Abstract

The purpose of this study is to obtain a margin of safety for material and process parameters in sheet metal forming. Commonly applied forming criteria are difficult to comprehensively evaluate the forming quality directly. Therefore, an image-driven criterion is suggested for uncertainty parameter identification of sheet metal forming. In this way, more useful characteristics, material flow, and distributions of safe and crack regions, can be considered. Moreover, to improve the efficiency for obtaining sufficient statistics of Approximate Bayesian Computation (ABC), a manifold learning-assisted ABC uncertainty inverse framework is proposed. Based on the framework, the design parameters of two sheet metal forming problems, an air conditioning cover and an engine inner hood, are identified.

References

1.
Coleman
,
H. W.
, and
Steele
,
W. G.
,
2018
,
Experimentation, Validation, and Uncertainty Analysis for Engineers
,
John Wiley & Sons
.
2.
Mathieu
,
M.
,
Couprie
,
C.
, and
LeCun
,
Y.
,
2016
, “
Deep Multi-Scale Video Prediction Beyond Mean Square Error
,” 4th International Conference on Learning Representations, ICLR 2016, Puerto Rico.
3.
Moore
,
E. Z.
,
Murphy
,
K. D.
, and
Nichols
,
J. M.
,
2011
, “
Crack Identification in a Freely Vibrating Plate Using Bayesian Parameter Estimation
,”
Mech. Syst. Signal Process
,
25
(
6
), pp.
2125
2134
.
4.
Nichols
,
J.
,
Link
,
W.
,
Murphy
,
K.
, and
Olson
,
C.
,
2010
, “
A Bayesian Approach to Identifying Structural Nonlinearity Using Free-Decay Response: Application to Damage Detection in Composites
,”
J. Sound Vib.
,
329
(
15
), pp.
2995
3007
.
5.
Pandita
,
P.
,
Bilionis
,
I.
, and
Panchal
,
J.
,
2019
, “
Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions
,”
ASME J. Mech. Des.
,
141
(
10
), p. 101404.
6.
Pritchard
,
J. K.
,
Seielstad
,
M. T.
,
Perez-Lezaun
,
A.
, and
Feldman
,
M. W.
,
1999
, “
Population Growth of Human Y Chromosomes: a Study of Y Chromosome Microsatellites
,”
Mol. Biol. Evol.
,
16
(
12
), pp.
1791
1798
.
7.
Prangle
,
D.
,
2018
,
Summary Statistics in Approximate Bayesian Computation
,
Chapman and Hall/CRC Press
,
London
.
8.
Joyce
,
P.
, and
Marjoram
,
P.
,
2008
, “
Approximately Sufficient Statistics and Bayesian Computation
,”
Stat. Appl. Genet. Mol. Biol.
,
7
(
1
), pp.
1
16
.
9.
Kabir
,
H.
,
Wang
,
Y.
,
Yu
,
M.
, and
Zhang
,
Q.-J.
,
2008
, “
Neural Network Inverse Modeling and Applications to Microwave Filter Design
,”
IEEE Trans. Microwave Theory Tech.
,
56
(
4
), pp.
867
879
.
10.
Wang
,
H.
,
Li
,
G.
, and
Cai
,
Y.
,
2010
, “
MPS-Based LS-SVR Metamodeling Technique for Sheet Forming Optimization
,”
AIP Conf. Proc.
,
1252
(
1
), pp.
1109
1117
.
11.
Jie
,
Y.
,
Pan
,
Q.-L.
,
An-De
,
L.
, and
Song
,
W.-B.
,
2017
, “
Flow Behavior of Al–6.2 Zn–0.70 Mg–0.30 Mn–0.17 Zr Alloy During Hot Compressive Deformation Based on Arrhenius and ANN Models
,”
Trans. Nonferrous Met. Soc. China
,
27
(
3
), pp.
638
647
.
12.
Li
,
H.
,
Liu
,
H. R.
,
Liu
,
N.
,
Sun
,
H.
,
Yang
,
H.
, and
Liu
,
B. Y.
,
2019
, “
Towards Sensitive Prediction of Wrinkling Instability in Sheet Metal Forming by Introducing Evolution of Triple Nonlinearity: Tube Forming
,”
Int. J. Mech. Sci.
,
161
, p.
105054
.
13.
Sehmi
,
M.
,
Christensen
,
J.
,
Bastien
,
C.
, and
Kanarachos
,
S.
,
2018
, “
Review of Topology Optimisation Refinement Processes for Sheet Metal Manufacturing in the Automotive Industry
,”
Struct. Multidiscipl. Optim.
