Large Scattered Data Fitting Based on Radial Basis Functions

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.

Plane wave fitting of the internal tidal sea-surface height signatures extracted from the TOPEX/Poseidon altimeter data along satellite tracks

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.

Data Mining Based Research of Development Direction of Waist Protection Equipment

[Objectives]To explore the trend of brands towards the design of waist protection products through data mining,and to provide reference for the design concept of the contour of waist protection pillow.[Methods]The structural design information of all waist protection equipment was collected from the national Internet platform,and the data were classified and a database was established.IBM SPSS 26.0 and MATLAB 2018a were used to analyze the data and tabulate them in Tableau 2022.4.After the association rules were clarified,the data were imported into Cinema 4D R21 to create the concept contour of waist protection pillow.[Results]The average and standard deviation of the single airbag design were the highest in all groups,with an average of 0.511 and a standard deviation of 0.502.The average and standard deviation of the upper and lower dual airbags were the lowest in all groups,with an average of 0.015 and a standard deviation of 0.120;the correlation coefficient between single airbag and 120°arc stretching was 0.325,which was positively correlated with each other(P<0.01);the correlation coefficient between multiple airbags and 360°encircling fitting was 0.501,which was positively correlated with each other and had the highest correlation degree(P<0.01).[Conclusions]The single airbag design is well recognized by companies,and has received the highest attention among all brand products.While focusing on single airbag design,most brands will consider the need to add 120°arc stretching elements in product design.At the time of focusing on multiple airbag design,some brands believe that 360°encircling fitting elements need to be added to the product,and the correlation between the two is the highest among all groups.

Neural network approach for modification and fitting of digitized data in reverse engineering~

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.

Research on the Model of Linear Data Fitting Method

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.

Study on Growth and Development Rules and Growth Curve Fitting of Minghua Black Minks

Growth curves of Minghua black minks at 0-180 days old were fitted and analyzed by using two growth models Logistic and Gompertz. The results showed that the growth curves of Minghua black minks could be fitted very well by Logistic model and Gompertz model （the degree of fitting FF≥0.99）, but Gompertz model was better at fitting and predicting their weight.

Dynamics and data fitting of a time-delayed SIRS hepatitis B model with psychological inhibition factor and limited medical resources

Hepatitis B is an infectious disease worthy of attention.Considering the incubation period,psychological inhibition factor,vaccine,limited medical resources and horizontal transmission,an SIRS model is proposed to describe hepatitis B transmission dynamics.In order to describe the behavior changes caused by people's psychological changes,the non-monotonic incidence rate is adopted in the model.We use the saturated treatment rate to describe the limited medical resources.Mathematical analysis shows the existence conditions of the equilibria,forward or backward bifurcation,Hopf bifurcation and the Bogdanov-Takens bifurcation.During the observation of the case data of hepatitis B in China,it is found that there are mainly three features,periodic outbreaks,aperiodic outbreaks,and periodic outbreaks turns to aperiodic outbreaks.According to the above features,we select three different representative regions,Jiangxi,Zhejiang province and Beijing,and then use our model to fit the actual monthly hepatitis B case data.The basic reproduction numbers that we estimated are 1.7712,1.4805 and 1.4132,respectively.The results of data fitting are consistent with those of theoretical analysis.According to the sensitivity analysis of Ro,we conclude that reducing contact,increasing treatment rate,strengthening vaccination and revaccinating can effectively prevent and control the prevalence of hepatitis B.

FAIR + FIT: Guiding Principles and Functional Metrics for Linked Open Data(LOD) KOS Products

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.

Least squares fitting of coordinate parameters model

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.

Comparison of Data Screening Methods for Evaluating School-Level Fitness Patterns in Youth: Findings from the NFL PLAY 60 FITNESSGRAM Partnership Project

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.

Goodness-of-fit tests for multi-dimensional copulas:Expanding application to historical drought data

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.

