Error modeling of 3-RSR parallel robot based on D-H transformation matrix

By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg （D-H） transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between po- sition and orientation error of the platform and the original geometric errors is simplified as a linear explicit function rela- tion. The results provide a basis for further studying error analysis and error compensation.

Research on the Applications of Probability Model and Matrix Transformation in Data Analysis and Management under the Environment of Information Time

In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the importance and the cross characteristics with other research direction to get the affirmation of the people. The probability theory and linear algebra act as the powerful tool for analyzing and mining data. The experimental result illustrates the effectiveness. In the near future, we plan to conduct more theoretical analysis on the topic.

Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model

Based on a simple coupled Lorenz model,we investigate how to assess a suitable initial perturbation scheme for ensemble forecasting in a multiscale system involving slow dynamics and fast dynamics.Four initial perturbation approaches are used in the ensemble forecasting experiments:the random perturbation(RP),the bred vector(BV),the ensemble transform Kalman filter(ETKF),and the nonlinear local Lyapunov vector(NLLV)methods.Results show that,regardless of the method used,the ensemble averages behave indistinguishably from the control forecasts during the first few time steps.Due to different error growth in different time-scale systems,the ensemble averages perform better than the control forecast after very short lead times in a fast subsystem but after a relatively long period of time in a slow subsystem.Due to the coupled dynamic processes,the addition of perturbations to fast variables or to slow variables can contribute to an improvement in the forecasting skill for fast variables and slow variables.Regarding the initial perturbation approaches,the NLLVs show higher forecasting skill than the BVs or RPs overall.The NLLVs and ETKFs had nearly equivalent prediction skill,but NLLVs performed best by a narrow margin.In particular,when adding perturbations to slow variables,the independent perturbations(NLLVs and ETKFs)perform much better in ensemble prediction.These results are simply implied in a real coupled air–sea model.For the prediction of oceanic variables,using independent perturbations(NLLVs)and adding perturbations to oceanic variables are expected to result in better performance in the ensemble prediction.

Mathematical Modeling and Control Algorithm Development for Bidirectional Power Flow in CCS-CNT System

As the demand for more efficient and adaptable power distribution systems intensifies, especially in rural areas, innovative solutions like the Capacitor-Coupled Substation with a Controllable Network Transformer (CCS-CNT) are becoming increasingly critical. Traditional power distribution networks, often limited by unidirectional flow capabilities and inflexibility, struggle to meet the complex demands of modern energy systems. The CCS-CNT system offers a transformative approach by enabling bidirectional power flow between high-voltage transmission lines and local distribution networks, a feature that is essential for integrating renewable energy sources and ensuring reliable electrification in underserved regions. This paper presents a detailed mathematical representation of power flow within the CCS-CNT system, emphasizing the control of both active and reactive power through the adjustment of voltage levels and phase angles. A control algorithm is developed to dynamically manage power flow, ensuring optimal performance by minimizing losses and maintaining voltage stability across the network. The proposed CCS-CNT system demonstrates significant potential in enhancing the efficiency and reliability of power distribution, making it particularly suited for rural electrification and other applications where traditional methods fall short. The findings underscore the system's capability to adapt to varying operational conditions, offering a robust solution for modern power distribution challenges.

COUPLING MODEL OF EXTENDED MANUFACTURING ORGANIZATION AND ITS APPLICATION

For the feature of complex weapon manufacturing on internet,a coupling model is proposed.By using the model,the correlation between manufacturing cells in an extended manufacturing organization can be evaluated quantitatively,so an appropriate control plan is determined.A strategy to improve and reduce the coupling relationship of the organization is studied.A correlation matrix of extended tasks is built to analyze the relationship between sub-tasks and manufacturing resources.An optimization method for manufacturing resource configuration is presented based on the coupling model.Finally,a software system for analyzing coupling model about manufacturing organization on internet is developed,and the result shows that the coupling model is effective.

MATHEMATICAL ANALYSIS OF DRUG RELEASE FROM A MONOLITHIC MATRIX WITH AN INITIALLY LINEAR CONCENTRATION DISTRIBUTION

Based on the principle of chemical engineering in the multisubject field—drug delivery, the release kinetics of the slab monolithic matrix with an initially linear concentration distribution is studied in this paper. It can be used to describe the later stage when drug loading is above its solubility limit. A comprehensive model is proposed and the generalized solutions are acquired by Laplace transformation, from which a special case, i.e. a perfect sink has been deduced. According to the derived equations, the concentration profiles in the matrix has been computed and illustrated and the effect of volume of extraction medium on release has been investigated.

