
,
Arendt
,
P.
, and
Huang
,
H. Z.
,
2011
, “
Toward a Better Understanding of Model Validation Metrics
,”
ASME J. Mech. Des.
,
133
(7), p.
071005
.
28.
Oberkampf
,
W. L.
, and
Trucano
,
T. G.
,
2008
, “
Verification and Validation Benchmarks
,”
Nucl. Eng. Des.
,
238
(3), pp.
716
743
.
29.
Ferson
,
S.
, and
Oberkampf
,
W. L.
,
2009
, “
Validation of Imprecise Probability Models
,”
Int. J. Reliab. Saf.
,
3
(1/2/3), pp.
3
22
.
30.
Kleijnen
,
J. P.
,
1995
, “
Statistical Validation of Simulation Models
,”
Eur. J. Oper. Res.
,
87
(1), pp.
21
34
.
31.
Buranathiti
,
T.
,
Cao
,
J.
,
Chen
,
W.
,
Baghdasaryan
,
L.
, and
Xia
,
Z. C.
,
2006
, “
Approaches for Model Validation: Methodology and Illustration on a Sheet Metal Flanging Process
,”
ASME J. Manuf. Sci. Eng.
,
128
(2), pp.
588
597
.
32.
Paez
,
T. L.
, and
Urbina
,
A.
,
2002
, “
Validation of Mathematical Models of Complex Structural Dynamic Systems
,” Ninth International Congress on Sound and Vibration, Orlando, FL, July 8–11.
33.
Hills
,
R. G.
, and
Leslie
,
I. H.
,
2003
, “
Statistical Validation of Engineering and Scientific Models: Validation Experiments to Application
,” Sandia National Laboratory, Albuquerque, NM, Report No.
SAND2003-0706
.http://prod.sandia.gov/techlib/access-control.cgi/2003/030706.pdf
34.
Dowding
,
K. J.
,
Leslie
,
I. H.
,
Hobbs
,
M. L.
,
Rutherford
,
B. M.
,
Hills
,
R. G.
, and
Pilch
,
M. M.
,
2004
, “
Case Study for Model Validation: Assessing a Model for Thermal Decomposition of Polyurethane Foam
,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2004-3632.
35.
Rutherford
,
B.
, and
Dowding
,
K.
,
2003
, “
An Approach to Model Validation and Model-Based Prediction—Polyurethane Foam Case Study
,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2003-2336.
36.
Chen
,
W.
,
Baghdasaryan
,
L.
,
Buranathiti
,
T.
, and
Cao
,
J.
,
2004
, “
Model Validation Via Uncertainty Propagation and Data Transformations
,”
AIAA J.
,
42
(7), pp.
1406
1415
.
37.
Rebba
,
R.
, and
Mahadevan
,
S.
,
2008
, “
Computational Methods for Model Reliability Assessment
,”
Reliab. Eng. Syst. Saf.
,
93
(8), pp.
1197
1207
.
38.
D'Agostino
,
R. B.
,
1986
,
Goodness-of-Fit-Techniques
, Vol.
68
,
CRC Press
, Boca Raton, FL.
39.
Ghanem
,
R. G.
,
Doostan
,
A.
, and
Red-Horse
,
J.
,
2008
, “
A Probabilistic Construction of Model Validation
,”
Comput. Methods Appl. Mech. Eng.
,
197
(29–32), pp.
2585
2595
.
40.
Massey
,
F. J.
, Jr.
,
1951
, “
The Kolmogorov–Smirnov Test for Goodness of Fit
,”
J. Am. Stat. Assoc.
,
46
(253), pp.
68
78
.
41.
Mahadevan
,
S.
, and
Haldar
,
A.
,
2000
,
Probability, Reliability and Statistical Method in Engineering Design
,
Wiley
, Hoboken, NJ.
42.
Sun
,
X.
,
Rosin
,
P. L.
,
Martin
,
R. R.
, and
Langbein
,
F. C.
,
2008
, “
Noise in 3D Laser Range Scanner Data
,”
IEEE International Conference on Shape Modeling and Applications
(
SMI
), Stony Brook, NY, June 4–6, pp.
37
45
.
43.
Boehnen
,
C.
, and
Flynn
,
P.
,
2005
, “
Accuracy of 3D Scanning Technologies in a Face Scanning Scenario
,”
Fifth International Conference on 3-D Digital Imaging and Modeling
(
3DIM
), Ottawa, ON, Canada, June 13–16, pp.
310
317
.
44.
Diebel
,
J. R.
,
Thrun
,
S.
, and
Brünig
,
M.
,
2006
, “
A Bayesian Method for Probable Surface Reconstruction and Decimation
,”
ACM Trans. Graph. (TOG)
,
25
(1), pp.
39
59
.
45.
Alexa
,
M.
,
2002
, “
Wiener Filtering of Meshes
,” Shape Modeling International (
SMI
), Banff, AB, Canada, May 17–22, pp.
51
57
.
46.
Cuillière
,
J.-C.
, and
Francois
,
V.
,
2014
, “
Integration of CAD, FEA and Topology Optimization Through a Unified Topological Model
,”
Comput. Aided Des. Appl.
,
11
(5), pp.
493
508
.
47.
Geuzaine
,
C.
, and
Remacle
,
J.-F.
,
2009
, “
Gmsh: A Three-Dimensional Finite Element Mesh Generator With Built-In Pre- and Post-Processing Facilities
,”
Int. J. Numer. Methods Eng.
,
79
(11), pp.
1309
1331
.
48.
Aidibe
,
A.
, and,
Tahan
,
A.
,
2015
, “
Adapting the Coherent Point Drift Algorithm to the Fixtureless Dimensional Inspection of Compliant Parts
,”
Int. J. Adv. Manuf. Technol.
,
79
(5–8), pp.
831
841
.
You do not currently have access to this content.