Non-overshooting and Non-undershooting Cubic Spline Interpolation for Empirical Mode Decomposition

To suppress the overshoots and undershoots in the envelope fitting for empirical mode decomposition （EMD）, an alternative cubic spline interpolation method without overshooting and undershooting is proposed. On the basis of the derived slope constraints of knots of a non-overshooting and non-undershooting cubic interpolant, together with ＂not-a-knot＂ conditions the cubic spline interpolants are constructed by replacing the requirement for equal second order derivatives at every knot with Brodlie＇ s derivative formula. Analysis and simulation experiments show that this approach can effectively avoid generating new extrema, shifting or exaggerating the existing ones in a signal, and thus significantly improve the decomposition performance of EMD.

Combining Cubic Spline Interpolation and Fast Fourier Transform to Extend Measuring Range of Reflectometry

The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.

Improvement of Orbit Prediction Algorithm for Spacecraft Through Simplified Precession-Nutation Model Using Cubic Spline Interpolation Method

For the on-orbit flight missions,the model of orbit prediction is critical for the tasks with high accuracy requirement and limited computing resources of spacecraft.The precession-nutation model,as the main part of extended orbit prediction,affects the efficiency and accuracy of on-board operation.In this paper,the previous research about the conversion between the Geocentric Celestial Reference System and International Terrestrial Reference System is briefly summarized,and a practical concise precession-nutation model is proposed for coordinate transformation computation based on Celestial Intermediate Pole(CIP).The idea that simplifying the CIP-based model with interpolation method is driven by characteristics of precession-nutation parameters changing with time.A cubic spline interpolation algorithm is applied to obtain the required CIP coordinates and Celestial Intermediate Origin locator.The complete precession nutation model containing more than 4000 parameters is simplified to the calculation of a cubic polynomial,which greatly reduces the computational load.In addition,for evaluating the actual performance,an orbit propagator is built with the proposed simplified precession-nutationmodel.Compared with the orbit prediction results obtained by the truncated series of IAU2000/2006 precession-nutation model,the simplified precession-nutation model with cubic spline interpolation can significantly improve the accuracy of orbit prediction,which implicates great practical application value in further on-orbit missions of spacecraft.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

A polynomial smooth epsilon-support vector regression based on cubic spline interpolation

Regression analysis is often formulated as an optimization problem with squared loss functions. Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to support vector regression models, this study takes cubic spline interpolation to generate a new polynomial smooth function ｜×｜ε^ 2, in g-insensitive support vector regression. Theoretical analysis shows that Sε^2 -function is better than pε^2 -function in properties, and the approximation accuracy of the proposed smoothing function is two order higher than that of classical pε^2 -function. The experimental data shows the efficiency of the new approach.

Theoretical Modeling and Surface Roughness Prediction of Microtextured Surfaces in Ultrasonic Vibration-Assisted Milling

Textured surfaces with certain micro/nano structures have been proven to possess some advanced functions,such as reducing friction,improving wear and increasing wettability.Accurate prediction of micro/nano surface textures is of great significance for the design,fabrication and application of functional textured surfaces.In this paper,based on the kinematic analysis of cutter teeth,the discretization of ultrasonic machining process,transformation method of coordinate systems and the cubic spline data interpolation,an integrated theoretical model was established to characterize the distribution and geometric features of micro textures on the surfaces machined by different types of ultrasonic vibration-assisted milling(UVAM).Based on the theoretical model,the effect of key process parameters(vibration directions,vibration dimensions,cutting parameters and vibration parameters)on tool trajectories and microtextured surface morphology in UVAM is investigated.Besides,the effect of phase difference on the elliptical shape in 2D/3D ultrasonic elliptical vibration-assisted milling(UEVAM)was analyzed.Compared to conventional numerical models,the method of the cubic spline data interpolation is applied to the simulation of microtextured surface morphology in UVAM,which is more suitable for characterizing the morphological features of microtextured surfaces than traditional methods due to the presence of numerous micro textures.The prediction of surface roughness indicates that the magnitude of ultrasonic amplitude in z-direction should be strictly limited in 1D rotary UVAM,2D and 3D UEVAM due to the unfavorable effect of axial ultrasonic vibration on the surface quality.This study can provide theoretical guidance for the design and fabrication of microtextured surfaces in UVAM.

Sub-pixel high precision dimensional measurement method for aero-engine hollow turbine blade based on industrial computed tomography image

Aero-engine hollow turbine blades are work under prolonged high temperature,requiring high dimensional accuracy.Blade profile and wall thickness are important parameters to ensure the comprehensive performance of blades,which need to be measured accurately during manufacturing process.In this study,a high accuracy industrial computed tomography(ICT)measuring method was developed based on standard cylindrical pin and ring workpieces of different sizes.Combining ICT with cubic spline interpolation,a sub-pixel accuracy was achieved in measuring the dimension of component.Compared with the traditional and whole-pixel level image measurement method,the cubic spline interpolation algorithm has the advantages of high accuracy in image edge detection and thus high accuracy of dimensional measurement.Further,the technique was employed to measure the profile and wall thickness of a typical aerospace engine turbine blade,and an accuracy higher than 0.015 mm was obtained.