Applications of Lodrigues Matrix in 3D Coordinate Transformation

Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms：① the traditional rotation angles θ,φ,ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.

Stability of GM(1,1) power model on vector transformation

The morbidity problem of the GM（1,1） power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM（1,1） power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM（1,1） power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM（1,1） power model.

Modeling and Decoupling of Coupling Tasks in Collaborative Development Process of Complicated Electronic Products

It is important to improve the development efficiency of decoupling a coupling task package according to the information relevancy relation between development tasks in the collaborative development process of complicated electronic products.In order to define the task coupling model in the development process,the weighted directed graph based on the information relevancy is established,and the correspondence between weighted directed graph model and numerical design structure matrix model of coupling tasks is introduced.The task coupling model is quantized,thereby the interactivity matrix of task package is built.A multi-goal task decoupling method based on improved genetic algorithm is proposed to decouple the task coupling model,which transforms the decoupling of task package into a multi-goal optimization issue.Then the improved genetic algorithm is used to solve the interactivity matrix of coupling tasks.Finally,the effectiveness of this decomposition method is proved by using the example of task package decoupling of collaborative development of a radar’s phased array antenna.

Mitigation of Transients in Capacitor Coupled Substations Using Traditional RLC Filter Techniques

This article presents an extensive examination and modeling of Capacitor Coupled Substations (CCS), noting some of their inherent constraints. The underlying implementation of a CCS is to supply electricity directly from high-voltage (HV) transmission lines to low-voltage (LV) consumers through coupling capacitors and is said to be cost-effective as compared to conventional distribution networks. However, the functionality of such substations is susceptible to various transient phenomena, including ferroresonance and overvoltage occurrences. To address these challenges, the study uses simulations to evaluate the effectiveness of conventional resistor-inductor-capacitor (RLC) filter in mitigating hazardous overvoltage resulting from transients. The proposed methodology entails using standard RLC filter to suppress transients and its associated overvoltage risks. Through a series of MATLAB/Simulink simulations, the research emphasizes the practical effectiveness of this technique. The study examines the impact of transients under varied operational scenarios, including no-load switching conditions, temporary short-circuits, and load on/off events. The primary aim of the article is to assess the viability of using an established technology to manage system instabilities upon the energization of a CCS under no-load circumstances or in case of a short-circuit fault occurring on the primary side of the CCS distribution transformer. The findings underscore the effectiveness of conventional RLC filters in suppressing transients induced by the CCS no-load switching.

Theoretical Investigations of the Local Structure Distortion and EPR Parameter for Ni2＋-doped Perovskite Fluorides

By analyzing the optical spectra and electron paramagnetic resonance parameter D, the local structure distortion of （NiF6）4- clusters in AMF3 （A=K, Rb; M=Zn, Cd, Ca） and K2ZnF4 series are studied using the complete energy matrix based on the double spin-orbit coupling parameter model for configuration ions in a tetragonal ligand field. The results indicate that the contribution of ligand to spin-orbit coupling interaction should be considered for our studied systems. Moreover, the relationships between D and the spin-obit coupling coefficients as well as the average parameter and the divergent parameter are discussed.

An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

Correlation of coordinate transformation parameters

Coordinate transformation parameters between two spatial Cartesian coordinate systems can be solved from the positions of non-colinear corresponding points. Based on the characteristics of translation, rotation and zoom components of the transformation, the complete solution is divided into three steps. Firstly, positional vectors are regulated with respect to the centroid of sets of points in order to separate the translation compo- nents. Secondly, the scale coefficient and rotation matrix are derived from the regulated positions independent- ly and correlations among transformation model parameters are analyzed. It is indicated that this method is applicable to other sets of non-position data to separate the respective attributions for transformation parameters.

3D numerical simulation of boreholes for gas drainage based on the pore–fracture dual media

A gas migration controlling equation was formulated based on the characteristics of the dual pore–fracture media of coal mass and in consideration of the matrix exchange between pores and fractures.A model of permeability dynamic evolution was established by analyzing the variation in effective stress during gas drainage and the action mechanism of the effect of coal matrix desorption on porosity and fracture in the coal body.A coupling model can then be obtained to characterize gas compressibility and coal deformability under the gas–solid coupling of loading coal.In addition,a 3D model of boreholes was established and solved for gas drainage based on the relevant physical parameters of real mines.The comparison and analysis results for the law of gas migration and the evolution of coal body permeability around the boreholes before and after gas extraction between the dual media and the single-seepage field models can provide a theoretical basis for further research on the action mechanism of gas drainage.

