A review of Bond-graph representation based
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paper_title: The mathematical foundations of bond graphs—III. Matroid theory

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Abstract The cycle and co-cycle matroids of a bond graph are defined using chain group matroids derived from the cycle and co-cycle vector spaces of a bond graph. The relationship between these structures is investigated and various results are proved. A precise equivalence is defined for bond graphs. Duality theory is seen to be very clear in the context of bond graph matroids.
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paper_title: Automated modeling to support design

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The need to consider, a number of different alternatives at an early stage in design has been well established. It is hypothesized that providing a tool for automatically modeling and analyzing behavior of an artifact would aid the conceptual designer by facilitating the consideration of more varied alternatives. We describe a tool for automatic formulation of dynamic system models from user specified interconnection of components. The underlying methods are based on Bond Graph formalism using causal reasoning to simplify the model. The simplified model is not only more tractable for analysis and simulation but also facilitates inferences about the dominant characteristics of the designed artifact. Introduction Conceptual design encompasses the development and evaluation of different design configurations. For each proposed configuration the designer must specify the basic layout of the device, identify appropriate components, visualize how the components will fit together and mentally simulate how the device will perform. Human designers are good at visualizing the geometric interaction among the components but they are not as good at understanding how the components function together as a group. In this paper we present some ideas underlying a design tool for evaluating the dynamic performance of a mechanical device. We believe that numerical simulation models, useful though they are, do not promote insight about design trade-offs. Models that preserve the relationships between the different components of the physical system seem to be more appropriate for this task. This research focuses on techniques that allow building and analyzing symbolic models of dynamic behavior given a description of the artifact in terms of its components and kinematic connections among them. An Environment for Conceptual Design of Dynamic Systems A conceptual design environment [Paz-SoHUn'88a, PazSoldan 88b] should meet certain primary requirements: First, it should allow the designer to interact in a natural and convenient fashion using sketches, references to standard components and brief description of custom-made components. A second set of requirements for such an environment relates to modeling flexibility. The user should be able to refine the modeling deuil is well as aggregate simple component models into more complex components that can be subsequently thought of and manipulated as a unit. Finally, it should give useful feedback about the performance of the designed artifact. A design environment built to simplify configuration evaluation has to emulate the modeling skills of a good engineer. Modeling of physical systems involves a good amount of engineering judgment and manipulation skill. Engineering judgment is called for in choosing an appropriate model for the situation under consideration. While modeling a bicycle, such as shown in Figure 1, ihe bicycle frame can be considered as a single inertia or as a large set of point masses in constrained motion. Modeling insight allots ihe engineer to concentrate on the relevant aspects of the problem, while ignoring dimensions where essentially nothing interesting is happening. Making such simplifying assumptions involves, in pan. reasoning about and deleting parts of the model which either correspond to constrained degrees of freedom or degrees of freedom * hich are not excited. The model of the bicycle, for example, may or may not include the rotary inertia of the frame depending on the boundary conditions of the problem. Proficient modelers do this frequently and make analysis simpler. The design environment should emulate this behavior as much as possible. Approach The natural interface and modeling flexibility requirements can be satisfied by adopting a component-based representation *here each component is represented as a collection of geometric and (~r,caonal primitive elements. The designer can build up a doue by aggregating components, a process which will involve specifying spatial component locations and the connections between components. The process of aggregation thus proceeds on two UNIVERSITY LIBRARIES CARNEGIE-MELLON UNIVERSITY PITTSBURGH, PENNSYLVANIA 1 5 2 1 3 Figure 1: A Bicycle with Two Different Boundary Conditions fronts: Component geometry is assembled to obtain device form and component level behavior is combined to model device function. The flexibility requirements can be satisfied since the dynamic and geometric model of each component can be individually modified without having to change the way the components are aggregated. The integrated representation of geometry and behavior models also facilitates using form-function component relations to relate parameter values [Rindcrle 87, Colburn 90). The modular aggregation and arbitrary resolution of dynamic models is accomplished through a novel use of Bond Graphs [Paynter 61, Rosenberg 75] a formal graph based representation used for physical system modeling. A modular fragment of a Bond Graph is associated with each component and as the components are connected the individual models are collected into a device model. Bond Graph theory provides a consistent basis for this process of aggregation, so that the kinematic constraints between components, specified by the designer, are sufficient information for assembling the component bond graph modules. The aggregate Bond Graph is simplified and reduced to a set of differential equations which are used to reason about the dynamic behavior of the designed system. connections to accommodate rotation as well u independent X and Y velocities. The forces at these ports excite the rotational and txmslational energy storage modes of the mass. The degree to which a force at one of the pom causes rotation or translation depends on the location of interaction. The -TFelements in the model account for this by transforming an arbitrary force and moment at a position to equivalent forces and moments about the center of gravity. The moduli of the transformer (TF) elements depends only on the location of force/moment application relative to the center of gravity. A mass may of course interact with other components at an arbitrary number of points. We define a composite mass to accommodate this arbitrary degree of connectivity by establishing rigid connections among many mass elements and thereby preserve the natural designer interface. The small hatched circles at the end of the bonds represent a consistent power-sense assignment Kinematic connections are also modeled as bond graph fragments. The model of a connector has a «1«, or common velocity, junction corresponding to every velocity, X, Y or rotational, that it constrains. A pinned connection includes two -1* junctions corresponding to common X and Y velocities. A rigid connection, as in Figure 4, includes an additional -1junction because rotation of two rigidly connected masses is identical.
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paper_title: A bond graph based approach to case--based synthesis

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Abstract : The paper presents an algorithm for case based synthesis of single input single output power drive systems based on dynamic behavior design specifications. The case base consists of electromechanical components modelled using the bond graph formalism. An hierarchical classification scheme for devices that distinguishes between the functional and structural aspects of a device is described. The synthesis algorithm also combines conceptual and parametric design in a coherent computational scheme. Examples illustrating the device representation and synthesis algorithm are described.
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Title: A Review of Bond-graph Representation Based

Section 1: Introduction
Description 1: Describe the research context, significance of bond graphs in electromechanical design, and summarize the hierarchical design phases.

Section 2: A brief review of Bond graphs
Description 2: Summarize the basic features of the bond-graph methodology and its application in modeling and analyzing the dynamics of physical systems.

Section 3: Bond-graph port models
Description 3: Discuss the dynamics of physical systems modeled by one-port, two-port, and three-port elements, including complex topologies and power conservation.

Section 4: Causality
Description 4: Explain the concept of causality in bond-graph terminology and its relevance to computation, focusing on the causality of one-port models.

Section 5: Analysis of physical systems using bond-graphs
Description 5: Describe how bond-graphs can be transformed into state-space differential equations for analyzing physical systems' behavior over time.

Section 6: Summary of bond-graph characteristics
Description 6: Summarize the advantages and drawbacks of the bond-graph methodology from the design perspective.

Section 7: Bond graphs and design
Description 7: Explore how bond graphs are used for dynamic analysis and behavior synthesis in design, and discuss their limitations in static systems and spatial form design.

Section 8: Reviews of research
Description 8: Summarize and critique various design methodologies proposed in the literature, focusing on design specifications, synthesis, and verification procedures using bond graphs.

Section 9: Clarifications and issues for further research
Description 9: Discuss inconsistencies, ambiguities, and fallacies in the reviewed methodologies, and propose how bond graphs can enable development of representations for synthesis.