Abstract

In order to impact physical mechanical system design decisions and realize the full promise of high-fidelity computational tools, simulation results must be integrated at the earliest stages of the design process. This is particularly challenging when dealing with uncertainty and optimizing for system-level performance metrics, as full-system models (often notoriously expensive and time-consuming to develop) are generally required to propagate uncertainties to system-level quantities of interest. Methods for propagating parameter and boundary condition uncertainty in networks of interconnected components hold promise for enabling design under uncertainty in real-world applications. These methods avoid the need for time consuming mesh generation of full-system geometries when changes are made to components or subassemblies. Additionally, they explicitly tie full-system model predictions to component/subassembly validation data which is valuable for qualification. These methods work by leveraging the fact that many engineered systems are inherently modular, being comprised of a hierarchy of components and subassemblies that are individually modified or replaced to define new system designs. By doing so, these methods enable rapid model development and the incorporation of uncertainty quantification earlier in the design process. The resulting formulation of the uncertainty propagation problem is iterative. We express the system model as a network of interconnected component models, which exchange solution information at component boundaries. We present a pair of approaches for propagating uncertainty in this type of decomposed system and provide implementations in the form of an open-source software library. We demonstrate these tools on a variety of applications and demonstrate the impact of problem-specific details on the performance and accuracy of the resulting UQ analysis. This work represents the most comprehensive investigation of these network uncertainty propagation methods to date.

