The classical Pauli particle(CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field(AVF) method in the computations of drift orbit...The classical Pauli particle(CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field(AVF) method in the computations of drift orbits. Demonstrating significantly higher efficiency, this advanced method is capable of accomplishing the simulation in less than one-third of the time of directly computing the guiding center motion. In contrast to the CPP-based Boris algorithm, this approach inherits the advantages of the AVF method, yielding stable trajectories even achieved with a tenfold time step and reducing the energy error by two orders of magnitude. By comparing these two CPP algorithms with the traditional RK4 method, the numerical results indicate a remarkable performance in terms of both the computational efficiency and error elimination. Moreover, we verify the properties of slow manifold integrators and successfully observe the bounce on both sides of the limiting slow manifold with deliberately chosen perturbed initial conditions. To evaluate the practical value of the methods, we conduct simulations in non-axisymmetric perturbation magnetic fields as part of the experiments,demonstrating that our CPP-based AVF method can handle simulations under complex magnetic field configurations with high accuracy, which the CPP-based Boris algorithm lacks. Through numerical experiments, we demonstrate that the CPP can replace guiding center dynamics in using energy-preserving algorithms for computations, providing a new, efficient, as well as stable approach for applying structure-preserving algorithms in plasma simulations.展开更多
Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to ca...Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential （or integro-differential） equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.展开更多
In order to solve the problem of metal impurities mixed in the production line of wood pulp nonwoven raw materials,intelligent metal detection and disposal automation equipment is designed.Based on the principle of el...In order to solve the problem of metal impurities mixed in the production line of wood pulp nonwoven raw materials,intelligent metal detection and disposal automation equipment is designed.Based on the principle of electromagnetic induction,the precise positioning of metal coordinates is realized by initial inspection and multi-directional re-inspection.Based on a geometry optimization driving algorithm,the cutting area is determined by locating the center of the circle that covers the maximum area.This approach aims to minimize the cutting area and maximize the use of materials.Additionally,the method strives to preserve as many fabrics at the edges as possible by employing the farthest edge covering circle algorithm.Based on a speed compensation algorithm,the flexible switching of upper and lower rolls is realized to ensure the maximum production efficiency.Compared with the metal detection device in the existing production line,the designed automation equipment has the advantages of higher detection sensitivity,more accurate metal coordinate positioning,smaller cutting material areas and higher production efficiency,which can make the production process more continuous,automated and intelligent.展开更多
In this paper, the dissipative and the forced terms of the Duffing equation are considered as the perturbations of nonlinear Hamiltonian equations and the perturbational effect is indicated by parameter ε. Firstly, b...In this paper, the dissipative and the forced terms of the Duffing equation are considered as the perturbations of nonlinear Hamiltonian equations and the perturbational effect is indicated by parameter ε. Firstly, based on the gradient- Hamiltonian decomposition theory of vector fields, by using splitting methods, this paper constructs structure-preserving algorithms （SPAs） for the Duffing equation. Then, according to the Liouville formula, it proves that the Jacobian matrix determinants of the SPAs are equal to that of the exact flow of the Duffing equation. However, considering the explicit Runge Kutta methods, this paper finds that there is an error term of order p＋l for the Jacobian matrix determinants. The volume evolution law of a given region in phase space is discussed for different algorithms, respectively. As a result, the sum of Lyapunov exponents is exactly invariable for the SPAs proposed in this paper. Finally, through numerical experiments, relative norm errors and absolute energy errors of phase trajectories of the SPAs and the Heun method （a second-order Runge-Kutta method） are compared. Computational results illustrate that the SPAs are evidently better than the Heun method when e is small or equal to zero.展开更多
To evaluate the performance of real time kinematic (RTK) network algorithms without applying actual measurements, a new method called geometric precision evaluation methodology (GPEM) based on covariance analysis was ...To evaluate the performance of real time kinematic (RTK) network algorithms without applying actual measurements, a new method called geometric precision evaluation methodology (GPEM) based on covariance analysis was presented. Three types of multiple reference station interpolation algorithms, including partial derivation algorithm (PDA), linear interpolation algorithms (LIA) and least squares condition (LSC) were discussed and analyzed. The geometric dilution of precision (GDOP) was defined to describe the influence of the network geometry on the interpolation precision, and the different GDOP expressions of above-mentioned algorithms were deduced. In order to compare geometric precision characteristics among different multiple reference station network algorithms, a simulation was conducted, and the GDOP contours of these algorithms were enumerated. Finally, to confirm the validation of GPEM, an experiment was conducted using data from Unite State Continuously Operating Reference Stations (US-CORS), and the precision performances were calculated according to the real test data and GPEM, respectively. The results show that GPEM generates very accurate estimation of the performance compared to the real data test.展开更多
