Incident Matrices Research Articles

Representation of planar kinematic chains with multiple joints based on a modified graph and isomorphism identification

The representation and isomorphism identification of kinematic chains (KCs) with multiple joints are crucial issues to be solved in mechanism research. In this paper, a modified graph—planar face graph (PF graph), is proposed. As a key concept, “face” has been put forward to represent the case that a single, specific relationship is incident with multiple incidents. Some other basic concepts relating to PF graph are also explained in detail. PF graph is used to represent KCs with multiple joints and it reflects the uniqueness of KCs and realizes the one-to-one correspondence between KCs and adjacency and incident matrices. It also establishes relationships with other methods for representing KCs and it is proved to be suitable for complex mechanical systems. Moreover, the sufficient and necessary condition of isomorphism are derived, and two properties of permutation similarity are analysed. Based on them, the modified eigenvalue eigenvector method and the maximum path method are proposed, and they are integrated to form a new algorithm. In addition, the reliability and efficiency of the algorithm are proved.

УПРАВЛЕНИЕ ТРАНСПОРТНО-ПРОИЗВОДСТВЕННЫМИ ПРОЦЕССАМИ В УСЛОВИЯХ НЕПЛАНОВОГО ПЕРЕРАСПРЕДЕЛЕНИЯ РЕСУРСОВ

Presents an algorithm and a mathematical model for controlling a technological process to minimize losses associated with an emergency in production. The conditions and features of the functioning of the technological process in the conditions of the flow method of performing work are presented. The conditions and schemes of pairing interconnected resources have been deter-mined, which allow their replacement to improve the efficiency of technological process control while observing the technology or organization of construction. Criteria are enclosed that assess the quality of the organisational-economic situation before and after the management of the tech-nological process of management. A matrix of incidents is given, which makes it possible to deter-mine the conditions of an emergency situation, to assess the loss and to make an operative decision about the compensation of these losses, which have arisen during an emergency stop of the pro-cess. The proposed model allows you to vary the parameters, change the search area to achieve the desired results. The model is invariant to the object of technological process control, which allows changing its parameters by adjusting the adjacency and incident matrices.

Consensus and Eigenvalue Estimation in Dynamic Consensus Networks with Strictly Positive Real Systems

The use of consensus networks in networking has received great attention due to its wide array of applications in fields such as robotics, transportation, sensor networking, communication networking, biology, and physics. The focus of this paper is to study a generalization of consensus problems whereby the weights of network edges are no longer static gains, but instead are dynamic systems, leading to the notion of dynamic consensus networks. Specifically, we consider networks whose nodes are transfer functions (typically integrators) and whose edges are strictly positive real transfer functions representing dynamical systems that couple the nodes. We transform each concept of static graph theory into dynamic terms, out of which a generalized dynamic graph theory naturally emerges. We present a framework for dynamic graphs and dynamic consensus networks. This framework introduces the idea of dynamic degree, adjacency, incident, and Laplacian matrices in a way that naturally extends these concepts from the static case. We show that strictly positive realness of the edges is a sufficient condition for dynamic networks to be stable (i.e., to reach consensus). To study the spectral properties of dynamic networks, we introduce the Dynamic Grounded Laplacian matrix, which is used to estimate lower and upper bounds for the real parts of the smallest and largest non-zero eigenvalues of the dynamic Laplacian matrix. These bounds can be used to obtain stability conditions using the Nyquist graphical stability test for undirected dynamic networks controlled using distributed controllers. Numerical simulations are provided to verify the effectiveness of the results.

Automatic topological structural synthesis algorithm of planar simple joint kinematic chains

Structural synthesis of kinematic chains is one of the most important and challenging mathematical problems in the field of conceptual design stage of mechanisms. In this article, an automatic topological structural synthesis algorithm has been proposed for planar simple joint kinematic chains. At first, the planar simple joint kinematic chains can be represented by single-color topological graph and corresponding link-joint incident matrix. Then, the corresponding incident matrices of planar simple joint kinematic chains with special input parameters can be formed with the single kinematic chain adding method with the help of isomorphic identification. Finally, based on the procedure for the single-color topological graph automatic drawing, an automatic topological structural synthesis algorithm of planar simple joint kinematic chains with specified degree of freedom F and number of links n can be synthesized in batch, while there are several examples to show the effectiveness of this method.

Non-full-rank Steiner quadruple systems S(v, 4, 3)

All different Steiner systems S(2 m , 4, 3) of order 2 m and rank 2 m ? m ? 1 + s over $$\mathbb{F}_2$$ , where 0 ≤ s ≤ m ? 1, are constructed. The number of different systems S(2 m , 4, 3) whose incident matrices are orthogonal to a fixed code is obtained. A connection between the number of different Steiner systems and of different Latin cubes is described.

