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.

Approximate solution of Volterra-Fredholm integral equations using generalized barycentric rational interpolant

It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation.However,classical rational interpolation has some deficiencies such as uncontrollable poles and low convergence order.In contrast with the classical rational interpolants,the generalized barycentric rational interpolants which depend linearly on the interpolated values,yield infinite smooth approximation with no poles in real numbers.In this paper,a numerical collocation approach,based on the generalized barycentric rational interpolation and Gaussian quadrature formula,was introduced to approximate the solution of Volterra-Fredholm integral equations.Three types of points in the solution domain are used as interpolation nodes.The obtained numerical results confirm that the barycentric rational interpolants are efficient tools for solving Volterra-Fredholm integral equations.Moreover,integral equations with Runge’s function as an exact solution,no oscillation occurrs in the obtained approximate solutions so that the Runge’s phenomenon is avoided.

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 Methods for Nitrate Interpolation in Wells in Aguascalientes, Mexico

The accuracy of interpolation models applied to groundwater depends, among other factors, on the interpolation method chosen. Therefore, it is necessary to compare different approaches. For this, different methods of interpolation of nitrate concentrations were contrasted in sixty-seven wells in an aquifer in Aguascalientes, Mexico. Four general interpolation methods were used in ArcGIS 10.5 to make the maps: IDW, Kriging, Natural Neighbor and Spline. In the modeling, only method type was varied. The input parameters (location, temporality, and nitrate concentration) were the same in the four interpolations;despite this, different maximum and minimum values were obtained for each interpolation method: for IDW, 0.2 to 22.0 mg/l, for Kriging, 3.5 to 16.5 mg/l, for Natural Neighbor, 0.3 to 21.7 mg/l and for Spline −30.8 to 37.2 mg/l. Finally, an assessment of the maps obtained was conducted by comparing them with the Official Mexican Standard (OMS), where 24 of the 67 wells were found outside the 10 mg/l that the OMS establishes as maximum permissible limit for human consumption. Taking as a starting point the measured values of nitrates (0.25 to 22.12 mg/l), as well as the spatial distribution of the interpolated values, it was determined that the Krigging method best fitted the data measured in the wells within the studied aquifer.

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.

Intelligent NURBS Interpolator Based on the Adaptive Feedrate Control

To satisfy the need for high-speed and high-accuracy machining of NURBS curve. Firstly the form of NURBS curve is analyzed and Talor＇s expansion of the parameter u with respect to time t is used to obtain the algorithm of the first order approximation interpolation. Secondly, based on the algorithm of the controlled chord error interpolator, an intelligent interpolation algorithm of the adaptive feedrate control is proposed. According to the actual machining capacity of machine tools, this algorithm uses look-ahead method, which dispenses with the complicated computation of the end point estimation of NURBS curve, to analyze the curve segment required by the maximum deceleration distance. Thus, the feedrate could decrease in advance and vary with the curvature and the variation ratio of curvature, which makes machining motion quite smooth. Not only could high accuracy and fine surface quality be achieved during high-speed machining, but also the overload of cutter tools is avoided on comers. Finally, in order to facilitate the calculation of interpolation, the dynamic matrix representation and efficient algorithm of curvature computation of the NURBS curve are presented,

NURBS CURVE INTERPOLATOR WITH ADAPTIVE ACCELERATION-DECELERATION CONTROL

The feedrate profile of non-uniform rational B-spline （NURBS） interpolation due to the contour errors is analyzed. A NURBS curve interpolator with adaptive acceleration-deceleration control is presented. In interpo- lation preprocessing, the sensitive zones of feedrate variations are processed with acceleration-deceleration control. By using the proposed algorithm, the machining accuracy is guaranteed and the feedrate is adaptively adjusted to he smoothed. The mechanical shock imposed in the servo system is avoided by the first and the second time derivatives of feedrates. A simulation of NURBS interpolation is given to demonstrate the validity and the effectiveness of the algorithm. The proposed interpolator can also be applied to the trajectory planning of the other parametric curves.

