Suitable region of dynamic optimal interpolation for efficiently altimetry sea surface height mapping

The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compared with the linear optimal interpolation(LOI)method,the DOI method can improve the accuracy of gridded ADT locally but with low computational efficiency.Consequently,considering both computational efficiency and accuracy,the DOI method is more suitable to be used only for regional applications.In this study,we propose to evaluate the suitable region for applying the DOI method based on the correlation between the absolute value of the Jacobian operator of the geostrophic stream function and the improvement achieved by the DOI method.After verifying the LOI and DOI methods,the suitable region was investigated in three typical areas:the Gulf Stream(25°N-50°N,55°W-80°W),the Japanese Kuroshio(25°N-45°N,135°E-155°E),and the South China Sea(5°N-25°N,100°E-125°E).We propose to use the DOI method only in regions outside the equatorial region and where the absolute value of the Jacobian operator of the geostrophic stream function is higher than1×10^(-11).

Research on Interpolation Method for Missing Electricity Consumption Data

Missing value is one of the main factors that cause dirty data.Without high-quality data,there will be no reliable analysis results and precise decision-making.Therefore,the data warehouse needs to integrate high-quality data consistently.In the power system,the electricity consumption data of some large users cannot be normally collected resulting in missing data,which affects the calculation of power supply and eventually leads to a large error in the daily power line loss rate.For the problem of missing electricity consumption data,this study proposes a group method of data handling(GMDH)based data interpolation method in distribution power networks and applies it in the analysis of actually collected electricity data.First,the dependent and independent variables are defined from the original data,and the upper and lower limits of missing values are determined according to prior knowledge or existing data information.All missing data are randomly interpolated within the upper and lower limits.Then,the GMDH network is established to obtain the optimal complexity model,which is used to predict the missing data to replace the last imputed electricity consumption data.At last,this process is implemented iteratively until the missing values do not change.Under a relatively small noise level(α=0.25),the proposed approach achieves a maximum error of no more than 0.605%.Experimental findings demonstrate the efficacy and feasibility of the proposed approach,which realizes the transformation from incomplete data to complete data.Also,this proposed data interpolation approach provides a strong basis for the electricity theft diagnosis and metering fault analysis of electricity enterprises.

Integer multiple quantum image scaling based on NEQR and bicubic interpolation

As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been studied.In this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral multiple.Firstly,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules.Then,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic modules.Finally,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these pixels.Through simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.

Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

Comparison of Spatial Interpolation Methods of Precipitation Data in Central Macedonia, Greece

The purpose of this paper is to investigate the spatial interpolation of rainfall variability with deterministic and geostatic inspections in the Prefecture of Kilkis (Greece). The precipitation data where recorded from 12 meteorological stations in the Prefecture of Kilkis for 36 hydrological years (1973-2008). The cumulative monthly values of rainfall were studied on an annual and seasonal basis as well as during the arid-dry season. In the deterministic tests, the I.D.W. and R.B.F. checks were inspected, while in the geostatic tests, Ordinary Kriging and Universal Kriging respectively. The selection of the optimum method was made based on the least Root Mean Square Error (R.M.S.E.), as well as on the Mean Error (M.E.), as assessed by the cross validation analysis. The geostatical Kriging also considered the impact of isotropy and anisotropy across all time periods of data collection. Moreover, for Universal Kriging, the study explored spherical, exponential and Gaussian models in various combinations. Geostatistical techniques consistently demonstrated greater reliability than deterministic techniques across all time periods of data collection. Specifically, during the annual period, anisotropy was the prevailing characteristic in geostatistical techniques. Moreover, the results for the irrigation and seasonal periods were generally comparable, with few exceptions where isotropic methods yielded lower (R.M.S.E.) in some seasonal observations.

Missing interpolation model for wind power data based on the improved CEEMDAN method and generative adversarial interpolation network

Randomness and fluctuations in wind power output may cause changes in important parameters(e.g.,grid frequency and voltage),which in turn affect the stable operation of a power system.However,owing to external factors(such as weather),there are often various anomalies in wind power data,such as missing numerical values and unreasonable data.This significantly affects the accuracy of wind power generation predictions and operational decisions.Therefore,developing and applying reliable wind power interpolation methods is important for promoting the sustainable development of the wind power industry.In this study,the causes of abnormal data in wind power generation were first analyzed from a practical perspective.Second,an improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)method with a generative adversarial interpolation network(GAIN)network was proposed to preprocess wind power generation and interpolate missing wind power generation sub-components.Finally,a complete wind power generation time series was reconstructed.Compared to traditional methods,the proposed ICEEMDAN-GAIN combination interpolation model has a higher interpolation accuracy and can effectively reduce the error impact caused by wind power generation sequence fluctuations.