,
58
(
1
), pp.
305
330
.
14.
Zhang
,
Y.
,
Kim
,
N. H.
, and
Haftka
,
R. T.
,
2019
, “
General-Surrogate Adaptive Sampling Using Interquartile Range for Design Space Exploration
,”
ASME. J. Mech. Des.
,
142
(
5
), pp. 051402.
15.
Jansson
,
T.
,
Nilsson
,
L.
, and
Redhe
,
M.
,
2003
, “
Using Surrogate Models and Response Surfaces in Structural Optimization–with Application to Crashworthiness Design and Sheet Metal Forming
,”
Struct. Multidiscipl. Optim.
,
25
(
2
), pp.
129
140
.
16.
Ye
,
F.
, and
Wang
,
H.
,
2017
, “A Novel Adaptive Region-Based Global Optimization Method for High Dimensional Problem,”
World Congress of Structural and Multidisciplinary Optimisation
,
Springer
,
New York
.
17.
Wang
,
H.
,
Ye
,
F.
,
Chen
,
L.
, and
Li
,
E.
,
2017
, “
Sheet Metal Forming Optimization by Using Surrogate Modeling Techniques
,”
Chin. J. Mech. Eng.
,
30
(
1
), pp.
22
36
.
18.
Huang
,
C.
,
Radi
,
B.
, and
El Hami
,
A.
,
2016
, “
Uncertainty Analysis of Deep Drawing Using Surrogate Model Based Probabilistic Method
,”
Int. J. Adv. Manuf. Technol.
,
86
(
9
), pp.
3229
3240
.
19.
Hamdaoui
,
M.
,
Le Quilliec
,
G.
,
Breitkopf
,
P.
, and
Villon
,
P.
,
2014
, “
POD Surrogates for Real-Time Multi-Parametric Sheet Metal Forming Problems
,”
Int. J. Mater. Form.
,
7
(
3
), pp.
337
358
.
20.
Wang
,
H.
,
Chen
,
L.
, and
Li
,
E.
,
2018
, “
Time Dependent Sheet Metal Forming Optimization by Using Gaussian Process Assisted Firefly Algorithm
,”
Int. J. Mater. Form.
,
11
(
2
), pp.
279
295
.
21.
Li
,
E.
, and
Wang
,
H.
,
2016
, “
An Alternative Adaptive Differential Evolutionary Algorithm Assisted by Expected Improvement Criterion and Cut-HDMR Expansion and its Application in Time-Based Sheet Forming Design
,”
Adv. Eng. Softw.
,
97
, pp.
96
107
.
22.
Barlet
,
O.
,
Batoz
,
J.-L.
,
Guo
,
Y.
,
Mercier
,
F.
,
Naceur
,
H.
, and
Knopf-Lenoir
,
C.
,
1996
,
The Inverse Approach and Mathematical Programming Techniques for Optimum Design of Sheet Forming Parts
,
ASME
.
23.
Dong
,
G.
,
Zhao
,
C.
,
Peng
,
Y.
, and
Li
,
Y.
,
2015
, “
Hot Granules Medium Pressure Forming Process of AA7075 Conical Parts
,”
Chin. J. Mech. Eng.
,
28
(
3
), pp.
580
591
.
24.
Goodfellow
,
I.
,
Bengio
,
Y.
,
Courville
,
A.
, and
Bengio
,
Y.
,
2016
,
Deep Learning
, Vol.
1
,
MIT Press Cambridge
.
25.
Deshpande
,
S.
, and
Purwar
,
A.
,
2019
, “
Computational Creativity via Assisted Variational Synthesis of Mechanisms Using Deep Generative Models
,”
ASME J. Mech. Des.
,
141
(
12
), p. 121402.
26.
Zeng
,
Y.
,
Wang
,
H.
,
Zhang
,
S.
,
Cai
,
Y.
, and
Li
,
E.
,
2019
, “
A Novel Adaptive Approximate Bayesian Computation Method for Inverse Heat Conduction Problem
,”
Int. J. Heat Mass Transfer
,
134
, pp.
185
197
.
27.
Luo
,
P.
,
Ren
,
J.
,
Peng
,
Z.
,
Zhang
,
R.
, and
Li
,
J.
,
2018
, “
Differentiable Learning-to-Normalize via Switchable Normalization
” arXiv preprint arXiv:1806.10779.
28.
He
,
K.
,
Zhang
,
X.
,
Ren
,
S.
, and
Sun
,
J.
