MANDELBROT enunciated the uncertainty of the length of a coastline in his paper "How long is the coastline of Britain?" published in Science in 1967. The fractal concept was presented for the first time in t...MANDELBROT enunciated the uncertainty of the length of a coastline in his paper "How long is the coastline of Britain?" published in Science in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. Although fractal dimensions of lots of phenomena were calculated by the box-counting method,the quantitative influence of series of square grids on them is ignored. The issue is systematically discussed as a case study of the mountains of China′s Mainland in this paper. And some significant conclusions are drawn as follows: 1) Although the fractal character objectively exists in the mountains of China′s Mainland,and it does not vary with the changes of series of square grids,the fractal dimensions of the mountains of China′s Mainland are different with these changes. 2) The fractal dimensions of the mountains of China′s Mainland vary with the average lengths of sides of series of square grids. The fractal dimension of the mountains of China′s Mainland is the function of the average length of side of square grid. They conform to the formula D=f(r) (where D is the fractal dimension,and r is the average length of side of square grid). 3) Different dots of data collection can affect the fractal dimension of the mountains of China′s Mainland. 4) The same range of length of side of square grid and dots of data collection can ensure the comparison of fractal dimensions of the mountains of China′s Mainland. The research is helpful to get the more understanding of fractal and fractal dimension,and ensure that the fractal studies would be scientific.展开更多
现有的500 k V/220 k V分区规划大多通过开断个别线路进行分区,未对整体性网架结构进行量化研究。基于此背景,提出了一种通过求取地理接线图的分形维数预测区域短路电流的方法。首先,结合电网的地理接线图,利用MATLAB编写的盒维数计算...现有的500 k V/220 k V分区规划大多通过开断个别线路进行分区,未对整体性网架结构进行量化研究。基于此背景,提出了一种通过求取地理接线图的分形维数预测区域短路电流的方法。首先,结合电网的地理接线图,利用MATLAB编写的盒维数计算程序对实际电网结构进行了分形维数的量化研究;其次,通过对电网结构分形维数与短路电流基本模型的研究,建立了电网结构分形维数与短路电流的数学关系,达到了预测短路电流的目的。算例结果验证了该思路的可行性。展开更多
基金Under the auspices of the National Natural Science Foundation of China(No.40301002) and the Key Program of the National Natural Science Foundation of China(No.40335046)
文摘MANDELBROT enunciated the uncertainty of the length of a coastline in his paper "How long is the coastline of Britain?" published in Science in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. Although fractal dimensions of lots of phenomena were calculated by the box-counting method,the quantitative influence of series of square grids on them is ignored. The issue is systematically discussed as a case study of the mountains of China′s Mainland in this paper. And some significant conclusions are drawn as follows: 1) Although the fractal character objectively exists in the mountains of China′s Mainland,and it does not vary with the changes of series of square grids,the fractal dimensions of the mountains of China′s Mainland are different with these changes. 2) The fractal dimensions of the mountains of China′s Mainland vary with the average lengths of sides of series of square grids. The fractal dimension of the mountains of China′s Mainland is the function of the average length of side of square grid. They conform to the formula D=f(r) (where D is the fractal dimension,and r is the average length of side of square grid). 3) Different dots of data collection can affect the fractal dimension of the mountains of China′s Mainland. 4) The same range of length of side of square grid and dots of data collection can ensure the comparison of fractal dimensions of the mountains of China′s Mainland. The research is helpful to get the more understanding of fractal and fractal dimension,and ensure that the fractal studies would be scientific.
文摘现有的500 k V/220 k V分区规划大多通过开断个别线路进行分区,未对整体性网架结构进行量化研究。基于此背景,提出了一种通过求取地理接线图的分形维数预测区域短路电流的方法。首先,结合电网的地理接线图,利用MATLAB编写的盒维数计算程序对实际电网结构进行了分形维数的量化研究;其次,通过对电网结构分形维数与短路电流基本模型的研究,建立了电网结构分形维数与短路电流的数学关系,达到了预测短路电流的目的。算例结果验证了该思路的可行性。
