Bond graph model-based system mode identification and mode-dependent fault thresholds for hybrid systems

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.     

On the modelling of heat exchangers and heat exchanger network dynamics using bond graphs

ABSTRACT

Heat exchanger networks are important systems in most thermal engineering systems and are found in applications ranging from power plants and the process industry to domestic heating. Achieving cost-effective design of heat exchanger networks relies heavily on mathematical modelling and simulation-based design. Today, stationary design calculations are carried out for all new designs, but for some special applications, the transient response of complete networks has been researched. However, simulating large heat exchanger networks poses challenges due to computational speed and stiff initial value problems when flow equations are cast in differential algebraic form. In this article, a systems approach to heat exchanger and heat exchanger network modelling is suggested. The modelling approach aims at reducing the cost of system model development by producing modular and interchangeable models. The approach also aims at improving the capability for large and complex network simulation by suggesting an explicit formulation of the network flow problem.     

Dynamic modelling and performance study of solar gas tunnel dryer

The work presented in this article focuses on the analysis and modelling of heat and mass transfers in the tunnel dryer during the drying of agricultural products. The main objective of this work is to establish a global modelling of the studied system based on the bond graph methodology. The pseudo-bond graph methodology was used in modelling the system. Such methodology was very suitable for this thermal process since it allows good management of the nonlinearity present in the system.

The thermal performance of the proposed dryer is analysed by solving the various energy balance equations. An application of drying tomatoes was achieved and a fair agreement was observed between predicted and experimental results.     

Staged and constrained two-dimensional guillotine cutting problems: An AND/OR-graph approach

An AND/OR-graph approach has been proposed by Morabito et al. to solve non-staged and unconstrained two-dimensional guillotine cutting problems. Basically, this approach consists of representing cutting patterns as complete paths in an AND/OR graph (where nodes and arcs correspond to rectangles and cuts, respectively) and choosing a search strategy to traverse or enumerate the nodes of the graph. In this present paper, the AND/OR-graph approach is extended to solve staged and constrained problems. Computational experiments with examples from the literature are performed and indicate that this approach generates good and fast solutions using a microcomputer. In addition to the fact that the AND/OR-graph approach can handle important constraints, it can be easily extended to solve cutting and packing problems with multiple dimensions.     

Pseudo bond graph tunnel greenhouse model with accurate longwave/shortwave radiations model

This research work is focused on the construction of an accurate longwave/shortwave radiation model on a tunnel greenhouse pseudo-bond graph model, widely used in Tunisia. This model includes sun position, useful incoming solar radiation model, sky longwave radiation model, inside longwave and shortwave radiation model. The key idea is to use bond graphs allowing a lumped modelling approach which is suitable for control applications. Furthermore, an evaluation of some longwave radiative model components was made, noting that these components are particularly sensitive regarding to the thermal behaviour of the model.

Experimental tunnel greenhouse data are used as validation elements for the present model with globally good results. A comparative study was also performed between the present model and a previous bond graph model containing a simplistic radiative model. Practical simulation results show a clear improvement compared with the previous model.     

Modelling of unilateral constraints using power-based restriction functions within Lagrangian mechanics

The consideration of unilateral contacts within multi-body systems is a common but also difficult task. Established modelling approaches such as the rigid body theory or the Hertzian contact are suitable for single-body systems but show serious problems with increasing system complexity. Indeed, there are different approaches to extend the existing models to multi-body systems, but with a growing number of contacts and the consideration of tangential friction, those enhancements are hardly applicable, showing numeric problems or becoming unmanageable. Thus, to overcome these limitations, a new modelling approach for unilateral contacts defined by power-based restriction functions is proposed in this contribution. The proposed contact model is based on continuous functions, making it numerically robust as well as applicable within Lagrangian mechanics. The approach is easily applicable and even remains manageable for multiple contacts since each constraint can be independently adapted by four physical parameters. The simple applicability and generalizability of the approach is demonstrated by several examples.     

