Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and the...Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and their influences are not fully investigated yet.In this work,three main factors,i.e.,the shape parameters,the influence domain size,and the nodal distribution,on the accuracy of the radial point interpolation method(RPIM)are systematically studied and conclusive results are obtained.First,the effect of shape parameters(R,q)of the multi-quadric basis function on the accuracy of RPIM is examined via global search.A new interpolation error index,closely related to the accuracy of RPIM,is proposed.The distribution of various error indexes on the R q plane shows that shape parameters q[1.2,1.8]and R[0,1.5]can give good results for general 3-D analysis.This recommended range of shape parameters is examined by multiple benchmark examples in 3D solid mechanics.Second,through numerical experiments,an average of 30 40 nodes in the influence domain of a Gauss point is recommended for 3-D solid mechanics.Third,it is observed that the distribution of nodes has significant effect on the accuracy of RPIM although it has little effect on the accuracy of interpolation.Nodal distributions with better uniformity give better results.Furthermore,how the influence domain size and nodal distribution affect the selection of shape parameters and how the nodal distribution affects the choice of influence domain size are also discussed.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
为设计高效稳定的演化算法,将方程求根的不动点迭代思想引入到优化领域,通过将演化算法的寻优过程看作为在迭代框架下方程不动点的逐步显示化过程,设计出一种基于数学模型的演化新算法,即不动点演化算法(fixed point evolution algorith...为设计高效稳定的演化算法,将方程求根的不动点迭代思想引入到优化领域,通过将演化算法的寻优过程看作为在迭代框架下方程不动点的逐步显示化过程,设计出一种基于数学模型的演化新算法,即不动点演化算法(fixed point evolution algorithm,FPEA).该算法的繁殖算子是由Aitken加速的不动点迭代模型导出的二次多项式,其整体框架继承传统演化算法(如差分演化算法)基于种群的迭代模式.试验结果表明:在基准函数集CEC2014、CEC2019上,本文算法的最优值平均排名在所有比较算法中排名第1;在4个工程约束设计问题上,FPEA与CSA、GPE等多个算法相比,能以较少的计算开销获得最高的求解精度.展开更多
随着新能源发电比例越来越高,其受电网三相不平衡的影响越来越明显,尤其负序超标是导致电力系统安全性降低的重要原因。统一潮流控制器(unified power flow controller,UPFC)具有调节各序电流输出的能力,可用于提升系统的平衡性。为此,...随着新能源发电比例越来越高,其受电网三相不平衡的影响越来越明显,尤其负序超标是导致电力系统安全性降低的重要原因。统一潮流控制器(unified power flow controller,UPFC)具有调节各序电流输出的能力,可用于提升系统的平衡性。为此,首先建立基于解耦-补偿原理的UPFC正序最优补偿潮流算法;其次构建UPFC的负序补偿电流控制模型,将电压不平衡补偿的优化求解问题归结为凸二次约束二次规划(quadratically constrained quadratic programming,QCQP)问题,并采用原-对偶内点法求取UPFC的负序电流最优输出值;最后提出计及正序网损与负序电压指标的负序电压补偿最优潮流(optimal power flow,OPF)计算方法以及区域负序电压总体补偿策略。通过算例分析验证所提出方法的可行性与有效性。展开更多
基金Project(2010CB732103)supported by the National Basic Research Program of ChinaProject(51179092)supported by the National Natural Science Foundation of ChinaProject(2012-KY-02)supported by the State Key Laboratory of Hydroscience and Engineering,China
文摘Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and their influences are not fully investigated yet.In this work,three main factors,i.e.,the shape parameters,the influence domain size,and the nodal distribution,on the accuracy of the radial point interpolation method(RPIM)are systematically studied and conclusive results are obtained.First,the effect of shape parameters(R,q)of the multi-quadric basis function on the accuracy of RPIM is examined via global search.A new interpolation error index,closely related to the accuracy of RPIM,is proposed.The distribution of various error indexes on the R q plane shows that shape parameters q[1.2,1.8]and R[0,1.5]can give good results for general 3-D analysis.This recommended range of shape parameters is examined by multiple benchmark examples in 3D solid mechanics.Second,through numerical experiments,an average of 30 40 nodes in the influence domain of a Gauss point is recommended for 3-D solid mechanics.Third,it is observed that the distribution of nodes has significant effect on the accuracy of RPIM although it has little effect on the accuracy of interpolation.Nodal distributions with better uniformity give better results.Furthermore,how the influence domain size and nodal distribution affect the selection of shape parameters and how the nodal distribution affects the choice of influence domain size are also discussed.
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.
文摘为设计高效稳定的演化算法,将方程求根的不动点迭代思想引入到优化领域,通过将演化算法的寻优过程看作为在迭代框架下方程不动点的逐步显示化过程,设计出一种基于数学模型的演化新算法,即不动点演化算法(fixed point evolution algorithm,FPEA).该算法的繁殖算子是由Aitken加速的不动点迭代模型导出的二次多项式,其整体框架继承传统演化算法(如差分演化算法)基于种群的迭代模式.试验结果表明:在基准函数集CEC2014、CEC2019上,本文算法的最优值平均排名在所有比较算法中排名第1;在4个工程约束设计问题上,FPEA与CSA、GPE等多个算法相比,能以较少的计算开销获得最高的求解精度.
文摘随着新能源发电比例越来越高,其受电网三相不平衡的影响越来越明显,尤其负序超标是导致电力系统安全性降低的重要原因。统一潮流控制器(unified power flow controller,UPFC)具有调节各序电流输出的能力,可用于提升系统的平衡性。为此,首先建立基于解耦-补偿原理的UPFC正序最优补偿潮流算法;其次构建UPFC的负序补偿电流控制模型,将电压不平衡补偿的优化求解问题归结为凸二次约束二次规划(quadratically constrained quadratic programming,QCQP)问题,并采用原-对偶内点法求取UPFC的负序电流最优输出值;最后提出计及正序网损与负序电压指标的负序电压补偿最优潮流(optimal power flow,OPF)计算方法以及区域负序电压总体补偿策略。通过算例分析验证所提出方法的可行性与有效性。
