Accurate numerical modeling of laser shock processing, a typical complex physical process, is very difficult because several input parameters in the model are uncertain in a range. And numerical simulation of this high dynamic process is very computational expensive. The Bayesian Gaussian process method dealing with multivariate output is introduced to overcome these difficulties by constructing a predictive model. Experiments are performed to collect the physical data of shock indentation profiles by varying laser power densities and spot sizes. A two-dimensional finite element model combined with an analytical shock pressure model is constructed to obtain the data from numerical simulation. By combining observations from experiments and numerical simulation of laser shock process, Bayesian inference for the Gaussian model is completed by sampling from the posterior distribution using Morkov chain Monte Carlo. Sensitivities of input parameters are analyzed by the hyperparameters of Gaussian process model to understand their relative importance. The calibration of uncertain parameters is provided with posterior distributions to obtain concentration of values. The constructed predictive model can be computed efficiently to provide an accurate prediction with uncertainty quantification for indentation profile by comparing with experimental data.

References

References
1.
Ye
,
C.
,
Liao
,
Y.
, and
Cheng
,
G. J.
,
2010
, “
Warm Laser Shock Peening Driven Nanostructures and Their Effects on Fatigue Performance in Aluminum Alloy 6160
,”
Adv. Eng. Mater.
,
12
(
4
), pp.
291
297
.10.1002/adem.200900290
2.
Hu
,
Y. X.
,
Xu
,
X. X.
,
Yao
,
Z. Q.
, and
Hu
,
J.
,
2010
, “
Laser Peen Forming Induced Two Way Bending of Thin Sheet Metals and Its Mechanisms
,”
J. Appl. Phys.
,
108
(
7
), p.
073117
.10.1063/1.3486218
3.
Huang
,
S.
,
Zhou
,
J. Z.
,
Sheng
,
J.
,
Lu
,
J. Z.
,
Sun
,
G. F.
,
Meng
,
X. K.
,
Zuo
,
L. D.
,
Ruan
,
H. Y.
, and
Chen
,
H. S.
,
2013
, “
Effects of Laser Energy on Fatigue Crack Growth Properties of 6061-T6 Aluminum Alloy Subjected to Multiple Laser Peening
,”
Eng. Fract. Mech.
,
99
, pp.
87
100
.10.1016/j.engfracmech.2013.01.011
4.
Hu
,
Y. X.
,
Han
,
Y. F.
,
Yao
,
Z. Q.
, and
Hu
,
J.
,
2010
, “
Three-Dimensional Numerical Simulation and Experimental Study of Sheet Metal Bending by Laser Peen Forming
,”
ASME J. Manuf. Sci. Eng.
,
132
(
6
), p.
061001
.10.1115/1.4002585
5.
Bhamare
,
S.
,
Ramakrishnan
,
G.
,
Mannava
,
S. R.
,
Langer
,
K.
,
Vasudevan
, V
. K.
, and
Qian
,
D.
,
2013
, “
Simulation-Based Optimization of Laser Shock Peening Process for Improved Bending Fatigue Life of Ti–6al–2sn–4zr–2mo Alloy
,”
Surf. Coat. Technol.
,
232
, pp.
464
474
.10.1016/j.surfcoat.2013.06.003
6.
Hu
,
Y. X.
, and
Yao
,
Z. Q.
,
2008
, “
Numerical Simulation and Experimentation of Overlapping Laser Shock Processing With Symmetry Cell
,”
Int. J. Mach. Tools Manuf.
,
48
(
2
), pp.
152
162
.10.1016/j.ijmachtools.2007.08.021
7.
Cao
,
Y.
,
Zhao
,
X.
, and
Shin
,
Y. C.
,
2013
, “
Analysis of Nanosecond Laser Ablation of Aluminum With and Without Phase Explosion in Air and Water
,”
J. Laser Appl.
,
25
(
3
), p.
032002
.10.2351/1.4794032
8.
Hu
,
Y. X.
,
Gong
,
C. M.
,
Yao
,
Z. Q.
, and
Hu
,
J.
,
2009
, “
Investigation on the Non-Homogeneity of Residual Stress Field Induced by Laser Shock Peening
,”
Surf. Coat. Technol.
,
203
(
23
), pp.
3503
3508
.10.1016/j.surfcoat.2009.04.029
9.
Sealy
,
M. P.
, and
Guo
,
Y. B.
,
2010
, “
Surface Integrity and Process Mechanics of Laser Shock Peening of Novel Biodegradable Magnesium–Calcium (Mg–Ca) Alloy
,”
J. Mech. Behav. Biomed. Mater.
,
3
(
7
), pp.
488
496
.10.1016/j.jmbbm.2010.05.003
10.
Park
,
I.
,
Amarchinta
,
H. K.
, and
Grandhi
,
R. V.
,
2010
, “
A Bayesian Approach for Quantification of Model Uncertainty
,”
Reliab. Eng. Syst. Saf.
,
95
(
7
), pp.
777
785
.10.1016/j.ress.2010.02.015
11.
Amarchinta
,
H.
,
Tarpey
,
T.
, and
Grandhi
,
R. V.
,
2010
, “
Regression Uncertainty Quantification Using Bootstrap Method for Residual Stress Field Predictions
,”
51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, S. Mahadevan, ed., Orlando, FL, Apr. 12–15.
