Component-based system simulation models are used throughout all development phases for design and verification of both physical systems and control software, not least in the aeronautical industry. However, the application of structured methods for uncertainty quantification (UQ) of system simulation models is rarely seen. To enable dimensionality reduction of a UQ problem and to thereby make UQ more feasible for industry-grade system simulation models, this paper describes a pragmatic method for uncertainty aggregation. The central idea of the proposed aggregation method is to integrate information obtained during common practice component-level validation directly into the components, and to utilize this information in model-level UQ. A generic component output uncertainty description has been defined and implemented in a Modelica library for modeling and simulation (M&S) of aircraft vehicle systems. An example is provided on how to characterize and quantify a component's aggregated output uncertainty based on the component-level bench test measurement data. Furthermore, the industrial applicability of the uncertainty aggregation method is demonstrated in an approximate UQ of an aircraft liquid cooling system simulation model. For cases when the concept of thorough UQ resulting in probability boxes is not feasible, the demonstrated approximate UQ using aggregated uncertainties is considered to be a pragmatic alternative fairly in reach for the common M&S practitioner within the area of system simulation.

References

References
1.
Steinkellner
,
S.
,
Andersson
,
H.
,
Gavel
,
H.
,
Lind
,
I.
, and
Krus
,
P.
,
2010
, “
Modeling and Simulation of Saab Gripens Vehicle Systems, Challenges in Processes and Data Uncertainties
,”
27th International Congress of the Aeronautical Sciences
(
ICAS
), Nice, France, Sept. 19–24.
2.
Cooke
,
R. M.
, and
Kelly
,
G. N.
,
2010
, “
Climate Change Uncertainty Quantification: Lessons Learned From the Joint EU-USNRC Project on Uncertainty Analysis of Probabilistic Accident Consequence Codes
,” Resources for the Future, Washington, DC,
RFF DP 10-29
.
3.
Katz
,
R. W.
,
Craigmile
,
P. F.
,
Guttorp
,
P.
,
Haran
,
M.
,
Sanso
,
B.
, and
Stein
,
M. L.
,
2013
, “
Uncertainty Analysis in Climate Change Assessments
,”
Nat. Clim. Change
,
3
(
9
): pp.
769
771
.
4.
Eek
,
M.
,
Kharrazi
,
S.
,
Gavel
,
H.
, and
Ölvander
,
J.
,
2015
, “
Study of Industrially Applied Methods for Verification, Validation & Uncertainty Quantification of Simulator Models
,”
Int. J. Model., Simul., Sci. Comput.
,
6
(
2
), p. 1550014.
5.
Carlsson
,
M.
,
Steinkellner
,
S.
,
Gavel
,
H.
, and
Ölvander
,
J.
,
2013
, “
Enabling Uncertainty Quantification of Large Aircraft System Simulation Models
,”
Council of European Aerospace Societies
(
CEAS
) Conference, Linköping, Sweden, Sept. 16–19, pp.
682
692
.
6.
Saltelli
,
A.
,
Ratto
,
M.
,
Andres
,
T.
,
Campolongo
,
F.
,
Cariboni
,
J.
,
Gatelli
,
D.
,
Saisana
,
M.
, and
Tarantola
,
S.
,
2008
,
Global Sensitivity Analysis: The Primer
,
Wiley
,
New York
.
7.
Helton
,
J. C.
,
Johnson
,
J. D.
,
Sallaberry
,
C. J.
, and
Storlie
,
C. B.
, “
Survey of Sampling-Based Methods for Uncertainty and Sensitivity Analysis
,”
Reliability Engineering & System Safety
,
91
(
10–11
): pp.
1175
1209
,
2006
.
8.
Zhang
,
Y.
,
Liu
,
Y.
,
Yang
,
X.
, and
Yue
,
Z.
,
2014
, “
A Global Nonprobabilistic Reliability Sensitivity Analysis in the Mixed Aleatory–Epistemic Uncertain Structures
,”
Proc. Inst. Mech. Eng., Part G
,
228
(
10
), pp.
1802
1814
.
9.
Roy
,
C. J.
, and
Oberkampf
,
W. L.
,
2011
, “
A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
25–28
), pp.
2131
2144
.
10.
Coleman
,
H. W.
, and
Steele
,
W. G.
,
2009
,
Experimentation, Validation, and Uncertainty Analysis for Engineers
,
3 ed.
,
Wiley
,
Hoboken, NJ
.
11.
Helton
,
J. C.
,
1994
, “
Treatment of Uncertainty in Performance Assessments for Complex Systems
,”
Risk Analysis
,
14
(
4
), pp.