Application of Newtonian approximate model to LIGO gravitational wave data processing

With the observation of a series of ground-based laser interferometer gravitational wave(GW)detectors such as LIGO and Virgo,nearly 100 GW events have been detected successively.At present,all detected GW events are generated by the mergers of compact binary systems and are identified through the data processing of matched filtering.Based on matched filtering,we use the GW waveform of the Newtonian approximate(NA)model constructed by linearized theory to match the events detected by LIGO and injections to determine the coalescence time and utilize the frequency curve for data fitting to estimate the parameters of the chirp masses of binary black holes(BBHs).The average chirp mass of our results is 22.05_(-6.31)^(+6.31)M_(⊙),which is very close to 23.80_(-3.52)^(+4.83)M_(⊙)provided by GWOSC.In the process,we can analyze LIGO GW events and estimate the chirp masses of the BBHs.This work presents the feasibility and accuracy of the low-order approximate model and data fitting in the application of GW data processing.It is beneficial for further data processing and has certain research value for the preliminary application of GW data.

从技术赋能到整体重塑:公共体育服务数字化治理的模式重构、组织变革及推进机制

数字时代我国公共体育服务从“技术赋能”到“整体重塑”的数字化进程被视为一个重塑多元主体治理关系及其能力的演变历程,对于提高公共体育服务供给效率具有重要意义。运用文献资料法、逻辑分析法等厘清了公共体育服务数字化治理的基本内涵及现存困境,重新审视了其模式重构的核心维度,深入阐释了其组织变革的动因特征,重点讨论了其推进机制的实践要素。研究认为:理念重构、价值重构、方式重构等形成模式重构的核心维度;管理思维转换、运行范式转换、决策方式转换等构成组织变革的动因特征;管理机制、考核机制、协调机制等为推进机制的实践要素。

智能手机GNSS数据质量分析与随机模型建立

为提高移动智能终端定位精度,利用小米8和华为Mate20手机采集多个卫星系统的观测数据并进行质量分析,通过不同卫星系统的伪距残差分别对信噪比模型参数进行估计,最后进行静态伪距单点定位实验。结果表明,手机端观测的BDS和GPS伪距精度接近,且高于GLONASS;相较于高度角,伪距残差与信噪比的相关性更强;在信噪比模型参数估计中,小米8拟合效果优于华为Mate20,BDS拟合效果差于其他卫星系统;参数拟合后的信噪比模型在水平和高程方向的定位精度分别为2.37 m和8.38 m,相较于高度角模型,定位精度提升约10%。

曲线曲面局部最小二乘渐进迭代逼近

作为一种有效的大数据拟合方法,曲线曲面最小二乘渐进迭代逼近方法(LSPIA)吸引了众多研究者的关注,并获得了广泛的应用。针对LSPIA算法拟合局部数据点效果较差的问题,提出了一种局部的LSPIA算法,称为LOCAL-LSPIA。首先,给定初始曲线(曲面)并从给定的数据点中选择部分数据点;然后在初始曲线(曲面)上选择需要调整的控制点;最后,LOCAL-LSPIA通过迭代调整这一部分控制点来生成一系列局部变化的拟合曲线(曲面),并且保证生成的曲线(曲面)的极限是在仅调整这部分控制点的情况下拟合部分数据点的最小二乘结果。在多个曲线曲面拟合上的实验结果表明,为达到相同的拟合精度,LOCAL-LSPIA算法比LSPIA算法需要的步骤和运算时间更少。因此,LOCAL-LSPIA是有效的,而且在拟合局部数据的情况下比LSPIA算法的收敛速度更快。

纬编电热针织物设计和性能评价

为了探究金属长丝作为电加热元件在纬编电热针织物中的应用,通过赛络菲尔纺工艺开发了棉/铜镁合金和棉/不锈钢复合导电纱,并与碳纤维进行比较,采用罗纹空气层加衬纬组织制作了电加热元件并联的3种电热织物,并对导电纱和纬编织物电热性能进行实测及数据拟合。结果显示:复合导电纱达到导电纱A类产品要求;在12 V电压时,棉/铜镁合金导电纱表面温度最高可达40.9℃;金属复合导电纱电热织物升温和时间、电压有关,电热织物的表面平衡温度与输入功率呈线性关系,温度达45℃以上时,电热织物电阻变化率低于2%,热稳定性好;相同条件下,棉/铜镁合金织物升温速度最快,输入功率最大,在4 V电压下最高温度达49.8℃;采用赛络菲尔复合导电纱开发罗纹空气层加衬纬的纬编电加热织物具有一定的可行性。

