In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presente...In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented.The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement.Several numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential directions.The comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in time.Moreover,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct implementation.All the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order.展开更多
This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve...This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.展开更多
We propose a suite of strategies for the parallel solution of fully implicit monolithic fluid-structure interaction(FSI).The solver is based on a modeling approach that uses the velocity and pressure as the primitive ...We propose a suite of strategies for the parallel solution of fully implicit monolithic fluid-structure interaction(FSI).The solver is based on a modeling approach that uses the velocity and pressure as the primitive variables,which offers a bridge between computational fluid dynamics(CFD)and computational structural dynamics.The spatiotemporal discretization leverages the variational multiscale formulation and the generalized-αmethod as a means of providing a robust discrete scheme.In particular,the time integration scheme does not suffer from the overshoot phenomenon and optimally dissipates high-frequency spurious modes in both subproblems of FSI.Based on the chosen fully implicit scheme,we systematically develop a combined suite of nonlinear and linear solver strategies.Invoking a block factorization of the Jacobian matrix,the Newton-Raphson procedure is reduced to solving two smaller linear systems in the multi-corrector stage.The first is of the elliptic type,indicating that the algebraic multigrid method serves as a well-suited option.The second exhibits a two-by-two block structure that is analogous to the system arising in CFD.Inspired by prior studies,the additive Schwarz domain decomposition method and the block-factorization-based preconditioners are invoked to address the linear problem.Since the number of unknowns matches in both subdomains,it is straightforward to balance loads when parallelizing the algorithm for distributed-memory architectures.We use two representative FSI benchmarks to demonstrate the robustness,efficiency,and scalability of the overall FSI solver framework.In particular,it is found that the developed FSI solver is comparable to the CFD solver in several aspects,including fixed-size and isogranular scalability as well as robustness.展开更多
We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the st...We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential.Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration,while the temporal dynamics are simulated using the fourth-order Runge-Kutta algorithm.The analysis reveals stable rhombus-shaped VS shapes with topological charges m=1 and 2 of the atomic component.The stability domains and spatial structure of these VSs are governed by three key parameters:the parametric-coupling strength(χ),atomicmolecular interaction strength(g_(12)),and the optical-lattice potential depth(V_(0)).By varyingχand g_(12),we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes,highlighting the nontrivial nonlinear dynamics of the system.This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.展开更多
This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute...This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute Error) polynomials. Additionally, metrics such as IAE (Integral Absolute Error), ISE (Integral of Square Error), ITSE (Integral of Time Squared Error), a MaxMin metric as well as LQR (Linear Quadratic Regulator) were evaluated. PSO (Particle Swarm Optimization) was employed for metric optimization. Time domain response to a step disturbance input was evaluated. The design which optimized the ISE metric proved to be the best performing, followed by IAE and MaxMin (with equivalent results) and then LQR.展开更多
This paper presents an innovative and effective control strategy tailored for a deregulated,diversified energy system involving multiple interconnected area.Each area integrates a unique mix of power generation techno...This paper presents an innovative and effective control strategy tailored for a deregulated,diversified energy system involving multiple interconnected area.Each area integrates a unique mix of power generation technologies:Area 1 combines thermal,hydro,and distributed generation;Area 2 utilizes a blend of thermal units,distributed solar technologies(DST),and hydro power;andThird control area hosts geothermal power station alongside thermal power generation unit and hydropower units.The suggested control system employs a multi-layered approach,featuring a blended methodology utilizing the Tilted Integral Derivative controller(TID)and the Fractional-Order Integral method to enhance performance and stability.The parameters of this hybrid TID-FOI controller are finely tuned using an advanced optimization method known as the Walrus Optimization Algorithm(WaOA).Performance analysis reveals that the combined TID-FOI controller significantly outperforms the TID and PID controllers when comparing their dynamic response across various system configurations.The study also incorporates investigation of redox flow batteries within the broader scope of energy storage applications to assess their impact on system performance.In addition,the research explores the controller’s effectiveness under different power exchange scenarios in a deregulated market,accounting for restrictions on generation ramp rates and governor hysteresis effects in dynamic control.To ensure the reliability and resilience of the presented methodology,the system transitions and develops across a broad range of varying parameters and stochastic load fluctuation.To wrap up,the study offers a pioneering control approach-a hybrid TID-FOI controller optimized via the Walrus Optimization Algorithm(WaOA)-designed for enhanced stability and performance in a complex,three-region hybrid energy system functioning within a deregulated framework.展开更多
In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of...To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.展开更多
The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficu...The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.展开更多
