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ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

作者： Bai, Lu Xue, Dingyu Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Shenyang Univ Sch Informat Engn Shenyang 110044 Liaoning Peoples R China

ISBN: (纸本)9780791857199

A numerical algorithm is presented to solve the initial value problem of linear and nonlinear Caputo fractional-order differential equations. Firstly, nonzero initial value problem should be transformed into zero initial value problem. Error analysis has been done to polynomial algorithm, the reason has been found why the calculation error of the algorithm is large. A new algorithm called exponential function algorithm is proposed based on the analysis. The obtained fractional-order differential equation is transformed into difference equation. If the differential equation is linear, the obtained difference equation is explicit, the numerical solution can be solved directly;otherwise, the obtained difference equation is implicit, the predictor of the numerical solution can be obtained with extrapolation algorithm, substitute the predictor into the equation, the corrector can be solved. Error analysis has been done to the new algorithm, the algorithm is of first order.

关键词： differential equation fractional-order initial value problem numerical algorithm

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A numerical algorithm for solving power-exponent type nonlinear inequalities with applications in calculating stabilizing parameters for LTI systems 16th

A numerical algorithm for solving power-exponent type nonlin...

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16th IFAC Symposium on Large Scale Complex Systems - Theory and Applications (LSS)

作者： Chen, Zhihua Guo, Yong Zhang, Kai Xie, Yongchun Beijing Inst Control Engn Beijing 100190 Peoples R China Northwestern Polytech Univ Sch Automat Xian 710072 Peoples R China Sichuan Univ Sch Aeronaut & Astronaut Chengdu 610225 Peoples R China

The paper proposes a numerical algorithm for finding a solution set of a class of power-exponent type nonlinear inequalities. The proposed numerical algorithm applies specifically to the case when the power-exponent is positive irrational number, which can't be effectively solved by using the existing methods. Firstly, by introducing a novel concept of margin variable and using the monotonicity of power-exponent function, this paper converts the problem of solving the nonlinear inequalities into a constrained nonlinear optimization (CNO) problem. Then the obtained CNO problem is solved by using the MATLAB function fmincon. Finally, a numerical algorithm to solve this class of inequalities is obtained. The proposed algorithm can find a solution set of the considered inequalities, not just one or few solutions. Further, the derived algorithm can be easily used to calculate the stabilizing parameter ranges for LTI systems based on the Routh-Hurwitz criterion. Moreover, an example of calculating the stabilizing parameters of a LTI system and an example of solving power-exponent type nonlinear inequalities are provided to show the effectiveness of the proposed algorithm.

关键词： Power-Exponent Function Nonlinear Inequalities Solution Set numerical algorithm LTI Systems Stabilizing Parameters State Feedback Control Constrained Nonlinear Optimization Margin Variable

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A numerical algorithm TO INITIAL VALUE PROBLEM OF LINEAR CAPUTO FRACTIONAL-ORDER DIFFERENTIAL EQUATION

A NUMERICAL ALGORITHM TO INITIAL VALUE PROBLEM OF LINEAR CAP...

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ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

作者： Bai, Lu Xue, Dingyu Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Shenyang Univ Sch Informat Engn Shenyang 110044 Liaoning Peoples R China

ISBN: (纸本)9780791857199

A numerical algorithm is presented to solve the initial value problem of linear Caputo fractional-order differential equations. Error analysis has been done to Taylor series algorithm, the reason has been found why the error of the algorithm is large, the condition of using Taylor series algorithm is presented. A new algorithm called exponential function algorithm is proposed based on the analysis. Nonzero initial value problem could be transformed into zero initial value problem. The obtained fractional order differential equation is transformed into difference equation, the numerical solution can be found with closed form solution formula. The error of the numerical solution can be modified with prediction-correction algorithm.

关键词： differential equation fractional-order initial value problem numerical algorithm

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A New numerical algorithm to Estimate the Average Travel Time of Workpiece in Packaging Equipments or Reliability Testers 24

A New Numerical Algorithm to Estimate the Average Travel Tim...

