Abstract

The consideration of uncertainty is especially important for the design of complex systems. Because of high complexity, the total system is normally divided into subsystems, which are treated in a hierarchical and ideally independent manner. In recent publications, e.g., (Zimmermann, M., and von Hoessle, J. E., 2013, “Computing Solution Spaces for Robust Design,” Int. J. Numer. Methods Eng., 94(3), pp. 290–307; Fender, J., Duddeck, F., and Zimmermann, M., 2017, “Direct Computation of Solution Spaces,” Struct. Multidiscip. Optim., 55(5), pp. 1787–1796), a decoupling strategy is realized via first the identification of the complete solution space (solutions not violating any design constraints) and second via derivation of a subset, a so-called box-shaped solution space, which allows for decoupling and therefore independent development of subsystems. By analyzing types of uncertainties occurring in early design stages, it becomes clear that especially lack-of-knowledge uncertainty dominates. Often, there is missing knowledge about overall manufacturing tolerances like limitations in production or subsystems are not even completely defined. Furthermore, flexibility is required to handle new requirements and shifting preferences concerning single subsystems arising later in the development. Hence, a set-based approach using intervals for design variables (i.e., interaction quantities between subsystems and the total system) is useful. Because in the published approaches, no uncertainty consideration was taken into account for the computation of these intervals, they can possibly have inappropriate size, i.e., being too narrow. The work presented here proposes to include these uncertainties related to design variables. This allows now to consider lack-of-knowledge uncertainty specific for early phase developments in the framework of complex systems design. An example taken from a standard crash load case (frontal impact against a rigid wall) illustrates the proposed methodology.

References

References
1.
Zimmermann
,
M.
, and
von Hoessle
,
J. E.
,
2013
, “
Computing Solution Spaces for Robust Design
,”
Int. J. Numer. Methods Eng.
,
94
(
3
), pp.
290
307
.10.1002/nme.4450
2.
Fender
,
J.
,
Duddeck
,
F.
, and
Zimmermann
,
M.
,
2017
, “
Direct Computation of Solution Spaces
,”
Struct. Multidiscip. Optim.
,
55
(
5
), pp.
1787
1796
.10.1007/s00158-016-1615-y
3.
Beyer
,
H.-G.
, and
Sendhoff
,
B.
,
2007
, “
Robust Optimization—A Comprehensive Survey
,”
Comput. Methods Appl. Mech. Eng.
,
196
(
33–34
), pp.
3190
3218
.10.1016/j.cma.2007.03.003
4.
Chakraborty
,
S.
,
Chatterjee
,
T.
,
Chowdhury
,
R.
, and
Adhikari
,
S.
,
2017
, “
Robust Design Optimization for Crashworthiness of Vehicle Side Impact
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B
,
3
(
3
), p.
031002
.10.1115/1.4035439
5.
Hendrix
,
E. M.
,
Mecking
,
C. J.
, and
Hendriks
,
T. H.
,
1996
, “
Finding Robust Solutions for Product Design Problems
,”
Eur. J. Oper. Res.
,
92
(
1
), pp.
28
36
.10.1016/0377-2217(95)00082-8
6.
Rocco
,
C. M.
,
Moreno
,
J. A.
, and
Carrasquero
,
N.
,
2003
, “
Robust Design Using a Hybrid-Cellular-Evolutionary and Interval-Arithmetic Approach: A Reliability Application
,”
Reliab. Eng. Syst. Saf.
,
79
(
2
), pp.
149
159
.10.1016/S0951-8320(02)00226-0
7.
Salazar
,
D. E.
, and
Rocco
,
C. M.
,
2007
, “
Solving Advanced Multi-Objective Robust Designs by Means of Multiple Objective Evolutionary Algorithms (MOEA): A Reliability Application
,”
Reliab. Eng. Syst. Saf.
,
92
(
6
), pp.
697
706
.10.1016/j.ress.2006.03.003
8.
Erschen
,
S.
,
Duddeck
,
F.
,
Gerdts
,
M.
, and
Zimmermann
,
M.
,
2018
, “
On the Optimal Decomposition of High-Dimensional Solution Spaces of Complex Systems
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B
,
4
(
2
), pp.
1
15
.10.1115/1.4037485
9.
Duddeck
,
F.
, and
Wehrle
,
E.
,
2015
, “
Recent Advances on Surrogate Modeling for Robustness Assessment of Structures With Respect to Crashworthiness Requirements
,”
Tenth European LS-DYNA Conference
, Würzburg, Germany, June 15–17.
10.
Nocedal
,
J.
, and
Wright
,
S. J.
,
2006
,
Numerical Optimization
,
Springer
,
New York
.
11.
Boyd
,
S.
, and
Vandenberghe
,
L.
,
2004
,
Convex Optimization
,
Cambridge University Press
,
New York
.
12.
Harwood
,
S. M.
, and
Barton
,
P. I.
,
2017
, “
How to Solve a Design Centering Problem
,”
Math. Methods Oper. Res.
,
86
(
1
), pp.
215
254
.10.1007/s00186-017-0591-3
13.
Fender
,
J.
,
2013
, “
Solution Spaces for Vehicle Crash Design
,”
Ph.D. thesis
, Technische Universität München, Munich, Germany.
14.
Lange
,
V. A.
,
Fender
,
J.
,
Song
,
L.
, and
Duddeck
,
F.
,
2018
, “
Early Phase Modeling of Frontal Impacts for Crashworthiness: From Lumped Mass–Spring Models to Deformation Space Models
,”
Inst. Mech. Eng., Part D
(epub).10.1177/0954407018814034
You do not currently have access to this content.