Time delay and integration （TDI） charge coupled device （CCD） noise sets a fundamental limit on image sensor performance, especially under low illumination in remote sensing applications. After introducing the comp...Time delay and integration （TDI） charge coupled device （CCD） noise sets a fundamental limit on image sensor performance, especially under low illumination in remote sensing applications. After introducing the complete sources of CCD noise, we study the effects of TDI operation mode on noise, and the relationship between different types of noise and number of the TDI stage. Then we propose a new technique to identify and measure sources of TDI CCD noise employing mathematical statistics theory, where theoretical analysis shows that noise estimated formulation converges well. Finally, we establish a testing platform to carry out experiments, and a standard TDI CCD is calibrated by using the proposed method. The experimental results show that the noise analysis and measurement methods presented in this paper are useful for modeling TDI CCDs.展开更多
This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditiona...This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.展开更多
There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in dire...There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.展开更多
The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integ...The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.展开更多
This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order...This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.展开更多
Finite element（FE） is a powerful tool and has been applied by investigators to real-time hybrid simulations（RTHSs）. This study focuses on the computational efficiency, including the computational time and accuracy...Finite element（FE） is a powerful tool and has been applied by investigators to real-time hybrid simulations（RTHSs）. This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time（TET） decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method（CDM）, the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ（λ = 4） method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.展开更多
In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thi...In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thing is to decompose a dynamic system into two sub-systems,a small-scale low-frequency system and a high-frequency system.The former can be analytically and efficiently solved with the mode superposition method,and the latter is dealt with through a time integration method such as the Newmark method.The summation of the responses of these two sub-systems is the responses of the original dynamic system.It is concluded that,with little sacrifice of efficiency,the combination method based on the strategy is more accurate than the combined time integration method,but it has the same accuracy order as that of the combined method.Numerical experiments validate the effectiveness of the proposed strategy.展开更多
Based on the weighted residual method,a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed,which is superior to the second-order accurate algorithms in trac...Based on the weighted residual method,a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed,which is superior to the second-order accurate algorithms in tracking long-term dynamics.For improving such a higher-order accurate algorithm,this paper proposes a two sub-step higher-order algorithm with unconditional stability and controllable dissipation.In the proposed algorithm,a time step interval[t_(k),t_(k)+h]where h stands for the size of a time step is divided into two sub-steps[t_(k),t_(k)+γh]and[t_(k)+γh,t_(k)+h].A non-dissipative fourth-order algorithm is used in the rst sub-step to ensure low-frequency accuracy and a dissipative third-order algorithm is employed in the second sub-step to lter out the contribution of high-frequency modes.Besides,two approaches are used to design the algorithm parameterγ.The rst approach determinesγby maximizing low-frequency accuracy and the other determinesγfor quickly damping out highfrequency modes.The present algorithm usesρ_(∞)to exactly control the degree of numerical dissipation,and it is third-order accurate when 0≤ρ_(∞)<1 and fourth-order accurate whenρ_(∞)=1.Furthermore,the proposed algorithm is self-starting and easy to implement.Some illustrative linear and nonlinear examples are solved to check the performances of the proposed two sub-step higher-order algorithm.展开更多
For the constrained nonlinear optimal control problem, by taking the first term of Taylor series, the dynamic equation is linearized. Thus by, introducing into the dual variable (Lagrange multiplier vector), the dynam...For the constrained nonlinear optimal control problem, by taking the first term of Taylor series, the dynamic equation is linearized. Thus by, introducing into the dual variable (Lagrange multiplier vector), the dynamic equation can be transformed into Hamilton system from Lagrange system on the basis of the original variable. Under the whole state, the problem discussed can be described from a new view, and the equation can be precisely solved by, the time precise integration method established in linear dynamic system. A numerical example shows the effectiveness of the method.展开更多
We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatia...We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.展开更多
We introduce a new transmit/receive dipole pair array to obtain a compact quasi\|monostatic antenna structure for ground penetrating radar systems.And we analyze this transmit/receive dipole pair array in time domain....We introduce a new transmit/receive dipole pair array to obtain a compact quasi\|monostatic antenna structure for ground penetrating radar systems.And we analyze this transmit/receive dipole pair array in time domain.The numerical results show that if the distance between the transmit antenna and receive antenna is appropriate the array configuration is adoptable.展开更多
文摘In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented.The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement.Several numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential directions.The comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in time.Moreover,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct implementation.All the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order.
基金the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).