The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the correspondin...The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhofflan systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.展开更多
This article seeks to outline an integrated and practical geometric optimization design system （GODS） incorporating hybrid graphical electromagnetic computing-wedge modeling （GRECO-WM） scheme and the genetic algor...This article seeks to outline an integrated and practical geometric optimization design system （GODS） incorporating hybrid graphical electromagnetic computing-wedge modeling （GRECO-WM） scheme and the genetic algorithm （GA） for calculating the radar cross section （RCS） and optimizing the geometric parameters of a large and complex target respectively. A new wedge modeling （WM） scheme is presented for calculating the high-frequency RCS of wedge with only one visible facet based on the method of equivalent currents （MEC）. The applications of GODS to 2D cross-section and 3D surface are respectively implemented by choosing an average of monostatic RCS values corresponding to a series of incident angles over a frequency band as the optimum objective function. And the results demonstrate that the RCS can be effectively and conveniently reduced by the GODS presented in this article.展开更多
The paper presents an algorithm for constructing geometric buffers for vector feature layers and dissolving those buffers using a sweep-line approach and vector algebra.The algorithm works by first constructing a geom...The paper presents an algorithm for constructing geometric buffers for vector feature layers and dissolving those buffers using a sweep-line approach and vector algebra.The algorithm works by first constructing a geometric buffer for a vector feature layer,then dissolving each single geometric buffer for that feature layer,and finally dissolving the overlapping buffers of the entire layer.The algorithm has been implemented successfully in a commercial Geographical Information System software package.展开更多
Structural shape monitoring plays a vital role in the structural health monitoring systems.The inverse finite element method(iFEM)has been demonstrated to be a practical method of deformation reconstruction owing to i...Structural shape monitoring plays a vital role in the structural health monitoring systems.The inverse finite element method(iFEM)has been demonstrated to be a practical method of deformation reconstruction owing to its unique advantages.Current iFEM formulations have been applied to small deformation of structures based on the small-displacement assumption of linear theory.However,this assumption may be inapplicable to some structures with large displacements in practical applications.Therefore,geometric nonlinearity needs to be considered.In this study,to expand the practical utility of iFEM for large displacement monitoring,we propose a nonlinear iFEM algorithm based on a four-node inverse quadrilateral shell element iQS4.Taking the advantage of an iterative iFEM algorithm,a nonlinear response is linearized to compute the geometrically nonlinear deformation reconstruction,like the basic concept of nonlinear FE analysis.Several examples are solved to verify the proposed approach.It is demonstrated that large displacements can be accurately estimated even if the in-situ sensor data includes different levels of randomly generated noise.It is proven that the nonlinear iFEM algorithm provides a more accurate displacement response as compared to the linear iFEM methodology for structures undergoing large displacement.Hence,the proposed approach can be utilized as a viable tool to effectively characterize geometrically nonlinear deformations of structures in real-time applications.展开更多
Traditional track dynamic geometric state(TDGS)simulation incurs substantial computational burdens,posing challenges for developing reliability assessment approach that accounts for TDGS.To overcome these,firstly,a si...Traditional track dynamic geometric state(TDGS)simulation incurs substantial computational burdens,posing challenges for developing reliability assessment approach that accounts for TDGS.To overcome these,firstly,a simulation-based TDGS model is established,and a surrogate-based model,grid search algorithm-particle swarm optimization-genetic algorithm-multi-output least squares support vector regression,is established.Among them,hyperparameter optimization algorithm’s effectiveness is confirmed through test functions.Subsequently,an adaptive surrogate-based probability density evolution method(PDEM)considering random track geometry irregularity(TGI)is developed.Finally,taking curved train-steel spring floating slab track-U beam as case study,the surrogate-based model trained on simulation datasets not only shows accuracy in both time and frequency domains,but also surpasses existing models.Additionally,the adaptive surrogate-based PDEM shows high accuracy and efficiency,outperforming Monte Carlo simulation and simulation-based PDEM.The reliability assessment shows that the TDGS part peak management indexes,left/right vertical dynamic irregularity,right alignment dynamic irregularity,and track twist,have reliability values of 0.9648,0.9918,0.9978,and 0.9901,respectively.The TDGS mean management index,i.e.,track quality index,has reliability value of 0.9950.These findings show that the proposed framework can accurately and efficiently assess the reliability of curved low-stiffness track-viaducts,providing a theoretical basis for the TGI maintenance.展开更多
