A New Method for Detection of Graph Isomorphism Based on the Quadratic Form

2003 ◽  
Vol 125 (3) ◽  
pp. 640-642 ◽  
Author(s):  
P. R. He and ◽  
W. J. Zhang ◽  
Q. Li and ◽  
F. X. Wu
Keyword(s):  
Quadratic Form ◽  
Graph Isomorphism ◽  
New Method ◽  
Eigenvalues And Eigenvectors ◽  
Kinematic Chains ◽  
Quadric Surfaces

This paper proposes a new method for detection of graph isomorphism using the concept of quadratic form. Graphs/kinematic chains are represented first by quadratic form, and the comparison of two graphs is thus reduced to the comparison of two quadratic form expressions. If both the lengths and the directions of the semiaxes of quadric surfaces, which are characterized by the eigenvalues and eigenvectors, are the same, the associated graphs/kinematic chains are isomorphic. An algorithm is developed based on this idea, and tested for the counter-examples known to other methods.

A Quadratic Form-Based Approach to Identification of Kinematic Chains in Structural Analysis and Synthesis of Mechanisms

2001 ◽  
Author(s):  
Peiren He ◽  
Wenjun Zhang ◽  
Qing Li
Keyword(s):  
Structural Analysis ◽  
Quadratic Form ◽  
Test Cases ◽  
Eigenvalues And Eigenvectors ◽  
New Approach ◽  
Kinematic Chains ◽  
Synthesis Of Mechanisms ◽  
Adjacency Matrices ◽  
Analysis And Synthesis

Abstract Identification of kinematic chains is needed when studying in structural analysis and synthesis of mechanisms. Research on detection of isomorphism in graphs/kinematic chains has a long history. Many algorithms or methods have been proposed. However, these methods have only achieved success in restricted conditions. This paper proposes a new approach using the concept of quadratic form. Graphs/kinematic chains are first represented by their adjacency matrices, the eigenvalues and their eigenvectors corresponding to these adjacency matrices are then calculated. Two graphs are represented by two quadratic expressions. The comparison of two graphs reduces to the comparison of two quadratic expressions. Quadratic expressions are characterized by the eigenvalues and eigenvectors. An algorithm is developed to compare, correspondingly, eigenvalues and eigenvectors of two graphs, known test cases are used to verify the effectiveness of the approach.

A New Method of Design of Epicyclic Gear Trains

2013 ◽  
Vol 457-458 ◽  
pp. 707-712
Author(s):  
Pei Wen An ◽  
Zhong Liang Lv
Keyword(s):  
New Method ◽  
Combination Method ◽  
Engineering Practice ◽  
Type Number ◽  
Practical Application ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Number Synthesis ◽  
Method Of Design

Epicyclic gear trains have been broadly applied in engineering practice. In this paper, kinematic chains (K.C.) with single-joint (S.J.) were applied to innovative synthesis of the epicyclic gear trains. The method of the innovative synthesis of the epicyclic gear trains was presented. Not only the epicyclic gear trains in common uses were obtained, but some new types of epicyclic gear trains that are got difficultly by means of conventional combination method were gained. Thereby, a new way has been offered for the innovative synthesis of the epicyclic gear trains, at the same time, a way has also been offered for practical application of some multi-link kinematic chains gained by using the theory of type-number synthesis of the K.C. with S.J.. Examples show that the method presented in this paper is right and feasible, and the method is efficient and practical for the innovative synthesis of the epicyclic gear trains.

A New Multivalued Neural Network for Isomorphism Identification of Kinematic Chains

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Gloria Galán-Marín ◽  
Domingo López-Rodríguez ◽  
Enrique Mérida-Casermeiro
Keyword(s):  
Neural Network ◽  
Intelligent Systems ◽  
Initial Conditions ◽  
Graph Isomorphism ◽  
Kinematic Chain ◽  
Parameter Tuning ◽  
Isomorphism Problem ◽  
Kinematic Chains ◽  
Graph Isomorphism Problem ◽  
Better Than

A lot of methods have been proposed for the kinematic chain isomorphism problem. However, the tool is still needed in building intelligent systems for product design and manufacturing. In this paper, we design a novel multivalued neural network that enables a simplified formulation of the graph isomorphism problem. In order to improve the performance of the model, an additional constraint on the degree of paired vertices is imposed. The resulting discrete neural algorithm converges rapidly under any set of initial conditions and does not need parameter tuning. Simulation results show that the proposed multivalued neural network performs better than other recently presented approaches.