文摘This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
基金This work was supported by the National Natural Science Foundation of China(Grant No.12172160)Shenzhen Science and Technology Program(Grant No.JCYJ20220818100600002)+1 种基金South-ern University of Science and Technology(Grant No.Y01326127)the Department of Science and Technology of Guangdong Province(Grant Nos.2020B1212030001 and 2021QN020642).
文摘We propose a suite of strategies for the parallel solution of fully implicit monolithic fluid-structure interaction(FSI).The solver is based on a modeling approach that uses the velocity and pressure as the primitive variables,which offers a bridge between computational fluid dynamics(CFD)and computational structural dynamics.The spatiotemporal discretization leverages the variational multiscale formulation and the generalized-αmethod as a means of providing a robust discrete scheme.In particular,the time integration scheme does not suffer from the overshoot phenomenon and optimally dissipates high-frequency spurious modes in both subproblems of FSI.Based on the chosen fully implicit scheme,we systematically develop a combined suite of nonlinear and linear solver strategies.Invoking a block factorization of the Jacobian matrix,the Newton-Raphson procedure is reduced to solving two smaller linear systems in the multi-corrector stage.The first is of the elliptic type,indicating that the algebraic multigrid method serves as a well-suited option.The second exhibits a two-by-two block structure that is analogous to the system arising in CFD.Inspired by prior studies,the additive Schwarz domain decomposition method and the block-factorization-based preconditioners are invoked to address the linear problem.Since the number of unknowns matches in both subdomains,it is straightforward to balance loads when parallelizing the algorithm for distributed-memory architectures.We use two representative FSI benchmarks to demonstrate the robustness,efficiency,and scalability of the overall FSI solver framework.In particular,it is found that the developed FSI solver is comparable to the CFD solver in several aspects,including fixed-size and isogranular scalability as well as robustness.
基金supported by the National Natural Science Foundation of China(Grant No.62275075)the Natural Science Foundation of Hubei Soliton Research Association(Grant No.2025HBSRA09)+1 种基金joint supported by Hubei Provincial Natural Science Foundation and Xianning of China(Grant Nos.2025AFD401 and 2025AFD405)Israel Science Foundation(Grant No.1695/22).
文摘We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential.Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration,while the temporal dynamics are simulated using the fourth-order Runge-Kutta algorithm.The analysis reveals stable rhombus-shaped VS shapes with topological charges m=1 and 2 of the atomic component.The stability domains and spatial structure of these VSs are governed by three key parameters:the parametric-coupling strength(χ),atomicmolecular interaction strength(g_(12)),and the optical-lattice potential depth(V_(0)).By varyingχand g_(12),we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes,highlighting the nontrivial nonlinear dynamics of the system.This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.
文摘This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute Error) polynomials. Additionally, metrics such as IAE (Integral Absolute Error), ISE (Integral of Square Error), ITSE (Integral of Time Squared Error), a MaxMin metric as well as LQR (Linear Quadratic Regulator) were evaluated. PSO (Particle Swarm Optimization) was employed for metric optimization. Time domain response to a step disturbance input was evaluated. The design which optimized the ISE metric proved to be the best performing, followed by IAE and MaxMin (with equivalent results) and then LQR.
文摘This paper presents an innovative and effective control strategy tailored for a deregulated,diversified energy system involving multiple interconnected area.Each area integrates a unique mix of power generation technologies:Area 1 combines thermal,hydro,and distributed generation;Area 2 utilizes a blend of thermal units,distributed solar technologies(DST),and hydro power;andThird control area hosts geothermal power station alongside thermal power generation unit and hydropower units.The suggested control system employs a multi-layered approach,featuring a blended methodology utilizing the Tilted Integral Derivative controller(TID)and the Fractional-Order Integral method to enhance performance and stability.The parameters of this hybrid TID-FOI controller are finely tuned using an advanced optimization method known as the Walrus Optimization Algorithm(WaOA).Performance analysis reveals that the combined TID-FOI controller significantly outperforms the TID and PID controllers when comparing their dynamic response across various system configurations.The study also incorporates investigation of redox flow batteries within the broader scope of energy storage applications to assess their impact on system performance.In addition,the research explores the controller’s effectiveness under different power exchange scenarios in a deregulated market,accounting for restrictions on generation ramp rates and governor hysteresis effects in dynamic control.To ensure the reliability and resilience of the presented methodology,the system transitions and develops across a broad range of varying parameters and stochastic load fluctuation.To wrap up,the study offers a pioneering control approach-a hybrid TID-FOI controller optimized via the Walrus Optimization Algorithm(WaOA)-designed for enhanced stability and performance in a complex,three-region hybrid energy system functioning within a deregulated framework.
