Inverse displacement analysis of the general six degree-of-freedom serial robot based on optimization method

The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot.The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the optimization method is adopted to solve the nonlinear least squares problem with the analytic form of new Jacobian matrix.In this way,joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three non-collinear end effector points are given.Compared with the general Newton iterative method,the proposed algorithm can search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method may also be the singular configuration.So the convergence domain is bigger than that of the general Newton iterative method.Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually much easier to be measured than the orientation of the end effector.The inverse displacement analysis of the general 6R(six-revolute-joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm.Because the three non-collinear points can be selected at random,the method can be applied to any other types of serial robots.

A General Calculating Method of Rotor’s Torsional Stiffness Based on Stiffness Influence Coefficient

In order to develop a general calculating rotor’s torsional stiffness based on stiffness influence coefficient for different rotor assembling, the calculation method of the torsional stiffness influence coefficient of equal thickness disc is researched in this paper at first. Then the torsional stiffness influence coefficient λ of equal thickness disc is fit to a binary curved face and a calculation equation is obtained based on a large quantity of calculating data, which lays the foundation for research on a general calculating method of rotor torsional stiffness. Thirdly a simplified calculation method for equivalent stiffness diameter of stepped equal thickness disc and cone disc in the steam turbine generators is suggested. Finally a general calculating program for calculating rotor’s torsional vibration features is developed, and the torsional vibration features of a verity of steam turbine rotors are calculated for verification. The calculating results show that stiffness influence coefficient λ of equal-thickness disc depends on parameters of B and H, as well as the stiffness influence coefficient λ;and discs with complex structure can be simplified to equal-thickness discs with little error by using the method suggested in this paper;error can be controlled within 1% when equivalent diameter of stiffness is calculated by this method.

B-CONVERGENCE PROPERTIES OF GENERAL LINEAR METHODS

In this paper, for general linear methods applied to strictly dissipative initial value problem in Hilbert spaces, we prove that algebraic stability implies B-convergence, which extends and improves the existing results on Runge-Kutta methods. Specializing our results for the case of multi-step Runge-Kutta methods, a series of B-convergence results are obtained.

THE VALIDITY OF THE MODIFIED MORI-TANAKA METHOD FOR COMPOSITES WITH SLIGHTLY WEAKENED INTERFACE

This paper presents a direct Mori-Tanaka approach to calculate the effective moduli of particle-reinforced composites and fiber-reinforced composites with spring-like imperfect interfaces. By a comparison between these results and those obtained from the approximate Mori-Tanaka method developed by Qu for composites with slightly weakened interface, the validity of the Qu's method is revealed.

APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS

Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method （GAOR） is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.

General displacement arch-cantilever element method for stress analysis of arch dam

Based on the general displacement method and the basic hypothesis of the trial load method, a new advanced trial load method, the general displacement arch-cantilever element method, was proposed to derive the transformation relation of displacements and loads between the surface nodes and middle plane nodes. This method considers the nodes on upstream and downstream surfaces of the arch dam to be exit nodes （master nodes）, and the middle plane nodes to be slave nodes. According to the derived displacement and load transformation matrices, the equilibrium equation treating the displacement of middle plane nodes as a basic unknown variable is transformed into one that treats the displacement of upstream and downstream nodes as a basic unknown variable. Because the surface nodes have only three degrees of freedom （DOF）, this method can be directly coupled with the finite element method （FEM）, which is used for foundation simulation to analyze the stress of the arch dam with consideration of dam-foundation interaction. Moreover, using the FEM, the nodal load of the arch dam can be easily obtained. Case studies of a typical cylindrical arch dam and the Wudongde arch dam demonstrate the robustness and feasibility of the proposed method.

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.

A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations

A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.

Secondary Nonlinear Stability of General Linear Methods for Stiff Initial Value Problems

In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.

Improvement and Exploration of Teaching Methods for General Entomology in Agriculture and Forestry Colleges and Universities

According to characteristics of General Entomology and existing problems in teaching process,it came up with methods and countermeasures for improving teaching General Entomology,including improving practical ability of students through enhancing all links of practice teaching,and stimulating learning interest of students through improving methods of course examination.

Parallel Implicit-Explicit General Linear Methods

High-order discretizations of partial differential equations(PDEs)necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner.Implicit-explicit(IMEX)integration based on general linear methods(GLMs)offers an attractive solution due to their high stage and method order,as well as excellent stability properties.The IMEX characteristic allows stiff terms to be treated implicitly and nonstiff terms to be efficiently integrated explicitly.This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel.The first approach is based on diagonally implicit multi-stage integration methods(DIMSIMs)of types 3 and 4.The second is a parallel generalization of IMEX Euler and has the interesting feature that the linear stability is independent of the order of accuracy.Numerical experiments confirm the theoretical rates of convergence and reveal that the new schemes are more efficient than serial IMEX GLMs and IMEX Runge-Kutta methods.

Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method

The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.

General Expression of LRC Method in Estimation of Bridge’s Equivalent Static Wind Load

According to the relationship between load and response, the equivalent static wind load(ESWL) of a structure can be estimated by load-response correlation(LRC) method, which can be accurately used to estimate the background ESWL of a structure. The derivation of the classical expression of LRC formula is based on a specific command response at a critical position, and the ESWL distribution has only one form in this case. In this paper, a general expression of LRC formula is derived based on a specific command response at all positions. For the general expression, ESWLs can be expressed by load-response correlation coefficients, response-response correlation coefficients, RMS values of the fluctuating wind loads, and peak factor in the form of matrices. By comparing the expressions of LRC method, it was found that the classical expression was only one form of the general one. The general expression which introduces the response-response correlation coefficients provided more options for structural engineers to estimate ESWLs and offered further insights into the LRC method. Finally, a cable-stayed bridge, a rigid three span continuous girder bridge, and a suspension bridge were used to verify the correctness of the general expression of LRC method.

