This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The pap...This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.展开更多
Utilizing the convex hull theory, a novel minimum zone circle （MZC） method, named im- proved minimum zone circle （IMZC） was developed in this paper. There were three steps for IMZC to evaluate the roundness error....Utilizing the convex hull theory, a novel minimum zone circle （MZC） method, named im- proved minimum zone circle （IMZC） was developed in this paper. There were three steps for IMZC to evaluate the roundness error. Firstly, with the convex hull algorithm, data points on the circle contour were categorized into two sets to determine two concentric circles which contained all points of the contour. Secondly, vertexes of the minimum circumscribed circle and the maximum inscribed circle were found out from the previously determined two sets, and then four tangent points for de- termining the two concentric circles were also found out. Lastly, according to the evaluation using the MZC method, the roundness error was figured out. In this paper l IMZC was used to evaluate roundness errors of some micro parts. The evaluation results showed that the measurement precision using the IMZC method was higher than the least squared circle （LSC） method for the same set of data points, and IMZC had the same accuracy as the traditional MZC but dramatically shortened com- putation time. The computation time of IMZC was 6. 89% of the traditional MZC.展开更多
Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, wh...Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, which can be used to solve directly the roundness of the measured round contour without Fourier transform, is presented. On the basis of the research and analysis of the rotation error movement which is separated by using the three-point method, a mathematical equation is derived, which can be used to separate the eccentric motion of least square center of measured round contour and the pure rotation motion error of spindle in rotation motion. The correctness of this method is validated by means of simulation.展开更多
with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hy...with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hyperbolic error which is caused in the process of processing cone, but about the discussion of hyperbolic error, there are two drawbacks in the current books and documents: (1) The error measuring plane is established on the rake face of tool, which doesn’t coincide with the actual measuring plane (axial plane) of work piece; (2) When the influential elements of error are analyzed, single parameter is only discussed. In order to overcome these demerits, the mathematical model of hyperbolic error on the axial plane of work piece is built in this paper when round body form tool processes cone. The fundamental reason which causes hyperbolic error when round body form tool processes cone is that the line profile replaces the curve profile of theory in the radial cut plane of tool in the design and manufacture of tool. In order to evaluate the mathematical formula of its error, firstly, the equation of cone of work piece must be established, secondly, the equation of cutting lip in the rake face is established, then, the profile equation of the radial plane of tool is evaluated on the condition that coordinate is changed, at last, the hyperbolic error is derived according to the equation and the substitutional line equation, and the error is converted to the axial plane of work piece which is coincided with the measuring plane. The actual calculation and the theory analysis indicated that if the cone length and the coning of the cone of work piece are fixed, the main elements which affect the hyperbolic error in the axial plane of work piece are the outside diameter R of round body form tool, the rake angle and the rear angle in "base point". If these three parameters are combined rationally, the hyperbolic error is minimum when round body form tool process cone, and the machining precision of work piece can be improved, on the condition that neither the work capacity of the tool design nor the manufacture cost of tool increases.展开更多
针对大数据传输中的数据机密性、完整性和数据丢失等问题,提出一种基于简化数据加密标准(Simplified Data Encryption Standard,SDES)和双轮差错控制的大数据集成安全系统。使用SDES加密算法生成加密字符串,并设计意外数据丢失备份系统...针对大数据传输中的数据机密性、完整性和数据丢失等问题,提出一种基于简化数据加密标准(Simplified Data Encryption Standard,SDES)和双轮差错控制的大数据集成安全系统。使用SDES加密算法生成加密字符串,并设计意外数据丢失备份系统以提高机密性和防止意外数据丢失。基于双轮差错控制以较低的空间开销控制传输过程中包含的任意数量的离散或连续错误位,基于固定长度编码(Fixed Length Coding,FLC)的无损压缩技术来减少数据开销。该算法具有较高的AE值、熵和压缩百分比,具有提供更高的数据机密性和完整性的潜力。展开更多
基金This study was supported by the National Key Basic Research and Development Project of China 2004CB418303 the National Natural Science foundation of China under Grant Nos. 40305012 and 40475027Jiangsu Key Laboratory of Meteorological Disaster KLME0601.
文摘This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.
基金Supported by the National Nature Science Foundation of China ( 51075035 )Beijing Training Program for the Talents( 210D00911000002)
文摘Utilizing the convex hull theory, a novel minimum zone circle （MZC） method, named im- proved minimum zone circle （IMZC） was developed in this paper. There were three steps for IMZC to evaluate the roundness error. Firstly, with the convex hull algorithm, data points on the circle contour were categorized into two sets to determine two concentric circles which contained all points of the contour. Secondly, vertexes of the minimum circumscribed circle and the maximum inscribed circle were found out from the previously determined two sets, and then four tangent points for de- termining the two concentric circles were also found out. Lastly, according to the evaluation using the MZC method, the roundness error was figured out. In this paper l IMZC was used to evaluate roundness errors of some micro parts. The evaluation results showed that the measurement precision using the IMZC method was higher than the least squared circle （LSC） method for the same set of data points, and IMZC had the same accuracy as the traditional MZC but dramatically shortened com- putation time. The computation time of IMZC was 6. 89% of the traditional MZC.
基金Henan Innovation Project for University Prominent Research Talents (2004KYCX006)Ph.D.Inital Foundation of Henan University of Science &Techonologythe Natural Science Foundation of Henan Education Agency (2008A460007)
文摘Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, which can be used to solve directly the roundness of the measured round contour without Fourier transform, is presented. On the basis of the research and analysis of the rotation error movement which is separated by using the three-point method, a mathematical equation is derived, which can be used to separate the eccentric motion of least square center of measured round contour and the pure rotation motion error of spindle in rotation motion. The correctness of this method is validated by means of simulation.
文摘with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hyperbolic error which is caused in the process of processing cone, but about the discussion of hyperbolic error, there are two drawbacks in the current books and documents: (1) The error measuring plane is established on the rake face of tool, which doesn’t coincide with the actual measuring plane (axial plane) of work piece; (2) When the influential elements of error are analyzed, single parameter is only discussed. In order to overcome these demerits, the mathematical model of hyperbolic error on the axial plane of work piece is built in this paper when round body form tool processes cone. The fundamental reason which causes hyperbolic error when round body form tool processes cone is that the line profile replaces the curve profile of theory in the radial cut plane of tool in the design and manufacture of tool. In order to evaluate the mathematical formula of its error, firstly, the equation of cone of work piece must be established, secondly, the equation of cutting lip in the rake face is established, then, the profile equation of the radial plane of tool is evaluated on the condition that coordinate is changed, at last, the hyperbolic error is derived according to the equation and the substitutional line equation, and the error is converted to the axial plane of work piece which is coincided with the measuring plane. The actual calculation and the theory analysis indicated that if the cone length and the coning of the cone of work piece are fixed, the main elements which affect the hyperbolic error in the axial plane of work piece are the outside diameter R of round body form tool, the rake angle and the rear angle in "base point". If these three parameters are combined rationally, the hyperbolic error is minimum when round body form tool process cone, and the machining precision of work piece can be improved, on the condition that neither the work capacity of the tool design nor the manufacture cost of tool increases.
