Vector-matrix Method Research Articles

Multiple Damaged Cables Identification in Cable-Stayed Bridges Using Basis Vector Matrix Method

A new damaged cable identification method using the basis vector matrix (BVM) is proposed to identify multiple damaged cables in cable-stayed bridges. The relationships between the cable tension stiffness and the girder bending strain of the cable-stayed bridge are established using a force method. The difference between the maximum bending strains of the bridges with intact and damaged cables is used to obtain the damage index vectors (DIXVs). Then, BVM is obtained by the normalized DIXV. Finally, the damage indicator vector (DIV) is obtained by DIXV and BVM to identify the damaged cables. The damage indicator is substituted into the damage severity function to identify the corresponding damage severity. A field cable-stayed bridge is used to verify the proposed method. The three-dimensional finite element model is established using ANSYS, and the model is validated using the field measurements. The validated model is used to simulate the strain response of the bridge with different damage scenarios subject to a moving vehicle load, including one, two, three, and four damaged cables with damage severity of 10%, 20%, and 30%, respectively. The noise effect is also discussed. The results show that the BVM method has good anti-noise capability and robustness.

Kinematics study for a spatial manipulator

For industrial robot design and control problems, it is necessary to determine both the positions of its parts relative to the stationary coordinate system, absolute positions of the parts, and their relative positions, generalised coordinates. The first problem is called the forward problem, and the second is the inverse problem for manipulator positions. The purpose of the paper is to solve the direct problem on manipulator positions, i.e., to determine and study positions of manipulator sections with known generalised coordinates. In the paper a spatial manipulator with four degrees of freedom is considered. Kinematic characteristics of the last link of the manipulator - grabber are defined. The kinematic characteristics are the coordinates of current position, velocity, and acceleration of the grip. Kinematic characteristics are found by applying the vector matrix method, based on the application of transition matrices from one reference system to another and rotation vector matrices. The vector matrix method belongs to the universal methods and is designed for use in mathematical computer simulation systems. Keywords: Vector matrix method, spatial manipulator, kinematic characteristics, mechanics of industrial robots.

Simulation of Controlled Motion of a Person When Walking in an Exoskeleton

Purpose of reseach. Robot exoskeletons open up new possibilities in the rehabilitation of patients with lower limb injuries. Despite the growing number of publications on this topic, many issues related to the development of design tools based on the simulation of human movement in an exoskeleton using the theoretical basis of stable movement in the upright position have not been studied well enough. Therefore, the purpose of this paper is to develop methods for improving the efficiency of the lower extremity exoskeleton control system for biped gait. Methods. The key feature of the paper is the application of modeling techniques determining the laws of the exoskeleton motion. Methods of mathematical modeling of the motion of sections are used, taking into account their subsequent possible use in modeling the motion of exoskeleton sections; trajectory equations are composed using the vector-matrix method. The trajectories of the exoskeleton's foot, lower leg, and hip movement during steady walking are studied.Results. To simulate the operation of a robotic complex - a prototype of an exoskeleton of the lower extremities with ten active degrees of freedom, kinematic definition the trajectory of the sections is used. To find the vector of generalized coordinates, the inverse kinematics problem is solved applying the vector-matrix method using the Jacobian matrix. The results of numerical simulation show high convergence and eficacy of the proposed method. The proposed method allows defining the trajectory of the operator in the exoskeleton in real devices.Conclusion. In the paper, the study of walking is performed from the standpoint of modeling a quasi-static gait using kinematic approaches. The developed method for determining the defining angles of rotation of the exoskeleton sections for different foot positions taking into account the position of the mass center projections, is used in the development of algorithms for controlling human motion in the exoskeleton.

Modeling Gait Patterns of a Patient with Orthopedic Injury Using an Exoskeleton

Purpose of reseach. The paper describes the EXOLITE-REHAB rehabilitation robotic complex which makes it possible to do rehabilitation exercises of lower limbs of patients by performing leg lifting, verticalization, squats and other types of movement. In many countries, research work is underway to create devices that allow a person to move in space when the musculo-skeletal system is damaged. Therefore, the purpose of this article is to study and set the basic regularities and algorithms based on mathematical models describing the controlled movement of the lower limbs exoskeleton by the example of modeling the movement of the exoskeleton's ankle joint.Methods. The key feature of the complex is the use of a follower-up control system that allows us to provide a prescribed movement of the human ankle joint with a high degree of accuracy in a wide range of parameters’ changes. Methods of mathematical modeling of the ankle joint movement are applied, taking into account their subsequent possible use in modeling the movement of exoskeleton links.Results. A kinematic setting of the ankle joint movement trajectory is used in order to simulate the operation of a robotic system. In order to find the vector of generalized coordinates, the inverse kinematics problem is solved using the vector-matrix method with the application of Jacobian matrix. The results of numerical simulation show high convergence and adequacy of the proposed method.Conclusion. The article considers the method of using a follower-up control system that has a sufficient degree of accuracy of copying the trajectory. The results of modeling the follower-up control system of the EXOLITE-REHAB rehabilitation exoskeleton, working according to the developed algorithm, show that it is able to repeat the required trajectory with sufficient accuracy. In the future, we plan to study the system more deeply on a three-dimensional model with electric drives.

