The stability analysis problems were put forward for the large-scale systems with time-delay by using the partial decomposition method. With the stability of the isolated subsystems without time- delay, some sufficien...The stability analysis problems were put forward for the large-scale systems with time-delay by using the partial decomposition method. With the stability of the isolated subsystems without time- delay, some sufficient criterions for the asymptotical stability of the whole system were obtained by making a Lyapunov function with the Razumikhin condition and a Lyapunov functional for the retarded type and neutral type, respectively.展开更多
The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and ...The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.展开更多
为了更合理有效地评价轨道质量,将轨道不平顺波长因素纳入轨道质量评价中,提出基于本征模函数(intrinsicmode function,IMF)的轨道质量评价方法——轨道质量能量指标(track quality energy index,TQEI).通过对轨道不平顺数据进行经验模...为了更合理有效地评价轨道质量,将轨道不平顺波长因素纳入轨道质量评价中,提出基于本征模函数(intrinsicmode function,IMF)的轨道质量评价方法——轨道质量能量指标(track quality energy index,TQEI).通过对轨道不平顺数据进行经验模态分解得到对应波长频段的不平顺IMF,利用频谱分析的方法求得各个IMF的能量;将各个IMF的能量与总能量的比值作为特征向量,并进行量纲一化处理,从而得到轨道不平顺IMF的能量系数;利用能量系数求得TQEI.通过理论推导证明了轨道质量数(track qualityindex,TQI)是在不考虑波长因素作用下轨道质量能量指标的特殊形式.最后,以京广提速干线轨道不平顺数据为例,对比分析了实际检测数据TQEI与TQI的关系.结果表明:轨道质量能量指标是对TQI的细化和延续,其既起到了TQI的幅值管理作用,又可以弥补TQI在波长及幅值管理方面的缺陷,可以准确有效地对轨道质量进行评价.展开更多
A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to...A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.展开更多
The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solu...The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffier functions of matric argument. The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1, the result here is simplified to that of first order differential equation.展开更多
文摘The stability analysis problems were put forward for the large-scale systems with time-delay by using the partial decomposition method. With the stability of the isolated subsystems without time- delay, some sufficient criterions for the asymptotical stability of the whole system were obtained by making a Lyapunov function with the Razumikhin condition and a Lyapunov functional for the retarded type and neutral type, respectively.
文摘The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.
文摘A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.
基金Supported by the NNSF of China(1027206710461005) the Scientific Research Foundation of Tianjin Education Committee(20050404).
文摘The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffier functions of matric argument. The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1, the result here is simplified to that of first order differential equation.