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24th International Conference on Electronic Packaging Technology (ICEPT)

作者： Sun, Niuyi Yang, Dan Mei, Na Sanechips Technol Co Ltd Reliabil Engn Dept State Key Lab Mobile Network & Mobile Multimedia Shenzhen Peoples R China

ISBN: (纸本)9798350338812;9798350338829

In order to reduce costs and improve the efficiency of production process in modern advanced manufacturing, one of premises in technology is to do some accurate travel-time estimations[1,2] of wrokpieces in machine systems. In this paper, we proposes a numerical algorithm for evaluating the average travel time of workpiece in the packaging equipments or reliability testers. Firstly, the above travel time problem is abstracted into a symbolic idea and expressed by a mathematical model for set-to-set mapping. Secondly, a new numerical algorithm combining both Monte Carlo method[3] and several computational geometry algorithms[4] is designed to solve the relevant travel-time model and mathematical equations as mentioned above. Finally, a numerical analysis is also provided to compare the differences between the new algorithm and the theoretical solution of a numerical example.

关键词： Travel Time numerical algorithm Monte Carlo Method Computational Geometry

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A Joint Optimization Method of Genetic algorithm and numerical algorithm Based on MATLAB

A Joint Optimization Method of Genetic Algorithm and Numeric...

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5th IEEE Conference on Industrial Electronics and Applications

作者： Zhang, Jingjun Zhong, Jitao Gao, Ruizhen He, Lili Hebei Univ Engn Dept Sci Res Coll Civil Engn Coll Mech & Elect Engn Handan Peoples R China

ISBN: (纸本)9781424450466

The mathematic model of a two-bar truss is built in MATLAB and the analysis is carried out by the genetic algorithm toolbox. In order to compare with each other, the parametric model of the planar truss is also established by the ANSYS Parametric Design Language and solutions are obtained using the first-order method native to ANSYS. The comparison of the results shows that genetic algorithms do not always display better properties than other algorithms for some problems. Finally, a joint optimization method which combines MATLAB genetic algorithm toolbox and the numerical algorithm based on the quasi-Newton method is proposed. Then the method is identified through the numerical example of the two-bar truss. The simulation results indicate that the joint optimization method can always converge to the global optimal solution.

关键词： genetic algorithm numerical algorithm optimization MATLAB ANSYS

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Adaptive step size numerical algorithm for fractional order control systems 29

Adaptive step size numerical algorithm for fractional order ...

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第29届中国控制与决策会议

作者： Yongkang He Zhidong Qi Yinyin Tang Di Hu School of automation Nanjing University of Science and Technology

ISBN: (纸本)9781509046584

For fractional order control systems,fast and accurate numerical algorithm is the key step in real-time control and *** the short memory method(SMM) and the constant weight memory method(CWMM)accelerate the computation speed through the choice and approximation of the historical information of the fractional differential operator,the computation precision decreases with the increase of *** CWMM is affected by input function and the error range is *** the limitation of fixed step size discretization(FSSD) of fractional differential operator,a variable step size discretization(VSSD) scheme is *** to the local error obtained by the step-doubling technique,the iterative step size is adjusted *** algorithm not only can achieve good accuracy,uniform error,but also fast calculation speed,which provides a feasible way for the numerical calculation of state space description of fractional order control ***,the reliability of the algorithm is verified by an example.

关键词： Fractional calculus numerical algorithm variable step size discretization adaptive step size

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Model and numerical algorithm for Analysis and Prediction of Fluid Distribution in a Porous Medium 4

Model and Numerical Algorithm for Analysis and Prediction of...

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4th International Conference on Technological Advancements in Computational Sciences, ICTACS 2024

作者： Ravshanov, Normakhmat Kholmatova, Iroda Shukurova, Markhabo Nematov, Asliddin Digital Technologies and Artificial Intelligence Research Institute Tashkent Uzbekistan Tashkent University of Information Technologies Karshi Branch Karshi Uzbekistan Jizzakh Polytechnic Institute Jizzakh Uzbekistan

ISBN: (纸本)9798350387490

We consider a problem related to the processes of fluid filtration in a heterogeneous porous medium, where the main hydrodynamic parameters of the object depend on the redistribution of pressure in the formation in order to increase the productivity of the formation, due to development of an optimal layout of vertical drainage wells and their capacities. To correctly select a strategy for solving problems, research work on mathematical modeling carried out over the past 5-10 years was analyzed. The work proposes a computer model for conducting computational experiments on a computer system, with the aim of forecasting and making management decisions for the design and development of an oil field,the results of which are presented in the form of graphic objects and tables. © 2024 IEEE.

