In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
In this paper, to begin with. the nonlinear differential equations of a truncaled shallow spherical shell with variable thickness under uniformal distributed load are linearized by step-by-step loading method. The lin...In this paper, to begin with. the nonlinear differential equations of a truncaled shallow spherical shell with variable thickness under uniformal distributed load are linearized by step-by-step loading method. The linear differential equations can be solved by spline collocanon method. Critical loads have been obtained accordingly.展开更多
An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aero...An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.展开更多
Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been dev...Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.展开更多
Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ord...Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied problems.This study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order ODEs.The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code.The order of the proposed method was then discussed in detail.The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively.In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff problems.The numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable methods.VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.展开更多
According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial,a variable-order and variable-step-size numeric...According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial,a variable-order and variable-step-size numerical method for solving differential equations is designed.The stability properties of the formulas are discussed and the stability regions are analyzed.The deduced methods are applied to a simulation problem.The results show that the numerical method can satisfy calculation accuracy,reduce the number of calculation steps and accelerate calculation speed.展开更多
Coastal wastewater-discharged effluents contain a mixture of pollutants with decay rates that vary with water depth. Analytical models using a two-dimensional advection-diffusion equation are presented to study the ef...Coastal wastewater-discharged effluents contain a mixture of pollutants with decay rates that vary with water depth. Analytical models using a two-dimensional advection-diffusion equation are presented to study the effects of a cross-stream sudden depth change and decay on mixing and dispersing steady discharge of effluents through a sea outfall. The solutions are illustrated graphically by plotting contours of concentration, resembling snapshots of discharged effluent plumes in the far-field. Different shapes of effluent plumes are observed due to the variability of length of the step seabed, and the concentration at the step seabed is formulated to measure how much has discharged effluents dispersed into or out of the shallow coastal waters.展开更多
最大功率点跟踪技术(Maximum Power Point Tracking, MPPT)是光伏发电系统中关键技术研究的热点之一。针对传统扰动观察法跟踪速度和精度无法兼顾的问题,文中提出了一种以功率变化量为步长控制量的自适应变步长扰动观察法,通过判断功率...最大功率点跟踪技术(Maximum Power Point Tracking, MPPT)是光伏发电系统中关键技术研究的热点之一。针对传统扰动观察法跟踪速度和精度无法兼顾的问题,文中提出了一种以功率变化量为步长控制量的自适应变步长扰动观察法,通过判断功率变化趋势,对远离最大功率点,采用大步长逼近;靠近最大功率点,采用小步长逼近。建立太阳能光伏电池数学模型得到其输出特性曲线,再利用MATLAB/Simulink搭建基于Boost电路的MPPT仿真模型,最后经仿真验证了所提出算法的稳定性、快速性和准确性,它比传统算法具有更好的MPPT暂态性能。展开更多
针对油浸式电力变压器瞬态温升计算效率过低的问题,该文提出本征正交分解-αATS(proper orthogonal decomposition-adaptive time stepping based onαfactor,POD-αATS)降阶自适应变步长瞬态计算方法。首先,推导变压器绕组瞬态温升计...针对油浸式电力变压器瞬态温升计算效率过低的问题,该文提出本征正交分解-αATS(proper orthogonal decomposition-adaptive time stepping based onαfactor,POD-αATS)降阶自适应变步长瞬态计算方法。首先,推导变压器绕组瞬态温升计算的有限元离散方程;其次,采用POD降阶算法改善传统瞬态计算中存在的条件数过大及方程阶数过高的问题;同时对于瞬态计算中的时间步长选择问题,提出适用于非线性问题的αATS变步长策略;然后,为验证方法的有效性,基于110 kV油浸式电力变压器绕组的基本结构建立二维八分区数值计算模型,同时将计算结果与基于110 kV绕组的温升实验结果进行对比。数值计算及实验结果表明,所提算法与全阶定步长算法在流场和温度场中的精度几乎相同,且流场计算效率提升约45倍,温度场计算效率提升约38倍,计算速度得到显著提高。这一点在温升实验中同样得到验证,说明该文所提算法的准确性、高效性及一定的工程实用性。展开更多
针对传统奇异值阈值(Singular Value Thresholding,SVT)数据恢复算法在对电力负荷数据恢复中忽视数据先验信息以及大规模数据计算效率低等问题,提出一种基于相空间重构与自适应变步长的改进SVT的数据恢复算法.为解决传统SVT容易忽视数...针对传统奇异值阈值(Singular Value Thresholding,SVT)数据恢复算法在对电力负荷数据恢复中忽视数据先验信息以及大规模数据计算效率低等问题,提出一种基于相空间重构与自适应变步长的改进SVT的数据恢复算法.为解决传统SVT容易忽视数据先验信息的问题,引入相空间重构算法将原始缺失数据映射到高维空间,利用数据间的关联性和结构特征,为后续数据恢复算法提供先验知识;结合对数与Sigmoid函数构建变步长基础函数,并利用等比项提高前期步长,构建自适应变步长SVT算法,克服传统SVT在大规模数据情况下计算效率低的问题.结合多项公用电力负荷数据集及多种常用电力负荷数据恢复算法进行对比实验分析,结果表明,改进SVT算法可获得更好的数据恢复效果,收敛速度、精度以及稳定性得到提升,具有较强的工程实用性.展开更多
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
文摘In this paper, to begin with. the nonlinear differential equations of a truncaled shallow spherical shell with variable thickness under uniformal distributed load are linearized by step-by-step loading method. The linear differential equations can be solved by spline collocanon method. Critical loads have been obtained accordingly.