Considering the characteristics of spatial straightness error, this paper puts forward a kind of evaluation method of spatial straightness error using Geometric Approximation Searching Algorithm (GASA). According to t...Considering the characteristics of spatial straightness error, this paper puts forward a kind of evaluation method of spatial straightness error using Geometric Approximation Searching Algorithm (GASA). According to the minimum condition principle of form error evaluation, the mathematic model and optimization objective of the GASA are given. The algorithm avoids the optimization and linearization, and can be fulfilled in three steps. First construct two parallel quadrates based on the preset two reference points of the spatial line respectively;second construct centerlines by connecting one quadrate each vertices to another quadrate each vertices;after that, calculate the distances between measured points and the constructed centerlines. The minimum zone straightness error is obtained by repeating comparing and reconstructing quadrates. The principle and steps of the algorithm to evaluate spatial straightness error is described in detail, and the mathematical formula and program flowchart are given also. Results show that this algorithm can evaluate spatial straightness error more effectively and exactly.展开更多
The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus.Not only can the combination ofand∇derivatives be beneficia...The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus.Not only can the combination ofand∇derivatives be beneficial to obtaining higher convergence order in numerical analysis,but also it prompts the timescale numerical computational scheme to have good properties,for instance,structure-preserving.In this letter,a structure-preserving algorithm for time-scale non-shifted Hamiltonian systems is proposed.By using the time-scale discrete variational method and calculus theory,and taking a discrete time scale in the variational principle of non-shifted Hamiltonian systems,the corresponding discrete Hamiltonian principle can be obtained.Furthermore,the time-scale discrete Hamilton difference equations,Noether theorem,and the symplectic scheme of discrete Hamiltonian systems are obtained.Finally,taking the Kepler problem and damped oscillator for time-scale non-shifted Hamiltonian systems as examples,they show that the time-scale discrete variational method is a structure-preserving algorithm.The new algorithm not only provides a numerical method for solving time-scale non-shifted dynamic equations but can be calculated with variable step sizes to improve the computational speed.展开更多
A creepy photoelectric endoscopy system with good performance is studied, and anexpansion and correction algorithm for a compressed photoelectric image with serious geometricdistortion is presented. The algorithm can ...A creepy photoelectric endoscopy system with good performance is studied, and anexpansion and correction algorithm for a compressed photoelectric image with serious geometricdistortion is presented. The algorithm can not only correct the geometric distortion, but alsorestore the gray-level distribution by means of ternary convolution algorithm. The details andthe outline in the image are very clear. It is proved to be of high performance in practice.展开更多
Support vector machine(SVM) has shown great potential in pattern recognition and regressive estima-tion.Due to the industrial development demands,such as the fermentation process modeling,improving the training perfor...Support vector machine(SVM) has shown great potential in pattern recognition and regressive estima-tion.Due to the industrial development demands,such as the fermentation process modeling,improving the training performance on increasingly large sample sets is an important problem.However,solving a large optimization problem is computationally intensive and memory intensive.In this paper,a geometric interpretation of SVM re-gression(SVR) is derived,and μ-SVM is extended for both L1-norm and L2-norm penalty SVR.Further,Gilbert al-gorithm,a well-known geometric algorithm,is modified to solve SVR problems.Theoretical analysis indicates that the presented SVR training geometric algorithms have the same convergence and almost identical cost of computa-tion as their corresponding algorithms for SVM classification.Experimental results show that the geometric meth-ods are more efficient than conventional methods using quadratic programming and require much less memory.展开更多