483
511
.
12.
Helton
,
J. C.
,
1996
, “
Probability, Conditional Probability and Complementary Cumulative Distribution Functions in Performance Assessment for Radioactive Waste Disposal
,”
Reliab. Eng. Syst. Safety
,
54
(
2–3
), pp.
145
163
.
13.
Pace
,
D. K.
,
2013
, “
Comprehensive Consideration of Uncertainty in Simulation Use
,”
J. Def. Model. Simul.: Appl., Methodol., Technol.
,
10
(
4
), pp.
367
380
.
14.
Pace
,
D. K.
,
2009
, “
Simulation Uncertainty and Validation
,”
Spring Simulation Interoperability Workshop
(SISO), San Diego, CA, Mar. 23–27, pp.
547
555
.
15.
Carlsson
,
M.
,
2013
, “
Methods for Early Model Validation: Applied on Simulation Models of Aircraft Vehicle Systems
,”
Lic.Eng. thesis
, Linköping University, Linköping, Sweden.
16.
Krus
,
P.
,
2005
, “
Robust System Modelling Using Bi-Lateral Delay Lines
,”
2nd Conference on Modeling and Simulation for Safety and Security
(
SimSafe
), Linköping, Sweden, May 30.
17.
Braun
,
R.
,
2013
, “
Multi-Threaded Distributed System Simulations: Using Bi-Lateral Delay Lines
,”
Lic.Eng. thesis
, Linköping University, Linköping, Sweden.
18.
Sjölund
,
M.
,
Braun
,
R.
,
Fritzon
,
P.
, and
Krus
,
P.
,
2010
, “
Towards Efficient Distributed Simulation in Modelica Using Transmission Line Modeling
,”
3rd International Workshop on Equation-Based Object-Oriented Languages and Tools
(
EOOLT
), Oslo, Norway, Oct. 3, pp.
71
77
.
19.
Borutzky
,
W.
,
2002
, “
Bond Graphs and Object-Oriented Modelling—A Comparison
,”
Proc. Inst. Mech. Eng.
, Part I,
216
(
1
), pp.
21
33
.
20.
Krus
,
P.
,
2008
, “
Distributed Modelling Techniques for System Simulation
,” Linköping University, Linköping, Sweden, Report No. LIU-IEI-R-08/0020-SE.
21.
Franke
,
R.
,
Casella
,
F.
,
Sielemann
,
M.
,
Proelss
,
K.
,
Otter
,
M.
, and
Wetter
,
M.
,
2009
, “
Standardization of Thermo-Fluid Modeling in Modelica Fluid
,”
7th International Modelica Conference
, Como, Italy, Sept. 20–22, pp.
122
131
.
22.
Fritzson
,
P.
,
2014
,
Principles of Object Oriented Modeling and Simulation With Modelica 3.3: A Cyber-Physical Approach
, 2nd ed.,
Wiley
,
Hoboken, NJ
.
23.
Pace
,
D. K.
,
2004
, “
Modeling and Simulation Verification and Validation Challenges
,”
Johns Hopkins APL Tech. Dig.
,
25
(
2
), pp.
163
172
.
24.
Carlsson
,
M.
,
Andersson
,
H.
,
Gavel
,
H.
, and
Ölvander
,
J.
,
2012
, “
Methodology for Development and Validation of Multipurpose Simulation Models
,”
AIAA
Paper No. 2012-0877.
25.
Simpson
,
T. W.
,
Poplinski
,
J. D.
,
Koch
,
P. N.
, and
Allen
,
J. K.
,
2001
, “
Metamodels for Computer-Based Engineering Design: Survey and Recommendations
,”
Eng. Comput.
,
17
(
2
), pp.
129
150
.
26.
Hemez
,
F.
,
Atamturktur
,
H. S.
, and
Unal
,
C.
,
2010
, “
Defining Predictive Maturity for Validated Numerical Simulations
,”
Comput. Struct.
,
88
(
7–8
), pp.
497
505
.
27.
Carlsson
,
M.
,
Gavel
,
H.
, and
Ölvander
,
J.
,
2012
, “
Utilizing Uncertainty Information in Early Model Validation
,”
AIAA
Paper No. 2012-4852.
28.
Carlsson
,
M.
,
Gavel
,
H.
, and
Ölvander
,
J.
,
2012
, “
Evaluating Model Uncertainty Based on Probabilistic Analysis and Component Output Uncertainty Descriptions
,”
ASME
Paper No. IMECE2012-85236.
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