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Q estimation using multifrequency point average method based on the taylor series expansion with a different order

Applied Geophysics 2021年第4期18卷 557-568,595页

作者： Zhang Jin Wang Yan-Guo Zhang Guo-Shu Lan Hui-Tian Zhang-Hua Hao Ya-Ju College of Geophysics and Measurement-control East China University of TechnologyNanchang 330013China State Key Laboratory of Nuclear Resources and Environment East China University of TechnologyNanchang 330013China College of Nuclear Science and Engineering East China University of TechnologyNanchang330013China Exploration and Development Research Institute of Daqing Oil Company Daqing 163712China.

The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave *** accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic *** this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order taylor series expansion of the amplitude attenuated ***,the multifrequency point average(MFPA)method is introduced to obtain a stable Q *** model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation *** addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex *** the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each *** contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average *** conclusion,the MFPA method has superior stability and practicability for the Q estimation.

关键词： Q estimation taylor series expansion Precision Stability

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A Nonlinear Optimal Control Approach for Bacterial Infections Under Antibiotics Resistance

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Journal of Systems Science & Complexity 2024年第6期37卷 2293-2317页

作者： RIGATOS Gerasimos ABBASZADEH Masoud SIANO Pierluigi AL-NUMAY Mohammed ZOUARI Farouk Unit of Industrial Automation Industrial Systems Institute26504Rion PatrasGreece Dept.of ECS Engineering Rensselaer Polytechnic Institute12065TroyNYUSA Dept.of Management and Innovation Systems University of Salerno84084FiscianoItaly Dept.of Electrical Eng. King Saud UniversityRiyadh 11421Saudi Arabia Laboratoire d'Automatique ENIT Tunisie1002 Tunis

The overuse and misuse of antibiotics has become a major problem for public *** become resistant to antibiotics and because of this the anticipated therapeutic effect is never ***-hospital infections are often aggravated and large amounts of money are spent for treating complications in the patients'*** this paper a nonlinear optimal(H-infinity)control method is developed for the dynamic model of bacterial infections exhibiting resistance to ***,differential flatness properties are proven for the associated state-space ***,the state-space description undergoes approximate linearization with the use of first-order taylor series expansion and through the computation of the associated Jacobian *** linearization process takes place at each sampling instance around a time-varying operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs *** the approximately linearized model of the system a stabilizing H-infinity feedback controller is *** compute the controller's gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control *** global stability properties of the control scheme are proven through Lyapunov *** proposed method achieves stabilization and remedy for the bacterial infection under moderate use of antibiotics.

关键词： Bacterial infection differential flatness properties global stability Jacobian matrices nonlinear H-infinity control resistance to antibiotics Riccati equation taylor series expansion

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Approximate Solutions to the Hamilton-Jacobi Equations for Generating Functions

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Journal of Systems Science & Complexity 2020年第2期33卷 261-288页

作者： HAO Zhiwei FUJIMOTO Kenji ZHANG Qiuhua Department of Astronautical Science and Mechanics Harbin Institute of TechnologyHarbin 150001China Department of Aeronautics and Astronautics Kyoto UniversityC3 Bldg.Kyotodaigaku-katsuraNishikyo-kuKyoto 615-8540Japan

For a nonlinear finite time optimal control problem,a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this *** algorithm allows one to obtain the taylor series expansion of the generating function up to any prescribed order by solving a sequence of first order ordinary differential equations ***,the coefficients of the taylor series expansion of the generating function can be computed exactly under a certain technical *** a generating function is found,it can be used to generate a family of optimal control for different boundary *** the generating function is computed off-line,the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional *** is useful to online optimal trajectory generation *** examples illustrate the effectiveness of the proposed algorithm.

关键词： Generating functions Hamilton-Jacobi equations optimal control taylor series expansion two-point boundary-value problems

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A Nonlinear Optimal Control Approach for Tracked Mobile Robots

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Journal of Systems Science & Complexity 2021年第4期34卷 1279-1300页

作者： RIGATOS Gerasimos Unit of Industrial Automation IndiLstrial Systems InstituteRion Patras 26504Greece

The article proposes a nonlinear optimal(H-infinity)control approach for the model of a tracked robotic *** kinematic model of such a tracked vehicle takes into account slippage effects due to the contact of the tracks with the *** solve the related control problem,the dynamic model of the vehicle undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control *** linearization process relies on first-order taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the *** the approximately linearized description of the tracked vehicle a stabilizing H-infinity feedback controller is *** compute the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control *** stability properties of the control scheme are proven through Lyapunov *** is also demonstrated that the control method retains the advantages of linear optimal control,that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

关键词： Approximate linearization global asymptotic stability H-infinity control Jacobian matrices Lyapunov analysis nonlinear optimal control taylor series expansion tracked robotic vehicle

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Accelerating spectral digital image correlation computation with taylor series image reconstruction

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Acta Mechanica Sinica 2024年第6期40卷 78-86页

作者： Shihao Han Yuming He Yiyu Hu Jian Lei Yongbo Yang Department of Mechanics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment Wuhan430074China Wuhan Sinorock Technology Co. LtdWuhan430074China

