In order to diminish the impacts of extemal disturbance such as parking speed fluctuation and model un- certainty existing in steering kinematics, this paper presents a parallel path tracking method for vehicle based ...In order to diminish the impacts of extemal disturbance such as parking speed fluctuation and model un- certainty existing in steering kinematics, this paper presents a parallel path tracking method for vehicle based on pre- view back propagation （BP） neural network PID controller. The forward BP neural network can adjust the parameters of PID controller in real time. The preview time is optimized by considering path curvature, change in curvature and road boundaries. A fuzzy controller considering barriers and different road conditions is built to select the starting po- sition. In addition, a kind of path planning technology satisfying the requirement of obstacle avoidance is introduced. In order to solve the problem of discontinuous curvature, cubic B spline curve is used for curve fitting. The simulation results and real vehicle tests validate the effectiveness of the proposed path planning and tracking methods.展开更多
This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numer...This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations （ODEs）, in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.展开更多
This paper deals with the computer modeling of structures starting from a point cloud. The CCTV （China Central Television） tower headquarters is the case for study because the shape of this building is non-stellar, ...This paper deals with the computer modeling of structures starting from a point cloud. The CCTV （China Central Television） tower headquarters is the case for study because the shape of this building is non-stellar, concave and multi-connected. It is composed of sowns and chains. The sown is the representation of a horizontal plane formed by dense points. The chain is a planar path modeled by rare points. The CCTV structure is defined only by the three orthogonal Cartesian coordinates of the points. The proposed computer modeling uses a sequence of procedures and the desired outputted 3D model is consistent. The first procedure is devoted to attributing points to their voxel and to estimating three values needed afterwards. The second procedure is devoted to analyzing clusters vertically and horizontally, to preliminarily distinguishing chains from sowns and to generating relational matching. The third procedure is devoted to building closed paths between all chains and all their projections on sowns. The fourth procedure is devoted to connecting points with triangles. The fifth procedure, still being implemented, is devoted to interpolating triangles with triangular splines. The results show it is possible to achieve the 3D model using the above mentioned procedures. These procedures are written, implemented and tested and they form a library of people＇s own software. The code is written using Matlab. It is not possible to obtain the required 3D model if the procedures are applied in the wrong order or one step is skipped. To conclude, it is possible to obtain the computer model of the CCTV using the provided sequence of procedures.展开更多
The authors study vanishing viscosity limits of solutions to the 3-dimensional incompressible Navier-Stokes system in general smooth domains with curved boundaries for a class of slip boundary conditions. In contrast ...The authors study vanishing viscosity limits of solutions to the 3-dimensional incompressible Navier-Stokes system in general smooth domains with curved boundaries for a class of slip boundary conditions. In contrast to the case of flat boundaries, where the uniform convergence in super-norm can be obtained, the asymptotic behavior of viscous solutions for small viscosity depends on the curvature of the boundary in general. It is shown, in particular, that the viscous solution converges to that of the ideal Euler equations in C（[0, T]; HI（Ω）） provided that the initial vorticity vanishes on the boundary of the domain.展开更多
基金Supported by the National Natural Science Foundation of China(No.11072106,No.51005133 and No.51375009)
文摘In order to diminish the impacts of extemal disturbance such as parking speed fluctuation and model un- certainty existing in steering kinematics, this paper presents a parallel path tracking method for vehicle based on pre- view back propagation （BP） neural network PID controller. The forward BP neural network can adjust the parameters of PID controller in real time. The preview time is optimized by considering path curvature, change in curvature and road boundaries. A fuzzy controller considering barriers and different road conditions is built to select the starting po- sition. In addition, a kind of path planning technology satisfying the requirement of obstacle avoidance is introduced. In order to solve the problem of discontinuous curvature, cubic B spline curve is used for curve fitting. The simulation results and real vehicle tests validate the effectiveness of the proposed path planning and tracking methods.
文摘This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations （ODEs）, in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.
文摘This paper deals with the computer modeling of structures starting from a point cloud. The CCTV （China Central Television） tower headquarters is the case for study because the shape of this building is non-stellar, concave and multi-connected. It is composed of sowns and chains. The sown is the representation of a horizontal plane formed by dense points. The chain is a planar path modeled by rare points. The CCTV structure is defined only by the three orthogonal Cartesian coordinates of the points. The proposed computer modeling uses a sequence of procedures and the desired outputted 3D model is consistent. The first procedure is devoted to attributing points to their voxel and to estimating three values needed afterwards. The second procedure is devoted to analyzing clusters vertically and horizontally, to preliminarily distinguishing chains from sowns and to generating relational matching. The third procedure is devoted to building closed paths between all chains and all their projections on sowns. The fourth procedure is devoted to connecting points with triangles. The fifth procedure, still being implemented, is devoted to interpolating triangles with triangular splines. The results show it is possible to achieve the 3D model using the above mentioned procedures. These procedures are written, implemented and tested and they form a library of people＇s own software. The code is written using Matlab. It is not possible to obtain the required 3D model if the procedures are applied in the wrong order or one step is skipped. To conclude, it is possible to obtain the computer model of the CCTV using the provided sequence of procedures.
基金Project supported by the National Natural Science Foundation of China(No.10971174)the Scientific Research Fund of Hunan Provincial Education Department(No.08A070)+1 种基金the Zheng Ge Ru Foundation, the Hong Kong RGC Earmarked Research Grants(Nos.CUHK-4040/06P,CUHK-4042/08P)a Focus Area Grant at The Chinese University of Hong Kong
文摘The authors study vanishing viscosity limits of solutions to the 3-dimensional incompressible Navier-Stokes system in general smooth domains with curved boundaries for a class of slip boundary conditions. In contrast to the case of flat boundaries, where the uniform convergence in super-norm can be obtained, the asymptotic behavior of viscous solutions for small viscosity depends on the curvature of the boundary in general. It is shown, in particular, that the viscous solution converges to that of the ideal Euler equations in C（[0, T]; HI（Ω）） provided that the initial vorticity vanishes on the boundary of the domain.