A New Method for Computing Eigenpairs of a Finite Element Structure

2014 ◽  
Vol 590 ◽  
pp. 672-676
Author(s):  
Ping Liang ◽  
Yu Hang Zhang ◽  
Jun Wei ◽  
Bing Yu
Keyword(s):  
Dynamical System ◽  
Finite Element ◽  
New Method ◽  
Stability And Convergence ◽  
Power Method ◽  
Value Iteration ◽  
Eigenvalues And Eigenvectors ◽  
Simpler Algorithm ◽  
Distribution Of Eigenvalues ◽  
D Value

Based on the weighted inverse topological change method and by introducing a new concept of mass submembers, a dynamical system can be transformed into a static one. Using the properties of the weighted D value, i.e. the weighted D value decreases monotonously with parameter λ increasing; a new method called the weighted D value iteration method is presented for computing the eigenpairs (eigenvalues and eigenvectors). Using this method a series of eigenpairs of a finite element structure can be obtained. It has a merit of simpler algorithm and less computation efforts. Not as the power method, its stability and convergence rate does not depend on the distribution of eigenvalues, and convergent quickly. An example is given to demonstrate the valid of this method.

New scheme for large-scale eigenvalue problems of the RPA-type matrix equation

1992 ◽  
Vol 70 (2) ◽  
pp. 296-300 ◽  
Author(s):  
Susumu Narita ◽  
Tai-ichi Shibuya
Keyword(s):  
Eigenvalue Problem ◽  
Convergence Rate ◽  
Matrix Equation ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Type Equation ◽  
Fast Convergence ◽  
New Method ◽  
Eigenvalues And Eigenvectors ◽  
Numerical Tests

A new method is proposed for obtaining a few eigenvalues and eigenvectors of a large-scale RPA-type equation. Some numerical tests are carried out to study the convergence behaviors of this method. It is found that the convergence rate is very fast and quite satisfactory. It depends strongly on the way of estimating the deviation vectors. Our proposed scheme gives a better estimation for the deviation vectors than Davidson's scheme. This scheme is applicable to the eigenvalue problems of nondiagonally dominant matrices as well. Keywords: large-scale eigenvalue problem, RPA-type equation, fast convergence.

Detection of small target in sea clutter via multiscale directional Lyapunov exponents

Sensor Review ◽  
2019 ◽  
Vol 39 (6) ◽  
pp. 752-762
Author(s):  
Rui Wang ◽  
Xiangyang Li ◽  
Hongguang Ma ◽  
Hui Zhang
Keyword(s):  
State Space ◽  
Lyapunov Exponents ◽  
Design Methodology ◽  
Radar Data ◽  
Nonstationary Time Series ◽  
New Method ◽  
Small Target ◽  
Sea Clutter ◽  
Eigenvalues And Eigenvectors ◽  
Content Type

Purpose This study aims to provide a new method of multiscale directional Lyapunov exponents (MSDLE) calculated based on the state space reconstruction for the nonstationary time series, which can be applied to detect the small target covered by sea clutter. Design/methodology/approach Reconstructed state space is divided into non-overlapping submatrices whose columns are equal to a predetermined scale. The authors compute eigenvalues and eigenvectors of the covariance matrix of each submatrix and extract the principal components σip and their corresponding eigenvectors. Then, the angles ψip of eigenvectors between two successive submatrices were calculated. The curves of (σip, ψip) reflect the nonlinear dynamics both in kinetic and directional and form a spectrum with multiscale. The fluctuations of (σip, ψip), which are sensitive to the differences of backscatter between sea wave and target, are taken out as the features for the target detection. Findings The proposed method can reflect the local dynamics of sea clutter and the small target within sea clutter is easily detected. The test on the ice multiparameter imaging X-ban radar data and the comparison to K distribution based method illustrate the effectiveness of the proposed method. Originality/value The detection of a small target in sea clutter is a compelling issue, as the conventional statistical models cannot well describe the sea clutter on a larger timescale, and the methods based on statistics usually require the stationary sea clutter. It has been proven that sea clutter is nonlinear, nonstationary or cyclostationary and chaotic. The new method of MSDLE proposed in the paper can effectively and efficiently detect the small target covered by sea clutter, which can be also introduced and applied to military, aerospace and maritime fields.

