Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficult...Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.展开更多
The sea-surface height （SSH） signatures of internal tides extracted from the TOPEX/Poseidon （T/P） altimeter data along satellite tracks are fitted with superposition of several plane waves which have different wav...The sea-surface height （SSH） signatures of internal tides extracted from the TOPEX/Poseidon （T/P） altimeter data along satellite tracks are fitted with superposition of several plane waves which have different wavenumber vectors. The key problem of plane wave fitting with iterative method is how to determine the initial value of wavenumber of each plane wave. The previous solving method is to analyze the internal tidal SSH signatures along each track with wavenumber spectrum. But it is found that the problem cannot be solved completely with the wavenumber spectrum analysis method only. The method based on the combination of wavenumber spectrum analysis method and the exhaustive method is proposed to determine the initial values of wavenumbers for iteration. Numerical results indicate that the proposed method is not only reasonable and feasible but also better than the previous method. The proposed method is an improvement of the previous one, which is beneficial to improving the precision of plane wave fitting of the T/P internal tidal SSH signatures and deepening the understanding of the internal tides in ocean.展开更多
Reverse engineering in the manufacturing field is a process in which the digitized data are obtained from an existing object model or a part of it, and then the CAD model is reconstructed. This paper presents an RBF n...Reverse engineering in the manufacturing field is a process in which the digitized data are obtained from an existing object model or a part of it, and then the CAD model is reconstructed. This paper presents an RBF neural network approach to modify and fit the digitized data. The centers for the RBF are selected by using the orthogonal least squares learning algorithm. A mathematically known surface is used for generating a number of samples for training the networks. The trained networks then generated a number of new points which were compared with the calculating points from the equations. Moreover, a series of practice digitizing curves are used to test the approach. The results showed that this approach is effective in modifying and fitting digitized data and generating data points to reconstruct the surface model.展开更多
By using the method of least square linear fitting to analyze data do not exist errors under certain conditions, in order to make the linear data fitting method that can more accurately solve the relationship expressi...By using the method of least square linear fitting to analyze data do not exist errors under certain conditions, in order to make the linear data fitting method that can more accurately solve the relationship expression between the volume and quantity in scientific experiments and engineering practice, this article analyzed data error by commonly linear data fitting method, and proposed improved process of the least distance squ^re method based on least squares method. Finally, the paper discussed the advantages and disadvantages through the example analysis of two kinds of linear data fitting method, and given reasonable control conditions for its application.展开更多
Purpose:To develop a set of metrics and identify criteria for assessing the functionality of LOD KOS products while providing common guiding principles that can be used by LOD KOS producers and users to maximize the f...Purpose:To develop a set of metrics and identify criteria for assessing the functionality of LOD KOS products while providing common guiding principles that can be used by LOD KOS producers and users to maximize the functions and usages of LOD KOS products.Design/methodology/approach:Data collection and analysis were conducted at three time periods in 2015–16,2017 and 2019.The sample data used in the comprehensive data analysis comprises all datasets tagged as types of KOS in the Datahub and extracted through their respective SPARQL endpoints.A comparative study of the LOD KOS collected from terminology services Linked Open Vocabularies(LOV)and BioPortal was also performed.Findings:The study proposes a set of Functional,Impactful and Transformable(FIT)metrics for LOD KOS as value vocabularies.The FAIR principles,with additional recommendations,are presented for LOD KOS as open data.Research limitations:The metrics need to be further tested and aligned with the best practices and international standards of both open data and various types of KOS.Practical implications:Assessment performed with FAIR and FIT metrics support the creation and delivery of user-friendly,discoverable and interoperable LOD KOS datasets which can be used for innovative applications,act as a knowledge base,become a foundation of semantic analysis and entity extractions and enhance research in science and the humanities.Originality/value:Our research provides best practice guidelines for LOD KOS as value vocabularies.展开更多
