Modal parameter has been considered as one of the indices in assessing the working state of hydraulic structures. The method for obtaining the modal parameter indices is crucial for health monitoring of hydraulic stru...Modal parameter has been considered as one of the indices in assessing the working state of hydraulic structures. The method for obtaining the modal parameter indices is crucial for health monitoring of hydraulic structures. Traditionally, model parameters are measured from the prototype dynamic test under the excitation of special equipment. The preparation is time-consuming and the method is difficult to carry out. We propose a method in this paper to denoise, reconstruct, determine the order and identify modal parameters based on singular entropy (SE) of eigenmatrix. It can be used to solve the problem of system eigenmatrix order determination, and to identify the modal order and the characteristics of structures under the working state. Finally, this method is applied to identify the operational modal parameters of Ertan arch dam under different flood discharging states and vibration frequencies of the powerhouse with a two-row placed unit in Lijiaxia hydropower station during the unit halting process. This new method provides a simple way to identify the modal parameters of large-scale hydraulic structures under ambient excitation.展开更多
Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of ...Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.展开更多
The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(...The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(mx-k)+∑p-kφ(k-mx) where m ≥ 2 is an integer. Based on the positive mask {pk+} and negative mask {p-k}, the conditions that guarantee the above equation has compactly distributional solutions or L2-stable solutions are established. Furthermore, the condition that the L2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of φ(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.展开更多
The increasing flexibility of active distribution systems(ADSs)coupled with the high penetration of renewable distributed generators(RDGs)leads to the increase of the complexity.It is of practical significance to achi...The increasing flexibility of active distribution systems(ADSs)coupled with the high penetration of renewable distributed generators(RDGs)leads to the increase of the complexity.It is of practical significance to achieve the largest amount of RDG penetration in ADSs and maintain the optimal operation.This study establishes an alternating current(AC)/direct current(DC)hybrid ADS model that considers the dynamic thermal rating,soft open point,and distribution network reconfiguration(DNR).Moreover,it transforms the optimal dispatching into a second-order cone programming problem.Considering the different control time scales of dispatchable resources,the following two-stage dispatching framework is proposed.d dispatch uses hourly input data with the goal(1)The day-ahea of minimizing the grid loss and RDG dropout.It obtains the optimal 24-hour schedule to determine the dispatching plans for DNR and the energy storage system.(2)The intraday dispatch uses 15-min input data for 1-hour rolling-plan dispatch but only executes the first 15 min of dispatching.To eliminate error between the actual operation and dispatching plan,the first 15 min is divided into three 5-min step-by-step executions.The goal of each step is to trace the tie-line power of the intraday rolling-plan dispatch to the greatest extent at the minimum cost.The measured data are used as feedback input for the rolling-plan dispatch after each step is executed.A case study shows that the comprehensive cooperative ADS model can release the line capacity,reduce losses,and improve the penetration rate of RDGs.Further,the two-stage dispatching framework can handle source-load fluctuations and enhance system stability.展开更多
Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the...Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.展开更多
To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of ...To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.展开更多
In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this...In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.展开更多
In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a...In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.展开更多
为了提高滤波器的带外抑制度和选择性,首次提出了一种双阶拓扑结构的带通滤波器。采用奇偶模方法对工字型双模谐振器的特性进行了分析,通带内具有四个谐振模式。滤波器有效尺寸为13.7 mm×5.35 mm,等于0.56λ_g×0.22λ_g(λ_g...为了提高滤波器的带外抑制度和选择性,首次提出了一种双阶拓扑结构的带通滤波器。采用奇偶模方法对工字型双模谐振器的特性进行了分析,通带内具有四个谐振模式。滤波器有效尺寸为13.7 mm×5.35 mm,等于0.56λ_g×0.22λ_g(λ_g为中心频率处的波导波长)。该滤波器的中心频率为7.34 GHz,相对带宽为20.9%,通带内最小插损为1.9 d B,阻带的三个传输零点分别位于3.17,8.36和9.61 GHz,上下阻带抑制度分别大于30 d B和46 d B,一次杂散抑制度大于18 d B。该滤波器具有结构紧凑,带外抑制度与选择性较高的优点。展开更多
By Riccati transformation, we establish some oscillation theorems for a class of two-dimensional nonlinear delay differential systems. The results obtained generalize some relatively known results.
The RGB2GRAY conversion model is the most popular and classical tool for image decolorization. A recent study showed that adapting the three weighting parameters in this first-order linear model with a discrete search...The RGB2GRAY conversion model is the most popular and classical tool for image decolorization. A recent study showed that adapting the three weighting parameters in this first-order linear model with a discrete searching solver has a great potential in its c6nversion ability. In this paper, we present a two-step strategy to efficiently extend the parameter searching solver to a two-order multivariance polynomial model, as a sum of three subspaces. We show that the first subspace in the two-order model is the most important and the second one can be seen as a refinement. In the first stage of our model, the gradient correlation similarity （Gcs） measure is used on the first subspace to obtain an immediate grayed image. Then, Gcs is applied again to select the optimal result from the immettiate grayed image plus the second subspace-induced candidate images. Experimental results show the advantages of the proposed approach in terms of quantitative evaluation, qualitative evaluation, and algorithm complexity.展开更多
基金Supported by the National Science Fund for Distinguished Young Scholars(Grant No.50725929)the National Science Foundation of China (Grant Nos.50539060 and 50679052)
文摘Modal parameter has been considered as one of the indices in assessing the working state of hydraulic structures. The method for obtaining the modal parameter indices is crucial for health monitoring of hydraulic structures. Traditionally, model parameters are measured from the prototype dynamic test under the excitation of special equipment. The preparation is time-consuming and the method is difficult to carry out. We propose a method in this paper to denoise, reconstruct, determine the order and identify modal parameters based on singular entropy (SE) of eigenmatrix. It can be used to solve the problem of system eigenmatrix order determination, and to identify the modal order and the characteristics of structures under the working state. Finally, this method is applied to identify the operational modal parameters of Ertan arch dam under different flood discharging states and vibration frequencies of the powerhouse with a two-row placed unit in Lijiaxia hydropower station during the unit halting process. This new method provides a simple way to identify the modal parameters of large-scale hydraulic structures under ambient excitation.