In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Co...In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Conventionally, the finite ele- ment methods （FEMs） or weak-form based meshfree methods have often been adopted to solve geometric nonlinear problems. However, issues, such as the mesh dependency, the numerical integration, and the boundary imposition, make these approaches com- putationally inefficient. Recently, strong-form collocation methods have been called on to solve the boundary value problems. The feasibility of the collocation method with the nodal discretization such as the radial basis collocation method （RBCM） motivates the present study. Due to the limited application to the nonlinear analysis in a strong form, we formulate the equation of equilibrium, along with the boundary conditions, in an incremental-iterative sense using the RBCM. The efficacy of the proposed framework is numerically demonstrated with the solution of two benchmark problems involving the geometric nonlinearity. Compared with the conventional weak-form formulation, the pro- posed framework is advantageous as no quadrature rule is needed in constructing the governing equation, and no mesh limitation exists with the deformed geometry in the increment al-it erative process.展开更多
In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this mo...In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.展开更多
Suppose C is an irreducible algebraic curve of genus g, C*(D,G) is an algebraic geometric code with designed minimum distance d* = deg(G)-2g + 2. In this paper, a decoding algorithm based on Fundamental Iterative Algo...Suppose C is an irreducible algebraic curve of genus g, C*(D,G) is an algebraic geometric code with designed minimum distance d* = deg(G)-2g + 2. In this paper, a decoding algorithm based on Fundamental Iterative Algorithm(FIA) is presented, also its reasonableness is proved. In fact, our decoding algorithm is a modification of the algorithm proposed by G. L. Fend and T. R. N. Rao(1993) and can correct any received words with errors not more than (d*-1)/2, whereas the complexity is only about one half as much as Feng and Rao’s. The procedure can be implemented easily by hardware or software.展开更多
Particles,including soot,aerosol and ash,usually exist as fractal aggregates.The radiative properties of the particle fractal aggregates have a great influence on studying the light or heat radiative transfer in the p...Particles,including soot,aerosol and ash,usually exist as fractal aggregates.The radiative properties of the particle fractal aggregates have a great influence on studying the light or heat radiative transfer in the particle medium.In the present work,the performance of the single-layer inversion model and the double-layer inversion model in reconstructing the geometric structure of particle fractal aggregates is studied based on the light reflectancetransmittance measurement method.An improved artificial fish-swarm algorithm(IAFSA)is proposed to solve the inverse problem.The result reveals that the accuracy of double-layer inversion model is more satisfactory as it can provide more uncorrelated information than the single-layer inversion model.Moreover,the developed IAFSA show higher accuracy and better robustness than the original artificial fish swarm algorithm(AFSA)for avoiding local optimization problems effectively.As a whole,the present work supplies a useful kind of measurement technology for predicting geometrical morphology of particle fractal aggregates.展开更多
基金supported by National Natural Science Foundation of China (Nos. 11975068 and 11925501)the National Key R&D Program of China (No. 2022YFE03090000)the Fundamental Research Funds for the Central Universities (No. DUT22ZD215)。
文摘The classical Pauli particle(CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field(AVF) method in the computations of drift orbits. Demonstrating significantly higher efficiency, this advanced method is capable of accomplishing the simulation in less than one-third of the time of directly computing the guiding center motion. In contrast to the CPP-based Boris algorithm, this approach inherits the advantages of the AVF method, yielding stable trajectories even achieved with a tenfold time step and reducing the energy error by two orders of magnitude. By comparing these two CPP algorithms with the traditional RK4 method, the numerical results indicate a remarkable performance in terms of both the computational efficiency and error elimination. Moreover, we verify the properties of slow manifold integrators and successfully observe the bounce on both sides of the limiting slow manifold with deliberately chosen perturbed initial conditions. To evaluate the practical value of the methods, we conduct simulations in non-axisymmetric perturbation magnetic fields as part of the experiments,demonstrating that our CPP-based AVF method can handle simulations under complex magnetic field configurations with high accuracy, which the CPP-based Boris algorithm lacks. Through numerical experiments, we demonstrate that the CPP can replace guiding center dynamics in using energy-preserving algorithms for computations, providing a new, efficient, as well as stable approach for applying structure-preserving algorithms in plasma simulations.
基金supported by National Natural Science Foundation of China (NSFC-11775219, 11775222, 11505186, 11575185 and 11575186)the National Key Research and Development Program (2016YFA0400600, 2016YFA0400601 and 2016YFA0400602)+3 种基金the ITER-China Program (2015GB111003, 2014GB124005)Chinese Scholar Council (201506340103)China Postdoctoral Science Foundation (2017LH002)the GeoA lgorithmic Plasma Simulator (GAPS) Project
文摘Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential （or integro-differential） equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.
