The microscopic characteristics of skeletal particles in rock and soil media have important effects on macroscopic mechanical properties.A mathematical procedure called spherical harmonic function analysis was here de...The microscopic characteristics of skeletal particles in rock and soil media have important effects on macroscopic mechanical properties.A mathematical procedure called spherical harmonic function analysis was here developed to characterize micromorphology of particles and determine the meso effects in a discrete manner.This method has strong mathematical properties with respect to orthogonality and rotating invariance.It was used here to characterize and reconstruct particle micromorphology in three-dimensional space.The applicability and accuracy of the method were assessed through comparison of basic geometric properties such as volume and surface area.The results show that the micromorphological characteristics of reproduced particles become more and more readily distinguishable as the reproduced order number of spherical harmonic function increases,and the error can be brought below 5%when the order number reaches 10.This level of precision is sharp enough to distinguish the characteristics of real particles.Reconstructed particles of the same size but different reconstructed orders were used to form cylindrical samples,and the stress-strain curves of these samples filled with different-order particles which have their mutual morphological features were compared using PFC3D.Results show that the higher the spherical harmonic order of reconstructed particles,the lower the initial compression modulus and the larger the strain at peak intensity.However,peak strength shows only a random relationship to spherical harmonic order.Microstructure reconstruction was here shown to be an efficient means of numerically simulating of multi-scale rock and soil media and studying the mechanical properties of soil samples.展开更多
高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于...高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于球谐函数的高斯过程近似模型(Variational Sparse Gaussian Processes based on Spherical Harmonic,SHVSGP),通过球谐函数将数据映射到超球面上,在一个不同于数据原始输入域的空间中寻找一个更紧凑的输入特征代表集,使得产生的稀疏高斯过程模型能够包含有更丰富的信息特征,同时获得诱导变量相关的对角协方差矩阵,这极大简化了矩阵运算的复杂度,节省了计算成本.本文将SHVSGP模型与当下流行的其他近似方法在大规模数据集上进行比较,结果表明SHVSGP模型可以获得高效且精确的预测.展开更多
提出了一种基于截断奇异值分解正则化(Truncated Singular Value Decomposition,TSVD)的电离层层析成像算法.该算法选择球谐函数与经验正交函数作为表征电离层电子密度空间变化的基函数,以降低背景模型对层析成像的影响;利用广义交叉验...提出了一种基于截断奇异值分解正则化(Truncated Singular Value Decomposition,TSVD)的电离层层析成像算法.该算法选择球谐函数与经验正交函数作为表征电离层电子密度空间变化的基函数,以降低背景模型对层析成像的影响;利用广义交叉验证法来选择合适的截断参数,提高了算法的稳定性和反演精度.基于中国区域23个观测站的电离层层析成像仿真结果表明:与乘法代数重构算法(Multiplicative Algebraic Reconstruction Technique,MART)相比,基于TSVD正则化的电离层层析成像算法能够在不需要背景电离层电子密度作为先验条件的情况下,实现电离层电子密度的有效反演.展开更多
基金Project(2015CB057903)supported by the National Basic Research Program of ChinaProjects(51679071,51309089)supported by the National Natural Science Foundation of China+2 种基金Project(BK20130846)supported by the Natural Science Foundation of Jiangsu Province,ChinaProject(2013BAB06B00)supported by the National Key Technology R&D Program,ChinaProject(2015B06014)supported by the Fundamental Research Funds for the Central Universities,China
文摘The microscopic characteristics of skeletal particles in rock and soil media have important effects on macroscopic mechanical properties.A mathematical procedure called spherical harmonic function analysis was here developed to characterize micromorphology of particles and determine the meso effects in a discrete manner.This method has strong mathematical properties with respect to orthogonality and rotating invariance.It was used here to characterize and reconstruct particle micromorphology in three-dimensional space.The applicability and accuracy of the method were assessed through comparison of basic geometric properties such as volume and surface area.The results show that the micromorphological characteristics of reproduced particles become more and more readily distinguishable as the reproduced order number of spherical harmonic function increases,and the error can be brought below 5%when the order number reaches 10.This level of precision is sharp enough to distinguish the characteristics of real particles.Reconstructed particles of the same size but different reconstructed orders were used to form cylindrical samples,and the stress-strain curves of these samples filled with different-order particles which have their mutual morphological features were compared using PFC3D.Results show that the higher the spherical harmonic order of reconstructed particles,the lower the initial compression modulus and the larger the strain at peak intensity.However,peak strength shows only a random relationship to spherical harmonic order.Microstructure reconstruction was here shown to be an efficient means of numerically simulating of multi-scale rock and soil media and studying the mechanical properties of soil samples.
文摘高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于球谐函数的高斯过程近似模型(Variational Sparse Gaussian Processes based on Spherical Harmonic,SHVSGP),通过球谐函数将数据映射到超球面上,在一个不同于数据原始输入域的空间中寻找一个更紧凑的输入特征代表集,使得产生的稀疏高斯过程模型能够包含有更丰富的信息特征,同时获得诱导变量相关的对角协方差矩阵,这极大简化了矩阵运算的复杂度,节省了计算成本.本文将SHVSGP模型与当下流行的其他近似方法在大规模数据集上进行比较,结果表明SHVSGP模型可以获得高效且精确的预测.