Modeling Wildfire Incident Complexity Dynamics

Wildfire management in the United States and elsewhere is challenged by substantial uncertainty regarding the location and timing of fire events, the socioeconomic and ecological consequences of these events, and the costs of suppression. Escalating U.S. Forest Service suppression expenditures is of particular concern at a time of fiscal austerity as swelling fire management budgets lead to decreases for non-fire programs, and as the likelihood of disruptive within-season borrowing potentially increases. Thus there is a strong interest in better understanding factors influencing suppression decisions and in turn their influence on suppression costs. As a step in that direction, this paper presents a probabilistic analysis of geographic and temporal variation in incident management team response to wildfires. The specific focus is incident complexity dynamics through time for fires managed by the U.S. Forest Service. The modeling framework is based on the recognition that large wildfire management entails recurrent decisions across time in response to changing conditions, which can be represented as a stochastic dynamic system. Daily incident complexity dynamics are modeled according to a first-order Markov chain, with containment represented as an absorbing state. A statistically significant difference in complexity dynamics between Forest Service Regions is demonstrated. Incident complexity probability transition matrices and expected times until containment are presented at national and regional levels. Results of this analysis can help improve understanding of geographic variation in incident management and associated cost structures, and can be incorporated into future analyses examining the economic efficiency of wildfire management.

An Optimal Design Approach for Fault-Tolerant Petri Net Controllers Using Arc Weights Minimization

This paper proposes an approach for the optimal design of fault-tolerant Petri net controllers using arc weights minimization. Given a system controller that is modeled as a Petri net, a fault-tolerant Petri net controller is obtained by embedding the given Petri net controller into a larger (redundant) Petri net controller that retains the properties of the original controller and allows the detection and identification of faults that may occur in the controller places. An algorithm is developed to systematically design this fault-tolerant Petri net controller in an optimal sense. The optimality is in terms of minimizing the sum of the entries in the input and output incident matrices of the fault-tolerant controller. Examples of the optimal design of fault-tolerant Petri net controllers for a manufacturing system are also provided to illustrate our approach.

A new method for isomorphism identification in topological graphs using incident matrices

A new method using incident matrices to identify the isomorphism of topological graphs is proposed in this paper. The technique of acquiring the necessary condition for identifying the isomorphism is developed by comparing the calculation of incident matrices. Furthermore, it can be automatically executed by programs. With the help of the results from the necessary condition, the technique to find the correspondence of different vertices is presented, and the sufficiency for the isomorphism identification is obtained. Three examples are presented to demonstrate the validity and reliability of this method.

Optimization of steering linkage and double-wishbone suspension via R-W multi-body dynamic analysis

By employing R-W (Roberson and Wittenburg) methodology of multi-body dynamic analysis, both the original and reduced digraph representation of a steering linkage and double-wishbone suspension system were made. The kinematical and constrain equations of this system was obtained after a deducing of its incident matrices and tach matrices. Finally, an optimization model of a steering and suspension mechanism aiming to minimize the steering error was established. The optimization model took the influence caused by wheel bouncing to the steering performance into account and employed two weight functions in order to simulate the actual working condition. This procedure was verified by an example of a passenger vehicle, a group of desirable design variables were defined. Kinematische Analyse und Optimierung der Einrichtungen der Doppelquerlenker-Radaufhangung und Lenkung

Matrix–matrix multiplication by using anisotropic self-diffraction in BaTiO_3

We propose a matrix-matrix multiplication by using anisotropic self-diffraction in BaTiO(3). The input matrices are carried by the two incident beams with special Bragg-matched incident angles. The output matrices are produced by anisotropic self-diffraction with the polarization orthogonal to those of the incident matrices. By thresholding the output this architecture is particularly suitable for the applications of optical interconnects and an optical switch.

Wave reflection and transmission in beams

The vibrational behaviour of beam systems can be expressed in terms of waves of both propagating and near field types. A propagating wave incident upon a discontinuity gives rise to reflected and transmitted waves of both kinds whose amplitudes may be found from well-known reflection and transmission coefficients. In this paper the approach is extended to the case of incident near field waves, reflection and transmission matrices being derived for the cases of a point support and a change in section. Reflection at a boundary and the effects of applied excitations are also considered. It is seen that incident near fields can give rise to substantial propagating components. The application of the results to the analysis of free and forced vibration of beams is then demonstrated. By adopting this approach the effects of the interaction of the near fields with neighbouring discontinuities are fully included.