In this paper,we introduce an accelerating algorithm based on the taylor series for reconstructing target images in the spectral digital image correlation method(SDIC).The taylor series image reconstruction method is employed instead of the previous direct Fourier transform(DFT)image reconstruction method,which consumes the majority of the computational time for target image *** partial derivatives in the taylor series are computed using the fast Fourier transform(FFT)of the entire image,following the principles of Fourier transform *** examine the impact of different orders of taylor series expansion on accuracy and efficiency,we employ third-and fourth-order taylor series image reconstruction methods and compare them with the DFT image reconstruction method through simulated *** a result of these enhancements,the computational efficiency using the third-and fourth-order taylor series improves by factors of 57 and 46,respectively,compared to the previous *** terms of analysis accuracy,within a strain range of 0–0.1 and without the addition of image noise,the accuracy of the proposed method increases with higher expansion orders,surpassing that of the DFT image reconstruction method when the fourth order is ***,when different levels of Gaussian noise are applied to simulated images individually,the accuracy of the third-or fourth-order taylor series expansion method is superior to that of the DFT reconstruction ***,we present the analyzed experimental results of a silicone rubber plate specimen with bilateral cracks under uniaxial tension.

关键词： Digital image correlation taylor series expansion Image reconstruction Strain measurement

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A collocation interval analysis method for interval structural parameters and stochastic excitation

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Science China(Physics,Mechanics & Astronomy) 2012年第1期55卷 66-77页

作者： QI WuChao QIU ZhiPing Institute of Solid Mechanics Beijing University of Aeronautics and Astronautics Beijing 100191 China

Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.

关键词： uncertainty propagation interval analysis taylor series expansion Chebyshev polynomial Pseudo excitation method

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A nonlinear optimal control approach for 3-DOF four-cable driven parallel robots

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Autonomous Intelligent Systems 2024年第1期4卷 233-258页

作者： G.Rigatos M.Abbaszadeh J.Pomares Unit Industrial Autom. Industrial Systems Inst.26504PatrasGreece Dept.ECS Eng. Rensselaer Polytech.Inst.Troy12065NYUSA Dept.of Systems Eng. Univ.of Alicante03690AlicanteSpain

In this article,a nonlinear optimal control approach is proposed for the dynamic model of 3-DOF four-cable driven parallel robots(CDPR).To solve the associated nonlinear optimal control problem,the dynamic model of the 3-DOF cable-driven parallel robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control *** linearization relies on taylor series expansion and on the associated Jacobian *** the linearized state-space model of the 3-DOF cable-driven parallel robot a stabilizing optimal(H-infinity)feedback controller is *** compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control *** stability properties of the control method are proven through Lyapunov *** proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs and a minimum dispersion of energy.

关键词： 3-DOF four-cable-driven parallel robot Fully-constrained cable-driven robots Nonlinear H-infinity control taylor series expansion Jacobian matrices Riccati equation Global stability

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Power system transient stability simulation under uncertainty based on taylor model arithmetic

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Frontiers of Electrical and Electronic Engineering in China 2009年第2期4卷 220-226页

作者： Shouxiang WANG Zhijie ZHENG Chengshan WANG School of Electrical Engineering and Automation Tianjin UniversityTianjin 300072China

The taylor model arithmetic is introduced to deal with *** uncertainty of model parameters is described by taylor models and each variable in functions is replaced with the taylor model(TM).Thus,time domain simulation under uncertainty is transformed to the integration of TM-based differential *** this paper,the taylor series method is employed to compute differential equations;moreover,power system time domain simulation under uncertainty based on taylor model method is *** method allows a rigorous estimation of the influence of either form of uncertainty and only needs one *** is computationally fast compared with the Monte Carlo method,which is another technique for uncertainty *** proposed method has been tested on the 39-bus New England *** test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.

关键词： interval arithmetic power systems taylor series expansion taylor model time domain simulation transient stability uncertainty

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A Nonlinear Optimal Control Method for Attitude Stabilization of Micro-Satellites

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Guidance, Navigation and Control 2022年第3期2卷 30-67页

作者： G.Rigatos M.Abbaszadeh K.Busawon L.Dala Unit of Industrial Automation Industrial Systems Institute 26504 Rion PatrasGreece Department of ECSE Rensselaer Polytechnic Institute New York 12065 USA Nonlinear Control Group University of Northumbria Newcastle NE18ST UK Department of Mechanical Engineering University of Northumbria Newcastle NE18ST UK

Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites'state-space *** this paper,a novel nonlinear optimal(H-infinity)control approach is developed for this control *** dynamic model of the satellite's attitude dynamics undergoesfirst approximate linearization around a temporary operating point which is updated at each iteration of the control *** linearization process relies on first-order taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite's attitude *** the approximately linearized description of the satellite's attitude a stabilizing H-infinity feedback controller is *** compute the controller's feedback gains,an algebraic Riccati equation is solved at each time-step of the control *** stability properties of the control scheme are proven through Lyapunov *** is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

关键词： Micro-satellites attitude control nonlinear optimal control H-infinity control differentialfiatness properties taylor series expansion Jacobian matrices Lyapunov analysis global asymptotic stability

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On Simplified Models for Dynamics of Pointlike Objects

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Journal of Applied Mathematics and Physics 2021年第8期9卷 1853-1869页

作者： Marijan Ribarič Luka Š uš terš ič Jož ef Stefan Institute Ljubljana Slovenia

Motivation: We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. Objective: Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable t ∈ (tm, +∞) and tm > 0 is large, say ! Method: We apply taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. Results: We make simplified models for the long-term dynamics of pointlike objects by taylor polynomials in time derivatives of the external force. Application: We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where t ≥ tm ≫ 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena.

关键词： Point Mass Long-Term Dynamics Harmonic Oscillator Drag Force Lorentz-Abraham-Dirac Equation taylor series expansion

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