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Energy-Based Bond Graph Model Reduction

  • L.S. LoucaEmail author
  • D.G. Rideout
  • T. Ersal
  • J.L. Stein
Chapter

Abstract

Model reduction refers to reducing the complexity of a given model to achieve a balance between model simplicity and accuracy. This chapter presents a set of model reduction techniques that are particularly amenable to bond graph models due to the common energy-based nature of these techniques and the bond graph language. Three techniques are presented that are developed with model order reduction, model partitioning, and simultaneous order and structure reduction in mind. Each technique utilizes a different energy-based metric that can be easily calculated from a bond graph model. These underlying metrics are presented first, followed by the algorithms, each with a simple illustrative example, as well as summaries of larger case studies performed with those algorithms to highlight their benefits. All three techniques are applicable to nonlinear models in differential–algebraic form, are realization preserving in the sense that the original meanings of the states and parameters are preserved, are trajectory dependent and thus explicitly take the specific inputs and parameter values into account, and can reduce models directly at the bond graph level.

Keywords

Model order reduction Model structure reduction Model partitioning Model simplification Model deduction Proper model Power and energy Activity Relative activity Junction inactivity Activity index Energetic contribution index Conditioning of bonds Decoupling Driving and driven subgraphs Driving and driven partitions Subgraph loop 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • L.S. Louca
    • 1
    Email author
  • D.G. Rideout
    • 2
  • T. Ersal
    • 3
  • J.L. Stein
    • 3
  1. 1.Department of Mechanical and Manufacturing EngineeringUniversity of CyprusNicosiaCyprus
  2. 2.Faculty of Engineering and Applied ScienceMemorial UniversitySt. John’sCanada
  3. 3.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA

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