Vector-matrix method for restoration of point spatial coordinates in stereo photography general case

Vector-matrix method for restoration of point spatial coordinates in stereo photography general case

Comparisons of Bitcoin Cryptosystem with Other Common Internet Transaction Systems by AHP Technique

This paper describes proposed methodology for evaluation of critical systems and prioritization of critical risks and assets identified in highly secured information systems. For different types of information assets or security environments it is necessary to apply different techniques and methods for their prioritization and evaluation. In this article, VECTOR matrix method for prioritization of critical assets and critical risks is explained and integrated into AHP (Analytic Hierarchy Process) technique as a set of fixed criteria for evaluation of defined alternatives. Bitcoin cryptocurrency was compared and evaluated along with other common Internet transaction systems by information security professionals according to defined VECTOR criteria. Also, the newly proposed hybrid AHP model is presented with potential case studies for future research. This article tries to discover security posture of Bitcoin cryptocurrency in the context of information security risks related to the existing most common online payment systems like e-banking, m-banking, and e-commerce

Применение векторно-матричного метода преобразования координат для манипуляторов лесных машин

Применение векторно-матричного метода преобразования координат для манипуляторов лесных машин

Adjustment of a rotated mirror analog of the Abbe prism

A construction of a mirror system manufactured from the AMg-6 aluminum alloy by diamond microsharpening and intended to take the place of the rotary Abbe prism in the infrared spectrum region is presented. Using the technique of reducing a three-mirror system to the simplest mirror equivalent and vector-matrix method, primary errors of a mirror system are revealed and their influence on the picture bounce is studied. An adjustment technique adapted to a real construction is developed for a mirror system.

On the method of investigation of mirror-prism systems and several features of analytical formulas applied for calculation of tolerance for prism angles

A simple example is used to demonstrate that, during the calculation of tolerance for prism angles, one should pay attention to their application conditions and to the mutual influence of primary errors, which has not been described in the literature. We propose a simple vector-matrix method as one of the possible solutions to the problem of error determination in mirror-prism systems and the specification of tolerances. Statistical analysis of tolerances for the AP-90 prism demonstrates the efficiency of the method.

Kinetostatical analysis of a lifting mechanism

This article considers the developed vector-matrix method for determining of driving forces and reaction forces in kinematic pairs of multilever linkage with adjustable closed circuit, which allows obtaining of analytical expressions of desired parameters in an explicit form. As a result of the kinetostatical analysis of lifting mechanism there are received recommendations for selection of a hydraulic cylinder.

Generalization of the Jones vector-matrix method and the regularity of the Weigert effect for partially polarized light

Generalization of the Jones vector for partially polarized radiation carried out by Kakichashvili is given. Partially polarized light is presented as two noncoherent components of mutually orthogonal polarization. The formal operation of amplitude summation of mutually noncoherent components and the symbol of this operation are introduced. The rules of operating with this symbol are determined. The regularity of the Weigert effect is modified for partial polarization of the inducing light. On this basis the modification of the Jones matrix for partially polarized light is made. The rules for the formation of the resulting matrix from the Jones matrices corresponding to the noncoherent components of partially polarized light are determined.

Holographic chiral structure on the basis of Weigert's effect

A simple analysis of the possibility of creating a holographic chiral structure on the basis of Weigert's effect with help of the Jones vector-matrix method was done, to my knowledge, for the first time. A corresponding experiment was also conducted. The results of the investigation show that the diffractive optical element obtained behaves similarly to liquid crystals or sculptured thin films with chiral structures.

Extension of a model analysis of the degree of polarization of light

A theoretical approach is developed in which partially polarized radiation can be represented as a sum of coherent and incoherent components and also of the action of some imaginary device with time-dependent birefringence. This approach allows the Jones vector matrix method to be used for the calculations, which is important for theoretical calculations of the polarization state.

Lambert scattering from a hyperboloid of one sheet

A generalized vector–matrix method is employed to determine the intensity of diffusely scattered light from a hyperboloid of one sheet. Solutions for both the elliptic and circular cross-section cases are obtained in integral form. For certain limiting conditions the latter results are shown to reduce to a form obtained earlier for a cylinder of circular cross section.

A characteristic vector matrix method for multicategory pattern classification†

Abstract An algorithm of classifying multicategory patterns using a characteristic vector matrix is described. It is shown that, if the training patterns are linearly separable, the algorithm will guarantee convergence. Furthermore, if the training patterns are not linearly separable, then a method for testing the existence of a limit cycle in the iteration procedure is developed. Examples indicate that the algorithm has rapid convergence and its usefulness is promising. Also a comparison of the convergence condition of the algorithm with that of the fractional correction rule is made.

Lambert Scattering from a Cone and Paraboloid of Revolution

Employing a vector-matrix method, the intensity of diffusely scattered light from a cone and paraboloid of revolution is calculated in the geometrical optics approximation. For the two quadric surfaces considered, different cases, determined principally by the direction of incident light and observer vectors, are examined. As a first approximation, multiple scattering is neglected in instances for which the surfaces are considered concave with respect to source and observer directions. When illuminated and viewed as convex surfaces, the effects of shadowing are introduced for those special orientations of light and observer vectors that permit easy determination of the geometry of the shadow lines.

A method for the exact determination of periodic motions in relay control systems

A vector matrix method for the exact determination of periodie motions in relay control systems with a dead zone and hysteresis is investigated. The conditions for the existence of harmonies, subharmonies and self-oscillations are obtained. A particular case of a third-order system is worked out and the results obtained on a digital and an analog computer are also discussed.