General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems

First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.

13 Galactic Star Clusters in Gaia DR3 Identified by An Improved FoF and UPMASK Hybrid Method Using MvC

Open clusters(OCs)serve as invaluable tracers for investigating the properties and evolution of stars and galaxies.Despite recent advancements in machine learning clustering algorithms,accurately discerning such clusters remains challenging.We re-visited the 3013 samples generated with a hybrid clustering algorithm of FoF and pyUPMASK.A multi-view clustering(MvC)ensemble method was applied,which analyzes each member star of the OC from three perspectives—proper motion,spatial position,and composite views—before integrating the clustering outcomes to deduce more reliable cluster memberships.Based on the MvC results,we further excluded cluster candidates with fewer than ten member stars and obtained 1256 OC candidates.After isochrone fitting and visual inspection,we identified 506 candidate OCs in the Milky Way.In addition to the 493 previously reported candidates,we finally discovered 13 high-confidence new candidate clusters.

A Localization Method of High Energy Transients for All-sky Gamma-ray Monitor

Fast and reliable localization of high-energy transients is crucial for characterizing the burst properties and guiding the follow-up observations.Localization based on the relative counts of different detectors has been widely used for all-sky gamma-ray monitors.There are two major methods for this count distribution localization:χ^(2)minimization method and the Bayesian method.Here we propose a modified Bayesian method that could take advantage of both the accuracy of the Bayesian method and the simplicity of the χ^(2)method.With comprehensive simulations,we find that our Bayesian method with Poisson likelihood is generally more applicable for various bursts than the χ^(2)method,especially for weak bursts.We further proposed a location-spectrum iteration approach based on the Bayesian inference,which could alleviate the problems caused by the spectral difference between the burst and location templates.Our method is very suitable for scenarios with limited computation resources or timesensitive applications,such as in-flight localization software,and low-latency localization for rapidly follow-up observations.

PSRDP:A Parallel Processing Method for Pulsar Baseband Data

To address the problem of real-time processing of ultra-wide bandwidth pulsar baseband data,we designed and implemented a pulsar baseband data processing algorithm(PSRDP)based on GPU parallel computing technology.PSRDP can perform operations such as baseband data unpacking,channel separation,coherent dedispersion,Stokes detection,phase and folding period prediction,and folding integration in GPU clusters.We tested the algorithm using the J0437-4715 pulsar baseband data generated by the CASPSR and Medusa backends of the Parkes,and the J0332+5434 pulsar baseband data generated by the self-developed backend of the Nan Shan Radio Telescope.We obtained the pulse profiles of each baseband data.Through experimental analysis,we have found that the pulse profiles generated by the PSRDP algorithm in this paper are essentially consistent with the processing results of Digital Signal Processing Software for Pulsar Astronomy(DSPSR),which verified the effectiveness of the PSRDP algorithm.Furthermore,using the same baseband data,we compared the processing speed of PSRDP with DSPSR,and the results showed that PSRDP was not slower than DSPSR in terms of speed.The theoretical and technical experience gained from the PSRDP algorithm research in this article lays a technical foundation for the real-time processing of QTT(Qi Tai radio Telescope)ultra-wide bandwidth pulsar baseband data.

Application of NSR-AISC Method in Reserve Estimation and Technical Economic Evaluation of Low-Grade Polymetallic Deposits: Taking a Low-Grade Copper-Molybdenum Mine in Guangdong Province as an Example

The development and utilization of low-grade polymetallic deposits with strategic mineral resources is one of the important measures to alleviate the current high dependence on strategic mineral resources in China. However, domestic mining enterprises and most mining consulting and design institutes usually use general industrial indicators to carry out reserve estimation and technical and economic feasibility studies on low-grade polymetallic deposits, which cannot truly reflect the economic value of such deposits. The article expounds on the definitions of net return value (NSR) and on-site total maintenance cost (AISC) of common ore smelters in the evaluation of overseas mineral resources. Taking a low-grade polymetallic copper-molybdenum mine in Guangdong Province as an example, comparing the research results showed the NSR-AISC method and the general industrial index method in low-grade polymetallic deposit. There are huge differences in the results of reserve estimation;through the further introduction of Taylor’s formula and the research results on the relationship between investment intensity and production scale, a more reasonable mine life and investment scale are recommended, and a more in-depth comparative study has been carried out in the dimension of technical and economic indicators. Based on the comparative study of the above two methods in reserve estimation and the evaluation results of technical and economic indicators, the author believes that the NSR-AISC method can better reflect the true value of low-grade polymetallic ore projects, and should be popularized and applied in resource evaluation and development practice. This article further describes the application status of the NSR-AISC method for reserve estimation and the evaluation of technical economic indicators, and suggests the main points that should be paid attention to in the use of the NSR-AISC method.

On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids

The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method.

EXACT SOLUTIONS FOR GENERAL VARIABLE-COEFFICIENT KdV EQUATION

By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don't exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable coefficient KdV equation is given.