文摘Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
基金This work was Supported by the Natural Science Foundation of Guangdong Province (Grant Nos.06105648,05008289,032038)the Doctoral Foundation of Guangdong Province (Grant No.04300917)
文摘The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(mx-k)+∑p-kφ(k-mx) where m ≥ 2 is an integer. Based on the positive mask {pk+} and negative mask {p-k}, the conditions that guarantee the above equation has compactly distributional solutions or L2-stable solutions are established. Furthermore, the condition that the L2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of φ(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.
基金supported by Universiti Sains Malaysia through Research University Team(RUTeam)Grant Scheme(No.1001/PELECT/8580011)。
文摘The increasing flexibility of active distribution systems(ADSs)coupled with the high penetration of renewable distributed generators(RDGs)leads to the increase of the complexity.It is of practical significance to achieve the largest amount of RDG penetration in ADSs and maintain the optimal operation.This study establishes an alternating current(AC)/direct current(DC)hybrid ADS model that considers the dynamic thermal rating,soft open point,and distribution network reconfiguration(DNR).Moreover,it transforms the optimal dispatching into a second-order cone programming problem.Considering the different control time scales of dispatchable resources,the following two-stage dispatching framework is proposed.d dispatch uses hourly input data with the goal(1)The day-ahea of minimizing the grid loss and RDG dropout.It obtains the optimal 24-hour schedule to determine the dispatching plans for DNR and the energy storage system.(2)The intraday dispatch uses 15-min input data for 1-hour rolling-plan dispatch but only executes the first 15 min of dispatching.To eliminate error between the actual operation and dispatching plan,the first 15 min is divided into three 5-min step-by-step executions.The goal of each step is to trace the tie-line power of the intraday rolling-plan dispatch to the greatest extent at the minimum cost.The measured data are used as feedback input for the rolling-plan dispatch after each step is executed.A case study shows that the comprehensive cooperative ADS model can release the line capacity,reduce losses,and improve the penetration rate of RDGs.Further,the two-stage dispatching framework can handle source-load fluctuations and enhance system stability.
基金supported by the NSFC Grant no.12271492the Natural Science Foundation of Henan Province of China Grant no.222300420550+1 种基金supported by the NSFC Grant no.12271498the National Key R&D Program of China Grant no.2022YFA1005202/2022YFA1005200.
文摘Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.
文摘To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.72031009 and 61473338)。
文摘In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.
基金supported by the National Natural Science Foundation of China (10701083 and 10425105)the National Basic Research Program of China (2005CB321704).
文摘In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.
文摘为了提高滤波器的带外抑制度和选择性,首次提出了一种双阶拓扑结构的带通滤波器。采用奇偶模方法对工字型双模谐振器的特性进行了分析,通带内具有四个谐振模式。滤波器有效尺寸为13.7 mm×5.35 mm,等于0.56λ_g×0.22λ_g(λ_g为中心频率处的波导波长)。该滤波器的中心频率为7.34 GHz,相对带宽为20.9%,通带内最小插损为1.9 d B,阻带的三个传输零点分别位于3.17,8.36和9.61 GHz,上下阻带抑制度分别大于30 d B和46 d B,一次杂散抑制度大于18 d B。该滤波器具有结构紧凑,带外抑制度与选择性较高的优点。
文摘By Riccati transformation, we establish some oscillation theorems for a class of two-dimensional nonlinear delay differential systems. The results obtained generalize some relatively known results.
基金Project supported by the National- Basic Research Program （973） of China （No. 2013CB035600）, the National Natural Science Foundation of China （Nos. 61261010, 61362001, and 61503176）, Jiangxi Provincial Advanced Projects for Post-Doctoral Research Funds of China （No. 2014KY02）, the International Postdoctoral Exchange Fellowship Program, and the International Scientific and Technological Cooperation Projects of Jiangxi Province, China （No. 20141BDH80001）
文摘The RGB2GRAY conversion model is the most popular and classical tool for image decolorization. A recent study showed that adapting the three weighting parameters in this first-order linear model with a discrete searching solver has a great potential in its c6nversion ability. In this paper, we present a two-step strategy to efficiently extend the parameter searching solver to a two-order multivariance polynomial model, as a sum of three subspaces. We show that the first subspace in the two-order model is the most important and the second one can be seen as a refinement. In the first stage of our model, the gradient correlation similarity （Gcs） measure is used on the first subspace to obtain an immediate grayed image. Then, Gcs is applied again to select the optimal result from the immettiate grayed image plus the second subspace-induced candidate images. Experimental results show the advantages of the proposed approach in terms of quantitative evaluation, qualitative evaluation, and algorithm complexity.