Background: There has been a great interest in tracking health-related fitness across the United States. The NFL PLAY 60 FITNESSGRAM Partnership Project (NFL P60FGPP) is a large participatory research network that inv...Background: There has been a great interest in tracking health-related fitness across the United States. The NFL PLAY 60 FITNESSGRAM Partnership Project (NFL P60FGPP) is a large participatory research network that involves the surveillance of fitness among more than 1000 schools spread throughout the country. Fitness data are collected by school staff and therefore these data can vary in quality and representativeness. Therefore, careful screening procedures are needed to ensure that the data can reflect actual patterns in the schools. This study examined the impact of different data screening procedures on outcomes of aerobic fitness (AF) collected from the NFL P60FGPP. Methods: Data were compiled from 149,101 youth from 504 schools and were processed using the established age- and gender-specific AF FITNESSGRAM health-related standards. Data were subjected to three different screening procedures (based on grade size and boy-to-girl ratio per grade). Linear models were computed to obtain unadjusted and adjusted (for age, BMI-Z, and socio-economic status) estimates of % youth in the Healthy Fitness Zone (HFZ) in order to determine if, 1) there were differences in % in the HFZ and 2) if differences could be explained by changes in the representativeness of the sample due to the different data screening procedures. Results: Depending on the screening procedure used, the final sample ranged from 96,999 (no screening) to 46,572 youth (most stringent criteria). The proportion of youth achieving appropriate levels of AF ranged from 56% to 61% with unscreened data resulting in consistently lower percentages of youth achieving the standard (P < 0.05). Overall, these differences were not explained by possible changes in demographic characteristics as the result of applying different screening criteria. Conclusions: The findings demonstrate the importance of establishing appropriate screening procedures that maximize sample size while also ensuring generalizability of the findings.展开更多
The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for mul...The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt＇s transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required.展开更多
This paper starts with untime-diversification of the time-diversification deformation model and gives displacement distribution model of untime-diversification and simplifies further the study of deformation model.The...This paper starts with untime-diversification of the time-diversification deformation model and gives displacement distribution model of untime-diversification and simplifies further the study of deformation model.The paper discusses the problem of least squares fitting of coordinate parameters model—parameters of deformation model.During discussion,the basic means of cubic B splines and two steps of multidimensional disorder datum fitting are adopted which can make fitting function calculated mostly approximate coordinate parameters model and it can make calculation easier.展开更多
