Rapid advancement of sensor technologies and computing power has led to wide availability of massive population-based shape data. In this paper, we present a Taylor expansion-based method for computing structural performance variation over its shape population. The proposed method consists of four steps: (1) learning the shape parameters and their probabilistic distributions through the statistical shape modeling (SSM), (2) deriving analytical sensitivity of structural performance over shape parameter, (3) approximating the explicit function relationship between the finite element (FE) solution and the shape parameters through Taylor expansion, and (4) computing the performance variation by the explicit function relationship. To overcome the potential inaccuracy of Taylor expansion for highly nonlinear problems, a multipoint Taylor expansion technique is proposed, where the parameter space is partitioned into different regions and multiple Taylor expansions are locally conducted. It works especially well when combined with the dimensional reduction of the principal component analysis (PCA) in the statistical shape modeling. Numerical studies illustrate the accuracy and efficiency of this method.

References

References
1.
Robinette
,
K. M.
,
Blackwell
,
S.
,
Daanen
,
H.
,
Boehmer
,
M.
, and
Fleming
,
S.
,
2002
, “
Civilian American and European Surface Anthropometry Resource (CAESAR) Final Report, Volume 1: Summary
,” SAE International, Warrendale, PA, accessed July 22, 2017, http://www.humanics-es.com/CAESARvol1.pdf
2.
Ball
,
R.
, and
Molenbroek
,
J.
,
2008
, “
Measuring Chinese Heads and Faces
,”
The Ninth International Congress of Physiological Anthropology. Human Diversity: Design for Life
, Delft, The Netherlands, Aug. 22–26, pp.
150
155
.
3.
OAI
,
2017
, “
OAI Design, Subject Characteristics, Data, and Images
,” The Osteoarthritis Initiative, San Francisco, CA, accessed July 22, 2017, https://oai.epi-ucsf.org/datarelease/About.asp
4.
Bryan
,
R.
,
Nair
,
P. B.
, and
Taylor
,
M.
,
2009
, “
Use of a Statistical Model of the Whole Femur in a Large Scale, Multi-Model Study of Femoral Neck Fracture Risk
,”
J. Biomech.
,
42
(
13
), pp.
2171
2176
.
5.
Bischoff
,
J. E.
,
Dai
,
Y.
,
Goodlett
,
C.
,
Davis
,
B.
, and
Bandi
,
M.
,
2014
, “
Incorporating Population-Level Variability in Orthopedic Biomechanical Analysis: A Review
,”
ASME J. Biomech. Eng.
,
136
(
2
), p.
021004
.
6.
Dryden
,
I. L.
, and
Mardia
,
K. V.
,
1998
,
Statistical Shape Analysis
, Vol.
4
,
Wiley
,
Chichester, UK
.
7.
Heimann
,
T.
, and
Meinzer
,
H.-P.
,
2009
, “
Statistical Shape Models for 3D Medical Image Segmentation: A Review
,”
Med. Image Anal.
,
13
(
4
), pp.
543
563
.
8.
Cremers
,
D.
,
2006
, “
Dynamical Statistical Shape Priors for Level Set-Based Tracking
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
28
(
8
), pp.
1262
1273
.
9.
Baek
,
S.-Y.
, and
Lee
,
K.
,
2012
, “
Parametric Human Body Shape Modeling Framework for Human-Centered Product Design
,”
Comput.-Aided Des.
,
44
(
1
), pp.
56
67
.
10.
Chu
,
C.-H.
,
Tsai
,
Y.-T.
,
Wang
,
C. C.
, and
Kwok
,
T.-H.
,
2010
, “
Exemplar-Based Statistical Model for Semantic Parametric Design of Human Body
,”
Comput. Ind.
,
61
(
6
), pp.
541
549
.
11.
Bryan
,
R.
,
Mohan
,
P. S.
,
Hopkins
,
A.
,
Galloway
,
F.
,
Taylor
,
M.
, and
Nair
,
P. B.
,
2010
, “
Statistical Modelling of the Whole Human Femur Incorporating Geometric and Material Properties
,”
Med. Eng. Phys.
,
32
(
1
), pp.
57
65
.
12.
Galloway
,
F.
,
Worsley
,
P.
,
Stokes
,
M.
,
Nair
,
P.
, and
Taylor
,
M.
