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A numerical algorithm FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第12期19卷 8602-8616页

作者： Zhao, Bowen Xu, Honglei Teo, Kok Lay Curtin Univ Sch Elect Engn Comp & Math Sci Perth 6102 Australia Sunway Univ Sch Math Sci Kuala Lumpur 47500 Malaysia

In this paper, we consider a general class of discrete-time optimal control problems subject to all-time-step constraints on the state and control variables. The derivations of the gradient formulas for the cost and constraint functions for this constrained discrete-time optimal control problem are rather involved. We present a simple approach to the derivations of these gradient formulas based on reversed automatic differentiation. On this basis, a numerical algorithm is developed to solve this all-time-step constrained discrete-time optimal control problem. We then consider a class of continuous-time optimal control problems subject to continuous state inequality constraints. This constrained continuous-time optimal control problem is discretized into a discrete time optimal control problem with all-time-step constraints using the Euler discretization method. Then, the algorithm developed for constrained discrete time optimal control problem is applied to solve this discretized optimal control problem. numerical examples are presented to verify the applicability of the methods.

关键词： Discrete-time optimal control problem continuous-time optimal con-trol problem automatic differentiation gradient formulas numerical algorithm all-time-step in-equality constraints continuous state inequality constraints

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Dynamic Analysis and Efficient numerical algorithm for Rocking Response of Freestanding Packages Under Transportation Excitations

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APPLIED SCIENCES-BASEL 2025年第9期15卷 5015-5015页

作者： Qi, Zhenmin Zhu, Dapeng Lanzhou Jiaotong Univ Sch Elect & Informat Engn Lanzhou 730070 Peoples R China Lanzhou Jiaotong Univ Sch Taff & Transportat Lanzhou 730070 Peoples R China

The transportation of freestanding packages, such as steel coils and prefabricated building components, poses significant safety challenges due to their susceptibility to dynamic responses like rocking, sliding, and overturning under vehicle acceleration. This study focuses on the critical rocking motion, which can lead to catastrophic accidents if the rocking angle exceeds a critical threshold. The package is modeled as a rigid block on a moving base, and its motion states, including static equilibrium, bouncing, rocking, and detachment, are analytically determined, with specific conditions identified for each state. A novel numerical algorithm, combining a time transformation method with the Runge-Kutta method, is proposed to efficiently determine collision time instants and analyze the piecewise-smooth rocking response. This approach partitions the solution into smooth intervals between impacts, significantly improving computational efficiency while maintaining accuracy. Experimental validation under sinusoidal and numerical analysis with random excitations confirms the algorithm's effectiveness in predicting rocking behavior. The results highlight the importance of the slenderness ratio and restitution coefficient in governing motion states and demonstrate the algorithm's superiority over traditional methods in terms of precision and efficiency. This work provides a robust framework for assessing transportation safety and optimizing package design, with implications for reducing overturning risks in practical scenarios.

关键词： freestanding packages rocking motion motion state numerical algorithm transportation safety overturning risk

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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 to solve a coupled system of fractional order using a novel reproducing kernel method

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ALEXANDRIA ENGINEERING JOURNAL 2021年第5期60卷 4583-4591页

作者： Saadeh, Rania Zarqa Univ Fac Sci Dept Math Zarqa 13110 Jordan

In this paper, a coupled system of fractional differential equations along with integral boundary conditions is discussed by means of the iterative reproducing kernel algorithm. Towards this end, a recently advanced analytical approach is proposed to obtain approximate solutions of nonclassical-types boundary value problems of fractional derivatives in Caputo sense. This approach optimizes approximate solutions based on the Gram-Schmidt process on Sobolev spaces that execute to generate Fourier expansion within a fast convergence rate, whereby the constructed kernel function fulfills homogeneous integral boundary conditions. Moreover, the solution is presented in the form of a fractional series over the entire Hilbert spaces without unwarranted assumptions on the considered models. The validity of the present algorithm is illustrated by expounding and testing two numerical examples. The achieved results indicate that the proposed algorithm is systematic, feasibility, stability, and convenient for dealing with other fractional systems emerging in the physical, technology and engineering. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.