OPTIMAL BIRKHOFF INTERPOLATION AND BIRKHOFF NUMBERS IN SOME FUNCTION SPACES

This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

Interpolation Technique for the Underwater DEM Generated by an Unmanned Surface Vessel

High-resolution underwater digital elevation models(DEMs)are important for water and soil conservation,hydrological analysis,and river channel dredging.In this work,the underwater topography of the Panjing River in Shanghai,China,was measured by an unmanned surface vessel.Five different interpolation methods were used to generate the underwater DEM and their precision and applicability for different underwater landforms were analyzed through cross-validation.The results showed that there was a positive correlation between the interpolation error and the terrain surface roughness.The five interpolation methods were all appropriate for the survey area,but their accuracy varied with different surface roughness.Based on the analysis results,an integrated approach was proposed to automatically select the appropriate interpolation method according to the different surface roughness in the surveying area.This approach improved the overall interpolation precision.The suggested technique provides a reference for the selection of interpolationmethods for underwater DEMdata.

Quantum color image scaling based on bilinear interpolation

As a part of quantum image processing, quantum image scaling is a significant technology for the development of quantum computation. At present, most of the quantum image scaling schemes are based on grayscale images, with relatively little processing for color images. This paper proposes a quantum color image scaling scheme based on bilinear interpolation, which realizes the 2^(n_(1)) × 2^(n_(2)) quantum color image scaling. Firstly, the improved novel quantum representation of color digital images(INCQI) is employed to represent a 2^(n_(1)) × 2^(n_(2)) quantum color image, and the bilinear interpolation method for calculating pixel values of the interpolated image is presented. Then the quantum color image scaling-up and scaling-down circuits are designed by utilizing a series of quantum modules, and the complexity of the circuits is analyzed.Finally, the experimental simulation results of MATLAB based on the classical computer are given. The ultimate results demonstrate that the complexities of the scaling-up and scaling-down schemes are quadratic and linear, respectively, which are much lower than the cubic function and exponential function of other bilinear interpolation schemes.

Two Families of Multipoint Root-Solvers Using Inverse Interpolation with Memory

In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.

The QCD Ground State Chiral Tetrahedron Symmetry

We propose that the exotic meson tetraquark ud~dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, dd~ and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The ud~dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũdd~ for the electrons and ud~dd~ for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state ud~dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.

考虑自由液面影响的多凸体结构浮态计算方法

针对液舱内自由液面对浮态和稳性的影响,文中提出了一种新的多凸体组合结构浮态算法。该方法将浮体和液舱分解成多个四面体单元,通过分析每个四面体与水面/液面的相对位置关系来确定浮体的浮力和浮心以及液舱液体的重心。该方法还提出了一种改进的双重迭代法用来确定多凸体组合结构的浮态:内层迭代法模拟浮体的升沉运动,得到浮体外的水面方程和液舱内的液面方程;通过外层迭代法模拟浮体的旋转运动。两种迭代方法交替进行,直至浮体的重力作用线和浮力作用线之间的距离满足精度要求,同时重力等于浮力。自编程序对某半潜船和某半潜式海洋平台的多种典型工况进行了浮态计算,同时也考虑了自由液面影响。此外利用Maxsurf建模进行了对比分析,还利用AUTOCAD进行了精度验证。对照结果表明:该研究提出的算法可以考虑自由液面对浮态的影响,原理清晰,收敛性好;算法无论对传统的单凸体结构(例如单体船),还是多凸体结构(例如多体船、漂浮式海洋平台等)均更容易取得准确解,且计算效率更高;算法可以实现“搭积木”式的建模方式,多工况建模时可以极大地减小工作量;算法无需依赖国外第三方图形平台(比如AUTOCAD、CATIA),可为我国相关工业软件的国产化打下良好的基础。

一种基于四平面的图像插值算法

针对现有图像插值算法存在的不足,提出了四平面插值算法,根据待插入点周围的4个像素点结合周边的像素点,从4个平面中选择一个作为插值平面,对于不符合平面插值的情况,则利用双线性插值,规避了用同一个插值公式对所有像素进行插值存在的不足,实验结果和数据分析表明了本方法的有效性。

应用时空复合趋势面Kriging方法插值地表沉降

通过布设监测点可反映地表沉降变化趋势,确保施工和运营期间安全,但沉降监测点数量有限,且易受施工作业、天气等因素干扰导致数据缺失或污染,因此需对监测区域数据进行插值处理。针对采用传统地统计插值方法估计地铁地表沉降趋势精度较低的问题,提出了一种基于时空复合趋势面的Kriging插值方法。以乌鲁木齐地铁3号线2017年6月24日—9月3日共15期地铁地表沉降观测值为实验数据,分别采用两种方法对沉降监测点缺失数据进行插补。结果表明,相较于传统方法,基于时空复合趋势面的Kriging插值方法的拟合精度更高,RMSE可降低约35%。

数控系统样条曲线插补技术研究综述

传统数控系统加工复杂曲线时,一般采用微小线段或圆弧段逼近的方法,加工精度低,易引发刀具抖动、机床振动等问题。随着CAD/CAM技术的发展,现代数控机床向高速度、高柔性方向发展,基于高质量加工的要求,提出样条曲线插补方法。对样条曲线插补方法进行综述,首先阐述了插补技术的重要性;其次从进给速度、加工精度等角度系统分析了样条曲线插补方法,分别介绍了A样条插补、B样条插补和C样条插补;最后描述了三种插补方法的发展过程和最新研究动态,对其未来趋势做了总结和展望。

