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.     

Cyclic cycle systems of the complete multipartite graph

In this paper, we study the existence problem for cyclic $?$‐cycle decompositions of the graph $K_m\left[n\right]$, the complete multipartite graph with $m$ parts of size $n$, and give necessary and sufficient conditions for their existence in the case that $2?|\left(m?1\right)n$.     

On the power graph and the reduced power graph of a finite group

In this paper, for a finite group, we investigate to what extent its directed (resp. undirected) reduced power graph determines its directed power graph (resp. reduced power graph). Moreover, we investigate the determination of the orders of the elements of a finite group from its directed (resp. undirected) reduced power graph. Consequently, we show that some classes of finite groups are recognizable from their undirected reduced power graphs. Also, we study the relationship between the isomorphism classes of groups corresponding to the equivalence relations induced by the isomorphism of each of these graphs on the set of all finite groups.     

Between the enhanced power graph and the commuting graph

The purpose of this note is to define a graph whose vertex set is a finite group $G$, whose edge set is contained in that of the commuting graph of $G$ and contains the enhanced power graph of $G$. We call this graph the deep commuting graph of $G$. Two elements of $G$ are joined in the deep commuting graph if and only if their inverse images in every central extension of $G$ commute. We give conditions for the graph to be equal to either of the enhanced power graph and the commuting graph, and show that automorphisms of $G$ act as automorphisms of the deep commuting graph.     

A procedure to linearize a class of non-linear systems modelled by bond graphs

A procedure is proposed to obtain the linearization of a class of non-linear physical systems using bond graphs. Also, a junction structure of a non-linear bond graph considering linearly dependent and independent state variables is described. From the junction structure of the non-linear bond graph a procedure to build a linearized bond graph is presented. Finally, an example of a Programmable Universal Manipulation Arm (PUMA) manipulator is given.     

Synchronized stationary distribution of stochastic coupled systems based on graph theory

This paper deals with the synchronized stationary distribution of stochastic coupled systems. The response system is constructed to help achieve a synchronized stationary distribution. Firstly, an error system obtained by the drive system and the response system is given and an appropriate Lyapunov function for the error system is constructed. On the basis of the graph theory and the Lyapunov method, some sufficient conditions are proposed to guarantee the existence of a stationary distribution for the error system, which reflects the coupling structure has a close relationship with synchronized stationary distribution. Then, an application to stochastic coupled oscillators is presented and sufficient conditions are obtained to illustrate the feasibility of the theoretical results. Finally, a numerical example is provided to demonstrate the effectiveness of theoretical results.     

Cyclic even cycle systems of the complete graph

In this article, it is proved that for each even integer m?4 and each admissible value n with n>2m, there exists a cyclic m‐cycle system of K_n, which almost resolves the existence problem for cyclic m‐cycle systems of K_n with m even. © 2011 Wiley Periodicals, Inc. J Combin Designs 20:23–39, 2012     

Allocating modelling resources in distributed model management systems

Due to the growing popularity of distributed computing systems and the increased level of modelling activity in most organizations, significant benefits can be realized through the implementation of distributed model management systems (DMMS). These systems can be defined as a collection of logically related modelling resources distributed over a computer network. In several ways, functions of DMMS are isomorphic to those of distributed database systems. In general, this paper examines issues viewed as central to the development of distributed model bases (DMB). Several criteria relevant to the overall DMB design problem are discussed. Specifically, this paper focuses on the problem of distributing decision models and tools (solvers), henceforth referred to as theModel Allocation Problem (MAP), to individual computing sites in a geographically dispersed organization. In this research, a 0/1 integer programming model is formulated for the MAP, and an efficient dual ascent heuristic is proposed. Our extensive computational study shows in most instances heuristic-generated solutions which are guaranteed to be within 1.5–7% of optimality. Further, even problems with 420 integer and 160,000 continuous variables took no more than 60 seconds on an IBM 3090-600E computer.     

