The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of chara...The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O( N^-1 ) is regained by using the B-splines smoothed rejection method in importance sampling.展开更多
We propose a new method for smoothly interpolating a given set of data points on Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm.To that end,we reduce interpolation problem to the ...We propose a new method for smoothly interpolating a given set of data points on Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm.To that end,we reduce interpolation problem to the classical Euclidean setting,allowing us to directly leverage the extensive toolbox of spline interpolation.The interpolated curve enjoy a number of nice properties:The solution exists and is optimal in many common situations.For applications,the structures with respect to chosen Riemannian metrics are detailed resulting in additional computational advantages.展开更多
This paper presents a parallel implementation of computing uniform bicubic B spline surfaces on Transputer networks. The work is essential for building Transputer based CAD and graphics systems.
Hydraulic valve block is an important part of the hydraulic system.The traditional hydraulic valve block is made by turning and milling,drilling and boring,which leads to many right-angle bending and closed cavity str...Hydraulic valve block is an important part of the hydraulic system.The traditional hydraulic valve block is made by turning and milling,drilling and boring,which leads to many right-angle bending and closed cavity structure of process holes in its internal flow channel,seriously affecting the flow performance of oil.Based on the new design space provided by additive manufacturing technology,the internal hydraulic flow channel of valve block is optimized by using B-spline curve.Computational fluid dynamics analysis is carried out on the hydraulic flow channel to determine the optimal flow channel structure with the smallest pressure drop.The weight reduction of hydraulic valve block is carried out through topology optimization.According to the results of topology optimization,using the method of selective laser melting(SLM),the printing of the hydraulic valve block is completed.The optimized hydraulic channel reduces the pressure loss by 31.4%compared with the traditional hydraulic channel.Compared with the traditional valve block,the hydraulic valve block manufactured by SLM with topology optimization reduces the weight by 33.9%.Therefore,the proposed flow channel optimization and valve block lightweight method provide a new reference for the performance improvement of the internal flow channel of hydraulic valve block and the overall lightweight design of valve block.展开更多
With application of the lock-up clutch in the torque converter（TC）, fuel economy is not much determined by its high-speed ratio transmission efficiency. As a benefit, more researches are focused on its low-speed rat...With application of the lock-up clutch in the torque converter（TC）, fuel economy is not much determined by its high-speed ratio transmission efficiency. As a benefit, more researches are focused on its low-speed ratio performance so as to improve vehicle gradeability and launching acceleration performance. According to the results of computational fluid dynamics（CFD） analysis, hydrodynamic loss inside the stator cascade accounts for 42% of the total energy loss at stalling speed ratio. It is found that upstream flow with large impingement angle results in boundary layer separation at the leading edge, which aggregates hydrodynamic loss and decreases circular flow rate dramatically at low-speed ratio. In this paper, a dual-blade stator is proposed to suppress the boundary layer separation, which is parameterized by using the non-uniform rational B spline（NURBS） method. The mean camber line and blade profile curve are expressed by a three control points quadratic open NURBS and a cubic closed one respectively. The key design parameters included the slot width and suction side shape of the primary blade are analyzed. The most effective slot width is found to be between 4% and 8% chord length, and the boundary layer separation can be suppressed completely by decreasing distribution of momentum moment at the primary blade and adding it to the leading edge of the secondary blade. As a result, circular flow rate and impeller torque capacity is increased by 17.9% and 9.6% respectively at stalling speed ratio, meanwhile, low-speed ratio efficiency is also improved. Maximum efficiency at high-speed ratio decreases by 0.5%, which can be ignored as the work of lock-up clutch. This research focuses on using the dual-blade stator to optimize low-speed ratio performance of the TC, which is benefit to vehicle power performance.展开更多
Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method n...Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.展开更多
In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable...In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.展开更多
Flatness and profile are important quality indexes of strip. Combining the influence function method to solve the elastic deformation of roll system with the variational method to solve the lateral flow of metal, the ...Flatness and profile are important quality indexes of strip. Combining the influence function method to solve the elastic deformation of roll system with the variational method to solve the lateral flow of metal, the flatness and profile of the strip during cold continuous rolling were simulated. The B 3 spline function was used to analogize the lateral distribution of strip thickness. The transverse distributions of the exit thickness and the front tension stress for each pass were obtained. Compared with the measured results, it is proved that using the spline function to analogize the lateral distribution of strip thickness can improve the calculation accuracy of flatness and profile largely.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
Curve and surface interpolation is the core of geometric modeling. The paper gives a new method to interpolate B spline curves and surfaces based on nonlinear optimization. The beauties of the method are: it is not ne...Curve and surface interpolation is the core of geometric modeling. The paper gives a new method to interpolate B spline curves and surfaces based on nonlinear optimization. The beauties of the method are: it is not necessary to calculate parameter values of data points, and the curves and surfaces generated have good behavior of fairness. The theory and procedures of the method are introduced in detail, the differences between the conventional method and the new one are discussed, and some figures generated by this new technique are presented.展开更多
文摘The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O( N^-1 ) is regained by using the B-splines smoothed rejection method in importance sampling.