Design and Implementation of a Novel Area-Efficient Interpolator

This paper presents the design considerations and implementation of an area-efficient interpolator suitable for a delta-sigma D/A converter. In an effort to reduce the area and design complexity, a method for designing an FIR filter as a tapped cascaded interconnection of identical subfilters is modified. The proposed subfilter structure further minimizes the arithmetic number. Experimental results show that the proposed interpolator achieves the design specification,exhibiting high performance and hardware efficiency,and also has good noise rejection capability. The interpolation filter can be applied to a delta-sigma DAC and is fully functional.

Analysis and Design of a Phase Interpolator for Clock and Data Recovery

In this paper,a detailed analysis of a phase interpolator for clock recovery is presented. A mathematical model is setup for the phase interpolator and we perform a precise analysis using this model. The result shows that the output amplitude and linearity of phase interpolator is primarily related to the difference between the two input phases. A new encoding pattern is given to solve this problem. Analysis in the circuit domain was also undertaken. The simulation results show that the relation between RC time-constant and time difference of input clocks affects the linearity of the phase interpolator. To alleviate this undesired effect, two adjustable-RC buffers are added at the input of the PI. Finally,a 90nm CMOS phase interpolator,which can work in the frequency from 1GHz to 5GHz,is proposed. The power dissipation of the phase interpolator is lmW with a 1.2V power supply. Experiment results show that the phase interpolator has a monotone output phase and good linearity.

Realization Methodology of a 5-axis Spline Interpolator in an Open CNC System

By making use of the advantages of non-uniform rational B-spline （NURBS） curves to represent spatial curves, an instruction format with double NURBS curves suitable for 5-axis coordinated real-time interpolation is presented to replace the current 5-axis coordinated linear interpolation method defective in low-speed, low-accuracy and enormous numerical control （NC） files in sculptured surface machining. A generation procedure of the NC files with the presented format is introduced and the method to realize the interpolation in an open computer numerical control （CNC） system is developed by ourselves. These illustrated the feasibility of the proposed method and its capability of avoiding all the shortages of 5-axis linear interpolation method.

Development of FPGA Based NURBS Interpolator and Motion Controller with Multiprocessor Technique

The high-speed computational performance is gained at the cost of huge hardware resource,which restricts the application of high-accuracy algorithms because of the limited hardware cost in practical use.To solve the problem,a novel method for designing the field programmable gate array(FPGA)-based non-uniform rational B-spline(NURBS) interpolator and motion controller,which adopts the embedded multiprocessor technique,is proposed in this study.The hardware and software design for the multiprocessor,one of which is for NURBS interpolation and the other for position servo control,is presented.Performance analysis and experiments on an X-Y table are carried out,hardware cost as well as consuming time for interpolation and motion control is compared with the existing methods.The experimental and comparing results indicate that,compared with the existing methods,the proposed method can reduce the hardware cost by 97.5% using higher-accuracy interpolation algorithm within the period of 0.5 ms.A method which ensures the real-time performance and interpolation accuracy,and reduces the hardware cost significantly is proposed,and it’s practical in the use of industrial application.

An Optimal Feed Interpolator Based on G^2 Continuous Bézier Curves for High-Speed Machining of Linear Tool Path