Some recent developments(accelerated expansion)in the Universe cannot be explained by the conventional formulation of general relativity.We apply the recently proposed f(T,B)gravity to investigate the accelerated expa...Some recent developments(accelerated expansion)in the Universe cannot be explained by the conventional formulation of general relativity.We apply the recently proposed f(T,B)gravity to investigate the accelerated expansion of the Universe.By parametrizing the Hubble parameter and estimating the best fit values of the model parameters b_(0),b_(1),and b_(2)imposed from Supernovae type la,Cosmic Microwave Background,B aryon Acoustic Oscillation,and Hubble data using the Markov Chain Monte Carlo method,we propose a method to determine the precise solutions to the field equations.We then observe that the model appears to be in good agreement with the observations.A change from the deceleration to the acceleration phase of the Universe is shown by the evolution of the deceleration parameter.In addition,we investigate the behavior of the statefinder analysis,equation of state(EoS)parameters,along with the energy conditions.Furthermore,to discuss other cosmological parameters,we consider some wellknown f(T,B)gravity models,specifically,f(T,B)=aT^(b)+cB^(d).Lastly,we find that the considered f(T,B)gravity models predict that the present Universe is accelerating and the EoS parameter behaves like the ACDM model.展开更多
普适图像传输系统(Flexible Image Transport System,FITS)是天文学领域应用最广泛的数据格式。自从20世纪80年代FITS格式被国际天文联合会(IAU)正式公布为国际标准以来,大部分的天文数据都是以FITS文件的形式在世界各地的数据中心和天...普适图像传输系统(Flexible Image Transport System,FITS)是天文学领域应用最广泛的数据格式。自从20世纪80年代FITS格式被国际天文联合会(IAU)正式公布为国际标准以来,大部分的天文数据都是以FITS文件的形式在世界各地的数据中心和天文学家手中保存和交换。采用文件系统方式保存管理的FITS数据文件,很难适应程序化的检索和定位需求。随着FITS文件数量的不断增加以及虚拟天文台技术的发展,为这些以文件形式保存的天文数据提供检索功能的需求越来越迫切。FITS头以关键词值对的形式确切定义了所属FITS文件的结构,还提供了数据本身诸多特性的重要信息。FITS头中保存的这些信息可以满足大部分FITS数据文件查询检索的需求。将FITS头中的信息利用数据库来保存和管理,可以极大的方便对FITS文件的检索和定位。FITS头归档入库系统(FitHAS)是中国虚拟天文台项目开发的一个简单实用的FITS头信息归档入库工具,能够方便的将单个或者多个FITS文件的主FITS头信息导入到数据库中,为FITS数据文件的查询检索奠定基础,进而为虚拟天文台等更高层次的数据访问服务部署创造条件。本文介绍FITS数据格式,FITS头的基本结构;探讨虚拟天文台环境下FITS数据文件检索定位的实现方式;阐述FitHAS的功能特点、设计开发和使用方法。展开更多
Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the m...Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme.展开更多
针对工业管道与容器在自动化装配、焊接及在线检测过程中,环状端面基准拟合易受边界噪声、局部形变与采样不均影响而导致精度不足的问题,提出一种曲率-拓扑双驱动的端面基准平面拟合方法。该方法基于局部协方差张量的谱分解提取主曲率,...针对工业管道与容器在自动化装配、焊接及在线检测过程中,环状端面基准拟合易受边界噪声、局部形变与采样不均影响而导致精度不足的问题,提出一种曲率-拓扑双驱动的端面基准平面拟合方法。该方法基于局部协方差张量的谱分解提取主曲率,构建平整度与退化度指标,实现点云的非均匀稀疏化;进一步引入拓扑数据分析(Topological Data Analysis,TDA),通过构建Vietoris-Rips复形与持久同调分析提取具有闭合拓扑特征的骨架点集,从而嵌入环形端面的结构先验。基于骨架点集协方差矩阵的最小特征向量确定平面法向,实现高鲁棒性的姿态估计。实验表明,该方法平均绝对角度误差小于0.03°,单次拟合耗时低于0.03 s,相较于最小中值平方法提速约300倍,在主元分析、随机采样一致性等传统方法基础上精度提升约10倍。该方法精度高、鲁棒性强、实时处理速度快,无需人工干预,适用于复杂工业环境下的管道端面自动化定位与基准构建,可为智能制造中的焊接路径规划与在线检测提供可靠技术支撑。展开更多
基金Supported by National Natural Science Youth Foundation (10401021).
文摘Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.
基金The National Natural Science Foundation of China under contract No. 41076006the State Ministry of Science and Technology of China under contract No. 2008AA09A402the Ministry of Education’s "111" Project of China under contract No. B07036
文摘The sea-surface height （SSH） signatures of internal tides extracted from the TOPEX/Poseidon （T/P） altimeter data along satellite tracks are fitted with superposition of several plane waves which have different wavenumber vectors. The key problem of plane wave fitting with iterative method is how to determine the initial value of wavenumber of each plane wave. The previous solving method is to analyze the internal tidal SSH signatures along each track with wavenumber spectrum. But it is found that the problem cannot be solved completely with the wavenumber spectrum analysis method only. The method based on the combination of wavenumber spectrum analysis method and the exhaustive method is proposed to determine the initial values of wavenumbers for iteration. Numerical results indicate that the proposed method is not only reasonable and feasible but also better than the previous method. The proposed method is an improvement of the previous one, which is beneficial to improving the precision of plane wave fitting of the T/P internal tidal SSH signatures and deepening the understanding of the internal tides in ocean.
文摘Reverse engineering in the manufacturing field is a process in which the digitized data are obtained from an existing object model or a part of it, and then the CAD model is reconstructed. This paper presents an RBF neural network approach to modify and fit the digitized data. The centers for the RBF are selected by using the orthogonal least squares learning algorithm. A mathematically known surface is used for generating a number of samples for training the networks. The trained networks then generated a number of new points which were compared with the calculating points from the equations. Moreover, a series of practice digitizing curves are used to test the approach. The results showed that this approach is effective in modifying and fitting digitized data and generating data points to reconstruct the surface model.
