Approximation methods are used in the analysis and prediction of data, especially laboratory data, in engineering projects. These methods are usually linear and are obtained by least-square-error approaches. There are...Approximation methods are used in the analysis and prediction of data, especially laboratory data, in engineering projects. These methods are usually linear and are obtained by least-square-error approaches. There are many problems in which linear models cannot be applied. Because of that there are logarithmic, exponential and polynomial curve-fitting models. These nonlinear models have a limited application in engineering problems. The variation of most data is such that the nonlinearity cannot be approximated by the above approaches. These methods are also not applicable when there is a large amount of data. For these reasons, a method of piecewise cubic spline approximation has been developed. The model presented here is capable of following the local nonuniformity of data in order to obtain a good fit of a curve to the data. There is C1 continuity at the limits of the piecewise elements. The model is tested and examined with four problems here. The results show that the model can approximate highly nonlinear data efficiently.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
文摘Approximation methods are used in the analysis and prediction of data, especially laboratory data, in engineering projects. These methods are usually linear and are obtained by least-square-error approaches. There are many problems in which linear models cannot be applied. Because of that there are logarithmic, exponential and polynomial curve-fitting models. These nonlinear models have a limited application in engineering problems. The variation of most data is such that the nonlinearity cannot be approximated by the above approaches. These methods are also not applicable when there is a large amount of data. For these reasons, a method of piecewise cubic spline approximation has been developed. The model presented here is capable of following the local nonuniformity of data in order to obtain a good fit of a curve to the data. There is C1 continuity at the limits of the piecewise elements. The model is tested and examined with four problems here. The results show that the model can approximate highly nonlinear data efficiently.
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.