Regularized Adaptation of Fuzzy Inference Systems. Modelling the Opinion of a Medical Expert about Physical Fitness: An Application

This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using regularization, since regularization improves the robustness of standard parameter estimation algorithms leading to stable fuzzy approximation. The proposed method can be used for modelling, identification and control of physical processes. A recursive method for on-line identification of fuzzy parameters employing Tikhonov regularization is suggested. The power of approach was shown by applying it to the modelling, identification, and adaptive control problems of dynamic processes. The proposed approach was used for modelling of human-decisions (experience) with a fuzzy inference system and for the fuzzy approximation of physical fitness with real world medical data.     

Dynamic Location-routeing Problems

Dynamic location-routeing problems involve the determination of the least-cost sequence of depot, vehicle fleet and route configurations in a distribution system, over a given planning horizon. This paper presents two solution approaches to such problems. The first is an exact method which is appropriate for small-scale problems. It consists of representing the problem by a suitable network and of solving to optimality an integer linear programme associated with the network. In the second approach, some of the system costs are approximated, and a global solution is then obtained by determining a shortest path on a directed graph. Under some hypotheses, this approach is suitable for large-scale problems. It is illustrated on a simple example.     

Quasi-steady state model determination for systems with singular perturbations modelled by bond graphs

A bond graph model for a singularly perturbed system is presented. This system is characterized by fast and slow dynamics. In addition, the bond graph can have storage elements with derivative and integral causality assignments for both dynamics. When the singular perturbation method is applied, the fast dynamic differential equation degenerates to an algebraic equation; the real roots of this equation can be determined by using another bond graph called singularly perturbed bond graph (SPBG). This SPBG has the characteristic that storage elements of the fast state and slow state have a derivative and integral causality assignment, respectively. Thus, a quasi-steady state model by using SPBG is obtained. A Lemma to get the junction structure from SPBG is proposed. Finally, the proposed methodology is applied to two examples.     

A Poroelastodynamic Plate Formulation of Extendable Order

In order to model the sound insulation properties of porous plate-like structures, an adequate poroelastic plate theory is needed. The approach used here to obtain such a theory consists in expanding the primal variables into power series in thickness direction. This allows an analytical integration over the thickness, thus reducing the dimension of the problem from 3d to 2d. The resulting out-of-plane and in-plane problems are discussed. Numerical calculations show a good agreement between the proposed model and the three-dimensional system. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Circle graphs and the cycle double cover conjecture

The long standing Cycle Double Cover Conjecture states that every bridgeless graph can be covered by a family of cycles such that every edge is covered exactly twice. Intimately related is the problem of finding, in an eulerian graph, a circuit decomposition compatible with a given transition system (transition systems are also known as decompositions into closed paths). One approach that seems promising consists in finding a black anticlique in the corresponding Sabidussi orbit of bicolored circle graphs.     

The birth of the giant component

Limiting distributions are derived for the sparse connected components that are present when a random graph on n vertices has approximately 1/2n edges. In particular, we show that such a graph consists entirely of trees, unicyclic components, and bicyclic components with probability approaching √2/3 cosh √5/18 ≈ 0.9325 as n→∞. The limiting probability that it is consists of trees, unicyclic components, and at most one another component is approximately 0.9957; the limiting probability that it is planar lies between 0.987 and 0.9998. When a random graph evolves and the number of edges passes 1/2n, its components grow in cyclic complexity according to an interesting Markov process whose asymptotic structure is derived. The probability that there never is more than a single component with more edges than vertices, throughout the veolution, approaches 5 π/18 ≈ 0.8727. A “uniform” model of random graphs, which allows self-loops and multiple edges, is shown to lead to formulas that are substanitially simpler than the analogous formulas for the classical random graphs of Erdõs and Rényi. The notions of “excess” and “deficiency,” which are significant characteristics of the generating function as well as of the graphs themselves, lead to a mathematically attractive structural theory for the uniform model. A general approach to the study of stopping configurations makes it possible to sharpen previously obtained estimates in a uniform manner and often to obtain closed forms for the constants of interest. Empirical results are presented to complement the analysis, indicating the typical behavior when n is near 2oooO. © 1993 John Wiley & Sons, Inc.     