基金National Key Research and Development Program of China(Nos.2022YFB4700600 and 2022YFB4700605)。
文摘In order to solve the problem of metal impurities mixed in the production line of wood pulp nonwoven raw materials,intelligent metal detection and disposal automation equipment is designed.Based on the principle of electromagnetic induction,the precise positioning of metal coordinates is realized by initial inspection and multi-directional re-inspection.Based on a geometry optimization driving algorithm,the cutting area is determined by locating the center of the circle that covers the maximum area.This approach aims to minimize the cutting area and maximize the use of materials.Additionally,the method strives to preserve as many fabrics at the edges as possible by employing the farthest edge covering circle algorithm.Based on a speed compensation algorithm,the flexible switching of upper and lower rolls is realized to ensure the maximum production efficiency.Compared with the metal detection device in the existing production line,the designed automation equipment has the advantages of higher detection sensitivity,more accurate metal coordinate positioning,smaller cutting material areas and higher production efficiency,which can make the production process more continuous,automated and intelligent.
基金Project supported by the National Natural Science Foundation of China (Grant No 10572021)the Doctoral Programme Foundation of Institute of Higher Education of China (Grant No 20040007022)
文摘In this paper, the dissipative and the forced terms of the Duffing equation are considered as the perturbations of nonlinear Hamiltonian equations and the perturbational effect is indicated by parameter ε. Firstly, based on the gradient- Hamiltonian decomposition theory of vector fields, by using splitting methods, this paper constructs structure-preserving algorithms （SPAs） for the Duffing equation. Then, according to the Liouville formula, it proves that the Jacobian matrix determinants of the SPAs are equal to that of the exact flow of the Duffing equation. However, considering the explicit Runge Kutta methods, this paper finds that there is an error term of order p＋l for the Jacobian matrix determinants. The volume evolution law of a given region in phase space is discussed for different algorithms, respectively. As a result, the sum of Lyapunov exponents is exactly invariable for the SPAs proposed in this paper. Finally, through numerical experiments, relative norm errors and absolute energy errors of phase trajectories of the SPAs and the Heun method （a second-order Runge-Kutta method） are compared. Computational results illustrate that the SPAs are evidently better than the Heun method when e is small or equal to zero.
基金Project(61273055) supported by the National Natural Science Foundation of ChinaProject(CX2010B012) supported by Hunan Provincial Innovation Foundation for Postgraduate Students, ChinaProject(B100302) supported by Innovation Foundation for Postgraduate Students of National University of Defense Technology, China
文摘To evaluate the performance of real time kinematic (RTK) network algorithms without applying actual measurements, a new method called geometric precision evaluation methodology (GPEM) based on covariance analysis was presented. Three types of multiple reference station interpolation algorithms, including partial derivation algorithm (PDA), linear interpolation algorithms (LIA) and least squares condition (LSC) were discussed and analyzed. The geometric dilution of precision (GDOP) was defined to describe the influence of the network geometry on the interpolation precision, and the different GDOP expressions of above-mentioned algorithms were deduced. In order to compare geometric precision characteristics among different multiple reference station network algorithms, a simulation was conducted, and the GDOP contours of these algorithms were enumerated. Finally, to confirm the validation of GPEM, an experiment was conducted using data from Unite State Continuously Operating Reference Stations (US-CORS), and the precision performances were calculated according to the real test data and GPEM, respectively. The results show that GPEM generates very accurate estimation of the performance compared to the real data test.
基金Supported by the National Natural Science Foundation of China (10932002,10972031)
文摘The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhofflan systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.
基金National Natural Science Foundation of China （20095251024）
文摘This article seeks to outline an integrated and practical geometric optimization design system （GODS） incorporating hybrid graphical electromagnetic computing-wedge modeling （GRECO-WM） scheme and the genetic algorithm （GA） for calculating the radar cross section （RCS） and optimizing the geometric parameters of a large and complex target respectively. A new wedge modeling （WM） scheme is presented for calculating the high-frequency RCS of wedge with only one visible facet based on the method of equivalent currents （MEC）. The applications of GODS to 2D cross-section and 3D surface are respectively implemented by choosing an average of monostatic RCS values corresponding to a series of incident angles over a frequency band as the optimum objective function. And the results demonstrate that the RCS can be effectively and conveniently reduced by the GODS presented in this article.
文摘The paper presents an algorithm for constructing geometric buffers for vector feature layers and dissolving those buffers using a sweep-line approach and vector algebra.The algorithm works by first constructing a geometric buffer for a vector feature layer,then dissolving each single geometric buffer for that feature layer,and finally dissolving the overlapping buffers of the entire layer.The algorithm has been implemented successfully in a commercial Geographical Information System software package.