基于三维点云的采后香蕉表征褐变定量评估方法

【目的】研究采后香蕉的表征褐变并评估其衰老程度对香蕉保鲜管理至关重要,本研究致力于解决传统人工测量香蕉表征褐变存在的劳动强度大、效率低下的问题。【方法】提出一种基于三维点云的采后香蕉表征褐变过程定量评估方法。首先利用三维扫描仪获取香蕉的三维点云模型,重构出香蕉的几何模型;然后使用欧式聚类对香蕉几何模型进行点云滤波降噪处理;再结合图像阈值分割法与散点轮廓算法(Alpha Shapes)求出香蕉的体积、表面积和黑斑面积;最后利用傅里叶函数对香蕉表面黑斑变化过程进行模拟,确定香蕉表征褐变过程的评估模型。设计本算法与溢水法测量实际香蕉体积、手绘测量面积的对比试验。【结果】拟合香蕉的生长函数,回归直线对观测值的拟合程度R2=0.9816>0.75,验证了算法的有效性。对比试验结果表明,本算法与实际测量值的平均相对误差小于1%,验证了该算法的准确性和可行性。【结论】本研究可为香蕉的保鲜管理提供数据及技术支撑。

一种在尺度空间下基于边缘的角点目标检测方法

图像中的目标角点位置是实现很多计算机视觉任务的关键数据。为了克服传统检测算法产生的数据冗余问题,提出了一种在尺度空间下基于边缘的角点目标检测方法。首先,构建一个分组多层的尺度空间,将原图投影到其中后得到多个平滑图像。与此同时,采用定义的边缘算子检出平滑图像中所有边缘而得到多个按序存放的像素点集,当点集数量稳定时停止更大尺度的变换。然后,在当前尺度下,计算点集中各元素反映其角点强度的特征值。根据这些特征值变化规律检出角点的支撑集区间,并在此区间中采用高斯拟合函数确定最终的目标角点。实验表明,该方法能够检出特征显著的目标角点及其角度,其中合成图像精度在像素级,应用案例中的平均误差与图幅比约为1.5/100。

基于体质测试大数据的灰色关联分析:建模与实证

目前,中国普遍采用电子仪器采集学生体质测试结果,积累了大量具有大数据特征的原始数据。在面对体质测试大数据时,如何利用数学模型找出测试项目之间的相关性,从而准确描述其相关性的强弱,具有科学意义。采用改进的灰色关联分析模型,对西部某高校31198名大学生体质测试大数据进行分析。该模型改变了传统邓氏模型的计算过程,使其适用于大数据。结果表明:BMI值对女生下肢耐力和爆发力有较大影响,是女生最重要的体质测试指标;肺活量对男生的耐力、灵活性和下肢爆发力有不同的影响,是男生最重要的体质测试指标;长跑,即男子1000 m跑、女子800 m跑和立定跳远,不仅是身体素质的2个最重要的指标,而且它们之间存在着很强的相关性。改进的灰色关联分析为大数据环境下体质测量指标之间的相关性分析提供了新的思路,为不同领域的大数据分析提供了建模参考。

基于小扰动频率量测数据的电网节点惯量分布评估方法

惯量在电力系统抵抗扰动中起到关键作用。随着新能源渗透率的提升,电力系统中低惯量与惯量时空分布不均的特征日益凸显,准确评估电网节点惯量分布具有重要意义。为此,文中提出一种基于小扰动频率量测数据的节点惯量分布评估方法。首先,分析了频率与惯量的数学耦合机理,揭示了新型电力系统惯量分布特征。然后,根据单次小扰动下的频率量测数据与系统电源参数,分别提出了考虑各节点频率相较于系统中心频率变化水平偏差的节点等效惯量定义方法,以及基于自适应阶数多项式拟合的节点频率变化率计算方法,两层方法相结合即可计算出单次小扰动下的节点等效惯量。进一步,鉴于单次小扰动下求出的节点等效惯量具有一定的随机误差,提出考虑多次扰动事件评估结果的动态聚合策略,形成适用于新型电力系统的节点等效惯量分布评估方法。最后,分别以IEEE 39节点系统、中国某省级电网为例验证了所提方法的有效性。结果表明,所提方法所需数据量少,仅需各节点同步相量测量单元采集的频率量测数据即可实现对电网惯量分布的有效评估,评估结果准确性高且时效性强。