Pseudo bond graphs for generalized compartmental models in engineering and physiology

True bond graphs, which use effort and flow variables whose product is power, can in principle be used to describe all types of physical systems. However, many system models do not use power variables and yet can be represented usefully as pseudo bond graphs. Pseudo bond graphs have been used particularly for open systems in which it is convenient to consider control volumes or compartments with boundaries across which mass can flow. In this paper, we show how the bond graph methods used for conductive and convective heat transfer can be generalized to account for diffusion, convection, and accumulation of a variety of physical quantities and how pseudo bond graphs can aid in constructing and representing such models. These models are known in mathematical biology as “compartmental models” and it is a main contribution of this paper to show that the same pseudo bond graphs apply to thermofluid and physiological dynamic models. The bond graphs build in some conservation principles automatically and yet have the flexibility to incorporate general multiport laws when necessary. Thus the pseudo bond graphs can exhibit system structure as do other network graphs and are very general in nature.     

Bond graph formulation of an optimal control problem for linear time invariant systems

A recent communication has proposed a conjectural procedure for representing a category of optimal control problems in bond graph language [W. Marquis-Favre, B. Chereji, D. Thomasset, S. Scavarda, Bond graph representation of an optimal control problem: the dc motor example, in: ICBGM’05 International Conference of Bond Graph Modelling and Simulation, New Orleans, USA, January 23-27, 2005, pp. 239-244]. This paper aims at providing a fundamental theory for proving the effectiveness of this procedure. The class of problem that the procedure can deal with has been extended. Its application was formerly restricted to linear time invariant siso system. The systems considered now are linear time invariant mimo systems. The optimization objective is the minimization of dissipation and input. The developments concerning the optimal control problem are based on the Pontryagin maximum principle and the proof of the effectiveness of the procedure makes a broad use of the port-Hamiltonian concept. As a result, the bond graph representation of the given optimization problem enables the analytical system, which provides the optimal solution, to be derived. The work presented in this paper is the first step in research with perspectives towards formulating dynamic optimization problems in bond graph and, towards coupling this formulation with a sizing methodology using bond graph language and a state-space inverse model approach. This sizing methodology, however, is not the topic of this paper and thus is not presented here.     

Examination of chaotic behaviours using bond graph model

In this paper, modelling and simulation of Chua's chaotic oscillator, which exhibits rich chaotic behaviours, are presented by using the bond graph model. Up to now modelling of Chua's chaotic oscillator using bond graph model is not yet developed. The non-linear resistor in the circuit is modelled in this contribution by linear time-invariant components and ideal switches using piecewise linearization approach. The bond graph model of all the circuit including switches is then generated. Simulations are provided via the computer program called as BOMAS using the obtained bond graph model. Finally, Chua's circuit is verified experimentally. It is shown that all experimental and simulation results well agree with the chaotic behaviours of Chua's circuit.     

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The theory of transient operations of synchronous machines—the so called two-reaction theory—was developed during the years 1926–1938. Doherty, Nickle and Park made the first efforts to find a complete theory. The problem then was solved by Kron for a general rotating electrical machine. In this paper the two-axis-model-machine is described using a bond graph. An example is given in which state-space-equations and output-equations are derived from the bond graph. A power-conserving transformation between the electrical quantities of the armature windings of the model machine and those of the real three phase armature windings is developed. This transformation is shown as a displacement modulated transformer structure which is central to the bond graph model.     

A Bond Graph Description of U-Tube Steam Generator Dynamics

Bond graph methods are used to derive a nonlinear model of a U-tube steam generator like those used in pressurized water reactor (PWR) power plants. A major advantage of bond graph modeling is the ease with which different subsystem models can be interconnected; this feature is demonstrated in the steam generator modeling. Individual models of primary water cooling, generator tube heat capacity, secondary and downcomer fluid mass and energy flows, the feedwater supply system, and the main steam control valve are developed. The complete bond graph model is validated using data from a test reactor steam generator.     

Three-axis platform simulation: Bond graph and Lagrangian approach

A bond graph model is derived for the geometric constraints of a three-axis flight table. Gimbal dynamics are easily added even in asymmetrical and unbalanced cases. A method is introduced to make the local dependent inertias computable. The bond graph compares favourably to the Lagrangian approach as to modelling effort and accessibility of intermediate variables as well as having computational advantages.     