基金supported by the NationalNatural Science Foundation of China(Grant No.11902253)the Fundamental Research Funds for the Central Universities of China.The authors are grateful for this support.
文摘Structural shape monitoring plays a vital role in the structural health monitoring systems.The inverse finite element method(iFEM)has been demonstrated to be a practical method of deformation reconstruction owing to its unique advantages.Current iFEM formulations have been applied to small deformation of structures based on the small-displacement assumption of linear theory.However,this assumption may be inapplicable to some structures with large displacements in practical applications.Therefore,geometric nonlinearity needs to be considered.In this study,to expand the practical utility of iFEM for large displacement monitoring,we propose a nonlinear iFEM algorithm based on a four-node inverse quadrilateral shell element iQS4.Taking the advantage of an iterative iFEM algorithm,a nonlinear response is linearized to compute the geometrically nonlinear deformation reconstruction,like the basic concept of nonlinear FE analysis.Several examples are solved to verify the proposed approach.It is demonstrated that large displacements can be accurately estimated even if the in-situ sensor data includes different levels of randomly generated noise.It is proven that the nonlinear iFEM algorithm provides a more accurate displacement response as compared to the linear iFEM methodology for structures undergoing large displacement.Hence,the proposed approach can be utilized as a viable tool to effectively characterize geometrically nonlinear deformations of structures in real-time applications.
基金Project(52072412)supported by the National Natural Science Foundation of China。
文摘Traditional track dynamic geometric state(TDGS)simulation incurs substantial computational burdens,posing challenges for developing reliability assessment approach that accounts for TDGS.To overcome these,firstly,a simulation-based TDGS model is established,and a surrogate-based model,grid search algorithm-particle swarm optimization-genetic algorithm-multi-output least squares support vector regression,is established.Among them,hyperparameter optimization algorithm’s effectiveness is confirmed through test functions.Subsequently,an adaptive surrogate-based probability density evolution method(PDEM)considering random track geometry irregularity(TGI)is developed.Finally,taking curved train-steel spring floating slab track-U beam as case study,the surrogate-based model trained on simulation datasets not only shows accuracy in both time and frequency domains,but also surpasses existing models.Additionally,the adaptive surrogate-based PDEM shows high accuracy and efficiency,outperforming Monte Carlo simulation and simulation-based PDEM.The reliability assessment shows that the TDGS part peak management indexes,left/right vertical dynamic irregularity,right alignment dynamic irregularity,and track twist,have reliability values of 0.9648,0.9918,0.9978,and 0.9901,respectively.The TDGS mean management index,i.e.,track quality index,has reliability value of 0.9950.These findings show that the proposed framework can accurately and efficiently assess the reliability of curved low-stiffness track-viaducts,providing a theoretical basis for the TGI maintenance.
文摘Considering the characteristics of spatial straightness error, this paper puts forward a kind of evaluation method of spatial straightness error using Geometric Approximation Searching Algorithm (GASA). According to the minimum condition principle of form error evaluation, the mathematic model and optimization objective of the GASA are given. The algorithm avoids the optimization and linearization, and can be fulfilled in three steps. First construct two parallel quadrates based on the preset two reference points of the spatial line respectively;second construct centerlines by connecting one quadrate each vertices to another quadrate each vertices;after that, calculate the distances between measured points and the constructed centerlines. The minimum zone straightness error is obtained by repeating comparing and reconstructing quadrates. The principle and steps of the algorithm to evaluate spatial straightness error is described in detail, and the mathematical formula and program flowchart are given also. Results show that this algorithm can evaluate spatial straightness error more effectively and exactly.
基金This work was supported by the National Natural Science Foundation of China(Nos.11972241,11572212)the Natural Science Foundation of Jiangsu Province(No.BK20191454)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYCX20_0251).
文摘The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus.Not only can the combination ofand∇derivatives be beneficial to obtaining higher convergence order in numerical analysis,but also it prompts the timescale numerical computational scheme to have good properties,for instance,structure-preserving.In this letter,a structure-preserving algorithm for time-scale non-shifted Hamiltonian systems is proposed.By using the time-scale discrete variational method and calculus theory,and taking a discrete time scale in the variational principle of non-shifted Hamiltonian systems,the corresponding discrete Hamiltonian principle can be obtained.Furthermore,the time-scale discrete Hamilton difference equations,Noether theorem,and the symplectic scheme of discrete Hamiltonian systems are obtained.Finally,taking the Kepler problem and damped oscillator for time-scale non-shifted Hamiltonian systems as examples,they show that the time-scale discrete variational method is a structure-preserving algorithm.The new algorithm not only provides a numerical method for solving time-scale non-shifted dynamic equations but can be calculated with variable step sizes to improve the computational speed.
