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- ARRs (3)
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- bond graph modelling (2)
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- power electronic systems (2)
- residual sinks (2)
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The paper proposes a bond graph approach to model based fault detection and isolation (FDI) that uses residual sinks. These elements couple a reference model of a process engineering system to a bond graph model of the system that is subject to disturbances caused by faults. In this paper it is assumed that two faults do not appear simultaneously. The underlying mathematical model is a Differential Algebraic Equations (DAE) system. The approach is illustrated by means of the often used hydraulic two tanks system.

Bond Graph Modelling and Simulation of Mechatronic Systems: An Introduction into the Methodology
(2006)

This paper introduces into a graphical, computer aided modelling methodology that is particularly suited for the concurrent design of mechatronic systems, viz. of engineering systems with mechanical, electrical, hydraulic or pneumatic components including interactions of physical effects from various energy domains. Beyond the introduction, bond graph modelling of multibody systems, as an example of an advanced topic, is briefly addressed in order to demonstrate the potential of this powerful approach to modelling mechatronic systems. It is outlined how models of multibody systems including flexible bodies can be build in a systematic manner.

This paper proposes a novel approach to a bond graph model-based failure prognosis for systems represented by a mode switching linear time-invariant model. A function for a degradation process is numerically determined by using a first stage and a second stage diagnostic bond graph model (DBG). Evaluation of the Analytical Redundancy Relations (ARRs) from the first stage DBG provides residuals that enable to detect the onset of incipient faults. The second stage DBG model accounts for parametric degradation by means of an unknown function. ARRs derived from the second stage DBG make use of the residuals of the first stage ARRs and constitute an implicit relation for the unknown degradation function. The computation takes place online concurrently to the monitoring of a real system and the measurement of its output signals. Once the time evolution of a degradation process has been computed up to some time instant, the time evolution of an ARR residual using it can be projected into the future in order to estimate the Remaining Useful Life (RUL) of a system. With progress of time the computation of a degradation process can be repeated and estimations of a RUL can be improved.

Hybrid system models exploit the modelling abstraction that fast state transitions take place instantaneously so that they encompass discrete events and the continuous time behaviour for the while of a system mode. If a system is in a certain mode, e.g. two rigid bodies stick together, then residuals of analytical redundancy relations (ARRs) within certain small bounds indicate that the system is healthy. An unobserved mode change, however, invalidates the current model for the dynamic behaviour. As a result, ARR residuals may exceed current thresholds indicating faults in system components that have not happened. The paper shows that ARR residuals derived from a bond graph cannot only serve as fault indicators but may also be used for bond graph model-based system mode identification. ARR residuals are numerically computed in an off-line simulation by coupling a bond graph of the faulty system to a non-faulty system bond graph through residual sinks. In real-time simulation, the faulty system model is to be replaced by measurements from the real system. As parameter values are uncertain, it is important to determine adaptive ARR thresholds that, given uncertain parameters, allow to decide whether the dynamic behaviour in a current system mode is the one of the healthy system so that false alarms or overlooking of true faults can be avoided. The paper shows how incremental bond graphs can be used to determine adaptive mode-dependent ARR thresholds for switched linear time-invariant systems with uncertain parameters in order to support robust fault detection. Bond graph-based hybrid system mode identification as well as the determination of adaptive fault thresholds is illustrated by application to a power electronic system easy to survey. Some simulation results have been analytically validated.

This paper introduces a graphical, computer aided modelling methodology that is particularly suited for the concurrent design of multidisciplinary systems, viz. of engineering systems with mechanical, electrical, hydraulic or pneumatic components, including interactions of physical effects from various energy domains. Following the introduction, bond graph modelling of multibody systems, as an example of an advanced topic, is briefly addressed in order to demonstrate the potential of this powerful approach to modelling multidisciplinary systems. It is shown how models of multibody systems including flexible bodies can be built in a systematic manner.

Incremental Bond Graphs
(2011)

Incremental true bond graphs are used for a matrix-based determination of first-order parameter sensitivities of transfer functions, of residuals of analytical redundancy relations, and of the transfer matrix of the inverse model of a linear multiple-input–multiple-output system given that the latter exists. Existing software can be used for this approach for the derivation of equations from a bond graph and from its associated incremental bond graph and for building the necessary matrices in symbolic form. Parameter sensitivities of transfer functions are obtained by multiplication of matrix entries. Symbolic differentiation of transfer functions is not needed. The approach is illustrated by means of hand derivation of results for small well-known examples.

