The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to...The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recur- sively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.展开更多
Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or...Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.展开更多
The steam turbine is a prime mover that converts kinetic energy in steam into rotational mechanical energy through the impact or reaction of the steam against the blades. The aim of this study is to design a steam tur...The steam turbine is a prime mover that converts kinetic energy in steam into rotational mechanical energy through the impact or reaction of the steam against the blades. The aim of this study is to design a steam turbine for a small scale steam power plant with target of producing electricity. The turbine is driven by the heat energy from palm kernel shells as a renewable energy source obtained at a lower or no cost. The study was concentrated on design of turbine elements and its validation using computer packages. Specifically, the microturbine design was limited to design, modeling, simulation and analysis of the rotor, blades and nozzle under the palm kernel shell as fuel for the micro power plant. In blade design, stress failures, efficiency and blade angle parameters were considered. In casing volume design, the overall heat transfer and mean temperature, and different concepts were applied. The thermal distribution on stator and rotor was considered in order to determine its level of tolerance. The design software packages used for design validation were Solidworks and Comsol Multiphysics for analysis. Simulation results showed that the designed steam turbine can adequately tolerate change in stress/load, torsion/compression, temperature and speeds.展开更多
稀疏线性方程组求解等高性能计算应用常常涉及稀疏矩阵向量乘(SpMV)序列Ax,A2x,…,Asx的计算.上述SpMV序列操作又称为稀疏矩阵幂函数(matrix power kernel,MPK).由于MPK执行多次SpMV且稀疏矩阵保持不变,在缓存(cache)中重用稀疏矩阵,可...稀疏线性方程组求解等高性能计算应用常常涉及稀疏矩阵向量乘(SpMV)序列Ax,A2x,…,Asx的计算.上述SpMV序列操作又称为稀疏矩阵幂函数(matrix power kernel,MPK).由于MPK执行多次SpMV且稀疏矩阵保持不变,在缓存(cache)中重用稀疏矩阵,可避免每次执行SpMV均从主存加载A,从而缓解SpMV访存受限问题,提升MPK性能.但缓存数据重用会导致相邻SpMV操作之间的数据依赖,现有MPK优化多针对单次SpMV调用,或在实现数据重用时引入过多额外开销.提出了缓存感知的MPK(cache-awareMPK,Ca-MPK),基于稀疏矩阵的依赖图,设计了体系结构感知的递归划分方法,将依赖图划分为适合缓存大小的子图/子矩阵,通过构建分割子图解耦数据依赖,根据特定顺序在子矩阵上调度执行SpMV,实现缓存数据重用.测试结果表明,Ca-MPK相对于Intel OneMKL库和最新MPK实现,平均性能提升分别多达约1.57倍和1.40倍.展开更多
The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly,the Matlab simulation models were established. Secondly,the Wiener kernel of power load...The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly,the Matlab simulation models were established. Secondly,the Wiener kernel of power load was found based on the Gaussian white noise as input. And then the uniform mathematical model of the power grid signal was established according to the homogeneous of the same order of Wiener functional series. Finally,taking three typical distortion sources which are semiconductor rectifier,electric locomotive and electric arc furnace in power grid as examples,we have validated the model through the Matlab simulation and analyzed the simulation errors. The results show that the uniform mathematical model of distortion signals in power grid can approximation the actual model by growing the items of the series under the condition of the enough storage space and computing speed.展开更多
Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function ...Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.展开更多
虚拟电厂(virtual power plants,VPP)可为电网运行提供容量可观的备用资源。准确评估和量化VPP的备用是VPP参与电网调控的关键。然而,分布式新能源出力、负荷用电、电价等具有较强的不确定性,可能导致传统基于确定性方法的备用评估结果...虚拟电厂(virtual power plants,VPP)可为电网运行提供容量可观的备用资源。准确评估和量化VPP的备用是VPP参与电网调控的关键。然而,分布式新能源出力、负荷用电、电价等具有较强的不确定性,可能导致传统基于确定性方法的备用评估结果不可靠。为此,结合VPP的特征,提出了考虑多重不确定性的可信备用定义及评估方法。首先,给出了VPP架构和可信备用定义。然后,构建了考虑各类资源聚合的VPP提供备用的模型。通过蒙特卡洛模拟各类不确定因素,利用核密度估计法确定具有不同置信度的可信备用集合,有效量化了VPP的可信备用。最后,以典型VPP为例进行仿真,验证了所提方法能够有效地刻画多重不确定性条件下VPP所能提供备用的概率特性,能够为调度机构提供更全面可靠的备用信息。展开更多
针对核电多回路耦合系统在升功率运行中异常传感器检测困难、检测延时及检测精度低等问题,提出了一种自联想核回归模型(auto-associative kernel regression,简称AAKR)与修正序贯概率比检验(sequential probability ratio test,简称SPRT...针对核电多回路耦合系统在升功率运行中异常传感器检测困难、检测延时及检测精度低等问题,提出了一种自联想核回归模型(auto-associative kernel regression,简称AAKR)与修正序贯概率比检验(sequential probability ratio test,简称SPRT)相结合的方法。首先,利用小波软阈值降噪方法对监测数据预处理,获取高质量的多源传感器解调信号;其次,采用AAKR构造传感器正常运行数据的估计值,并获取多源传感器测量值与估计值之间的残差;然后,运用滑动时间窗获取不同阶段残差向量的均值和方差,设计一种SPRT检测规则对传感器残差进行异常检测;最后,用核电一、二回路耦合系统模拟机实验数据进行方法验证与性能分析。结果表明,所提传感器异常检测方法的准确率达到99.52%,异常检测延时降低了81.73%,可有效提高现有核电厂传感器异常检测的稳定性。展开更多
文摘The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recur- sively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.
