Effective and efficient simulation-based design is facilitated by models of appropriate complexity. A single model will not have the most appropriate level of complexity throughout all phases of a simulation maneuver if inputs or parameters vary. Ideally, a model for which complexity can be varied as necessary will achieve the best possible trade-off between accuracy and computational efficiency. A method is presented for switching system model elements on and off as their importance changes, and predicting the response of the resulting variable-complexity model. A modified transformer element removes the dynamic output of a model element to the rest of the system when the moving average of its absolute power falls below a user-defined threshold. When the element is “off,” the input from the system to the element is still passed through the transformer so that an estimate of element power and importance can continue to be calculated and the element switched back “on” if necessary. The bond graph formalism is used to facilitate implementation. Switch configurations are defined for both causally weak and causally strong energy storage and dissipative elements. The method is applicable to linear or nonlinear systems that can be modeled with lumped parameter elements. The approach is demonstrated for quarter- and half-car vehicle models subject to a road profile of varying frequency. The appropriate model complexity at all stages is determined and implemented continuously without prior knowledge of input or parameter changes.

1.
Sendur
,
P.
,
Stein
,
J. L.
,
Louca
,
L. S.
, and
Peng
,
H.
, 2002, “
A Model Accuracy and Validation Algorithm
,”
Proceedings of the 2002 ASME IMECE
, New Orleans, LA.
2.
Bell
,
D. G.
, and
Taylor
,
D. L.
, 1990, “
Determining Optimal Model Complexity in an Iterative Design Process
,”
Proceedings of the ASME Design Theory and Methodology—DTM ‘90
, Chicago, IL, pp.
291
297
.
3.
2009, 20SIM, Version 4.1, Controllab Products B.V., Enschede, The Netherlands.
4.
Karnopp
,
D.
,
Margolis
,
D.
, and
Rosenberg
,
R.
, 2006,
System Dynamics: Modeling and Simulation of Mechatronic Systems
, 4th ed.,
Wiley
,
New York
.
5.
Rosenberg
,
R. C.
, and
Zhou
,
T.
, 1988, “
Power-Based Model Insight
,”
Proceedings of the 1988 ASME Winter Annual Meeting, Symposium on Automated Modeling for Design
, Chicago, IL, ASME Book No. G00460, pp.
61
67
.
6.
Louca
,
L. S.
,
Stein
,
J. L.
,
Hulbert
,
G. M.
, and
Sprague
,
J.
, 1997, “
Proper Model Generation: An Energy-Based Methodology
,”
Proceedings of the International Conference on Bond Graph Modeling ICGBM ‘97
, Phoenix, AZ,
Society for Computer Simulation
,
San Diego, CA
.
7.
Rideout
,
D. G.
,
Stein
,
J. L.
, and
Louca
,
L. S.
, 2007, “
A Systematic Identification of Decoupling in Dynamic System Models
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
129
(
4
), pp.
503
513
.
8.
Kypuros
,
J. A.
, and
Longoria
,
R. G.
, 2002 “
Variable Fidelity Modeling of Vehicle Ride Dynamics Using an Element Activity Metric
,”
Proceedings of the ASME IMECE 2002
, New Orleans, LA, pp.
525
534
.
9.
MATLAB R2007A, The MathWorks, Natick, MA.
10.
Kypuros
,
J. A.
, and
Longoria
,
R. G.
, 2003, “
Model Synthesis for Design of Switched Systems Using a Variable Structure System Formulation
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
125
(
4
), pp.
618
629
.
11.
Stein
,
J. L.
, and
Tseng
,
Y. -T.
, 1991, “
Strategies for Automating the Modeling Process
,”
Proceedings of the 1991 ASME Winter Annual Meeting, Symposium on Automated Modeling
, Atlanta, GA, ASME DSC-Vol.
34
, pp.
69
87
.
12.
Asher
,
G. M.
, 1993, “
The Robust Modelling of Variable Topology Circuits Using Bond Graphs
,”
Proceedings of ICBGM ‘93
, San Diego, CA, pp.
126
131
.
13.
Ducreux
,
J. P.
,
Dauphin-Tanguy
,
G.
, and
Rombaut
,
C.
, 1993, “
Bond Graph Modelling of Commutation Phenomena in Power Electronics Circuits
,”
Proceedings of ICBGM ‘93
, San Diego, CA, pp.
132
136
.
14.
Garcia
,
J.
,
Dauphin-Tanguy
,
G.
, and
Rombaut
,
C.
, 1997, “
A Bond Graph Approach for Modeling Switching Losses of Power Semiconductor Devices
,”
Proceedings of the International Conference on Bond Graph Modeling ICBGM ‘97
, pp.
207
212
.
15.
Strömberg
,
J. -E.
,
Top
,
J. L.
, and
Söderman
,
U.
, 1993, “
Variable Causality in Bond Graphs Caused by Discrete Effects
,”
Proceedings of ICBGM’93
, San Diego, CA, pp.
115
119
.
16.
Mosterman
,
P. J.
, and
Biswas
,
G.
, 1998, “
A Theory of Discontinuities in Dynamic Physical Systems
,”
J. Franklin Inst.
0016-0032,
335B
(
3
), pp.
401
438
.
17.
Demİir
,
Y.
,
Poyraz
,
M.
, and
Köksal
,
M.
, 1997, “
Derivation of State and Output Equations for Systems Containing Switches and a Novel Definition of a Switch Using the Bond Graph Method
,”
J. Franklin Inst.
0016-0032,
334
(
2
), pp.
191
197
.
18.
Umarikar
,
A. C.
, and
Umanand
,
L.
, 2005, “
Modelling of Switching Systems in Bond Graphs Using the Concept of Switched Power Junctions
,”
J. Franklin Inst.
0016-0032,
342
, pp.
131
147
.
19.
Junco
,
S.
, et al.
, 2007, “
On Commutation Modeling in Bond Graphs
,”
Proceedings of ICBGM ‘07
, San Diego, CA, pp.
12
19
.
20.
Dauphin-Tanguy
,
G.
, and
Rombaut
,
C.
, 1993, “
Why a Unique Causality in the Elementary Commutation Cell Bond Graph Model of a Power Electronics Converter
,”
Proceedings of the IEEE International Conference on Systems, Man and Cybernetics
, pp.
257
263
.
21.
Karnopp
,
D.
, 1985, “
General Method for Including Rapidly Switched Devices in Dynamic System Simulation Models
,”
Trans. Soc. Comput. Simul. Int.
0740-6797,
2
(
2
), pp.
155
168
.
22.
Paynter
,
H. M.
, and
Longoria
,
R. G.
, 1997, “
Two-Port Canonical Bond Graph Models of Lossy Power Transduction
,”
Proceedings of the IEEE International Conference on Systems, Man and Cybernetics
, Vol.
2
, pp.
1533
1537
.
23.
Louca
,
L. S.
, and
Stein
,
J. L.
, 2002, “
Ideal Physical Element Representation From Reduced Bond Graphs
,”
Proc. IMechE Part I: J. Systems and Control Engineering Special Issue
,
216
, pp.
73
83
.
24.
Karnopp
,
D.
, and
Margolis
,
D.
, 1979, “
Analysis and Simulation of Planar Mechanism Systems Using Bond Graphs
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
101
, pp.
187
191
.
You do not currently have access to this content.