Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symm...Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, the positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.展开更多
Road horizontal alignment contains three elements: straight line,circular arc,and clothoid.In AutoCAD,clothoid can only be fitted by polyline or spline,and the graphics which are separated from the road data are indep...Road horizontal alignment contains three elements: straight line,circular arc,and clothoid.In AutoCAD,clothoid can only be fitted by polyline or spline,and the graphics which are separated from the road data are independent of each other.Therefore,it is necessary to develop a new curve for road horizontal alignment.Firstly,the differential approximation and series integration methods for clothoid were discussed.Secondly,the geometric formulae for road line which contain the three elements were derived as a whole.Then,the advantages and feasibility of customizing a road line class,which was derived from the curve base class,were analyzed based on ObjectARX(AutoCAD Runtime eXtension) techniques.Finally,the data structure and operations for the road line class were stressed.The experimental results show that the road line can integrate the road elements,graphics and data to implement the graphics-oriented design,which can be widely used in road alignment design.展开更多
There is still an obstacle to prevent neural network from wider and more effective applications, i.e., the lack of effective theories of models identification. Based on information theory and its generalization, this ...There is still an obstacle to prevent neural network from wider and more effective applications, i.e., the lack of effective theories of models identification. Based on information theory and its generalization, this paper introduces a universal method to achieve nonlinear models identification. Two key quantities, which are called nonlinear irreducible auto-correlation (NIAC) and generalized nonlinear irreducible auto-correlation (GNIAC), are defined and discussed. NIAC and GNIAC correspond with intrinstic irreducible auto-(dependency) (IAD) and generalized irreducible auto-(dependency) (GIAD) of time series respectively. By investigating the evolving trend of NIAC and GNIAC, the optimal auto-regressive order of nonlinear auto-regressive models could be determined naturally. Subsequently, an efficient algorithm computing NIAC and GNIAC is discussed. Experiments on simulating data sets and typical nonlinear prediction models indicate remarkable correlation between optimal auto-regressive order and the highest order that NIAC-GNIAC have a remarkable non-zero value, therefore demonstrate the validity of the proposal in this paper.展开更多
We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the ...We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.展开更多
文摘为了全面反映高速铁路线路空间线形作用下的轮轨动态相互作用特征,基于车辆-轨道耦合动力学理论,综合考虑车辆系统与轨道系统的动力响应,提出了高速铁路线路空间线形的动力学评价指标体系研究方法.针对高速铁路平纵断面参数,确定了变化敏感的动力学指标,并给出了具体的高速铁路空间线形评价指标.以高速铁路纵断面线形评价为例,详细介绍了该研究方法的应用与实施过程,在此基础上,给出了高速铁路纵断面的参数设计建议.研究结果表明:在时速为350 km高速铁路线路线形参数的设计过程中,竖曲线的设计原则是应尽可能采用较小的坡度及较大的竖曲线半径,且夹坡段长度不小于300 m.
基金Project(40674071) supported by the National Natural Science Foundation of Chinaproject(KFAS2002-2003) supported by Korea Foundation for Advanced Studies
文摘Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, the positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.
基金Project(51108049)supported by the National Natural Science Foundation of ChinaProject(kfj090207)supported by Open Fund of Key Laboratory of Road Structure and Material of Ministry of Transport(Changsha University of Science and Technology),China
文摘Road horizontal alignment contains three elements: straight line,circular arc,and clothoid.In AutoCAD,clothoid can only be fitted by polyline or spline,and the graphics which are separated from the road data are independent of each other.Therefore,it is necessary to develop a new curve for road horizontal alignment.Firstly,the differential approximation and series integration methods for clothoid were discussed.Secondly,the geometric formulae for road line which contain the three elements were derived as a whole.Then,the advantages and feasibility of customizing a road line class,which was derived from the curve base class,were analyzed based on ObjectARX(AutoCAD Runtime eXtension) techniques.Finally,the data structure and operations for the road line class were stressed.The experimental results show that the road line can integrate the road elements,graphics and data to implement the graphics-oriented design,which can be widely used in road alignment design.
文摘There is still an obstacle to prevent neural network from wider and more effective applications, i.e., the lack of effective theories of models identification. Based on information theory and its generalization, this paper introduces a universal method to achieve nonlinear models identification. Two key quantities, which are called nonlinear irreducible auto-correlation (NIAC) and generalized nonlinear irreducible auto-correlation (GNIAC), are defined and discussed. NIAC and GNIAC correspond with intrinstic irreducible auto-(dependency) (IAD) and generalized irreducible auto-(dependency) (GIAD) of time series respectively. By investigating the evolving trend of NIAC and GNIAC, the optimal auto-regressive order of nonlinear auto-regressive models could be determined naturally. Subsequently, an efficient algorithm computing NIAC and GNIAC is discussed. Experiments on simulating data sets and typical nonlinear prediction models indicate remarkable correlation between optimal auto-regressive order and the highest order that NIAC-GNIAC have a remarkable non-zero value, therefore demonstrate the validity of the proposal in this paper.
基金supported by the National Natural Science Foundation ofChina (No. 60673031)the National Basic Research Program(973) of China (No. 2004CB719400)
文摘We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.