A simple approach for the estimation of CO_2 penetration depth into a caprock layer

Caprock is a water-saturated formation with a sufficient entry capillary pressure to prevent the upward migration of a buoyant fluid. When the entry capillary pressure of caprock is smaller than the pressure exerted by the buoyant CO2plume, CO2gradually penetrates into the caprock. The CO2penetration depth into a caprock layer can be used to measure the caprock sealing efficiency and becomes the key issue to the assessment of caprock sealing efficiency. On the other hand, our numerical simulations on a caprock layer have revealed that a square root law for time and pore pressure exists for the CO2penetration into the caprock layer. Based on this finding, this study proposes a simple approach to estimate the CO2penetration depth into a caprock layer. This simple approach is initially developed to consider the speed of CO2invading front. It explicitly expresses the penetration depth with pressuring time, pressure difference and pressure magnitude. This simple approach is then used to fit three sets of experimental data and good fittings are observed regardless of pressures, strengths of porous media, and pore fluids(water,hydrochloric acid, and carbonic acid). Finally, theoretical analyses are conducted to explore those factors affecting CO2penetration depth. The effects of capillary pressure, gas sorption induced swelling, and fluid property are then included in this simple approach. These results show that this simple approach can predict the penetration depth into a caprock layer with sufficient accuracy, even if complicated interactions in penetration process are not explicitly expressed in this simple formula.

A Generic Kinematic Model for Three Main Types of Five-axis Machine Tools

Material removal is one of the most used processes in manufacturing. Five-axis CNC machines are believed to be the best tools in sculptured surface machining. In this study, a generic and unified kinematic model was developed as a viable alternative to the particular solutions that are only applicable to individual machine configurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of a five-axis machine-tool. This versatile model is very useful applied to the design of five-axis machine tools.

Theoretical investigations of the local distortion and electron paramagnetic resonance parameter for CdCl_2:V^(2+) and CsMgX_3:V_^(2+)(X=Cl,Br) systems

This paper systematically investigates the local distortion and electron paramagnetic resonance （EPR） parameter for CdCl2：V^2＋ and CsMgX3：V^2＋ （X=Cl, Br） systems on the basis of the complete energy matrix, in which not only the contributions due to the spin-orbit coupling of the central ions but also that of the ligands are considered. To describe the difference of overlapping between d-orbits and p orbit, two spin-orbit coupling coefficients are introduced. By simulating the crystal field parameter and EPR parameter, the local distortion parameters are studied and the relationships between the EPR parameter and the spin-orbit coupling coefficients as well as divergent parameter are discussed. These results show that the local structures exhibit compression distortion for CdCl2：V^2＋ and elongation distortions for CsMgX3：V^2＋ （X：Cl, Br）, respectively. It notes that the empirical formula R≈RH T （ri - rh）/2 is not suitable for CdCl2：V^2＋ and CsMgX3：V^2＋ （X=Cl, Br） systems. The contributions of ligand to spin-orbit coupling interaction cannot be neglected for strong covalent systems, especially for V^2＋ doped in CsMgBr3：V^2＋.

Underwater Digital Terrain Model with GPS-aided High-resolution Profile-scan Sonar Images

The whole procedures of underwater digital terrain model (DTM) were presented by building with the global positioning system (GPS) aided high-resolution profile-scan sonar images.The algorithm regards the digital image scanned in a cycle as the raw data.First the label rings are detected with the improved Hough transform (HT) method and followed by curve-fitting for accurate location;then the most probable window for each ping is detected with weighted neighborhood gray-level co-occurrence matrix;and finally the DTM is built by integrating the GPS data with sonar data for 3D visualization.The case of an underwater trench for immersed tube road tunnel is illustrated.

Hydraulics Management Model of Response Function Solved by Laplace Transform Boundary Element Method

In solving a response function by the boundary element method, the use of the singular valued method and the Laplace transform in a time domain makes the solving process be simplified and the result be accurate. The restricted condition matrix formed by the response matrix method is much smaller than that by embedding method. In addition, the response function may realize directly the management decision making. So it is efficient for establishing and solving hydraulics management models.

Structural Reanalysis of Dynamic Systems Using Model Updating Method

Model updating methodologies are invariably successful when used on noise-free simulated data, but tend to be unpredictable when presented with real experimental data that are unavoidably corrupted with uncorrelated noise content. In this paper, reanalysis using frequency response functions for correlating and updating dynamic systems is presented. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the modified damping matrix of the system. The modified mass and stiffness matrices are identified from the normal frequency response functions by using the least squares method. A numerical example is employed to illustrate the applicability of the proposed method. The result indicates that the present method is effective.