We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner...We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.展开更多
The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed...The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed based on the geometric barycenter of whitenization weight function in the two-dimensional coordinate plane,and the calculation of kernel is converted to the calculation of barycenter in geometric figures.The method fully considers the effect of all information contained in whitenization weight function on the calculation result of kernel,and is the extension and perfection of the existing methods in the scope of application.展开更多
传统统计局部核主元分析(statistical local kernel principal component analysis, SLKPCA)在构造改进残差时未考虑样本的差异性,使得故障样本信息易于被其他样本所掩盖,针对该问题,提出一种基于加权统计局部核主元分析(weighted stati...传统统计局部核主元分析(statistical local kernel principal component analysis, SLKPCA)在构造改进残差时未考虑样本的差异性,使得故障样本信息易于被其他样本所掩盖,针对该问题,提出一种基于加权统计局部核主元分析(weighted statistical local kernel principal component analysis, WSLKPCA)的非线性化工过程微小故障诊断方法。该方法首先利用KPCA获取过程的得分向量和特征值并构建初始残差。然后设计了一种基于测试样本与训练样本之间距离的加权策略构建加权改进残差,对含有较强微小故障信息的样本赋予较大权值,以增强故障样本的影响。最后,采用基于测量变量与监控统计量之间的加权互信息构建贡献图以识别故障源变量。在连续搅拌反应釜和田纳西伊斯曼(Tennessee Eastman, TE)化工过程上的仿真结果表明,所提方法具有良好的微小故障检测与识别性能。展开更多
文摘We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.
基金Supported by the National Natural Science Foundation of China(71271226,70971064,71101159)the Humanities and Social Science Foundation of Ministry of Education(11YJC630273,12YJC630140)+4 种基金the Program for Chongqing Innovation Team in University(KJTD201313)the Science and Technology Research Projects of Chongqing Education Commission(KJ120706)the Open Foundation of Chongqing Key Laboratory of Electronic Commerce and Supply Chain System(2012ECSC0101)the Special Fund of Chongqing Key Laboratory of Electronic Commerce and Supply Chain System(2012ECSC0217)the Chongqing City Board of Education Science and Technology Research Projects(1202010)
文摘The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed based on the geometric barycenter of whitenization weight function in the two-dimensional coordinate plane,and the calculation of kernel is converted to the calculation of barycenter in geometric figures.The method fully considers the effect of all information contained in whitenization weight function on the calculation result of kernel,and is the extension and perfection of the existing methods in the scope of application.
文摘传统统计局部核主元分析(statistical local kernel principal component analysis, SLKPCA)在构造改进残差时未考虑样本的差异性,使得故障样本信息易于被其他样本所掩盖,针对该问题,提出一种基于加权统计局部核主元分析(weighted statistical local kernel principal component analysis, WSLKPCA)的非线性化工过程微小故障诊断方法。该方法首先利用KPCA获取过程的得分向量和特征值并构建初始残差。然后设计了一种基于测试样本与训练样本之间距离的加权策略构建加权改进残差,对含有较强微小故障信息的样本赋予较大权值,以增强故障样本的影响。最后,采用基于测量变量与监控统计量之间的加权互信息构建贡献图以识别故障源变量。在连续搅拌反应釜和田纳西伊斯曼(Tennessee Eastman, TE)化工过程上的仿真结果表明,所提方法具有良好的微小故障检测与识别性能。