A new method for high precsion instantaneous speedmeasurement of hydraulic system

The instantaneous speed of a hydraulic system contains a wealth of operational information,and its accurate extraction is the basis for condition monitoring and fault diagnosis.In order to solve the problem of high hardware requirement for instantaneous speed measurement based on data acquisition card,a new method of high precision measurement is proposed.In this method,the time-displacement information of each tooth is obtained from the pulsed square wave signal of the gear disk collected by magnetoelectric sensors.The time-displacement curve is interpolated by the cubic spline interpolation method,and then the instantaneous speed is calculated by the five-point digital differential formula.The experimental results show that the method improves the speed measurement resolution and reduces the quantization error.The high precision instantaneous speed signal can also be acquired by hardware devices with less teeth and low sampling frequency.The related research results provide a theoretical basis and a method for improving the accuracy of instantaneous speed measurement.

A PMU data recovering method based on preferred selection strategy

Nowadays, the technology of renewable sources grid-connection and DC transmission has a rapid development. And phasor measurement units(PMUs) become more notable in power grids, due to the necessary of real time monitoring and close-loop control applications. However, the PMUs data quality issue affects applications based on PMUs a lot. This paper proposes a simple yet effective method for recovering PMU data. To simply the issue, two different scenarios of PMUs data loss are first defined. Then a key combination of preferred selection strategies is introduced. And the missing data is recovered by the function of spline interpolation. This method has been tested by artificial data and field data obtained from on-site PMUs. The results demonstrate that the proposed method recovers the missing PMU data quickly and accurately. And it is much better than other methods when missing data are massive and continuous. This paper also presents the interesting direction for future work.

Curve length estimation based on cubic spline interpolation in gray-scale images

This paper deals with a novel local arc length estimator for curves in gray-scale images.The method first estimates a cubic spline curve fit for the boundary points using the gray-level information of the nearby pixels,and then computes the sum of the spline segments’lengths.In this model,the second derivatives and y coordinates at the knots are required in the computation;the spline polynomial coefficients need not be computed explicitly.We provide the algorithm pseudo code for estimation and preprocessing,both taking linear time.Implementation shows that the proposed model gains a smaller relative error than other state-of-the-art methods.

Two Times Spline Interpolant in Power Exponent Form under the First Boundary Condition

In this paper the concept of first boundary condition （i）（i = 0, 1, 2,…, n） is proposed based on [1], the existence of two times spline interpolant under first boundary condition is proved using constructivity method and the uniqueness of the two times spline interpolant under first boundary condition（n） is proved too.

Interpolation Method Research and Precision Analysis of GPS Satellite Position

According to the precise ephemeris has only provided satellite position that is discrete not any time,so propose that make use of interpolation method to calculate satellite position at any time.The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation,Newton interpolation,Hermite interpolation,Cubic spline interpolation method,Chebyshev fitting method respectively,which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst,the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore,Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.

Self-Collimation for Two-Dimensional Micro-Angle Measurement in Space

How to measure the two-dimensional attitude angle of space target and achieve stable tracking and aiming has become an important problem. The self-collimation is often measured via one-dimensional motion of the object in space. This paper proposes a micro-angle measurement system based on self-collimation to obtain the two-dimensional angle information of moving objects in space, and a thrice reflecting optical path structure is built to improve the compactness of the system. First, by establishing a posture angle measurement and decomposition model, the two-dimensional deflection angle value of the reflecting mirror is derived from the rotation angle equation;Second, the self-collimating measurement process is simulated to show the relationship between the reflecting mirror rotation angle and the imaging spot distortion of detector;Third, a two-dimensional micro-angle experimental platform is established based on the Position Sensitive Detector(PSD). Finally, nonlinear error of PSD is improved by the cubic spline interpolation method. The case results show a 15% reduction in the angle error.

Comparison of modeling methods for wind power prediction:a critical study

Prediction of power generation of a wind turbine is crucial,which calls for accurate and reliable models.In this work,six different models have been developed based on wind power equation,concept of power curve,response surface methodology(RSM)and artificial neural network(ANN),and the results have been compared.To develop the models based on the concept of power curve,the manufacturer’s power curve,and to develop RSM as well as ANN models,the data collected from supervisory control and data acquisition(SCADA)of a 1.5 MW turbine have been used.In addition to wind speed,the air density,blade pitch angle,rotor speed and wind direction have been considered as input variables for RSM and ANN models.Proper selection of input variables and capability of ANN to map input-output relationships have resulted in an accurate model for wind power prediction in comparison to other methods.

Numerical study of the flow in the Yellow River with non-monotonous banks

A 2-D depth averaged RNG k- ε model is developed to simulate the flow in a typical reach of the Upper Yellow River with non-monotonic banks. In order to take account of the effect of the secondary flow in a bend, the momentum equations are modified by adding an additional source term. A comparison between the numerical simulation and the field measurements indicates that the improved 2-D depth averaged RNG k- ε model can improve the accuracy of the numerical simulation. An arc spline interpolation method is developed to interpolate the non-monotonic river banks. The method can also be reasonably applied for the 2-D interpolation of the river bed level. Through a comparison of the water surface gradients simulated in the seven bends of the studied reach, some analytical formulae are improved to reasonably calculate the longitudinal and transverse gradients in meandering river reaches. Furthermore, the positions of the maximum water depth and the maximum velocity in a typical bend are discussed.