References

1.
Carlberg
,
K.
,
Guzzetti
,
S.
,
Khalil
,
M.
, and
Sargsyan
,
K.
,
2019
, “
The Network Uncertainty Quantification Method for Propagating Uncertainties in Component-Based Systems
,” arXiv:1908.11476 [math.NA].
2.
Liao
,
Q.
, and
Willcox
,
K.
,
2015
, “
A Domain Decomposition Approach for Uncertainty Analysis
,”
SIAM J. Sci. Comput.
,
37
(
1
), pp.
A103
A133
.10.1137/140980508
3.
Martin
,
J. D.
, and
Simpson
,
T. W.
,
2006
, “
A Methodology to Manage System-Level Uncertainty During Conceptual Design
,”
ASME J. Mech. Des.
,
128
(
4
), pp.
959
968
.10.1115/1.2204975
4.
Rojas
,
E.
, and
Tencer
,
J.
,
2021
, “
Performance of Iterative Network Uncertainty Quantification for Multicomponent System Qualification
,”
ASME
Paper No. IMECE2021-72345.10.1115/IMECE2021-72345
5.
Le Maître
,
O.
, and
Knio
,
O. M.
,
2010
,
Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics
,
Springer Science & Business Media
,
Berlin, Germany
.
6.
Ghanem
,
R. G.
, and
Spanos
,
P. D.
,
2003
,
Stochastic Finite Elements: A Spectral Approach
,
Courier Corporation
,
New York
.
7.
Xiu
,
D.
, and
Karniadakis
,
G. E.
,
2002
, “
The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations
,”
SIAM J. Sci. Comput.
,
24
(
2
), pp.
619
644
.10.1137/S1064827501387826
8.
Xiu
,
D.
,
2010
, “
Numerical Methods for Stochastic Computations
,”
Numerical Methods for Stochastic Computations
,
Princeton University Press
,
Princeton, NJ
.
9.
Smith
,
B. F.
,
1997
, “
Domain Decomposition Methods for Partial Differential Equations
,”
Parallel Numerical Algorithms
,
Springer
,
Berlin, Germany
, pp.
225
243
.
10.
Chan
,
T. F.
, and
Mathew
,
T. P.
,
1994
, “
Domain Decomposition Algorithms
,”
Acta Numer.
,
3
, pp.
61
143
.10.1017/S0962492900002427
11.
Toselli
,
A.
, and
Widlund
,
O.
,
2004
,
Domain Decomposition Methods-Algorithms and Theory
, Vol.
34
,
Springer Science & Business Media
,
Berlin, Germany
.
12.
Sargsyan
,
K.
,
Safta
,
C.
,
Johnston
,
K.
,
Khalil
,
M.
,
Chowdhary
,
K. S.
,
Rai
,
P.
,
Casey
,
T. A.
,
Boll
,
L. D.
,
Zeng
,
X.
, and
Debusschere
,
B.
,
2021
, “
UQTk Version 3.1.1 User Manual sand2021-3655
,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2021-3655.
13.
Yang
,
X. I.
, and
Mittal
,
R.
,
2014
, “
Acceleration of the Jacobi Iterative Method by Factors Exceeding 100 Using Scheduled Relaxation
,”
J. Comput. Phys.
,
274
, pp.
695
708
.10.1016/j.jcp.2014.06.010
14.
Pratapa
,
P. P.
,
Suryanarayana
,
P.
, and
Pask
,
J. E.
,
2016
, “
Anderson Acceleration of the Jacobi Iterative Method: An Efficient Alternative to Krylov Methods for Large, Sparse Linear Systems
,”
J. Comput. Phys.
,
306
, pp.
43
54
.10.1016/j.jcp.2015.11.018
15.
Eyert
,
V.
,
1996
, “
A Comparative Study on Methods for Convergence Acceleration of Iterative Vector Sequences
,”
J. Comput. Phys.
,
124
(
2
), pp.
271
285
.10.1006/jcph.1996.0059
16.
Anderson
,
D. G.
,
1965
, “
Iterative Procedures for Nonlinear Integral Equations
,”
J. ACM (JACM)
,
12
(
4
), pp.
547
560
.10.1145/321296.321305
17.
Fang
,
H-R.
, and
Saad
,
Y.
,
2009
, “
Two Classes of Multisecant Methods for Nonlinear Acceleration
,”
Numer. Linear Algebra Appl.
,
16
(
3
), pp.
197
221
.10.1002/nla.617
18.
Toth
,
A.
, and
Kelley
,
C.
,
2015
, “
Convergence Analysis for Anderson Acceleration
,”
SIAM J. Numer. Anal.
,
53
(
2
), pp.
805
819
.10.1137/130919398
19.
Walker
,
H. F.
, and
Ni
,
P.
,
2011
, “
Anderson Acceleration for Fixed-Point Iterations
,”
SIAM J. Numer. Anal.
,
49
(
4
), pp.
1715
1735
.10.1137/10078356X
20.
SIERRA Thermal/Fluid Development Team
,
2019
, “
SIERRA Multimechanics Module: Aria User Manual - Version 4.52
,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2019-3786.
21.
Schroeder
,
B.
,
Hetzler
,
A.
,
Mills
,
B.
, and
Shelton
,
J.
,
2018
, “
An Effort Towards a Consistent VVUQ Approach for Thermal Systems Analyses
,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2018-5411 PE.
22.
Scott
,
S. N.
,
Dodd
,
A. B.
,
Larsen
,
M. E.
,
Suo-Anttila
,
J. M.
, and
Erickson
,
K. L.
,
2016
, “
Validation of Heat Transfer, Thermal Decomposition, and Container Pressurization of Polyurethane Foam Using Mean Value and Latin Hypercube Sampling Approaches
,”
Fire Technol.
,
52
(
1
), pp.
121
147
.10.1007/s10694-014-0448-8
23.
Benner
,
P.
,
Gugercin
,
S.
, and
Willcox
,
K.
,
2015
, “
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
,”
SIAM Rev.
,
57
(
4
), pp.
483
531
.10.1137/130932715
24.
Peherstorfer
,
B.
,
Willcox
,
K.
, and
Gunzburger
,
M.
,
2018
, “
Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
,”
Siam Rev.
,
60
(
3
), pp.
550
591
.10.1137/16M1082469
25.
Brunini
,
V.
,
Parish
,
E. J.
,
Tencer
,
J.
, and
Rizzi
,
F.
,
2022
, “
Projection-Based Model Reduction for Coupled Conduction–Enclosure Radiation Systems
,”
ASME J. Heat Transfer-Trans. ASME
,
144
(
6
), p. 062101.10.1115/1.4053994
26.
Gelsomino
,
F.
, and
Rozza
,
G.
,
2011
, “
Comparison and Combination of Reduced-Order Modelling Techniques in 3d Parametrized Heat Transfer Problems
,”
Math. Comput. Modell. Dyn. Syst.
,
17
(
4
), pp.
371
394
.10.1080/13873954.2011.547672
27.
Brunton
,
S. L.
, and
Kutz
,
J. N.
,
2022
,
Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
,
Cambridge University Press
,
Cambridge, UK
.
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