Reduction of models of large scale lumped structures using normal modes and bond graphs

Margolis, Donald L.; Young, Greg

doi:10.1016/0016-0032(77)90107-7

Cited by 22 publications

(2 citation statements)

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“…Elements with small contribution are eliminated in order to produce a reduced model. The element activity metric provides more flexibility from frequency-based metrics that address the issue of model complexity by the frequency content of the model (Margolis and Young, 1977). In contrast, the activity metric considers the importance of all energetic elements, and therefore, the significance of all energy elements in the model can be described.…”

Section: Introductionmentioning

confidence: 99%

Power Conserving Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

Louca

2014

Journal of Dynamic Systems, Measurement, and Control

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Dynamic analysis is extensively used to study the behavior of continuous and lumped parameter linear systems. In addition to the physical space, analyses can also be performed in the modal space where very useful frequency information of the system can be extracted. More specifically, modal analysis can be used for the analysis and controller design of dynamic systems, where reduction of model complexity without degrading its accuracy is often required. The reduction of modal models has been extensively studied and many reduction techniques are available. The majority of these techniques use frequency as the metric to determine the reduced model. This paper describes a new method for calculating modal decompositions of lumped parameter systems with the use of the bond graph formulation. The modal decomposition is developed through a power conserving coordinate transformation. The generated modal decomposition model is then used as the basis for reducing its size and complexity. The model reduction approach is based on the previously developed model order reduction algorithm (MORA), which uses the energy-based activity metric in order to generate a series of reduced models. The activity metric was originally developed for the generic case of nonlinear systems; however, in this work, the activity metric is adapted for the case of linear systems with single harmonic excitation. In this case closed form expressions are derived for the calculation of activity. An example is provided to demonstrate the power conserving transformation, calculation of the modal power and the elimination of unimportant modes or modal elements.

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Section: Introductionmentioning

confidence: 99%

Power Conserving Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

Louca

2014

Journal of Dynamic Systems, Measurement, and Control

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“…The literature presents many model reduction techniques including component cost analysis [2], balanced truncation [3], polynomial approximation methods [4][5][6], optimal Hankel norm approximation [7], optimization-based methods [8,9], proper orthogonal decomposition [10,11], singular perturbation [12], and modal analysis [13,14]. A thorough review of these techniques is omitted herein, but provided in a companion to this paper [15].…”

Section: Introductionmentioning

confidence: 99%

Realization-Preserving Structure and Order Reduction of Nonlinear Energetic System Models Using Energy Trajectory Correlations

Ersal

Fathy

Stein

2009

Journal of Dynamic Systems, Measurement, and Control

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Previous work by the authors developed algorithms for simplifying the structure of a lumped dynamic system model and reducing its order. This paper extends this previous work to enable simultaneous model structure and order reduction. Specifically, it introduces a new energy-based metric to evaluate the relative importance of energetic connections in a model. This metric (1) accounts for correlations between energy flow patterns in a model using the Karhunen–Loève expansion; (2) examines all energetic connections in a model, thereby assessing the relative importance of both energetic components and their interactions, and enabling both order and structural reduction; and (3) is realization preserving, in the sense of not requiring a state transformation. A reduction scheme based on this metric is presented and illustrated using a simple example. The example shows that the proposed method can successfully concurrently reduce model order and structure without requiring a realization change, and that it can provide an improved assessment of the importance of various model components due to its correlation-based nature.

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Rigid Body, Flexible Body, and Micro Electromechanical Systems

Samantaray

Pathak

Bouamama

2012

Intelligent Mechatronic Systems

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Reduction of models of large scale lumped structures using normal modes and bond graphs

Cited by 22 publications

References 1 publication

Power Conserving Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

Power Conserving Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

Realization-Preserving Structure and Order Reduction of Nonlinear Energetic System Models Using Energy Trajectory Correlations

Rigid Body, Flexible Body, and Micro Electromechanical Systems

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