12.
Kennedy
,
M. C.
, and
O'Hagan
,
A.
,
2001
, “
Bayesian Calibration of Computer Models
,”
J. R. Stat. Soc.: Ser. B
,
63
(
3
), pp.
425
464
.10.1111/1467-9868.00294
13.
Bayarri
,
M. J.
,
Berger
,
J. O.
,
Paulo
,
R.
,
Sacks
,
J.
,
Cafeo
,
J. A.
,
Cavendish
,
J.
,
Lin
,
C.-H.
, and
Tu
,
J.
,
2007
, “
A Framework for Validation of Computer Models
,”
Technometrics
,
49
(
2
), pp.
138
154
.10.1198/004017007000000092
14.
Higdon
,
D.
,
Gattiker
,
J.
,
Williams
,
B.
, and
Rightley
,
M.
,
2008
, “
Computer Model Calibration Using High-Dimensional Output
,”
J. Am. Stat. Assoc.
,
103
(
482
), pp.
570
583
.10.1198/016214507000000888
15.
Sollier
,
A.
,
Berthe
,
L.
, and
Fabbro
,
R.
,
2001
, “
Numerical Modeling of the Transmission of Breakdown Plasma Generated in Water During Laser Shock Processing
,”
Eur. Phys. J.: Appl. Phys.
,
16
(
2
), pp.
131
139
.10.1051/epjap:2001202
16.
Fabbro
,
R.
,
Fournier
,
J.
,
Ballard
,
P.
,
Devaux
,
D.
, and
Virmont
,
J.
,
1990
, “
Physical Study of Laser-Produced Plasma in Confined Geometry
,”
J. Appl. Phys.
,
68
(
2
), pp.
775
784
.10.1063/1.346783
17.
Berthe
,
L.
,
Fabbro
,
R.
,
Peyre
,
P.
,
Tollier
,
L.
, and
Bartnicki
,
E.
,
1997
, “
Shock Waves From a Water-Confined Laser-Generated Plasma
,”
J. Appl. Phys.
,
82
(
6
), pp.
2826
2832
.10.1063/1.366113
18.
Zhang
,
W.
,
Yao
,
Y. L.
, and
Noyan
,
I. C.
,
2004
, “
Microscale Laser Shock Peening of Thin Films, Part 1: Experiment, Modeling and Simulation
,”
ASME J. Manuf. Sci. Eng.
,
126
(
1
), pp.
10
17
.10.1115/1.1645878
19.
Johnson
,
G.
, and
Cook
,
W.
,
1983
, “
A Constitutive Model and Data for Metals Subjected to Large Strains, High Srain Rates and High Temperatures
,”
Proceedings of the 7th International Symposium on Ballistics
, M. J. M ed., The Netherlands, Apr. 19–21.
20.
Holloway
,
J. P.
,
Bingham
,
D.
,
Chou
,
C.-C.
,
Doss
,
F.
,
Paul Drake
,
R.
,
Fryxell
,
B.
,
Grosskopf
,
M.
,
Van Der Holst
,
B.
,
Mallick
,
B. K.
,
Mcclarren
,
R.
,
Mukherjee
,
A.
,
Nair
,
V.
,
Powell
,
K. G.
,
Ryu
,
D.
,
Sokolov
,
I.
,
Toth
,
G.
, and
Zhang
,
Z.
,
2011
, “
Predictive Modeling of a Radiative Shock System
,”
Reliab. Eng. Syst. Saf.
,
96
(
9
), pp.
1184
1193
.10.1016/j.ress.2010.08.011
21.
Rasmussen
,
C. E.
, and
Williams
,
C.
,
2006
,
Gaussian Processes for Machine Learning
,
MIT Press
,
Boston, MA
.
22.
Higdon
,
D.
,
Kennedy
,
M.
,
Cavendish
,
J.
,
Cafeo
,
J.
, and
Ryne
,
R.
,
2004
, “
Combining Field Data and Computer Simulations for Calibration and Prediction
,”
SIAM J. Sci. Comput.
,
26
(
2
), pp.
448
466
.10.1137/S1064827503426693
23.
Metropolis
,
N.
,
Rosenbluth
,
A. W.
,
Rosenbluth
,
M. N.
,
Teller
,
A. H.
, and
Teller
,
E.
,
1953
, “
Equation of State Calculations by Fast Computing Machines
,”
J. Chem. Phys.
,
21
(
6
), pp.
1087
1092
.10.1063/1.1699114
24.
Robert
,
C.
, and
Casella
,
G.
,
2004
,
Monte Carlo Statistical Methods
,
Springer-Verlag
,
New York
.
25.
Bates
,
R. A.
,
Buck
,
R. J.
,
Riccomagno
,
E.
, and
Wynn
,
H. P.
,
1996
, “
Experimental Design and Observation for Large Systems
,”
J. R. Stat. Soc. Ser. B
,
58
(
1
), pp.
77
94
.10.2307/2346166
26.
Johnson
,
M.
,
Moore
,
L.
, and
Ylvisaker
,
D.
,
1990
, “
Minimax and Maximin Distance Designs
,”
J. Stat. Plann. Inference
26
(
2
), pp.
131
148
.10.1016/0378-3758(90)90122-B
You do not currently have access to this content.