文摘We propose a new method for smoothly interpolating a given set of data points on Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm.To that end,we reduce interpolation problem to the classical Euclidean setting,allowing us to directly leverage the extensive toolbox of spline interpolation.The interpolated curve enjoy a number of nice properties:The solution exists and is optimal in many common situations.For applications,the structures with respect to chosen Riemannian metrics are detailed resulting in additional computational advantages.
文摘This paper presents a parallel implementation of computing uniform bicubic B spline surfaces on Transputer networks. The work is essential for building Transputer based CAD and graphics systems.
基金supported by the National Natural Science Foundation of China(No.51775273)the Jiangsu Province Science and Technology Support Plan Project(No.BE2018010-2)+2 种基金the National Defence Basic Scientific Research Program of China(No.JCKY2018605C010)the Frontiers of Science and Technology Program of China (No.1816312ZT00406301)the Aeronautical Science Foundation of China(No.2020Z049052002)
文摘Hydraulic valve block is an important part of the hydraulic system.The traditional hydraulic valve block is made by turning and milling,drilling and boring,which leads to many right-angle bending and closed cavity structure of process holes in its internal flow channel,seriously affecting the flow performance of oil.Based on the new design space provided by additive manufacturing technology,the internal hydraulic flow channel of valve block is optimized by using B-spline curve.Computational fluid dynamics analysis is carried out on the hydraulic flow channel to determine the optimal flow channel structure with the smallest pressure drop.The weight reduction of hydraulic valve block is carried out through topology optimization.According to the results of topology optimization,using the method of selective laser melting(SLM),the printing of the hydraulic valve block is completed.The optimized hydraulic channel reduces the pressure loss by 31.4%compared with the traditional hydraulic channel.Compared with the traditional valve block,the hydraulic valve block manufactured by SLM with topology optimization reduces the weight by 33.9%.Therefore,the proposed flow channel optimization and valve block lightweight method provide a new reference for the performance improvement of the internal flow channel of hydraulic valve block and the overall lightweight design of valve block.
基金Supported by National Natural Science Foundation of China(Grant No.51575393)
文摘With application of the lock-up clutch in the torque converter（TC）, fuel economy is not much determined by its high-speed ratio transmission efficiency. As a benefit, more researches are focused on its low-speed ratio performance so as to improve vehicle gradeability and launching acceleration performance. According to the results of computational fluid dynamics（CFD） analysis, hydrodynamic loss inside the stator cascade accounts for 42% of the total energy loss at stalling speed ratio. It is found that upstream flow with large impingement angle results in boundary layer separation at the leading edge, which aggregates hydrodynamic loss and decreases circular flow rate dramatically at low-speed ratio. In this paper, a dual-blade stator is proposed to suppress the boundary layer separation, which is parameterized by using the non-uniform rational B spline（NURBS） method. The mean camber line and blade profile curve are expressed by a three control points quadratic open NURBS and a cubic closed one respectively. The key design parameters included the slot width and suction side shape of the primary blade are analyzed. The most effective slot width is found to be between 4% and 8% chord length, and the boundary layer separation can be suppressed completely by decreasing distribution of momentum moment at the primary blade and adding it to the leading edge of the secondary blade. As a result, circular flow rate and impeller torque capacity is increased by 17.9% and 9.6% respectively at stalling speed ratio, meanwhile, low-speed ratio efficiency is also improved. Maximum efficiency at high-speed ratio decreases by 0.5%, which can be ignored as the work of lock-up clutch. This research focuses on using the dual-blade stator to optimize low-speed ratio performance of the TC, which is benefit to vehicle power performance.
基金Project (No. G1998030401) supported by the National Natural Sci-ence Foundation of China
文摘Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.
文摘In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.
基金Item Sponsored by National Natural Science Foundation of China(50275130)Provincial Natural Science Foundation of Hebei of China(E200400223)
文摘Flatness and profile are important quality indexes of strip. Combining the influence function method to solve the elastic deformation of roll system with the variational method to solve the lateral flow of metal, the flatness and profile of the strip during cold continuous rolling were simulated. The B 3 spline function was used to analogize the lateral distribution of strip thickness. The transverse distributions of the exit thickness and the front tension stress for each pass were obtained. Compared with the measured results, it is proved that using the spline function to analogize the lateral distribution of strip thickness can improve the calculation accuracy of flatness and profile largely.
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.
文摘Curve and surface interpolation is the core of geometric modeling. The paper gives a new method to interpolate B spline curves and surfaces based on nonlinear optimization. The beauties of the method are: it is not necessary to calculate parameter values of data points, and the curves and surfaces generated have good behavior of fairness. The theory and procedures of the method are introduced in detail, the differences between the conventional method and the new one are discussed, and some figures generated by this new technique are presented.
