Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in detai...Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.展开更多
径向基函数(Radial Basis Function,RBF)是一种确定性的多维空间插值模型,可以有效逼近任意维度的空间数据。RBF插值模型中,基函数形态参数直接影响插值精度。为了快速求解最佳形态参数,获取准确的插值结果,该文采用改进的逐点交叉验证(...径向基函数(Radial Basis Function,RBF)是一种确定性的多维空间插值模型,可以有效逼近任意维度的空间数据。RBF插值模型中,基函数形态参数直接影响插值精度。为了快速求解最佳形态参数,获取准确的插值结果,该文采用改进的逐点交叉验证(Improved Leave One Out Cross Validation,ILOOCV)方法求取最优形态参数,首先从形态参数取值区间内选定初始形态参数α,然后从n个已知点中顺序选出一个点,使用剩下的n-1个已知点构建RBF插值模型,计算被取出点处真实值与插值结果的误差,循环n次,累计交叉验证误差,再依次从形态参数取值区间选取下一个值,重复操作,建立形态参数α与累计交叉验证误差之间的函数映射关系,最后通过最小化交叉验证误差来获取最佳形态参数。以我国东北地区气象观测数据进行实验,对ILOOCV方法进行验证,结果表明ILOOCV方法选取最佳形态参数使其插值结果比较精确,是一种可行的RBF形态参数优化方法。展开更多
选择合适的插值预测模型对揭示干旱区绿洲地下水与表层土壤特征空间变化特征具有重要意义。根据克里雅绿洲实测地下水(埋深、电导率、水温)与表层土壤(含水率、电导率、土温)数据,系统评价不同空间插值方法(RBF、IDW、Ordinary Kriging...选择合适的插值预测模型对揭示干旱区绿洲地下水与表层土壤特征空间变化特征具有重要意义。根据克里雅绿洲实测地下水(埋深、电导率、水温)与表层土壤(含水率、电导率、土温)数据,系统评价不同空间插值方法(RBF、IDW、Ordinary Kriging)对不同特征预测精度的影响。结果表明:克里雅绿洲区域地下水埋深主要在3 m以下,电导率在5 m S·cm-1以下,温度在15℃以下;表层土壤含水量主要在0.5以下,电导率在2.5 m S·cm-1以下,温度在13℃以下。地下水埋深采用RBF插值的精度较高,电导率采用IDW的精度较高,水温采用RBF的精度较高;表层土壤含水率采用Kriging插值的精度较高,电导率采用RBF的精度较高,土温采用RBF的精度较高;除土壤含水率外,其余指标采用对数转化后插值精度较高。展开更多
[摘要]给出了一种陀螺仪转子悬浮结构.建立了悬浮磁场 B 样条小波有限元模型;研究了一类新的有限元空间.它以 B 样条小波函数作为正四面体有限等参元的形状函数。利用 B 样条小波函数的变尺度特性在不改变网格的剖分下提高分辨率。最后...[摘要]给出了一种陀螺仪转子悬浮结构.建立了悬浮磁场 B 样条小波有限元模型;研究了一类新的有限元空间.它以 B 样条小波函数作为正四面体有限等参元的形状函数。利用 B 样条小波函数的变尺度特性在不改变网格的剖分下提高分辨率。最后对悬浮系统模型进行了仿真,给出了磁力线的走向、分布及空间各点的磁场强度,并对结果进行了分析。展开更多
The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, e...The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.展开更多
基金Supported by the National Natural Science Foundation of China( 1 9971 0 1 7,1 0 1 2 5 1 0 2 )
文摘Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.
文摘径向基函数(Radial Basis Function,RBF)是一种确定性的多维空间插值模型,可以有效逼近任意维度的空间数据。RBF插值模型中,基函数形态参数直接影响插值精度。为了快速求解最佳形态参数,获取准确的插值结果,该文采用改进的逐点交叉验证(Improved Leave One Out Cross Validation,ILOOCV)方法求取最优形态参数,首先从形态参数取值区间内选定初始形态参数α,然后从n个已知点中顺序选出一个点,使用剩下的n-1个已知点构建RBF插值模型,计算被取出点处真实值与插值结果的误差,循环n次,累计交叉验证误差,再依次从形态参数取值区间选取下一个值,重复操作,建立形态参数α与累计交叉验证误差之间的函数映射关系,最后通过最小化交叉验证误差来获取最佳形态参数。以我国东北地区气象观测数据进行实验,对ILOOCV方法进行验证,结果表明ILOOCV方法选取最佳形态参数使其插值结果比较精确,是一种可行的RBF形态参数优化方法。
文摘选择合适的插值预测模型对揭示干旱区绿洲地下水与表层土壤特征空间变化特征具有重要意义。根据克里雅绿洲实测地下水(埋深、电导率、水温)与表层土壤(含水率、电导率、土温)数据,系统评价不同空间插值方法(RBF、IDW、Ordinary Kriging)对不同特征预测精度的影响。结果表明:克里雅绿洲区域地下水埋深主要在3 m以下,电导率在5 m S·cm-1以下,温度在15℃以下;表层土壤含水量主要在0.5以下,电导率在2.5 m S·cm-1以下,温度在13℃以下。地下水埋深采用RBF插值的精度较高,电导率采用IDW的精度较高,水温采用RBF的精度较高;表层土壤含水率采用Kriging插值的精度较高,电导率采用RBF的精度较高,土温采用RBF的精度较高;除土壤含水率外,其余指标采用对数转化后插值精度较高。
文摘[摘要]给出了一种陀螺仪转子悬浮结构.建立了悬浮磁场 B 样条小波有限元模型;研究了一类新的有限元空间.它以 B 样条小波函数作为正四面体有限等参元的形状函数。利用 B 样条小波函数的变尺度特性在不改变网格的剖分下提高分辨率。最后对悬浮系统模型进行了仿真,给出了磁力线的走向、分布及空间各点的磁场强度,并对结果进行了分析。
基金financially supported by the Key Program of National Natural Science Foundation of China(No.41530320)China Natural Science Foundation for Young Scientists(No.41404093)+1 种基金Key National Research Project of China(Nos2016YFC0303100 and 2017YFC0601900)China Natural Science Foundation(No.41774125)
文摘The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.