关键词： Caputo fractional derivative Coupled system Non-classical boundary condition Reproducing kernel function numerical algorithm

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Calculation boundary vulnerability of numerical algorithm in milling stability prediction

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2022年第11-12期119卷 8271-8286页

作者： Dai, Yuebang Li, Hongkun Liu, Bo Yang, Chao Dalian Univ Technol Sch Mech Engn Dalian 116024 Peoples R China

Though considerable efforts have been made to improve the precision of numerical algorithms for obtaining more accurate chatter stability prediction in milling process, a calculation boundary vulnerability, existing generally in numerical predictive methods, is usually ignored, which can significantly reduce accuracy of chatter stability prediction in certain calculated step lengths. Starting from the numerical solution of delay differential equation, this paper first gives a detailed mathematical derivation to demonstrate the beingness of the numerical calculation errors at the crucial step for two equal interval calculation methods of cutting force coefficients, and then discusses the impact of the errors on the convergence effect and prediction accuracy. Afterwards, the methods seeking and repairing the discrete number of time period with vulnerability are proposed, which are verified by the classic milling models. The presented technique could prevent this undesirable boundary vulnerability happening in numerical prediction of milling stability, and help the path planers obtain more accurate parameters which can achieve chatter free in the manufacturing process.

关键词： Chatter stability prediction numerical algorithm Calculation boundary vulnerability

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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 numerical algorithm for damage progression of reinforced concrete bridge piers during air temperature and solar radiation cycles

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ENGINEERING STRUCTURES 2024年 319卷

作者： Zhang, Kai Lei, Jinshan Wang, Zhiyong Yuan, Qiang Cent South Univ Sch Civil Engn Changsha 410075 Peoples R China Natl Engn Res Ctr High Speed Railway Construct Tec Changsha 410075 Peoples R China Anhui Engineer Mat Technol Co Ltd CTCE Grp Hefei 230041 Peoples R China

Reinforced concrete (RC) solid piers are unavoidably affected by air temperature changes and solar radiation during service life. Nevertheless, the deterioration of pier concrete with increased exposure age remains unclear. A novel thermal-mechanical numerical algorithm (finite element model) for characterizing the deterioration characteristics of RC structures under cyclic environmental loads has been suggested. The deterioration of RC pier concrete after 100 years of air temperature and solar radiation cycles is simulated. The numerical results demonstrate that tensile damage of pier concrete during air temperature and solar radiation cycles increases continuously with exposure age. After one year of exposure, the tensile damage value of pier surface concrete increased to 0.201 and further increased to 0.286 and 0.357 as the exposure age grew to 10 and 100 years. Pier concrete tensile damage can be mitigated by using surface short-wave absorption-reducing methods, controlling the thermal properties of concrete, and raising the concrete peak tensile strain. The proposed finite element framework and numerical solutions enable a viable simulation-based method for the analysis of bridge structural long-term deterioration behavior and design of the bridge engineering.

关键词： Reinforced concrete (RC) piers Elastoplastic behavior Environment loading Damage evolution 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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Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton's principle: The numerical algorithm

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2023年第1期180卷

作者： Fan, Chengkai Steinmann, Paul Wang, Jiong South China Univ Technol Sch Civil Engn & Transportat Guangzhou 510640 Guangdong Peoples R China South China Univ Technol State Key Lab Subtrop Bldg Sci Guangzhou 510640 Guangdong Peoples R China Univ Erlangen Nurnberg Inst Appl Mech Egerlandstr 5 D-91058 Erlangen Germany Univ Glasgow Glasgow Computat Engn Ctr Glasgow Scotland