Bond Graph Methodology
(2010)

Nowadays, engineering systems are becoming increasingly complex and, for design purposes, must be considered as multidisciplinary systems made up of components from different engineering disciplines. With regard to the systematic development and the analysis of models, interdisciplinary methodologies supported by software become more and more important. Bond graphs are a graphical description formalism particularly suited for multidisciplinary systems and used by modellers across the world.
Bond Graph Methodology gives a comprehensive, in-depth representation of the state of the art, including recent results gathered from research articles, dissertations and contributions by the author on a number of topics. The structured and rigorous presentation systematically covers model development, analysis of models, numerical computation of models and modern software that can be used for a bond graph approach. The book also includes a range of case studies illustrating various applications of the methodology and provides a glossary.
Bond Graph Methodology addresses fundamentals, as well as advanced topics, e.g., models of variable structure, bond graphs for sensitivity analysis and generation of equations for the study of robustness. The compilation and presentation of the material has been inspired by the author's extensive experience in research and teaching.
A useful text for advanced courses in modelling, simulation and control, Bond Graph Methodology can also be used for self-study. It has been designed to serve readers interested in the subject of bond graph modelling and those with expertise in related areas, as well as members of the worldwide community of bond graph modellers.

Switched power electronic subsystems are widely used in various applications. A fault in one of their components may have a significant effect on the system’s load or may even cause a damage. Therefore, it is important to detect and isolate faults and to report true faults to a supervisory system in order to avoid malfunction of or damage to a load. If, in a model-based approach to fault detection and isolation of hybrid systems, switching devices are considered as ideal switches then some equations must be reformulated whenever some devices have switched. In this paper, a fixed causality bond graph representation of hybrid system models is used, i.e., computational causalities assigned according to the Standard Causality Assignment Procedure (SCAP) are independent of system modes of operation. The latter are taken into account by transformer moduli mi(t) ∈ {0, 1} ∀t ≥ 0 in a unique set of equations of motion. In a case study, this approach is used for fault diagnosis in a three-phase full-wave rectifier. Residuals of Analytical Redundancy Relations (ARRs) holding for all modes of operations and serving as fault indicators are computed in an offline simulation as part of a DAE system by using a bond graph model of the faulty system instead of the real one and by coupling it to a bond graph of the healthy system by means of residual sinks.

In this paper, residual sinks are used in bond graph model-based quantitative fault detection for the coupling of a model of a faultless process engineering system to a bond graph model of the faulty system. By this way, integral causality can be used as the preferred computational causality in both models. There is no need for numerical differentiation. Furthermore, unknown variables do not need to be eliminated from power continuity equations in order to obtain analytical redundancy relations (ARRs) in symbolic form. Residuals indicating faults are computed numerically as components of a descriptor vector of a differential algebraic equation system derived from the coupled bond graphs. The presented bond graph approach especially aims at models with non-linearities that make it cumbersome or even impossible to derive ARRs from model equations by elimination of unknown variables. For illustration, the approach is applied to a non-controlled as well as to a controlled hydraulic two-tank system. Finally, it is shown that not only the numerical computation of residuals but also the simultaneous numerical computation of their sensitivities with respect to a parameter can be supported by bond graph modelling.

This book presents bond graph model-based fault detection with a focus on hybrid system models. The book addresses model design, simulation, control and model-based fault diagnosis of multidisciplinary engineering systems. The text beings with a brief survey of the state-of-the-art, then focuses on hybrid systems. The author then uses different bond graph approaches throughout the text and provides case studies.

For the case when the abstraction of instantaneous state transitions is adopted, this paper proposes to start fault detection and isolation in an engineering system from a single time-invariant causality bond graph representation of a hybrid model. To that end, the paper picks up on a long-known proposal to model switching devices by a transformer modulated by a Boolean variable and a resistor in fixed conductance causality accounting for its ON resistance. Bond graph representations of hybrid system models developed in this way have been used so far mainly for the purpose of simulation. The paper shows that they can well constitute an approach to the bond-graph-based quantitative fault detection and isolation of hybrid models. Advantages are that the standard sequential causality assignment procedure can be a used without modification. A single set of analytical redundancy relations valid for all physically feasible system modes can be (automatically) derived from the bond graph. Stiff model equations due to small values of the ON resistance in the switch model may be avoided by symbolic reformulation of equations and letting the ON resistance of some switches tend to zero, turning them into ideal switches.
First, for two examples considered in the literature, it is shown that the approach proposed in this paper can produce the same analytical redundancy relations as were obtained from a hybrid bond graph with controlled junctions and the use of a sequential causality assignment procedure especially for fault detection and isolation purpose. Moreover, the usefulness of the proposed approach is illustrated in two case studies by its application to standard switching circuits extensively used in power electronic systems and by simulation of some fault scenarios. The approach, however, is not confined to the fault detection and isolation of such systems. Analytically validated simulation results obtained by means of the program Scilab give confidence in the approach.