文摘A creepy photoelectric endoscopy system with good performance is studied, and anexpansion and correction algorithm for a compressed photoelectric image with serious geometricdistortion is presented. The algorithm can not only correct the geometric distortion, but alsorestore the gray-level distribution by means of ternary convolution algorithm. The details andthe outline in the image are very clear. It is proved to be of high performance in practice.
基金Supported by the National Natural Science Foundation of China (20476007,20676013)
文摘Support vector machine(SVM) has shown great potential in pattern recognition and regressive estima-tion.Due to the industrial development demands,such as the fermentation process modeling,improving the training performance on increasingly large sample sets is an important problem.However,solving a large optimization problem is computationally intensive and memory intensive.In this paper,a geometric interpretation of SVM re-gression(SVR) is derived,and μ-SVM is extended for both L1-norm and L2-norm penalty SVR.Further,Gilbert al-gorithm,a well-known geometric algorithm,is modified to solve SVR problems.Theoretical analysis indicates that the presented SVR training geometric algorithms have the same convergence and almost identical cost of computa-tion as their corresponding algorithms for SVM classification.Experimental results show that the geometric meth-ods are more efficient than conventional methods using quadratic programming and require much less memory.
基金Project supported by the Ministry of Science and Technology of Taiwan(No.MOST 104-2221-E-009-193)
文摘In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Conventionally, the finite ele- ment methods （FEMs） or weak-form based meshfree methods have often been adopted to solve geometric nonlinear problems. However, issues, such as the mesh dependency, the numerical integration, and the boundary imposition, make these approaches com- putationally inefficient. Recently, strong-form collocation methods have been called on to solve the boundary value problems. The feasibility of the collocation method with the nodal discretization such as the radial basis collocation method （RBCM） motivates the present study. Due to the limited application to the nonlinear analysis in a strong form, we formulate the equation of equilibrium, along with the boundary conditions, in an incremental-iterative sense using the RBCM. The efficacy of the proposed framework is numerically demonstrated with the solution of two benchmark problems involving the geometric nonlinearity. Compared with the conventional weak-form formulation, the pro- posed framework is advantageous as no quadrature rule is needed in constructing the governing equation, and no mesh limitation exists with the deformed geometry in the increment al-it erative process.
基金Supported by the NSF Jiangsu Province(BK2003211)Supported by the NSF of Henan Province(2003120001)
文摘In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θ positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.
文摘Suppose C is an irreducible algebraic curve of genus g, C*(D,G) is an algebraic geometric code with designed minimum distance d* = deg(G)-2g + 2. In this paper, a decoding algorithm based on Fundamental Iterative Algorithm(FIA) is presented, also its reasonableness is proved. In fact, our decoding algorithm is a modification of the algorithm proposed by G. L. Fend and T. R. N. Rao(1993) and can correct any received words with errors not more than (d*-1)/2, whereas the complexity is only about one half as much as Feng and Rao’s. The procedure can be implemented easily by hardware or software.
基金supported by the National Natural Science Foundation of China(No.51806103)the Natural Science Foundation of Jiangsu Province(No.BK20170800)Aeronautical Science Foundation of China(No.201928052002)。
文摘Particles,including soot,aerosol and ash,usually exist as fractal aggregates.The radiative properties of the particle fractal aggregates have a great influence on studying the light or heat radiative transfer in the particle medium.In the present work,the performance of the single-layer inversion model and the double-layer inversion model in reconstructing the geometric structure of particle fractal aggregates is studied based on the light reflectancetransmittance measurement method.An improved artificial fish-swarm algorithm(IAFSA)is proposed to solve the inverse problem.The result reveals that the accuracy of double-layer inversion model is more satisfactory as it can provide more uncorrelated information than the single-layer inversion model.Moreover,the developed IAFSA show higher accuracy and better robustness than the original artificial fish swarm algorithm(AFSA)for avoiding local optimization problems effectively.As a whole,the present work supplies a useful kind of measurement technology for predicting geometrical morphology of particle fractal aggregates.