基金The National Natural Science Foundation of China(No50475073,50775036)the High Technology Research Program of Jiangsu Province(NoBG2006035)
文摘An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.
基金supported by an NSERC Canada Postgraduate Scholarshipsupported by a grant from NSERC Canada
文摘Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.
基金funded by Fundamental Research Grant Scheme Universiti Sains Malaysia,Grant No.203/PJJAUH/6711688 received by S.A.M.Yatim.Url at http://www.research.usm.my/default.asp?tag=3&f=1&k=1.
文摘Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied problems.This study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order ODEs.The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code.The order of the proposed method was then discussed in detail.The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively.In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff problems.The numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable methods.VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.
基金supported by the National Natural Science Foundation of China Under Grant No.61773008.
文摘According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial,a variable-order and variable-step-size numerical method for solving differential equations is designed.The stability properties of the formulas are discussed and the stability regions are analyzed.The deduced methods are applied to a simulation problem.The results show that the numerical method can satisfy calculation accuracy,reduce the number of calculation steps and accelerate calculation speed.
文摘Coastal wastewater-discharged effluents contain a mixture of pollutants with decay rates that vary with water depth. Analytical models using a two-dimensional advection-diffusion equation are presented to study the effects of a cross-stream sudden depth change and decay on mixing and dispersing steady discharge of effluents through a sea outfall. The solutions are illustrated graphically by plotting contours of concentration, resembling snapshots of discharged effluent plumes in the far-field. Different shapes of effluent plumes are observed due to the variability of length of the step seabed, and the concentration at the step seabed is formulated to measure how much has discharged effluents dispersed into or out of the shallow coastal waters.
文摘最大功率点跟踪技术(Maximum Power Point Tracking, MPPT)是光伏发电系统中关键技术研究的热点之一。针对传统扰动观察法跟踪速度和精度无法兼顾的问题,文中提出了一种以功率变化量为步长控制量的自适应变步长扰动观察法,通过判断功率变化趋势,对远离最大功率点,采用大步长逼近;靠近最大功率点,采用小步长逼近。建立太阳能光伏电池数学模型得到其输出特性曲线,再利用MATLAB/Simulink搭建基于Boost电路的MPPT仿真模型,最后经仿真验证了所提出算法的稳定性、快速性和准确性,它比传统算法具有更好的MPPT暂态性能。
文摘针对油浸式电力变压器瞬态温升计算效率过低的问题,该文提出本征正交分解-αATS(proper orthogonal decomposition-adaptive time stepping based onαfactor,POD-αATS)降阶自适应变步长瞬态计算方法。首先,推导变压器绕组瞬态温升计算的有限元离散方程;其次,采用POD降阶算法改善传统瞬态计算中存在的条件数过大及方程阶数过高的问题;同时对于瞬态计算中的时间步长选择问题,提出适用于非线性问题的αATS变步长策略;然后,为验证方法的有效性,基于110 kV油浸式电力变压器绕组的基本结构建立二维八分区数值计算模型,同时将计算结果与基于110 kV绕组的温升实验结果进行对比。数值计算及实验结果表明,所提算法与全阶定步长算法在流场和温度场中的精度几乎相同,且流场计算效率提升约45倍,温度场计算效率提升约38倍,计算速度得到显著提高。这一点在温升实验中同样得到验证,说明该文所提算法的准确性、高效性及一定的工程实用性。
文摘针对传统奇异值阈值(Singular Value Thresholding,SVT)数据恢复算法在对电力负荷数据恢复中忽视数据先验信息以及大规模数据计算效率低等问题,提出一种基于相空间重构与自适应变步长的改进SVT的数据恢复算法.为解决传统SVT容易忽视数据先验信息的问题,引入相空间重构算法将原始缺失数据映射到高维空间,利用数据间的关联性和结构特征,为后续数据恢复算法提供先验知识;结合对数与Sigmoid函数构建变步长基础函数,并利用等比项提高前期步长,构建自适应变步长SVT算法,克服传统SVT在大规模数据情况下计算效率低的问题.结合多项公用电力负荷数据集及多种常用电力负荷数据恢复算法进行对比实验分析,结果表明,改进SVT算法可获得更好的数据恢复效果,收敛速度、精度以及稳定性得到提升,具有较强的工程实用性.