关键词： Computational experiment Fluid filtration Hydrogeological parameters Mathematical model numerical algorithm Porous media

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numerical algorithm for Dynamic Impedance of Bridge Pile-Group Foundation and Its Validation

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algorithmS 2021年第8期14卷 247-247页

作者： Wang, Chenyu Qiao, Hong Wang, Yi Du, Xianting Beijing Univ Civil Engn & Architecture Sch Civil & Transportat Engn Beijing 100044 Peoples R China Tsinghua Univ Dept Civil Engn Beijing 100084 Peoples R China Beijing Jiaotong Univ Sch Civil Engn Beijing 100044 Peoples R China

The characteristics of bridge pile-group foundation have a significant influence on the dynamic performance of the superstructure. Most of the existing analysis methods for the pile-group foundation impedance take the trait of strong specialty, which cannot be generalized in practical projects. Therefore, a project-oriented numerical solution algorithm is proposed to compute the dynamic impedance of bridge pile-group foundation. Based on the theory of viscous-spring artificial boundary, the derivation and solution of the impedance function are transferred to numerical modeling and harmonic analysis, which can be carried out through the finite element method. By taking a typical pile-group foundation as a case study, the results based on the algorithm are compared with those from existing literature. Moreover, an impact experiment of a real pile-group foundation was implemented, the results of which are also compared with those resulting from the proposed numerical algorithm. Both comparisons show that the proposed numerical algorithm satisfies engineering precision, thus showing good effectiveness in application.

关键词： numerical algorithm pile-group foundation bridge dynamic impedance viscous-spring artificial boundary harmonic analysis

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A numerical algorithm for the Resolution of Boolean Equations

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IEEE Transactions on Computers 1974年第9期C-23卷 983-986页

作者： Del Picchia, Walter The Departamento de Engenharia de Eletricidade Escola Politdcnica da Universidade de Sao Paulo Sao Paulo Brazil

This correspondence presents the remainder-quotient (RQ)-algorithm for the resolution of Boolean equations. If w = w ( xkl, xj2, … XkN) = 1 is the Boolean equation equivalent to the system whose solution is desired, we want to determine the Boolean functions xk, = Xkp ( xhj+1,… -xkN) with p = 1,2,… j, which verify the equivalent equation. We start with the function w given by its minterm numbers and performing usual divisions we determine the solutions in the domain of the numerical transform (NT), introduced in a previous paper. An alternative way is also presented, which is advantageous when the number of minterms in the equivalent equation is large. Examples which show the great systematization of the methods are given. Copyright © 1974 by The Institute of Electrical and Electronics Engineers, Inc.

关键词： Boolean Equation Computation Consistence numerical algorithm Transformation

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numerical algorithm for Distribution-Map Derivations of Switching Converters

Numerical Algorithm for Distribution-Map Derivations of Swit...

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Annual Conference of the IEEE Industrial Electronics Society

作者： Yuta Yamada Tomoharu Nagashima Yoshifumi Ibuki Yoshiki Fukumoto Hiroo Sekiya Graduate School of Advanced Integration Science Chiba University DAIHEN Corp.

ISBN: (纸本)9781479940318

This paper proposes a numerical algorithm for drawing distribution maps of switching power-converter characteristics on parameter spaces. The concept of the proposed algorithm is that parameters satisfying the assigned conditions are derived and followed with low computation cost. Zero-Voltage-Switching (ZVS) region, output power distribution map, and contour map of power-conversion efficiency of the phase-controlled class-D inverter are drawn as application examples of the proposed algorithm. It is possible from these maps to design the phase-controlled class-D inverter achieving the ZVS at entire control regions. The validity and effectiveness of the proposed algorithm were confirmed by carrying out circuit experiments.

关键词： numerical algorithm Distribution map Switching power converter Converter design ZVS region Phase-controlled class-D inverter

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