When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The q...When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.展开更多
In response to the problems of low sampling efficiency,strong randomness of sampling points,and the tortuous shape of the planned path in the traditional rapidly-exploring random tree(RRT)algorithm and bidirectional R...In response to the problems of low sampling efficiency,strong randomness of sampling points,and the tortuous shape of the planned path in the traditional rapidly-exploring random tree(RRT)algorithm and bidirectional RRT algorithm used for unmanned aerial vehicle(UAV)path planning in complex environments,an improved bidirectional RRT algorithm was proposed.The algorithm firstly adopted a goal-oriented strategy to guide the sampling points towards the target point,and then the artificial potential field acted on the random tree nodes to avoid collision with obstacles and reduced the length of the search path,and the random tree node growth also combined the UAV’s own flight constraints,and by combining the triangulation method to remove the redundant node strategy and the third-order B-spline curve for the smoothing of the trajectory,the planned path was better.The planned paths were more optimized.Finally,the simulation experiments in complex and dynamic environments showed that the algorithm effectively improved the speed of trajectory planning and shortened the length of the trajectory,and could generate a safe,smooth and fast trajectory in complex environments,which could be applied to online trajectory planning.展开更多
Modern high speed machining (HSM) machine tools often operates at high speed and high feedrate with high ac- celerations,in order to deliver the rapid feed motion.This paper presents an interpolation algorithm to gene...Modern high speed machining (HSM) machine tools often operates at high speed and high feedrate with high ac- celerations,in order to deliver the rapid feed motion.This paper presents an interpolation algorithm to generate continuous quintic spline toolpaths,with a constant travel increment at each step,while the smoother accelerations and jerks of two-order curve are obtained.Then an approach for reducing the feedrate fluctuation in high speed spline interpolation is presented.The presented ap- proach has been validated to quickly,reliably and effective with the simulation.展开更多
As electro-hydrostatic actuator(EHA)technology advances towards lightweight and integration,the demand for enhanced internal flow pathways in hydraulic valve blocks intensifies.However,owing to the constraints imposed...As electro-hydrostatic actuator(EHA)technology advances towards lightweight and integration,the demand for enhanced internal flow pathways in hydraulic valve blocks intensifies.However,owing to the constraints imposed by traditional manufacturing processes,conventional hydraulic integrated valve blocks fail to satisfy the demands of a more compact channel layout and lower energy dissipation.Notably,the subjectivity in the arrangement of internal passages results in a time-consuming and labor-intensive process.This study employed additive manufacturing technology and the ant colony algorithm and B-spline curves for the meticulous design of internal passages within an aviation EHA valve block.The layout environment for the valve block passages was established,and path optimization was achieved using the ant colony algorithm,complemented by smoothing using B-spline curves.Three-dimensional modeling was performed using SolidWorks software,revealing a 10.03%reduction in volume for the optimized passages compared with the original passages.Computational fluid dynamics(CFD)simulations were performed using Fluent software,demonstrating that the algorithmically optimized passages effectively prevented the occurrence of vortices at right-angled locations,exhibited superior flow characteristics,and concurrently reduced pressure losses by 34.09%-36.36%.The small discrepancy between the experimental and simulation results validated the efficacy of the ant colony algorithm and B-spline curves in optimizing the passage design,offering a viable solution for channel design in additive manufacturing.展开更多
The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plan...The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.展开更多
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （...Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.展开更多
Directly applying the B-spline interpolation function to process plate cams in a computer numerical control(CNC)system may produce verbose tool-path codes and unsmooth trajectories.This paper is devoted to addressing ...Directly applying the B-spline interpolation function to process plate cams in a computer numerical control(CNC)system may produce verbose tool-path codes and unsmooth trajectories.This paper is devoted to addressing the problem of B-splinefitting for cam pitch curves.Considering that the B-spline curve needs to meet the motion law of the follower to approximate the pitch curve,we use the radial error to quantify the effects of thefitting B-spline curve and the pitch curve.The problem thus boils down to solving a difficult global optimization problem tofind the numbers and positions of the control points or data points of the B-spline curve such that the cumulative radial error between thefitting curve and the original curve is minimized,and this problem is attempted in this paper with a double deep Q-network(DDQN)reinforcement learning(RL)algorithm with data points traceability.Specifically,the RL envir-onment,actions set and current states set are designed to facilitate the search of the data points,along with the design of the reward function and the initialization of the neural network.The experimental results show that when the angle division value of the actions set isfixed,the proposed algorithm can maximize the number of data points of the B-spline curve,and accurately place these data points to the right positions,with the minimum average of radial errors.Our work establishes the theoretical foundation for studying splinefitting using the RL method.展开更多
Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an...Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an image,including different translations, scales, and orientations, can be performedusing these parametric curves. For this, Bézier and B-spline curves can be generatedusing a point set that belongs to the outer boundary of the object. Theresulting object shape can be used in computer vision fields, such as searchingand segmentation methods and training machine learning algorithms. Theprerequisite for reconstructing the shape with parametric curves is to obtainsequentially the points in the point set. In this study, a novel algorithm hasbeen developed that sequentially obtains the pixel locations constituting theouter boundary of the object. The proposed algorithm, unlike the methods inthe literature, is implemented using a filter containing weights and an outercircle surrounding the object. In a binary format image, the starting point ofthe tracing is determined using the outer circle, and the next tracing movementand the pixel to be labeled as the boundary point is found by the filter weights.Then, control points that define the curve shape are selected by reducing thenumber of sequential points. Thus, the Bézier and B-spline curve equationsdescribing the shape are obtained using these points. In addition, differenttranslations, scales, and rotations of the object shape are easily provided bychanging the positions of the control points. It has also been shown that themissing part of the object can be completed thanks to the parametric curves.展开更多
According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a k...According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N>2) patch B-spline surfaces meeting at a common corner are given at the end.展开更多
Through a precise recursion of B-spline bases and the resursive expression of the derivatives of rational surfaces, this paper presents an efficient algorithm for the calculation of NURBS surfaces and all their direct...Through a precise recursion of B-spline bases and the resursive expression of the derivatives of rational surfaces, this paper presents an efficient algorithm for the calculation of NURBS surfaces and all their directional derivatives. The algorithm requires less storage and proves to be stable.展开更多
Through a precise recursion of B-spline bases, this paper presents an efficient algorithm for the calculation of NURBS curves and all their derivatives. The algorithm requires less storage and is proved to be stable.
文摘When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.
基金supported by Gansu Provincial Science and Technology Program Project(No.23JRRA868)Lanzhou Municipal Talent Innovation and Entrepreneurship Project(No.2019-RC-103)。
文摘In response to the problems of low sampling efficiency,strong randomness of sampling points,and the tortuous shape of the planned path in the traditional rapidly-exploring random tree(RRT)algorithm and bidirectional RRT algorithm used for unmanned aerial vehicle(UAV)path planning in complex environments,an improved bidirectional RRT algorithm was proposed.The algorithm firstly adopted a goal-oriented strategy to guide the sampling points towards the target point,and then the artificial potential field acted on the random tree nodes to avoid collision with obstacles and reduced the length of the search path,and the random tree node growth also combined the UAV’s own flight constraints,and by combining the triangulation method to remove the redundant node strategy and the third-order B-spline curve for the smoothing of the trajectory,the planned path was better.The planned paths were more optimized.Finally,the simulation experiments in complex and dynamic environments showed that the algorithm effectively improved the speed of trajectory planning and shortened the length of the trajectory,and could generate a safe,smooth and fast trajectory in complex environments,which could be applied to online trajectory planning.
文摘Modern high speed machining (HSM) machine tools often operates at high speed and high feedrate with high ac- celerations,in order to deliver the rapid feed motion.This paper presents an interpolation algorithm to generate continuous quintic spline toolpaths,with a constant travel increment at each step,while the smoother accelerations and jerks of two-order curve are obtained.Then an approach for reducing the feedrate fluctuation in high speed spline interpolation is presented.The presented ap- proach has been validated to quickly,reliably and effective with the simulation.