非理想相贯焊缝自动化焊接的运动控制研究

为了实现对加工装配存在误差的大构件相贯焊缝的多层多道自动化焊接,在介绍四轴联动焊接机器人结构及工作原理的基础上,建立了集斜交、偏置的通用相贯焊缝数学模型,提出一种连续控制焊枪位置参数及姿态调整值的计算方法,利用关键点示教+分段空间圆弧插补确定焊枪位置,主法面二分角法给出焊枪姿态,最后采用PC机+运动控制卡的方式构成伺服控制系统,驱动电机执行运动控制算法。该运动控制算法通用性较强,对管管焊缝工程化应用具有重要的参考价值。

中国舞蹈艺术的审美文化观——内外部相融的舞蹈研究方法论探讨

舞蹈创作和批评研究既包括“生命体”身体意识和时空关系的内部规律探讨,也要阐释舞蹈与人类其他社会实践的外部规律联系,内外部结合的方法论很有意义。舞蹈分析与动作分析并非相同概念。舞蹈创作和研究从业者除了提升动作分析理论,还应密切关注新的编舞走向和跨学科的舞蹈研究趋势。20世纪八九十年代以来,西方舞蹈学者的舞蹈分析框架,融入了文化研究,揭示出仅作动作分析或内部研究的局限性;中国舞蹈学者的元素分析、形态分析也与舞蹈文化密切相关。在全球在地化和全媒体时代,作为一种方法论,舞蹈艺术的“审美文化观”将舞蹈创作到批评视为审美文化活动,承袭了古今中西文化汇通的中国美学、文学、理论界和舞蹈学的相关研究,自律论、他律论与通律论相辅相成,重视具体的真实的人本体,一方面强调侧重内部研究的“跨媒介性”视角,另一方面也倡导将内外部打通的“跨文化”观,尝试既在审美中看舞蹈文化,也在文化中看舞蹈审美,是一种具有“中国式现代化”路径的文艺观和方法论。“点线面体”充分融合的审美文化四面体图式,基于艾布拉姆斯“四要素”三角和格里斯沃尔德“文化菱形”理论基础,融入拉班动作分析四面体思路,并与中国人文社科学术界倡导多年的“审美文化”研究相通。

基于高倍过采样与加窗插值FFT的电力谐波分析

为提高谐波分析精度,分析了信号加窗引起的信噪比损失以及AD转换产生的量化误差,阐述了过采样技术提高信噪比的原理。在此基础上,提出了基于高倍过采样和加窗插值快速傅里叶变换(fast Fourier transform, FFT)的谐波分析方法。该方法充分利用AD转换器的潜力,以尽量高的采样速率进行AD采样,同时通过均值滤波避免高倍过采样引起的采样数据量激增问题。详细研究了所提谐波分析方法对信号中谐波分量幅值和相位的影响,并给出了简洁实用的谐波幅值和相位校正方法。仿真表明,所提方法可在不增加系统成本的前提下改善加窗插值FFT的抗噪声能力,提高谐波分析精度。

紫外可见波长溶液标准物质的研制

以紫外可见区无吸收的高氯酸溶液作为空白基体,利用稀土元素钬和钕在紫外可见光区丰富的光谱特征吸收,研制一种可以覆盖200~900nm的紫外可见区的波长溶液标准物质。采用对峰值点附近进行3次样条插值进行数据处理,并以插值后的峰值数据作为峰值波长,分辨力可到小数点后两位。经过均匀性和稳定性检验,由9家实验室采用高精度紫外可见分光光度计对该标准物质进行协同定值,并进行不确定度评定。结果表明,该标准物质均匀性良好,在25℃下保存稳定性在1年以上。该标准物质可应用于光谱光度测量仪器的波长校准和期间核查等。

基于GRA-GRU的淮河流域水质预测研究

水质指标具有多元相关性、时序性和非线性的特点,为有效预测河流水质变化,针对水质数据存在缺失和异常的问题,提出基于灰色关联分析-门控循环单元(Grey Relational Analysis-Gated Recurrent Unit, GRA-GRU)的水质预测模型。以淮河流域水质数据为样本,使用线性插值修补缺失数据和剔除的异常数据。使用灰色关联分析计算不同水质指标间的相关性,选择高相关性的水质指标以确定输入变量,并使用门控循环单元(Gated Recurrent Unit, GRU)预测不同的水质指标。将GRA-GRU的预测结果与反向传播神经网络(Back Propagation Neural Network, BPNN)、循环神经网络(Recurrent Neural Network, RNN)、长短期记忆神经网络(Long Short Term Memory, LSTM)、GRU及灰色关联分析-长短期记忆神经网络(Grey Relational Analysis-Long Short Term Memory, GRA-LSTM)进行对比分析,结果显示GRA-GRU在不同水质指标预测上具有较好的适应性,可以有效降低预测误差。其中,与其他模型相比,GRA-GRU预测的化学需氧量在均方根误差上分别降低了3.617%、0.681%、0.478%、1.505%和0.471%。