Bond graph fluid line models for inclusion with dynamic systems simulations

A procedure is presented whereby the control volume equations for one-dimensional, compressible gas dynamics are cast into first-order, state variable form. These equations are interpreted using causal bond graphs. The resulting bond graph is shown to reduce to the classic I-C chain under acoustic constraints and to a more recently developed model of low speed thermal energy transport subject to associated constraints.Through example it is demonstrated that the control volume bond graph is easily coupled to an overall system model and thus can be digitally simulated as part of the overall nonlinear state space representation. The result is that a very accurate gas dynamic model can be coupled with an overall dynamic system model without requiring a prohibitively large number of equations.     

Bond graphs in control: Physical state variables and observers

Bond graph modeling techniques yield state equations intimately related to energy storage in physical systems. The easy physical interpretation of the state variables from a bond graph model aids in the realization of modern automatic control schemes involving state variable feedback. When it is inconvenient or impossible or measure certain state variables, the useful device of an observer may be used to estimate the missing state variables. It is shown that the same bond graph used to model the system can be used to derive a complete or reduced order observer. The partial observers use derivative causality in a new way and in some cases, the effects of completely unknown disturbances may be accounted for.     

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

Bond graphs are an extremely useful modeling procedure for representing the actual energy exchange mechanisms of interacting dynamic systems. Governing state equations are straightforwardly obtained from the bond graph; however, for large structures, a restrictively large number of equations can result. A procedure is developed whereby the original equations are reduced to a form suitable for modal decomposition. The resulting modes are reinterpreted in bond graph form with the resulting model being an extremely accurate system representation while requiring only a fraction of the original number of equations. The procedure is demonstrated through example.     

Modelling and Passivity Based Control of switched systems from bond graph formalism: Application to multicellular converters

This paper addresses the modelling and control of switched systems with Boolean inputs. A generalization of Passivity Based Control (PBC) is proposed and fitted to bond graph formalism. The state equations of the equivalent average model are first deduced from the original bond graph using the notion of commutation cells and then interpreted according to Port Controlled Hamiltonian formalism. The whole approach is presented in a formal way. This method is then applied on a multicellular serial converter, which is widespread in power systems and of growing interest. The application of PBC associated to a modelling approach using commutation cells on a non-trivial example shows its efficiency to determine a generic controller, the number of elementary cells being considered as a parameter.     

Modeling of musculoskeletal structure and function using a modular bond graph approach

The dynamic effects of muscle strength, timing of muscle activations, and body geometry have been modeled for a wide variety of human activities. These types of models require the development of complex system equations that account for the effects of rigid-body dynamics, musculotendon actuators, passive and active resistance to motion, and other physiological structures. One way in which model refinement can be expedited is through the use of bond graph modeling techniques. While bond graph techniques have been used extensively in a broad variety of applications, they have been used only sparingly in the field of biomechanics, despite the potential suitability of a modular, multidomain approach to the modeling of musculoskeletal function. In the current paper, bond graph modules representing muscle function and rigid-body motions of underlying bone structures are introduced. The system equations generated with the use of these models are equivalent to those developed with more traditional techniques, but the modules can be more easily used in conjunction with control models of neuromuscular function for the simulation of overall dynamic motor performance.     

Robust graph learning with graph convolutional network

Graph convolutional network (GCN) is a powerful tool to process the graph data and has achieved satisfactory performance in the task of node classification. In general, GCN uses a fixed graph to guide the graph convolutional operation. However, the fixed graph from the original feature space may contain noises or outliers, which may degrade the effectiveness of GCN. To address this issue, in this paper, we propose a robust graph learning convolutional network (RGLCN). Specifically, we design a robust graph learning model based on the sparse constraint and strong connectivity constraint to achieve the smoothness of the graph learning. In addition, we introduce graph learning model into GCN to explore the representative information, aiming to learning a high-quality graph for the downstream task. Experiments on citation network datasets show that the proposed RGLCN outperforms the existing comparison methods with respect to the task of node classification.     