On decomposing a graph into nontrivial bonds

We show that for every 2‐connected bipartite graph which is not a multiple edge and which has no K₅‐minor there is an edge‐disjoint collection of nontrivial bonds (i.e., not stars) which partition the edges of the graph. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 109–127, 2000     

A Multinomial Model for a Bond Market

In this paper, we generalize the classical binomial bond market model of Ho and Lee [2] to the multinomial model. We establish necessary and sufficient conditions for such a bond market model to be arbitrage-free and path independent. We study the bond option pricing and forward-rate equation in the trinomial case.Research is supported by the Lithuanian State Science and Studies Foundation, program Mathematical models of Lithuanian economy for forecasting of the macroeconomic processes (registration No C-03004).__________Translated from Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 413–428, October–December, 2004.     

Density and power graphs in graph homomorphism problem

We introduce two necessary conditions for the existence of graph homomorphisms based on the concepts of density and power graph. As corollaries, we obtain a lower bound for the fractional chromatic number, and we set forward elementary proofs of the facts that the circular chromatic number of the Petersen graph is equal to three and the fact that the Coxeter graph is a core.     

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.     

Every 4-connected line graph of a quasi claw-free graph is hamiltonian connected

Let G be a graph. For u,vV(G) with dist_G(u,v)=2, denote J_G(u,v)={wN_G(u)∩N_G(v)|N_G(w)N_G(u)N_G(v){u,v}}. A graph G is called quasi claw-free if J_G(u,v)≠ for any u,vV(G) with dist_G(u,v)=2. In 1986, Thomassen conjectured that every 4-connected line graph is hamiltonian. In this paper we show that every 4-connected line graph of a quasi claw-free graph is hamiltonian connected.     

On the independence number of the power graph of a finite group

The power graph ${\Gamma }_G$ of a finite group $G$ is the graph whose vertex set is $G$, two distinct elements being adjacent if one is a power of the other. In this paper, we give sharp lower and upper bounds for the independence number of ${\Gamma }_G$ and characterize the groups achieving the bounds. Moreover, we determine the independence number of ${\Gamma }_G$ if $G$ is cyclic, dihedral or generalized quaternion. Finally, we classify all finite groups $G$ whose power graphs have independence number 3 or $n?2$, where $n$ is the order of $G$.     

Linearization of a class of non-linear systems modelled by multibond graphs

Based on non-linear systems described by multibond graphs, a procedure designed to present symbolic linearization of these multibond graphs, is presented in this paper. Firstly, a junction structure of a multibond graph with multiport gyrators that represent Eulerian junction structures is proposed. In addition, non-linear multiport resistors are considered. By knowing the non-linear causal paths and loops of the non-linear multibond graph, the linearization is obtained by two steps: (1) The original multibond graph on the nominal operating point is evaluated; (2) New and additional paths based on the non-linear causal paths and loops are included. The state space representation of the linearized multibond graph using the corresponding junction structure is presented. An advantage of this methodology is its ability to allow the user to define a nominal operating point in which the linearization will be carried out.

In order to apply the proposed methodology, two physical systems are modelled and linearized by multibond graphs: a synchronous generator and a two degrees of freedom PUMA. Simulation results of these non-linear and linearized systems are shown.     

Switching synchronized chaotic systems applied to secure communication

The purpose of this paper is to study the behavior of the solutions of two synchronized chaotic systems when the solutions switch from the first to the second system and vice-versa. The initial condition is chosen in the first system and the solutions travels for time $t \in [0, h]$, where $h>0$. The value of the solution at time $h$ is then chosen as the initial condition for the solution of the second system and this solution travels for time $t \in [h, 2h]$. The value of the solution at time $2h$ is then chosen as the initial value for the solution of the first system and so on. The first system is composed of two subsystems, Master and Slave that are synchronized. We present applications using the Lorenz, Chua and Chen systems. Some simulations using Matlab are presented.