Topological Synthesis and Analysis of Geared Linkages Based on Matrix Powers

1989 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Adjacency Matrix ◽  
Digital Computer ◽  
Visual Inspection ◽  
Kinematic Chain ◽  
New Method ◽  
Graph Representation ◽  
Kinematic Chains ◽  
Degree Matrix ◽  
Topological Synthesis

Abstract A new method for transforming pin-jointed kinematic chains into geared linkages is introduced. The method utilizes the graph representation in the form of the adjacency matrix and the “degree matrix” [20], and the powers of these matrices. The method involves first determining the feasible locations for assigning gear pairs in a kinematic chain, followed by determining which of the choices are distinct, and finally, determining the distinct possible ways of assigning the ground link for each distinct “geared kinematic chain” so formed. Because the method is based on matrix manipulations and does not rely on visual inspection, it is easily implemented on a digital computer. The method is applied to an example class of geared mechanism, the single-dof geared seven-bar linkages.

A distinct matrix representation of the planar kinematic chains and isomorphism recognition

2019 ◽  
Vol 13 (4) ◽  
pp. 5717-5734
Author(s):  
M. S. Alam ◽  
M. Suhaib
Keyword(s):  
Mechanism Design ◽  
Design Problem ◽  
Matrix Representation ◽  
Degree Of Freedom ◽  
New Method ◽  
Structural Synthesis ◽  
Primary Condition ◽  
Secondary Conditions ◽  
Kinematic Chains ◽  
Three Degree Of Freedom

Structural synthesis of kinematic chains has been an indispensable area of the mechanism-design problem. The duplication may occur while developing kinematic chains. Therefore, an isomorphic test is required to eliminate duplication. For this purpose, the numbers of methods are proposed during recent years. However, most of the methods are complex and difficult to understand, and fulfil the only primary condition, but not the secondary conditions for isomorphism detection. In the present work, a new method is introduced to detect isomorphism in planar kinematic chains (KCs) fulfilling both primary and secondary conditions. First, KC’s are topologically transformed into skeleton diagrams, and then skeleton matrices [S] and identification strings [IS] are formulated consequently. In order to detect isomorphism, the IS is considered as an invariant string of a KC which in turn, enables the detection of isomorphism between the KCs. The proposed method accurately recognizes isomorphism up to 12 links KCs with no counter examples found in the literature. Three examples with one degree of freedom having 10 links 12 joints, 10 links 13 joints and 12 links three degree of freedom systems are introduced to reveal the reliability and strength of the proposed method.

A Method for Substructural Sensitivity Synthesis

1991 ◽  
Vol 113 (2) ◽  
pp. 201-208 ◽  
Author(s):  
Joo Ho Heo ◽  
K. F. Ehmann
Keyword(s):  
Dynamic Characteristics ◽  
Computational Efficiency ◽  
Synthesis Method ◽  
Simple Calculation ◽  
Component Mode Synthesis ◽  
New Method ◽  
Eigenvalues And Eigenvectors ◽  
Modal Data ◽  
Entire Structure ◽  
Design Variables

A new method, termed the substructural sensitivity synthesis method, which utilizes the computational merits of the component mode synthesis technique was proposed for the simple calculation of design sensitivities of the dynamic characteristics of substructurally combined structures. It has been shown that the modal sensitivities of the entire structure can be obtained by synthesizing the substructural modal data and the sensitivities of the modal data for the design variables of the modifiable substructure. For a truss structure, as an example, the sensitivities of the eigenvalues and eigenvectors obtained by the new method were compared with exact solutions in terms of accuracy and computational efficiency.

scholarly journals Identifying the Isomorphism of Kinematic Chains

2016 ◽  
Vol 10 (3) ◽  
pp. 195-200
Author(s):  
Krystyna Romaniak
Keyword(s):  
Eigenvalues And Eigenvectors ◽  
Kinematic Chains ◽  
Precise Result ◽  
Key Issues

Abstract Identification of isomorphic kinematic chains is one of the key issues in researching the structure of mechanisms. As a result the structures which duplicate are eliminated and further research is carried out on kinematic chains that do not duplicate. This dilemma has been taken up by many scholars who have come up with a variety of ideas how to solve it. The review of the methods for identifying the isomorphism of kinematic chains suggested by researchers is contained in this study, including Hamming Number Technique, eigenvalues and eigenvectors, perimeter graphs, dividing and matching vertices. The spectrum of methods applied to the issue of identifying the iso-morphism of mechanisms reflects the researchers’ efforts to obtain a precise result in the shortest time possible.

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