Analytical redundancy relations are fundamental in model-based fault detection and isolation. Their numerical evaluation yields a residual that may serve as a fault indicator. Considering switching linear time-invariant system models that use ideal switches, it is shown that analytical redundancy relations can be systematically deduced from a diagnostic bond graph with fixed causalities that hold for all modes of operation. Moreover, as to a faultless system, the presented bond graph–based approach enables to deduce a unique implicit state equation with coefficients that are functions of the discrete switch states. Devices or phenomena with fast state transitions, for example, electronic diodes and transistors, clutches, or hard mechanical stops are often represented by ideal switches which give rise to variable causalities. However, in the presented approach, fixed causalities are assigned only once to a diagnostic bond graph. That is, causal strokes at switch ports in the diagnostic bond graph reflect only the switch-state configuration in a specific system mode. The actual discrete switch states are implicitly taken into account by the discrete values of the switch moduli. The presented approach starts from a diagnostic bond graph with fixed causalities and from a partitioning of the bond graph junction structure and systematically deduces a set of equations that determines the wanted residuals. Elimination steps result in analytical redundancy relations in which the states of the storage elements and the outputs of the ideal switches are unknowns. For the later two unknowns, the approach produces an implicit differential algebraic equations system. For illustration of the general matrix-based approach, an electromechanical system and two small electronic circuits are considered. Their equations are directly derived from a diagnostic bond graph by following causal paths and are reformulated so that they conform with the matrix equations obtained by the formal approach based on a partitioning of the bond graph junction structure. For one of the three mode-switching examples, a fault scenario has been simulated.

Bond Graphs are well suited for modelling multibody systems. In this paper modelling of planar flexible beams undergoing large overall motions are studied based on finite element (FE) technique. Two well-known approaches are used - the co-rotational (CR) and absolute nodal coordinate (ANC) formulation. Two ANC formulations are analyzed - one in which elastic forces is described using classical beam theory in a local coordinate frame, and another based on a global continuum mechanics approach. Starting from these classical formulations velocity formulations are developed and used to develop Bond Graph FE components. The effect of gravity has been considered as well. These components can be put in libraries and used for systematic Bond Graph flexible body model development. It is shown that Bond Graph technique is capable of dealing with different flexible body formulations and can be used as a general approach in parallel to other modelling approaches. Models are developed and simulations are performed using the object oriented environment of BondSim. Owing to the object oriented approach, transformation from one to the other model is relatively simply. The results are illustrated by suitable examples and they confirm accuracy of the developed models. It was shown that the CR approach offers much better performance than the both ANC formulations.

Bond graph modelling
(2006)

A bond graph representation of switching devices known for a long time has been a modulated transformer with a modulus b(t)∈{0,1}∀t≥0 in conjunction with a resistor R:Ron accounting for the ON-resistance of a switch considered non-ideal. Besides other representations, this simple model has been used in bond graphs for simulation of the dynamic behaviour of hybrid systems. A previous article of the author has proposed to use the transformer–resistor pair in bond graphs for fault diagnosis in hybrid systems. Advantages are a unique bond graph for all system modes, the application of the unmodified standard Sequential Causality Assignment Procedure, fixed computational causalities and the derivation of analytical redundancy relations incorporating ‘Boolean’ transformer moduli so that they hold for all system modes. Switches temporarily connect and disconnect model parts. As a result, some independent storage elements may temporarily become dependent, so that the number of state variables is not time-invariant. This article addresses this problem in the context of modelling and simulation of fault scenarios in hybrid systems. In order to keep time-invariant preferred integral causality at storage ports, residual sinks previously introduced by the author are used. When two storage elements become dependent at a switching time instance ts, a residual sink is activated. It enforces that the outputs of two dependent storage elements become immediately equal by imposing the conjugate3 power variable of appropriate value on their inputs. The approach is illustrated by the bond graph modelling and simulation of some fault scenarios in a standard three-phase switched power inverter supplying power into an RL-load in a delta configuration. A well-developed approach to model-based fault detection and isolation is to evaluate the residual of analytical redundancy relations. In this article, analytical redundancy relation residuals have been computed numerically by coupling a bond graph of the faulty system to one of the non-faulty systems by means of residual sinks. The presented approach is not confined to power electronic systems but can be used for hybrid systems in other domains as well. In further work, the RL-load may be replaced by a bond graph model of an alternating current motor in order to study the effect of switch failures in the power inverter on to the dynamic behaviour of the motor.

Bond graph software can simulate bond graph models without the user needing to manually derive equations. This offers the power to model larger and more complex systems than in the past. Multibond graphs (those with vector bonds) offer a compact model which further eases handling multibody systems. Although multibond graphs can be simulated successfully, the use of vector bonds can present difficulties. In addition, most qualitative, bond graph–based exploitation relies on the use of scalar bonds. This article discusses the main methods for simulating bond graphs of multibody systems, using a graphical software platform. The transformation between models with vector and scalar bonds is presented. The methods are then compared with respect to both time and accuracy, through simulation of two benchmark models. This article is a tutorial on the existing methods for simulating three-dimensional rigid and holonomic multibody systems using bond graphs and discusses the difficulties encountered. It then proposes and adapts methods for simulating this type of system directly from its bond graph within a software package. The value of this study is in giving practical guidance to modellers, so that they can implement the adapted method in software.