A numerical control (NC) tool path of digital CAD model is widely generated as a set of short line segments in machining. However, there are three shortcomings in the linear tool path, such as discontinuities of tangency and curvature, huge number of line segments, and short lengths of line segments. These disadvantages hinder the development of high speed machining. To smooth the linear tool path and improve machining efficiency of short line segments, this paper presents an optimal feed interpolator based on G^2 continuous Bézier curves for the linear tool path. First, the areas suitable for fitting are screened out based on the geometric characteristics of continuous short segments (CSSs). CSSs in every area are compressed and fitted into a G^2 Continuous Bézier curve by using the least square method. Then a series of cubic Bézier curves are generated. However, the junction between adjacent Bézier curves is only G^0 continuous. By adjusting the control points and inserting Bézier transition curves between adjacent Bézier curves, the G^2 continuous tool path is constructed. The fitting error is estimated by the second-order Taylor formula. Without iteration, the fitting algorithm can be implemented in real-time environment. Second, the optimal feed interpolator considering the comprehensive constraints (such as the chord error constraint, the maximum normal acceleration, servo capacity of each axis, etc.) is proposed. Simulation and experiment are conducted. The results shows that the proposed method can generate smooth path, decrease the amount of segments and reduce machining time for machining of linear tool path. The proposed research provides an effective method for high-speed machining of complex 2-D/3-D profiles described by short line segments.

A Real-time NURBS Surface Interpolator for 5-axis Surface Machining

A real-time non-uniform rational B-spline （NURBS） surface interpolator is proposed and 5-axis machining method with a flat-end cutter is discussed. With the Taylor expansion and the coordinate transformation, the algorithms of NURBS interpolation, cutter effective machining radius, cutter offsetting and.inverse kinematics are deduced and implemented, respectively. Different from the conventional free-form surface machining, the proposed interpolator can real-time generate the motion commands of computer numerical control （CNC） machines with CC feedrate, rather than that of CL. An example part surface is demonstrated and the results of simulation show that the proposed method can be applied in actual 5-axis surface machining.

LOOK-AHEAD ALGORITHM FOR VELOCITY CONTROL BASED ON PARAMETERIZED CURVE INTERPOLATOR

To avoid suffering gouge and transient overshooting in high speed cutting machining, a novel parametefized curve interpolator model with velocity look-ahead algorithm is proposed. Based on a prearrangement step interpolation algorithm for parameterized curves and considering high curvature points, parameterized curve tool path is divided into acceleration segments and deceleration segments by look-ahead algorithm. Under condition of characteristics of acceleration and deceleration stored in control system, deceleration before high curvature points and acceleration after high curvature points are realized in real-time in high speed cutting machining. Based on new parameterized curve interpolator model with velocity look-ahead algorithm, a real cubic spline is machined simulativly. The simulation results show that velocity look-ahead algorithm improves velocity changing more smoothly.

A Universal Approach to Designing an Image Interpolator with an Image Smoothing Filter

A number of conventional interpolation techniques have been proposed. However, it seems that there do not exist good criteria for the design of optimal linear interpolators. Also, such an interpolator can hardly provide a satisfactory solution for interpolating noisy images. In this paper, the novelty of this research is that a universal approach is proposed to design an image interpolator with any one image smoothing filter, thereby not only interpolating a down-sampled image but also preserving the characteristics of the performing filtering.

Study on Real-time Look-ahead and Adaptive Parametric Curve Interpolator

The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpolation, which considering the maximum acceleration/deceleration of the machine tool. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, the look-ahead function was designed and illustrated. It can detect and adjust the feedrate adaptively. With the help of real-time look-ahead, the acceleration/deceleration can be limited to the range of the machine tool capacity. Thus, feedrate fluctuation is reduced. A NURBS curve interpolation experiment was provided to verify the feasibility and advantages of the proposed interpolator with a real-time look-ahead function.

A Phase Interpolator CDR with Low-Voltage CML Circuits

In this paper, a phase interpolator clock and data recovery （CDR） with low-voltage current mode logic （CML） latched, buffers, and muxes is presented. Because of using the CML circuits, the CDR can operate in a low supply voltage. And the original swing of the differential inputs and outputs is less than that of the CMOS logic. The power supply voltage is 1.2 V, and the static current consumption is about 20 mA. In this phase interpolator CDR, the charge pump and loop filter are replaced by a digital filter. And this structure offers the benefits of increased system stability and faster acquisition.

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.