文摘In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
基金The project supported by the National Key Program for Developing Basic Sciences (G1999043408 and G1998040901-1)the National Natural Sciences Foundation of China (40175024 and 40035010)
文摘To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.
基金financial support from Hunan Provincial Natura1 Science Foundation of China,Grant Number:02JJY2085,for this study
文摘The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2006AA06A208)
文摘Time delay and integration （TDI） charge coupled device （CCD） noise sets a fundamental limit on image sensor performance, especially under low illumination in remote sensing applications. After introducing the complete sources of CCD noise, we study the effects of TDI operation mode on noise, and the relationship between different types of noise and number of the TDI stage. Then we propose a new technique to identify and measure sources of TDI CCD noise employing mathematical statistics theory, where theoretical analysis shows that noise estimated formulation converges well. Finally, we establish a testing platform to carry out experiments, and a standard TDI CCD is calibrated by using the proposed method. The experimental results show that the noise analysis and measurement methods presented in this paper are useful for modeling TDI CCDs.
基金The project supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China （G2000048702, 2003CB716707）the National Science Fund for Distinguished Young Scholars （10025208）+1 种基金 the National Natural Science Foundation of China （Key Program） （10532040） the Research Fund for 0versea Chinese （10228028）.
文摘This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.
文摘There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.
文摘The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.
基金supported by the National Natural Science Foun-dation of China (11172334)
文摘This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.
基金National Natural Science Foundation of China under Grant Nos.51639006 and 51725901
文摘Finite element（FE） is a powerful tool and has been applied by investigators to real-time hybrid simulations（RTHSs）. This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time（TET） decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method（CDM）, the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ（λ = 4） method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11872090 and 12172023).
文摘In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thing is to decompose a dynamic system into two sub-systems,a small-scale low-frequency system and a high-frequency system.The former can be analytically and efficiently solved with the mode superposition method,and the latter is dealt with through a time integration method such as the Newmark method.The summation of the responses of these two sub-systems is the responses of the original dynamic system.It is concluded that,with little sacrifice of efficiency,the combination method based on the strategy is more accurate than the combined time integration method,but it has the same accuracy order as that of the combined method.Numerical experiments validate the effectiveness of the proposed strategy.
基金supported by the National Natural Science Foundation of China(Grant Numbers 11872090,11672019,11472035).
文摘Based on the weighted residual method,a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed,which is superior to the second-order accurate algorithms in tracking long-term dynamics.For improving such a higher-order accurate algorithm,this paper proposes a two sub-step higher-order algorithm with unconditional stability and controllable dissipation.In the proposed algorithm,a time step interval[t_(k),t_(k)+h]where h stands for the size of a time step is divided into two sub-steps[t_(k),t_(k)+γh]and[t_(k)+γh,t_(k)+h].A non-dissipative fourth-order algorithm is used in the rst sub-step to ensure low-frequency accuracy and a dissipative third-order algorithm is employed in the second sub-step to lter out the contribution of high-frequency modes.Besides,two approaches are used to design the algorithm parameterγ.The rst approach determinesγby maximizing low-frequency accuracy and the other determinesγfor quickly damping out highfrequency modes.The present algorithm usesρ_(∞)to exactly control the degree of numerical dissipation,and it is third-order accurate when 0≤ρ_(∞)<1 and fourth-order accurate whenρ_(∞)=1.Furthermore,the proposed algorithm is self-starting and easy to implement.Some illustrative linear and nonlinear examples are solved to check the performances of the proposed two sub-step higher-order algorithm.
文摘For the constrained nonlinear optimal control problem, by taking the first term of Taylor series, the dynamic equation is linearized. Thus by, introducing into the dual variable (Lagrange multiplier vector), the dynamic equation can be transformed into Hamilton system from Lagrange system on the basis of the original variable. Under the whole state, the problem discussed can be described from a new view, and the equation can be precisely solved by, the time precise integration method established in linear dynamic system. A numerical example shows the effectiveness of the method.
文摘We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.
基金Supported jointly by a Grand Project of the National Natural Science Foundation of China and the Changjiang Water Resources Commission(50099620)
文摘We introduce a new transmit/receive dipole pair array to obtain a compact quasi\|monostatic antenna structure for ground penetrating radar systems.And we analyze this transmit/receive dipole pair array in time domain.The numerical results show that if the distance between the transmit antenna and receive antenna is appropriate the array configuration is adoptable.