文摘By using the method of least square linear fitting to analyze data do not exist errors under certain conditions, in order to make the linear data fitting method that can more accurately solve the relationship expression between the volume and quantity in scientific experiments and engineering practice, this article analyzed data error by commonly linear data fitting method, and proposed improved process of the least distance squ^re method based on least squares method. Finally, the paper discussed the advantages and disadvantages through the example analysis of two kinds of linear data fitting method, and given reasonable control conditions for its application.
基金College of Communication and Information(CCI)Research and Creative Activity Fund,Kent State University
文摘Purpose:To develop a set of metrics and identify criteria for assessing the functionality of LOD KOS products while providing common guiding principles that can be used by LOD KOS producers and users to maximize the functions and usages of LOD KOS products.Design/methodology/approach:Data collection and analysis were conducted at three time periods in 2015–16,2017 and 2019.The sample data used in the comprehensive data analysis comprises all datasets tagged as types of KOS in the Datahub and extracted through their respective SPARQL endpoints.A comparative study of the LOD KOS collected from terminology services Linked Open Vocabularies(LOV)and BioPortal was also performed.Findings:The study proposes a set of Functional,Impactful and Transformable(FIT)metrics for LOD KOS as value vocabularies.The FAIR principles,with additional recommendations,are presented for LOD KOS as open data.Research limitations:The metrics need to be further tested and aligned with the best practices and international standards of both open data and various types of KOS.Practical implications:Assessment performed with FAIR and FIT metrics support the creation and delivery of user-friendly,discoverable and interoperable LOD KOS datasets which can be used for innovative applications,act as a knowledge base,become a foundation of semantic analysis and entity extractions and enhance research in science and the humanities.Originality/value:Our research provides best practice guidelines for LOD KOS as value vocabularies.
文摘Background: There has been a great interest in tracking health-related fitness across the United States. The NFL PLAY 60 FITNESSGRAM Partnership Project (NFL P60FGPP) is a large participatory research network that involves the surveillance of fitness among more than 1000 schools spread throughout the country. Fitness data are collected by school staff and therefore these data can vary in quality and representativeness. Therefore, careful screening procedures are needed to ensure that the data can reflect actual patterns in the schools. This study examined the impact of different data screening procedures on outcomes of aerobic fitness (AF) collected from the NFL P60FGPP. Methods: Data were compiled from 149,101 youth from 504 schools and were processed using the established age- and gender-specific AF FITNESSGRAM health-related standards. Data were subjected to three different screening procedures (based on grade size and boy-to-girl ratio per grade). Linear models were computed to obtain unadjusted and adjusted (for age, BMI-Z, and socio-economic status) estimates of % youth in the Healthy Fitness Zone (HFZ) in order to determine if, 1) there were differences in % in the HFZ and 2) if differences could be explained by changes in the representativeness of the sample due to the different data screening procedures. Results: Depending on the screening procedure used, the final sample ranged from 96,999 (no screening) to 46,572 youth (most stringent criteria). The proportion of youth achieving appropriate levels of AF ranged from 56% to 61% with unscreened data resulting in consistently lower percentages of youth achieving the standard (P < 0.05). Overall, these differences were not explained by possible changes in demographic characteristics as the result of applying different screening criteria. Conclusions: The findings demonstrate the importance of establishing appropriate screening procedures that maximize sample size while also ensuring generalizability of the findings.
基金supported by the Program of Introducing Talents of Disciplines to Universities of the Ministry of Education and State Administration of the Foreign Experts Affairs of China (the 111 Project, Grant No.B08048)the Special Basic Research Fund for Methodology in Hydrology of the Ministry of Sciences and Technology of China (Grant No. 2011IM011000)
文摘The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt＇s transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required.