A tabu thresholding algorithm for arc crossing minimization in bipartite graphs

Acyclic directed graphs are commonly used to model complex systems. The most important criterion to obtain a readable map of an acyclic graph is that of minimizing the number of arc crossings. In this paper, we present a heuristic for solving the problem of minimizing the number of arc crossings in a bipartite graph. It consists of a novel and easier implementation of fundamental tabu search ideas without explicit use of memory structures (a tabu thresholding approach). Computational results are reported on a set of 250 randomly generated test problems. Our algorithm has been compared with the two best heuristics published in the literature and with the optimal solutions for the test problems, size permitting.This research was partially supported by the C.I.C.Y.T. with code tap92-0639.     

Model predictive control of nonlinear hybrid systems with discrete inputs employing a hybrid fuzzy model

The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed.

An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented.

The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor.

Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used.     

Bond graph model of an induction machine with hysteresis nonlinearities

An induction machine is one of the most convenient devices for conversion of electrical energy to mechanical rotational energy. Induction machine is a typical member of a multi-domain, nonlinear, high-order dynamic system. To reduce its complexity, the mathematical models used for designing their control have several assumptions built into them. The most striking of these assumptions is that of linear magnetics. Bond graph is a convenient tool for modelling nonlinear elements. This paper proposes the use of the bond graph methodology to develop a model of an induction machine that includes the nonlinearities due to magnetics.     

Report on the activities of the working group on discrete mathematics

In the past decade there have been significant developments in computer technology and solution techniques for analysing business and industrial decision problems. In recent years good modelling systems have become available to ease the burden of model communication. Currently the single most important barrier to increased use of structured approaches to decision modelling is the acquisition of the necessary skills to initially develop models of complex decision systems. This paper examines the modelling process with reference to linear programming. Two related production planning problems are presented and their associated models developed. The relationship between the two problems is such that student modellers are forced to become involved in the important details of the problems and, by examining the nature of solution spaces in constrained optimisation, students are able to rapidly gain confidence and skills in modelling.     

Switchable structured bond: A bond graph device for modeling power coupling/decoupling of physical systems

This paper presents a controlled Bond Graph interconnection structure named Switchable Structured Bond, or SS-Bond for short, basically intended for modeling and simulation of ideal switching phenomena (zero transition time) with fixed causality. Serving to model the presence or absence of a power preserving connection between two power ports, these new structures are inspired in the idea yielding the switchable bond (or SB) formalism, but embody some features correcting the shortcomings of the latter. Indeed, when both power ports are connected, both the SB and the SS-Bond behave like a standard power bond, but when the power connection is absent, the SS-Bond fully captures the possible states of the adjacent power ports, unlike the SB, which in many cases leaves undefined the situation of these ports. As SS-Bonds are originally defined to model ideal switching, these possible states are zero-flow or zero-effort for each of the disconnected power ports. These four situations, together with the normally connected state, define the five possible switching modes of an SS-Bond.The SS-Bonds can be internally represented with standard bond graph elements. To keep fixed the causality assignment even under switching, some algebraic constraints are added to the equation set of the switched structure, which in the Bond Graph domain can be represented with residual sinks. A minor modification on the internal implementation of the SS-Bonds allows the formalism for commutation modeling with the non-ideal approach consisting in adding parasitic components to avoid causality changes. Besides some models of electric–electronic circuits, slip-stick friction in a simple mechanical system and abrupt faults in a hydraulic two tank system are used to illustrate the new formalism and its performance in modeling and simulation.     

Modal analysis reduction of multi-body systems with generic damping

Modal analysis of multi-body systems is broadly used to study the behavior and controller design of dynamic systems. In both cases, model reduction that does not degrade accuracy is necessary for the efficient use of these models. Previous work by the author addressed the reduction of modal representations by eliminating entire modes or individual modal elements (inertial, compliant, resistive). In that work, the bond graph formulation was used to model the system and the modal decomposition was limited to systems with proportional damping. The objective of the current work is to develop a new methodology such that model reduction can be implemented to modal analysis of multi-body systems with non-proportional damping that were not modeled using bond graphs. This extension also makes the methodology applicable to realistic systems where the importance of modal coupling terms is quantified and potentially eliminated. The new methodology is demonstrated through an illustrative example.