According to differential geometry and gear geometry, the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth ...According to differential geometry and gear geometry, the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion. The correct meshing condition, contact line, contact ratio, calculating method for pin tooth's maximum contact point are developed. Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1, 2, 3 and ?1, respectively. A general method called enveloping method to generate hypocycloid and epicycloid is put forward. The correct meshing condition for cycloid pin wheel gearing is provided, and the contact line and the contact ratio are also discussed.展开更多
The convergence properties of the Fletcher-Reeves method for unconstrained optimization are further studied with the technique of generalized line search. Two conditions are given which guarantee the global convergenc...The convergence properties of the Fletcher-Reeves method for unconstrained optimization are further studied with the technique of generalized line search. Two conditions are given which guarantee the global convergence of the Fletcher-Reeves method using generalized Wolfe line searches or generalized Arjimo line searches, whereas an example is constructed showing that the conditions cannot be relaxed in certain senses.展开更多
The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient...The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient method, however, heavily restricted the use of conjugate gradient method for largescale nonlinear optimization. This is, to the great extent, due to the requirement of a relatively exact line search at each iteration and the loss of conjugacy property of the search directions in various occasions. On the contrary, the limited-memory BFGS method and the Barzilai-Bowein gradient method share the so-called asymptotical one stepsize per line-search property, namely, the trial stepsize in the method will asymptotically be accepted by the line search when the iteration is close to the solution. This paper will focus on the analysis of the subspace minimization conjugate gradient method by Yuan and Stoer(1995). Specifically, if choosing the parameter in the method by combining the Barzilai-Borwein idea, we will be able to provide some efficient Barzilai-Borwein conjugate gradient(BBCG) methods. The initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches. This variant of the BBCG method might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization.展开更多
With the wide application of power electronized resources(PERs),the amplitude and frequency of voltages show significant time-varying characteristics under asymmetrical faults.As a result,the traditional phasor model,...With the wide application of power electronized resources(PERs),the amplitude and frequency of voltages show significant time-varying characteristics under asymmetrical faults.As a result,the traditional phasor model,impedance model,and symmetrical components method based on the constant amplitude and frequency of voltages are facing great challenges.Hence,a novel asymmetrical fault analysis method based on conjugate vectors is proposed in this paper which can meet the modeling and analysis requirements of the network excited by voltages with time-varying amplitude/frequency.Furthermore,asymmetrical fault characteristics are extracted.As an application,a faulted phase identification(FPI)strategy is proposed based on the fault characteristics.The correctness and superiority of the asymmetrical fault analysis method and FPI strategy are verified in time-domain simulations and a real-time digital simulator.展开更多
Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the ...Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.展开更多
3D inversion of borehole-surface electrical data for complex geo-electrical models is still a challenging problem in geophysical exploration. We have developed a program for 3D inversion to borehole-surface electrical...3D inversion of borehole-surface electrical data for complex geo-electrical models is still a challenging problem in geophysical exploration. We have developed a program for 3D inversion to borehole-surface electrical data based on the quasi-analytical approximation （QA） and re-weighted regularized conjugate gradient method （RRCG） algorithms using Visual Fortran 6.5. Application of the QA approximation to forward modeling and Frechet derivative computations speeds up the calculation dramatically. The trial calculation for synthetic data of theoretical model showed that the program is fast and highly precise.展开更多
This paper aims to search for the solutions of the(2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation.Lump solutions,breather solutions,mixed solutions with solitons,and lump-breather solutions can be o...This paper aims to search for the solutions of the(2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation.Lump solutions,breather solutions,mixed solutions with solitons,and lump-breather solutions can be obtained from the N-soliton solution formula by using the long-wave limit approach and the conjugate complex method.We use both specific circumstances and general higher-order forms of the hybrid solutions as examples.With the help of maple software,we create density and 3D graphs to summarize the dynamic properties of these solutions.Additionally,it is possible to observe how the solutions'trajectory,velocity,and shape vary over time.展开更多
Highly precise acoustic impedance inversion is a key technology for pre-drilling prediction by VSP data. In this paper, based on the facts that VSP data has high resolution, high signal to noise ratio, and the downgoi...Highly precise acoustic impedance inversion is a key technology for pre-drilling prediction by VSP data. In this paper, based on the facts that VSP data has high resolution, high signal to noise ratio, and the downgoing and upgoing waves can be accurately separated, we propose a method of predicting the impedance below the borehole in front of the bit using VSP data. First, the method of nonlinear iterative inversion is adopted to invert for impedance using the VSP corridor stack. Then, by modifying the damping factor in the iteration and using the preconditioned conjugate gradient method to solve the equations, the stability and convergence of the inversion results can be enhanced. The results of theoretical models and actual data demonstrate that the method is effective for pre-drilling prediction using VSP data.展开更多
In this paper,a three-term derivative-free projection method is proposed for solving nonlinear monotone equations.Under someappropriate conditions,the global convergence and R-linear convergence rate of the proposed m...In this paper,a three-term derivative-free projection method is proposed for solving nonlinear monotone equations.Under someappropriate conditions,the global convergence and R-linear convergence rate of the proposed method are analyzed and proved.With no need of any derivative information,the proposed method is able to solve large-scale nonlinear monotone equations.Numerical comparisons show that the proposed method is effective.展开更多
基金the National Science and Technology Supporting Program (Grant No. No. 2006BAF01B08)Chongqing Science and Technology Key Task (Grant No. CSCT2006AA3010-6)
文摘According to differential geometry and gear geometry, the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion. The correct meshing condition, contact line, contact ratio, calculating method for pin tooth's maximum contact point are developed. Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1, 2, 3 and ?1, respectively. A general method called enveloping method to generate hypocycloid and epicycloid is put forward. The correct meshing condition for cycloid pin wheel gearing is provided, and the contact line and the contact ratio are also discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19801033).
