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.

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.

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.

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.

Research on the Spatial Interpolation Method for Temperature inInner Mongolia

以内蒙古自治区为研究区，采用反距离权重法、样条函数法和普通克里金法对研究区119个气象观测站点的气温数据进行空间插值，结果表明，普通克里金法由于能够最优地描述气温在空间上的连续性变化特征，插值精度最高；反距离权重法插值精度次之，但其模拟结果趋于产生牛眼模式，且结果不能外推；样条函数法由于受到边界效应的影响，插值精度最低。

High Accurate Interpolation of NURBS Tool Path for CNC Machine Tools

Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation.Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.

A comparative study of spatial interpolation methods fordetermining fishery resources density in the Yellow Sea

Spatial interpolation is a common tool used in the study of fishery ecology, especially for the construction of ecosystem models. To develop an appropriate interpolation method of determining fishery resources density in the Yellow Sea, we tested four frequently used methods, including inverse distance weighted interpolation(IDW), global polynomial interpolation(GPI), local polynomial interpolation(LPI) and ordinary kriging(OK).A cross-validation diagnostic was used to analyze the efficacy of interpolation, and a visual examination was conducted to evaluate the spatial performance of the different methods. The results showed that the original data were not normally distributed. A log transformation was then used to make the data fit a normal distribution. During four survey periods, an exponential model was shown to be the best semivariogram model in August and October 2014, while data from January and May 2015 exhibited the pure nugget effect.Using a paired-samples t test, no significant differences(P>0.05) between predicted and observed data were found in all four of the interpolation methods during the four survey periods. Results of the cross-validation diagnostic demonstrated that OK performed the best in August 2014, while IDW performed better during the other three survey periods. The GPI and LPI methods had relatively poor interpolation results compared to IDW and OK. With respect to the spatial distribution, OK was balanced and was not as disconnected as IDW nor as overly smooth as GPI and LPI, although OK still produced a few "bull's-eye" patterns in some areas.However, the degree of autocorrelation sometimes limits the application of OK. Thus, OK is highly recommended if data are spatially autocorrelated. With respect to feasibility and accuracy, we recommend IDW to be used as a routine interpolation method. IDW is more accurate than GPI and LPI and has a combination of desirable properties, such as easy accessibility and rapid processing.

Water distribution extracted from mining subsidence area using Kriging interpolation algorithm

By comprehensively analyzing the data of geology and mining, Kriging algorithm was introduced to analyze the thematic information of geological data, to rapidly extract mining parameters for predicting mining subsidence, and to effectively integrate geomorphology and predict information. As a result, the change information of water body is successfully detected from the prediction of surface subsidence due to mining activity. Analysis shows that the elevation of farmland in the west side of water body will be lower than ever, and the west part farmland will be submerged. However, there is no evidence for impacting the villages. All the information provides a reference for efficiently assessing environmental impact due to mining activity, which can help to govern the subsidence of the area reasonably.

Circular Interpolation Algorithms of 5-Axis Simultaneous CNC System

Spatial circular arc can be machined conveniently by a 5-axis NC machine tool.Based on the data sampling method,circular interpolation in two-dimensional plane is discussed briefly.The key is to solve the problem of circular center ex- pressed in the workpiece coordinate system by means of the transformation matrix.Circular interpolation in three-dimensional space is analyzed in detail.The method of undetermined coefficient is used to solve the center of the spatial circle and the method of coor- dinate transformation is used to transform the spatial circle into the XY-plane.Circular arc in three-dimensional space can be ma- chined by the positional 5-axis machining and the conical surface can be machined by the continuous 5-axis machining.The velocity control is presented to avoid the feedrate fluctuation.The interpolation algorithms are tested by a simulation example and the inter- polation algorithms are proved feasible.The algorithms are applied to the 5-axis CNC system software.

A Study on Spatial Interpolation of Temperature in Anhui Province Based on ANUSPLIN

To achieve refined temperature grid data with high accuracy and high spatial resolution,hourly temperature grid dataset with spatial resolution of 1 km in Anhui Province from January to December in 2016 was established using the ANUSPLIN thin plate spline algorithm,which meets the needs of climate change research and meteorological disaster risk assessment. And the interpolation error was analyzed. The results show that the interpolated values of hourly temperature by ANUSPLIN are close to the observed values in 2016. The error is generally below 1. 5 ℃,and the root mean square error is 0. 937 6 ℃. On monthly scale,the interpolated values of hourly temperature by ANUSPLIN are also close to the observed values.In October,November,June and May,the interpolation accuracy is the highest,and the proportion of absolute error of hourly temperature lower than 2 ℃ is up to 99%,97. 4%,98. 1% and 97. 4% respectively. In February,March,August and December,the interpolation accuracy is the lowest,and the proportion of absolute error higher than 2 ℃ is 8. 1%,5. 3%,4. 1% and 4. 2% respectively. Due to the effect of complex topography in Anhui,the interpolation accuracy is the lowest in the mountainous areas of southern and western Anhui,and the interpolation error in these regions even exceeds 1. 5 ℃ annually and 1. 8 ℃ monthly.

Sinogram Interpolation Method for Sparse-Angle Tomography

In sparse-angle X-ray tomography reconstruction, where only a small number of projection images are taken around the object, appropriate sinogram interpolation has a significant impact on image quality. A novel sinogram interpolation method is introduced for extreme sparse tomographic reconstruction where only nine measured projection images are available. The sinogram is interpolated by solving characteristics of the so-called warps, which can be considered as approximation sine waves in a limited region. The numerical evidence suggests that this approach gives superior results over standard interpolation methods when the tomographic data are extremely sparse and noisy.

Performance of global look-up table strategy in digital image correlation with cubic B-spline interpolation and bicubic interpolation

Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation(DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss–Newton(IC-GN) algorithm.The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.

Study on Control Algorithm for Continuous Segments Trajectory Interpolation

In CNC machining,the complexity of the part contour causes a series of problems including the repeated start-stop of the motor,low machining efficiency,and poor machining quality.To relieve those problems,a new interpolation algorithm was put forward to realize the interpolation control of continuous sections trajectory.The relevant error analysis of the algorithm was also studied.The feasibility of the algorithm was proved by machining experiment using a laser machine to carve the interpola- tion trajectory in the CNC system GT100.This algorithm effectively improved the machining efficiency and the contour quality.

Accuracy Assessment and Comparative Analysis of IDW, Spline and Kriging in Spatial Interpolation of Landform (Topography): An Experimental Study

It is practically impossible and unnecessary to obtain spatial-temporal information of any given continuous phenomenon at every point within a given geographic area. The most practical approach has always been to obtain information about the phenomenon as in many sample points as possible within the given geographic area and estimate the values of the unobserved points from the values of the observed points through spatial interpolation. However, it is important that users understand that different interpolation methods have their strength and weaknesses on different datasets. It is not correct to generalize that a given interpolation method (e.g. Kriging, Inverse Distance Weighting (IDW), Spline etc.) does better than the other without taking into cognizance, the type and nature of the dataset and phenomenon involved. In this paper, we theoretically, mathematically and experimentally evaluate the performance of Kriging, IDW and Spline interpolation methods respectively in estimating unobserved elevation values and modeling landform. This paper undertakes a comparative analysis based on the prediction mean error, prediction root mean square error and cross validation outputs of these interpolation methods. Experimental results for each of the method on both biased and normalized data show that Spline provided a better and more accurate interpolation within the sample space than the IDW and Kriging methods. The choice of an interpolation method should be phenomenon and data set structure dependent.