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
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
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
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.
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.
