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 ...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.展开更多
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 e...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.展开更多
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 refle...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.展开更多
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.
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 pixel...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.展开更多
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 blad...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.展开更多
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 monit...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.展开更多
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 advanta...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.展开更多
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...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.展开更多
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,respon...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.展开更多
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...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.展开更多
基金the Ministerial Level Advanced Research Foundation (445030705QB0301)
文摘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.
基金The authors would like to express gratitude for supporting funding from the Natural Science Foundation of China(No.51905272).
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No 11604115the Educational Commission of Jiangsu Province of China under Grant No 17KJA460004the Huaian Science and Technology Funds under Grant No HAC201701
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundationof China(Nos.61170092,61133011,61272208,61103091,and61202308)the Fundamental Research Funds for the CentralUniversities,China(Nos.450060445674 and 450060481512)
文摘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.
基金financially supported by the National Science and Technology Major Project "Aero Engine and Gas Turbine"(No.2017-Ⅶ-0008-0102)National Nature Science Foundation of China (No.51701112 and No.51690162)+1 种基金Shanghai Rising-Star Program (No.20QA1403800 and No.21QC1401500)Shanghai Science and Technology Committee (No.21511103600)
文摘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.
基金supported in part by National Natural Science Foundation of China(NSFC)(51627811,51707064)Project Supported by the National Key Research and Development Program of China(2017YFB090204)Project of State Grid Corporation of China(SGTYHT/16-JS-198)
文摘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.
基金Supported by the National Natural Science Foundation of China(41474020)
文摘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.
基金Supported by the National Natural Science Foundation of China (61701296, U1831133)the Natural Science Foundation of Shanghai (17ZR1443500)the Shanghai Aerospace Science and Engineering Fund (SAST2017-062)。
文摘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.
文摘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.
基金supported by the National Natural Science Foun-dation of China(Grant Nos.91230111,11361002)the Natural Science Foundation of Ningxia Hui Autonomous Region(Grant No.NZ13086)
文摘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.