基金Supported by National Natural Science Foundation of China(Grant No.51890881)。
文摘As electro-hydrostatic actuator(EHA)technology advances towards lightweight and integration,the demand for enhanced internal flow pathways in hydraulic valve blocks intensifies.However,owing to the constraints imposed by traditional manufacturing processes,conventional hydraulic integrated valve blocks fail to satisfy the demands of a more compact channel layout and lower energy dissipation.Notably,the subjectivity in the arrangement of internal passages results in a time-consuming and labor-intensive process.This study employed additive manufacturing technology and the ant colony algorithm and B-spline curves for the meticulous design of internal passages within an aviation EHA valve block.The layout environment for the valve block passages was established,and path optimization was achieved using the ant colony algorithm,complemented by smoothing using B-spline curves.Three-dimensional modeling was performed using SolidWorks software,revealing a 10.03%reduction in volume for the optimized passages compared with the original passages.Computational fluid dynamics(CFD)simulations were performed using Fluent software,demonstrating that the algorithmically optimized passages effectively prevented the occurrence of vortices at right-angled locations,exhibited superior flow characteristics,and concurrently reduced pressure losses by 34.09%-36.36%.The small discrepancy between the experimental and simulation results validated the efficacy of the ant colony algorithm and B-spline curves in optimizing the passage design,offering a viable solution for channel design in additive manufacturing.
基金Supported by Hi -tech Research and Development Program of China(No. 2001AA421200).
文摘The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.
基金financially supported by the National Natural Science Foundation of China(11202081,11272124,and 11472109)the State Key Lab of Subtropical Building Science,South China University of Technology(2014ZC17)
文摘Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
基金supported by Fujian Province Nature Science Foundation under Grant No.2018J01553.
文摘Directly applying the B-spline interpolation function to process plate cams in a computer numerical control(CNC)system may produce verbose tool-path codes and unsmooth trajectories.This paper is devoted to addressing the problem of B-splinefitting for cam pitch curves.Considering that the B-spline curve needs to meet the motion law of the follower to approximate the pitch curve,we use the radial error to quantify the effects of thefitting B-spline curve and the pitch curve.The problem thus boils down to solving a difficult global optimization problem tofind the numbers and positions of the control points or data points of the B-spline curve such that the cumulative radial error between thefitting curve and the original curve is minimized,and this problem is attempted in this paper with a double deep Q-network(DDQN)reinforcement learning(RL)algorithm with data points traceability.Specifically,the RL envir-onment,actions set and current states set are designed to facilitate the search of the data points,along with the design of the reward function and the initialization of the neural network.The experimental results show that when the angle division value of the actions set isfixed,the proposed algorithm can maximize the number of data points of the B-spline curve,and accurately place these data points to the right positions,with the minimum average of radial errors.Our work establishes the theoretical foundation for studying splinefitting using the RL method.
文摘Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an image,including different translations, scales, and orientations, can be performedusing these parametric curves. For this, Bézier and B-spline curves can be generatedusing a point set that belongs to the outer boundary of the object. Theresulting object shape can be used in computer vision fields, such as searchingand segmentation methods and training machine learning algorithms. Theprerequisite for reconstructing the shape with parametric curves is to obtainsequentially the points in the point set. In this study, a novel algorithm hasbeen developed that sequentially obtains the pixel locations constituting theouter boundary of the object. The proposed algorithm, unlike the methods inthe literature, is implemented using a filter containing weights and an outercircle surrounding the object. In a binary format image, the starting point ofthe tracing is determined using the outer circle, and the next tracing movementand the pixel to be labeled as the boundary point is found by the filter weights.Then, control points that define the curve shape are selected by reducing thenumber of sequential points. Thus, the Bézier and B-spline curve equationsdescribing the shape are obtained using these points. In addition, differenttranslations, scales, and rotations of the object shape are easily provided bychanging the positions of the control points. It has also been shown that themissing part of the object can be completed thanks to the parametric curves.
文摘According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N>2) patch B-spline surfaces meeting at a common corner are given at the end.
基金Supported by National Science Foundation of China,China Postdoctral Science Foundation863 projects。
文摘Through a precise recursion of B-spline bases and the resursive expression of the derivatives of rational surfaces, this paper presents an efficient algorithm for the calculation of NURBS surfaces and all their directional derivatives. The algorithm requires less storage and proves to be stable.
文摘Through a precise recursion of B-spline bases, this paper presents an efficient algorithm for the calculation of NURBS curves and all their derivatives. The algorithm requires less storage and is proved to be stable.