文摘This paper starts with untime-diversification of the time-diversification deformation model and gives displacement distribution model of untime-diversification and simplifies further the study of deformation model.The paper discusses the problem of least squares fitting of coordinate parameters model—parameters of deformation model.During discussion,the basic means of cubic B splines and two steps of multidimensional disorder datum fitting are adopted which can make fitting function calculated mostly approximate coordinate parameters model and it can make calculation easier.
基金the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan provided funding for this study(Grant No.AP09058240)。
文摘Some recent developments(accelerated expansion)in the Universe cannot be explained by the conventional formulation of general relativity.We apply the recently proposed f(T,B)gravity to investigate the accelerated expansion of the Universe.By parametrizing the Hubble parameter and estimating the best fit values of the model parameters b_(0),b_(1),and b_(2)imposed from Supernovae type la,Cosmic Microwave Background,B aryon Acoustic Oscillation,and Hubble data using the Markov Chain Monte Carlo method,we propose a method to determine the precise solutions to the field equations.We then observe that the model appears to be in good agreement with the observations.A change from the deceleration to the acceleration phase of the Universe is shown by the evolution of the deceleration parameter.In addition,we investigate the behavior of the statefinder analysis,equation of state(EoS)parameters,along with the energy conditions.Furthermore,to discuss other cosmological parameters,we consider some wellknown f(T,B)gravity models,specifically,f(T,B)=aT^(b)+cB^(d).Lastly,we find that the considered f(T,B)gravity models predict that the present Universe is accelerating and the EoS parameter behaves like the ACDM model.
文摘普适图像传输系统(Flexible Image Transport System,FITS)是天文学领域应用最广泛的数据格式。自从20世纪80年代FITS格式被国际天文联合会(IAU)正式公布为国际标准以来,大部分的天文数据都是以FITS文件的形式在世界各地的数据中心和天文学家手中保存和交换。采用文件系统方式保存管理的FITS数据文件,很难适应程序化的检索和定位需求。随着FITS文件数量的不断增加以及虚拟天文台技术的发展,为这些以文件形式保存的天文数据提供检索功能的需求越来越迫切。FITS头以关键词值对的形式确切定义了所属FITS文件的结构,还提供了数据本身诸多特性的重要信息。FITS头中保存的这些信息可以满足大部分FITS数据文件查询检索的需求。将FITS头中的信息利用数据库来保存和管理,可以极大的方便对FITS文件的检索和定位。FITS头归档入库系统(FitHAS)是中国虚拟天文台项目开发的一个简单实用的FITS头信息归档入库工具,能够方便的将单个或者多个FITS文件的主FITS头信息导入到数据库中,为FITS数据文件的查询检索奠定基础,进而为虚拟天文台等更高层次的数据访问服务部署创造条件。本文介绍FITS数据格式,FITS头的基本结构;探讨虚拟天文台环境下FITS数据文件检索定位的实现方式;阐述FitHAS的功能特点、设计开发和使用方法。
基金Supported by the National Basic Research Program of China(2012CB025904)Zhengzhou Shengda University of Economics,Business and Management(SD-YB2025085)。
文摘Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme.
文摘针对工业管道与容器在自动化装配、焊接及在线检测过程中,环状端面基准拟合易受边界噪声、局部形变与采样不均影响而导致精度不足的问题,提出一种曲率-拓扑双驱动的端面基准平面拟合方法。该方法基于局部协方差张量的谱分解提取主曲率,构建平整度与退化度指标,实现点云的非均匀稀疏化;进一步引入拓扑数据分析(Topological Data Analysis,TDA),通过构建Vietoris-Rips复形与持久同调分析提取具有闭合拓扑特征的骨架点集,从而嵌入环形端面的结构先验。基于骨架点集协方差矩阵的最小特征向量确定平面法向,实现高鲁棒性的姿态估计。实验表明,该方法平均绝对角度误差小于0.03°,单次拟合耗时低于0.03 s,相较于最小中值平方法提速约300倍,在主元分析、随机采样一致性等传统方法基础上精度提升约10倍。该方法精度高、鲁棒性强、实时处理速度快,无需人工干预,适用于复杂工业环境下的管道端面自动化定位与基准构建,可为智能制造中的焊接路径规划与在线检测提供可靠技术支撑。