文摘The convergence properties of the Fletcher-Reeves method for unconstrained optimization are further studied with the technique of generalized line search. Two conditions are given which guarantee the global convergence of the Fletcher-Reeves method using generalized Wolfe line searches or generalized Arjimo line searches, whereas an example is constructed showing that the conditions cannot be relaxed in certain senses.
基金supported by National Natural Science Foundation of China (Grant Nos. 81173633, 11401038 and 11331012)the Chinese Academy of Sciences Grant (Grant No. kjcx-yw-s7-03)+2 种基金National Natural Science Foundation of China for Distinguished Young Scientists (Grant No. 11125107)the Key Project of Chinese National Programs for Fundamental Research and Development (Grant No. 2015CB856000)the Fundamental Research Funds for the Central Universities (Grant No. 2014RC0904)
文摘The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient method, however, heavily restricted the use of conjugate gradient method for largescale nonlinear optimization. This is, to the great extent, due to the requirement of a relatively exact line search at each iteration and the loss of conjugacy property of the search directions in various occasions. On the contrary, the limited-memory BFGS method and the Barzilai-Bowein gradient method share the so-called asymptotical one stepsize per line-search property, namely, the trial stepsize in the method will asymptotically be accepted by the line search when the iteration is close to the solution. This paper will focus on the analysis of the subspace minimization conjugate gradient method by Yuan and Stoer(1995). Specifically, if choosing the parameter in the method by combining the Barzilai-Borwein idea, we will be able to provide some efficient Barzilai-Borwein conjugate gradient(BBCG) methods. The initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches. This variant of the BBCG method might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization.
基金supported in part by the National Natural Science Foundation of China(52107096)in part by the Young Elite Scientists Sponsorship Program by CAST(2021QNRC001)in part by the National Science Foundation for Distinguished Young Scholars of China(52225704).
文摘With the wide application of power electronized resources(PERs),the amplitude and frequency of voltages show significant time-varying characteristics under asymmetrical faults.As a result,the traditional phasor model,impedance model,and symmetrical components method based on the constant amplitude and frequency of voltages are facing great challenges.Hence,a novel asymmetrical fault analysis method based on conjugate vectors is proposed in this paper which can meet the modeling and analysis requirements of the network excited by voltages with time-varying amplitude/frequency.Furthermore,asymmetrical fault characteristics are extracted.As an application,a faulted phase identification(FPI)strategy is proposed based on the fault characteristics.The correctness and superiority of the asymmetrical fault analysis method and FPI strategy are verified in time-domain simulations and a real-time digital simulator.
基金supported by the National Natural Science Foundation of China(Grant No.12161030)by the Hainan Provincial Natural Science Foundation of China(Grant No.121RC537).
文摘Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.
文摘3D inversion of borehole-surface electrical data for complex geo-electrical models is still a challenging problem in geophysical exploration. We have developed a program for 3D inversion to borehole-surface electrical data based on the quasi-analytical approximation （QA） and re-weighted regularized conjugate gradient method （RRCG） algorithms using Visual Fortran 6.5. Application of the QA approximation to forward modeling and Frechet derivative computations speeds up the calculation dramatically. The trial calculation for synthetic data of theoretical model showed that the program is fast and highly precise.
文摘This paper aims to search for the solutions of the(2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation.Lump solutions,breather solutions,mixed solutions with solitons,and lump-breather solutions can be obtained from the N-soliton solution formula by using the long-wave limit approach and the conjugate complex method.We use both specific circumstances and general higher-order forms of the hybrid solutions as examples.With the help of maple software,we create density and 3D graphs to summarize the dynamic properties of these solutions.Additionally,it is possible to observe how the solutions'trajectory,velocity,and shape vary over time.
文摘Highly precise acoustic impedance inversion is a key technology for pre-drilling prediction by VSP data. In this paper, based on the facts that VSP data has high resolution, high signal to noise ratio, and the downgoing and upgoing waves can be accurately separated, we propose a method of predicting the impedance below the borehole in front of the bit using VSP data. First, the method of nonlinear iterative inversion is adopted to invert for impedance using the VSP corridor stack. Then, by modifying the damping factor in the iteration and using the preconditioned conjugate gradient method to solve the equations, the stability and convergence of the inversion results can be enhanced. The results of theoretical models and actual data demonstrate that the method is effective for pre-drilling prediction using VSP data.
文摘In this paper,a three-term derivative-free projection method is proposed for solving nonlinear monotone equations.Under someappropriate conditions,the global convergence and R-linear convergence rate of the proposed method are analyzed and proved.With no need of any derivative information,the proposed method is able to solve large-scale nonlinear monotone equations.Numerical comparisons show that the proposed method is effective.
