Energy-Based Model Reduction Methodology for Automated Modeling

[+] Author and Article Information
Loucas S. Louca

Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia 1678, Cypruslslouca@ucy.ac.cy

Jeffrey L. Stein

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125stein@umich.edu

Gregory M. Hulbert

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125hulbert@umich.edu

J. Dyn. Sys., Meas., Control 132(6), 061202 (Oct 28, 2010) (16 pages) doi:10.1115/1.4002473 History: Received February 05, 2009; Revised July 22, 2010; Published October 28, 2010; Online October 28, 2010

In recent years, algorithms have been developed to help automate the production of dynamic system models. Part of this effort has been the development of algorithms that use modeling metrics for generating minimum complexity models with realization preserving structure and parameters. Existing algorithms, add or remove ideal compliant elements from a model, and consequently do not equally emphasize the contribution of the other fundamental physical phenomena, i.e., ideal inertial or resistive elements, to the overall system behavior. Furthermore, these algorithms have only been developed for linear or linearized models, leaving the automated production of models of nonlinear systems unresolved. Other model reduction techniques suffer from similar limitations due to linearity or the requirement that the reduced models be realization preserving. This paper presents a new modeling metric, activity, which is based on energy. This metric is used to order the importance of all energy elements in a system model. The ranking of the energy elements provides the relative importance of the model parameters and this information is used as a basis to reduce the size of the model and as a type of parameter sensitivity information for system design. The metric is implemented in an automated modeling algorithm called model order reduction algorithm (MORA) that can automatically generate a hierarchical series of reduced models that are realization preserving based on choosing the energy threshold below which energy elements are not included in the model. Finally, MORA is applied to a nonlinear quarter car model to illustrate that energy elements with low activity can be eliminated from the model resulting in a reduced order model, with physically meaningful parameters, which also accurately predicts the behavior of the full model. The activity metric appears to be a valuable metric for automating the reduction of nonlinear system models—providing in the process models that provide better insight and may be more numerically efficient.

Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Energy elements and power variables shown in bond graph form

Grahic Jump Location
Figure 2

Comparison of the energy stored in an energy storage element versus the activity as provided by Eq. 1 for an oscillation of power

Grahic Jump Location
Figure 4

Activity index sorting

Grahic Jump Location
Figure 5

Detail of reduce model procedure in Fig. 3

Grahic Jump Location
Figure 6

Nonlinear quarter car model representations—full model

Grahic Jump Location
Figure 7

Road profile—road elevation, Zr(x) and velocity, Vr(x)

Grahic Jump Location
Figure 8

Element activity, VF=1 m/s

Grahic Jump Location
Figure 9

Model reduction, VF=1 m/s, β=95%

Grahic Jump Location
Figure 10

Full versus reduced model and error (full minus reduced), VF=1 m/s

Grahic Jump Location
Figure 11

Element activity, VF=5 m/s

Grahic Jump Location
Figure 12

Model reduction, VF=5 m/s, β=95%

Grahic Jump Location
Figure 13

Full versus reduced model and error, VF=5 m/s

Grahic Jump Location
Figure 14

Series of reduced models by varying the reduction threshold

Grahic Jump Location
Figure 15

Accuracy of reduced models (Note that the responses of the full and reduced 1 models are not visible since they are overlaid by the almost identical response of the reduced 2 model)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In