,
2016
, “
Deep Residual Learning for Image Recognition
,”
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
,
Las Vegas, NV
,
June 27–30
, pp.
770
778
.
29.
Zhu
,
H.
,
Zeng
,
H.
,
Liu
,
J.
, and
Zhang
,
X.
,
2021
, “
Logish: A New Nonlinear Nonmonotonic Activation Function for Convolutional Neural Network
,”
Neurocomputing
,
458
, pp.
490
499
.
30.
Constantinides
,
G. A.
,
Cheung
,
P. Y.
, and
Luk
,
W.
,
2003
, “
Synthesis of Saturation Arithmetic Architectures
,”
ACM Trans. Des. Autom. Electron. Syst.
,
8
(
3
), pp.
334
354
.
31.
Breitkopf
,
P.
,
Naceur
,
H.
,
Rassineux
,
A.
, and
Villon
,
P.
,
2005
, “
Moving Least Squares Response Surface Approximation: Formulation and Metal Forming Applications
,”
Comput. Struct.
,
83
(
17–18
), pp.
1411
1428
.
32.
Wang
,
H.
,
Li
,
G.
, and
Li
,
E.
,
2010
, “
Time-Based Metamodeling Technique for Vehicle Crashworthiness Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
199
(
37–40
), pp.
2497
2509
.
33.
Welstead
,
S. T.
,
1999
,
Fractal and Wavelet Image Compression Techniques
,
SPIE Optical Engineering Press Bellingham
,
Washington
.
34.
Wang
,
Z.
,
Bovik
,
A. C.
,
Sheikh
,
H. R.
, and
Simoncelli
,
E. P.
,
2004
, “
Image Quality Assessment: From Error Visibility to Structural Similarity
,”
IEEE Trans. Image Process.
,
13
(
4
), pp.
600
612
.
35.
Kamiński
,
B.
,
Jakubczyk
,
M.
, and
Szufel
,
P.
,
2018
, “
A Framework for Sensitivity Analysis of Decision Trees
,”
Cent. Eur. J. Oper. Res.
,
26
(
1
), pp.
135
159
.
36.
Ho
,
T. K.
,
1995
, “
Random Decision Forests
,”
Proceedings of 3rd International Conference on Document Analysis and Recognition
,
Canada
,
IEEE
, Vol. 1, pp.
278
282
.
37.
Geurts
,
P.
,
Ernst
,
D.
, and
Wehenkel
,
L.
,
2006
, “
Extremely Randomized Trees
,”
Mach. Learn.
,
63
(
1
), pp.
3
42
.
38.
Friedman
,
J. H.
,
2001
, “
Greedy Function Approximation: a Gradient Boosting Machine
,”
Ann. Stat.
,
29
(
5
), pp.
1189
1232
.
39.
Joglekar
,
S.
, “
Adaboost—Sachin Joglekar’s Blog
,” https://codesachin.wordpress.com
40.
Ord
,
J. K.
,
2006
,
Kriging
, Encyclopedia of Statistical Sciences,
John Wiley & Sons, Inc
.
41.
Cortes
,
C.
, and
Vapnik
,
V.
,
1995
, “
Support-vector Networks
,”
Mach. Learn.
,
20
(
3
), pp.
273
297
.
42.
Bhatt
,
D.
,
Aggarwal
,
P.
,
Bhattacharya
,
P.
, and
Devabhaktuni
,
V.
,
2012
, “
An Enhanced Mems Error Modeling Approach Based on Nu-Support Vector Regression
,”
Sensors
,
12
(
7
), pp.
9448
9466
.
43.
Saunders
,
C.
,
Gammerman
,
A.
, and
Vovk
,
V.
,
1998
, “
Ridge Regression Learning Algorithm in Dual Variables
,”
Proceedings of the 15th International Conference on Machine Learning, ICML '98
,
Madison, WI
.
44.
Fan
,
J.
, and
Yao
,
Q.
,
2008
,
Nonlinear Time Series: Nonparametric and Parametric Methods
,
Springer Science & Business Media
,
New York
.
45.
Rumelhart
,
D. E.
,
Hinton
,
G. E.
, and
Williams
,
R. J.
,
1985
,
Learning Internal Representations by Error Propagation
,
California University, San Diego, La Jolla Institute for Cognitive Science
.
46.
Lemmens
,
A.
, and
Croux
,
C.
,
2006
, “
Bagging and Boosting Classification Trees to Predict Churn
,”
J. Mark. Res.
,
43
(
2
), pp.
276
286
.
You do not currently have access to this content.