This paper is the second part of a variational modeling work on the dynamic magneto mechanical response of magnetic shape memory alloys (MSMA). In the first part of this series work, the governing equations system for modeling the dynamic response of MSMA samples has been derived based on Hamilton's principle, which contains the Maxwell's equations, the magneto-mechanic equations, the evolution equations of internal variables and the twin interface motion criteria. In this paper, we aim to conduct comprehensive numerical simulations on the dynamic magneto-mechanical response of MSMA samples. To solve the governing system, the space-time finite element method is applied and a double-loop iterative numerical algorithm is proposed. By using this algorithm, the independent variables in the governing system and the motion of twin interfaces in the MSMA sample can be determined separately and iteratively. Besides that, a specific discretization of the sample is adopted to simplify the calculation of variant state distribution in the sample. To show the efficiency of the numerical algorithm, the magneto-mechanical response of a MSMA sample in stress-assisted dynamic field loading tests and field-assisted dynamic mechanical loading tests are studied. Based on the numerical results, some global response curves of the MSMA sample are plotted, which show good consistency with the experimental results. Furthermore, the current configuration of the sample and the distributions of some important physical fields in the sample can be simulated. The current work will be helpful for the design of novel actuators or energy harvesters with MSMA.

关键词： Magnetic shape memory alloy Dynamic response numerical algorithm Finite element simulation Mechanism analysis

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Parameter calibration and numerical algorithm realization of physically visco-hyperelastic constitutive model based on compression experiment of EPDM

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INTERNATIONAL JOURNAL OF IMPACT ENGINEERING 2023年第1期181卷

作者： Xu, Yude Hu, Shuchuan Hu, Meng Lu, Hongyao Liu, Silei Zhang, Wanqing Xue, Zhiqiang Li, Shaozheng Xu, Guoyao Wu, Xuanqing Ren, Zeqi Zhang, Xi Shi, Zixuan Wang, Zhang Tongji Univ Minist Educ Key Lab Rd & Traff Engn Shanghai 201804 Peoples R China Shanghai Key Lab Rail Infrastruct Durabil & Syst S Shanghai 201804 Peoples R China Tongji Univ Coll Transportat Engn Shanghai 201804 Peoples R China Shanghai Univ Engn Sci Sch Urban Rail Transportat Shanghai 201620 Peoples R China Shanghai Shentong Metro Grp Co Ltd Shanghai 201103 Peoples R China Shanghai Marine Diesel Engine Res Inst Shanghai 201108 Peoples R China Shanghai Tunnel Engn & Rail Transit Design & Res I Shanghai 200235 Peoples R China Liaoning Prov Traff Planning & Design Inst Co Ltd Shenyang 110166 Peoples R China

Multi-constitutive models integrated with microstructure parameters are suitable to capture different rubberlike material mechanical characteristics such as large deformation, hysteresis. However, the typical models are less often adopted to analyze realistic engineering problems due to difficult derivation of numerical algorithm which can be embedded into FEM models. Therefore, we take numerical algorithm derivation of physically visco-hyperelastic constitutive model proposed by Yuhai Xiang as an application example to analyze mechanic performance of EPDM (Ethylene Propylene Diene Monomer), which is widely utilized as cushion members of rail structure. After numerical algorithm is derived, static and dynamic compression tests are designed to calibrate mechanical parameters of EPDM. Finally, FEM models integrated with above numerical algorithm and calibration parameters are established to simulate mechanical response under different boundary conditions. In comparison of results between experiments and FEM simulations, accuracy and precision of numerical iteration formula and practicality can meet demands of engineering design and application when deformation and distortion of the FEM model mesh are not severe. We hope our work can supply some inspiration and be expanded to characterize, analyze, simulate and even predict performance of other similar rubberlike materials by applying suitable constitutive models in future.

关键词： Visco-hyperelasticity numerical algorithm nonlinear FEM Parameter calibration EPDM Compression test

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