基金This work was supported by the Natural Science Foundation of China(Grant Nos.61673169,11701176,11626101,11601485).
文摘Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.
文摘The steam turbine is a prime mover that converts kinetic energy in steam into rotational mechanical energy through the impact or reaction of the steam against the blades. The aim of this study is to design a steam turbine for a small scale steam power plant with target of producing electricity. The turbine is driven by the heat energy from palm kernel shells as a renewable energy source obtained at a lower or no cost. The study was concentrated on design of turbine elements and its validation using computer packages. Specifically, the microturbine design was limited to design, modeling, simulation and analysis of the rotor, blades and nozzle under the palm kernel shell as fuel for the micro power plant. In blade design, stress failures, efficiency and blade angle parameters were considered. In casing volume design, the overall heat transfer and mean temperature, and different concepts were applied. The thermal distribution on stator and rotor was considered in order to determine its level of tolerance. The design software packages used for design validation were Solidworks and Comsol Multiphysics for analysis. Simulation results showed that the designed steam turbine can adequately tolerate change in stress/load, torsion/compression, temperature and speeds.
文摘稀疏线性方程组求解等高性能计算应用常常涉及稀疏矩阵向量乘(SpMV)序列Ax,A2x,…,Asx的计算.上述SpMV序列操作又称为稀疏矩阵幂函数(matrix power kernel,MPK).由于MPK执行多次SpMV且稀疏矩阵保持不变,在缓存(cache)中重用稀疏矩阵,可避免每次执行SpMV均从主存加载A,从而缓解SpMV访存受限问题,提升MPK性能.但缓存数据重用会导致相邻SpMV操作之间的数据依赖,现有MPK优化多针对单次SpMV调用,或在实现数据重用时引入过多额外开销.提出了缓存感知的MPK(cache-awareMPK,Ca-MPK),基于稀疏矩阵的依赖图,设计了体系结构感知的递归划分方法,将依赖图划分为适合缓存大小的子图/子矩阵,通过构建分割子图解耦数据依赖,根据特定顺序在子矩阵上调度执行SpMV,实现缓存数据重用.测试结果表明,Ca-MPK相对于Intel OneMKL库和最新MPK实现,平均性能提升分别多达约1.57倍和1.40倍.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51277043)
文摘The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly,the Matlab simulation models were established. Secondly,the Wiener kernel of power load was found based on the Gaussian white noise as input. And then the uniform mathematical model of the power grid signal was established according to the homogeneous of the same order of Wiener functional series. Finally,taking three typical distortion sources which are semiconductor rectifier,electric locomotive and electric arc furnace in power grid as examples,we have validated the model through the Matlab simulation and analyzed the simulation errors. The results show that the uniform mathematical model of distortion signals in power grid can approximation the actual model by growing the items of the series under the condition of the enough storage space and computing speed.
文摘Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.
文摘虚拟电厂(virtual power plants,VPP)可为电网运行提供容量可观的备用资源。准确评估和量化VPP的备用是VPP参与电网调控的关键。然而,分布式新能源出力、负荷用电、电价等具有较强的不确定性,可能导致传统基于确定性方法的备用评估结果不可靠。为此,结合VPP的特征,提出了考虑多重不确定性的可信备用定义及评估方法。首先,给出了VPP架构和可信备用定义。然后,构建了考虑各类资源聚合的VPP提供备用的模型。通过蒙特卡洛模拟各类不确定因素,利用核密度估计法确定具有不同置信度的可信备用集合,有效量化了VPP的可信备用。最后,以典型VPP为例进行仿真,验证了所提方法能够有效地刻画多重不确定性条件下VPP所能提供备用的概率特性,能够为调度机构提供更全面可靠的备用信息。
文摘针对核电多回路耦合系统在升功率运行中异常传感器检测困难、检测延时及检测精度低等问题,提出了一种自联想核回归模型(auto-associative kernel regression,简称AAKR)与修正序贯概率比检验(sequential probability ratio test,简称SPRT)相结合的方法。首先,利用小波软阈值降噪方法对监测数据预处理,获取高质量的多源传感器解调信号;其次,采用AAKR构造传感器正常运行数据的估计值,并获取多源传感器测量值与估计值之间的残差;然后,运用滑动时间窗获取不同阶段残差向量的均值和方差,设计一种SPRT检测规则对传感器残差进行异常检测;最后,用核电一、二回路耦合系统模拟机实验数据进行方法验证与性能分析。结果表明,所提传感器异常检测方法的准确率达到99.52%,异常检测延时降低了81.73%,可有效提高现有核电厂传感器异常检测的稳定性。