,
2012
, “
Development of a Statistical Model of Knee Kinetics for Applications in Pre-Clinical Testing
,”
J. Biomech.
,
45
(
1
), pp.
191
195
.
13.
Rao
,
C.
,
Fitzpatrick
,
C. K.
,
Rullkoetter
,
P. J.
,
Maletsky
,
L. P.
,
Kim
,
R. H.
, and
Laz
,
P. J.
,
2013
, “
A Statistical Finite Element Model of the Knee Accounting for Shape and Alignment Variability
,”
Med. Eng. Phys.
,
35
(
10
), pp.
1450
1456
.
14.
Galloway
,
F.
,
Kahnt
,
M.
,
Ramm
,
H.
,
Worsley
,
P.
,
Zachow
,
S.
,
Nair
,
P.
, and
Taylor
,
M.
,
2013
, “
A Large Scale Finite Element Study of a Cementless Osseointegrated Tibial Tray
,”
J. Biomech.
,
46
(
11
), pp.
1900
1906
.
15.
Chui
,
H.
, and
Rangarajan
,
A.
,
2003
, “
A New Point Matching Algorithm for Non-Rigid Registration
,”
Comput. Vision Image Understanding
,
89
(
2
), pp.
114
141
.
16.
Wang
,
X.
, and
Qian
,
X.
,
2016
, “
A Statistical Atlas Based Approach to Automated Subject-Specific FE Modeling
,”
Comput.-Aided Des.
,
70
, pp.
67
77
.
17.
KwoK
,
T.-H.
,
Zhang
,
Y.
, and
Wang
,
C. C.
,
2012
, “
Efficient Optimization of Common Base Domains for Cross Parameterization
,”
IEEE Trans. Visualization Comput. Graphics
,
18
(
10
), pp.
1678
1692
.
18.
Gower
,
J. C.
,
1975
, “
Generalized Procrustes Analysis
,”
Psychometrika
,
40
(
1
), pp.
33
51
.
19.
Reh
,
S.
,
Beley
,
J.-D.
,
Mukherjee
,
S.
, and
Khor
,
E. H.
,
2006
, “
Probabilistic Finite Element Analysis Using ANSYS
,”
Struct. Safety
,
28
(
1
), pp.
17
43
.
20.
Choi
,
K. K.
, and
Kim
,
N.-H.
,
2006
,
Structural Sensitivity Analysis and Optimization 1: Linear Systems
,
Springer Science & Business Media
,
New York
.
21.
Qian
,
X.
,
2010
, “
Full Analytical Sensitivities in NURBS Based Isogeometric Shape Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
199
(
29
), pp.
2059
2071
.
22.
Bookstein
,
F. L.
,
1989
, “
Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
11
(
6
), pp.
567
585
.
23.
Sederberg
,
T. W.
, and
Parry
,
S. R.
,
1986
, “
Free-Form Deformation of Solid Geometric Models
,”
ACM SIGGRAPH Comput. Graphics
,
20
(
4
), pp.
151
160
.
24.
Wang
,
X.
, and
Qian
,
X.
,
2014
, “
An Optimization Approach for Constructing Trivariate B-Spline Solids
,”
Comput.-Aided Des.
,
46
, pp.
179
191
.
25.
Hammersley
,
J. M.
,
1960
, “
Monte Carlo Methods for Solving Multivariable Problems
,”
Ann. N. Y. Acad. Sci.
,
86
(
3
), pp.
844
874
.
26.
Stegmann
,
M. B.
, and
Gomez
,
D. D.
,
2002
, “
A Brief Introduction to Statistical Shape Analysis
,” Vol.
15
,
Informatics and Mathematical Modelling
, Technical University of Denmark, DTU, Kongens Lyngby, Denmark, p.
11
.
27.
Hasler
,
N.
,
Stoll
,
C.
,
Sunkel
,
M.
,
Rosenhahn
,
B.
, and
Seidel
,
H.-P.
,
2009
, “
A Statistical Model of Human Pose and Body Shape
,”
Computer Graphics Forum
, Vol.
28
,
Wiley
,
Hoboken, NJ
, pp.
337
346
.
28.
Chen
,
X.
,
Zheng
,
C.
, and
Zhou
,
K.
,
2016
, “
Example-Based Subspace Stress Analysis for Interactive Shape Design
,”
IEEE Trans. Visualization Comput. Graphics
,
PP
(99), p. 1.
You do not currently have access to this content.