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).

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.

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.

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.

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.

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.

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.

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。

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。

基于插值修正ACER的脐带缆响应短期极值预测方法研究

针对脐带缆在随机载荷作用下其响应难以准确预测的问题,本文提出了一种基于插值技术与平均条件超越率(average conditional exceedance rate,ACER)的海洋脐带缆响应极值预测方法。构造随机波浪荷载作用下脐带缆结构响应的数值模型,获取脐带缆关键位置处的张力与曲率响应时程数据。分别求解张力和曲率时间序列对应的1~4阶ACER函数值,选取合适阶数的ACER函数,采用三次样条插值与B样条插值技术对平均条件超越点的尾部区域进行插值。对插值曲线外推,实现在不同超越概率下脐带缆的结构响应极值预测。本方法适用于非独立同分布下的海洋脐带缆张力与曲率响应数据的极值预测,并利用Gumbel极值分布模型进行对比,讨论并验证本文所提方法在海洋脐带缆响应极值预测中的适用性。

铁路路基动力响应的2.5D有限元方法研究现状及展望

作为一种频域计算方法,2.5D有限元具备计算效率高、内存占用小等优势,同时也存在诸多局限。经过20余年的发展,2.5D有限元方法已经具备了描述复杂土体本构关系和复杂路基几何特征条件下铁路路基动力响应的能力。荷载输入方法、建模策略和波动吸收边界的持续优化使得2.5D有限元方法的精度不断提高,二维插值方法则为进一步提升计算效率提供了思路。目前,2.5D有限元已经成为铁路路基动力响应研究中的常用方法。为了理清铁路路基动力响应2.5D有限元方法的发展脉络,分别从荷载输入、路基系统、响应输出和计算精度及效率的提升方面总结了其发展现状,介绍了2.5D有限元在发展过程中遇到的瓶颈问题及解决对策。在此基础上,针对算法的精度和效率、研究的对象和内容进行了进一步的讨论和展望。

机械臂多目标最优轨迹的自适应惩罚MOEA/D规划

为了减少机械臂的工作时间和工作过程中的冲击量,提出了基于自适应惩罚MOEA/D算法的时间-冲击多目标规划方法。介绍了PUMA560机械臂结构,并建立了机械臂的连杆坐标系。建立了以减小机械臂工作时间和冲击为综合目标的优化模型,并分析了5次多项式插值函数。通过编码和建立适应度函数,将轨迹规划问题转化为最优基因搜索问题。根据邻域内解的密度设置了自适应惩罚因子,提出了机械臂轨迹的自适应惩罚MOEA/D规划方法。经仿真验证,自适应惩罚MOEA/D算法搜索的Pareto前沿解质量高于标准MOEA/D算法、文献[10]新型MOEA/D算法。且经过优化,机械臂工作时间减少了7.68%,冲击减少了17.32%。实验结果表明,自适应惩罚MOEA/D算法在机械臂轨迹规划中具有优越性。

装载机自动铲掘轨迹及轨迹误差补偿研究

根据装载机工作装置各杆件几何关系和试验点位数据,计算出了试验自动铲掘轨迹。通过对不同铲掘深度下的轨迹误差计算分析,提出了一种通过修正初始规划轨迹的误差补偿方法,并使用插值法对误差补偿效果进行了初步验证。最后,通过试验对误差补偿前后的轨迹误差大小以及试验铲掘效果进行了对比分析。试验结果表明,补偿后的铲掘轨迹误差减小了51.39%,铲掘质量提高了10.55%,单位时间铲装量增大了3.33%。

基于细化等值面拓扑的病灶切片三维重建方法

脑组织病灶切片的三维重构对于了解神经胶质神经瘤状态具有重要意义,可用于鉴别诊断、手术模拟等。移动立方体(MC)算法是经典的多边形曲面重建算法,具有简单易实现的优点,但其存在低效且梯级现象明显的情况。针对该问题,本研究提出一种细化等值面拓扑的病灶切片空间堆叠重建方法(SSR-RI),旨在实现拓扑构形与运行效率的优化。SSR-RI通过构建空间坐标系对磁共振图像(MRI)切片邻近图进行处理,为了改善双线性插值法中图像分量易受损的问题,提出一种自适应空间插值法,根据灰度值变化自适应选择插值点,对周围进行扩充。在结合等法线顶点的基础上,设计了一种细化等值面提取方式的堆叠重建方法,以提高堆叠速度,并减少梯级问题。为了进一步优化SSR-RI的三维重建效果,提出一种改进的局部反射光照法(PR)以绘制三维病变,利用镜面颜色反射(SCR)与镜面指数(SE)对重建体进行渲染优化。使用公开脑肿瘤分割数据集BraTS的618例病例开展三维重建实验,以验证所提出方法性能。实验结果显示,所提算法的重建时间只需2.124 s,F-score值达到0.845,SSIM值达到0.81,相较于MC算法减少了38%的重建时间,F-score值和SSIM值分别提高了30.89%和38.4%。重构体序列间结构紧密,视觉效果更富立体感和纹理感,有效地提高了三维重建的绘制效率。