Complementary formulations in vibrations: bond graph structures and modal transformations

Lumped parameter, undamped vibratory system models are studied starting from a vector bond graph representation which yields a symmetric set of equations of motion in terms of momenta and displacements. Four additional formulations are obtained depending upon the choices of displacement or impulse-momentum degrees of freedom including the classical formulation in terms of mass displacements. Differences in terms of forcing and response variables are found among the alternative formulations and differences in system order are explained. A new form of normal mode equations is developed using first order symmetric variables and a bond graph representation is given. Advantages in the use of the new model analysis for subsystem coupling are discussed.     

Bond graph representation of a photoreception model

A bond graph network representation of a photoreception model of Limulus is derived. The admitted nerwork elements are exclusively restricted to the microscopically realistic processes of storage, diffusion and chemical reactions of molecules. All kinds of coupling in the network are explicitly expressed in terms of the above processes. The model is numerically evaluated and the results are compared with experimental data.     

Reduction of models of interacting lumped and distributed systems using bond graphs and repeated modal decomposition

Previous works have shown the usefulness of bond graphs for modeling and simulation of interacting lumped and distributed systems. Frequently, when damping is included in the model, the overall system is “stiff”, possessing widely disparate characteristic times. This makes simulation difficult and time consuming.Bond graphs are used here to represent the interacting lumped and modal dynamics of a system while treating the damping as an external forcing onto the system. By performing a second modal decomposition, a second bond graph model can be formulated where the damping can now be physically represented. The result is a total system model in which the characteristic times can be controlled through elimination of high frequency modes.     

SimilCatch: Enhanced social spammers detection on Twitter using Markov Random Fields

The problem of social spam detection has been traditionally modeled as a supervised classification problem. Despite the initial success of this detection approach, later analysis of proposed systems and detection features has shown that, like email spam, the dynamic and adversarial nature of social spam makes the performance achieved by supervised systems hard to maintain. In this paper, we investigate the possibility of using the output of previously proposed supervised classification systems as a tool for spammers discovery. The hypothesis is that these systems are still highly capable of detecting spammers reliably even when their recall is far from perfect. We then propose to use the output of these classifiers as prior beliefs in a probabilistic graphical model framework. This framework allows beliefs to be propagated to similar social accounts. Basing similarity on a who-connects-to-whom network has been empirically critiqued in recent literature and we propose here an alternative definition based on a bipartite users-content interaction graph. For evaluation, we build a Markov Random Field on a graph of similar users and compute prior beliefs using a selection of state-of-the-art classifiers. We apply Loopy Belief Propagation to obtain posterior predictions on users. The proposed system is evaluated on a recent Twitter dataset that we collected and manually labeled. Classification results show a significant increase in recall and a maintained precision. This validates that formulating the detection problem with an undirected graphical model framework permits to restore the deteriorated performances of previously proposed statistical classifiers and to effectively mitigate the effect of spam evolution.     

Using bond graphs in simulating an electro-hydraulic system

The paper describes the preparation of a dynamic model required for simulation of a 30 kW electro-hydraulic system used to induce controlled vibration of a wide range of components, machines or structures. The vibrator system is associated with a 28 tonne seismic block. The model is highly detailed to allow study of the system to its dynamic performance limits of around 300 Hz. The model consists of nearly eighty equations some of them nonlinear and discontinuous. The paper describes the orderly development of the model emanating from the bond graph approach. Some simulation results, with limited experimental correlation, are included.     

基于符号有向图的故障诊断系统及其软件平台

基于符号有向图(SDG)的故障诊断系统不依赖精确数学模型和在线数据,适用于外场通用故障诊断设备实施现场诊断。建立图形化SDG模型开发平台是实现其通用性的关键。基于Visio的软件实现通过模具设计和功能扩展降低了平台开发成本,提高了平台运行的可靠性,也使得现场维护人员可以方便地利用其扩展诊断设备功能。     

Bond graph models of structured parameter uncertainties

Taking into account uncertainties in model parameter values is a crucial point for studying robustness in modeling and in control. This paper proposes to construct in a systematic and graphical procedure two forms of the linear state equation usually found in the literature for dealing with the robustness problem in the case of structured uncertainties on parameters. It is shown how to model uncertainties in a bond graph approach, in the case of additive or multiplicative parametric variations.