地磁活动的神经网络预测：使用局部Hölder指数的方法
Neural network prediction of geomagnetic activity: a method using local Hölder exponents
摘要：
利用Hölder指数$α$分析了太阳风和地磁时间序列的局部标度和奇异性。结果表明，在分析的情况下，由于多重分形的波动$α$的变化从点到点。我们认为，存在着一个特殊的规则性/不规则性和波动的幅度特性，可以用来改善预测的地磁活动之间的相互作用。为此，采用具有反馈连接的分层反向传播人工神经网络模型研究太阳风-磁层耦合和地磁$D_{st}$指数预测。太阳风输入取自行星际磁场、质子密度和体速度的主成分分析。在将本地Hölder指数信息添加到输入层的情况下，实现了卓越的网络性能。
英文摘要：
Local scaling and singularity properties of solar wind and geomagnetic time series were analysed using Hölder exponents $α$. It was shown that in analysed cases due to multifractality of fluctuations $α$ changes from point to point. We argued there exists a peculiar interplay between regularity / irregularity and amplitude characteristics of fluctuations which could be exploited for improvement of predictions of geomagnetic activity. To this end layered backpropagation artificial neural network model with feedback connection was used for the study of the solar wind - magnetosphere coupling and prediction of geomagnetic $D_{st}$ index. The solar wind input was taken from principal component analysis of interplanetary magnetic field, proton density and bulk velocity. Superior network performance was achieved in cases when the information on local Hölder exponents was added to the input layer.
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