悬浮颗粒散射脉冲信号群的统计分形特性

The statistical fractal characteristic of aerosol scattering pulse signal group

将PCI-9812高速数据采集卡与激光尘埃粒子计数光电传感器结合,对空气中悬浮颗粒群产生的散射脉冲信号数随幅度的统计分布p(l)进行高分辨率的测定.实验数据表明,在大样本条件下,脉冲信号集合整体及不同脉宽信号子集的p(l)函数在幅度定义域(V0,VM)内均以很高的精度满足对数正态分布形式,即该随机脉冲信号群具有统计分形(自相似)特征.进一步理论研究表明,p(l)函数具有非线性缩放不变性;且当统计参数满足(lnl-lnl)2>lnl时,该函数与幂函数l-(1-ε)表现出几何相似性,其中ε1.

The amplitude statistical distribution funetion p（l） of the aerosol scattering pulse signals is measured with high resolution through combining the high-speed data acquisition card PCI-9812 and the photoelectric sensor of laser airborne particle counter.The experimental results show that the distribution founction p（l） of the whole signal group and the different pulse width subsets all fit the lognormal distribution with very high precision in the range of amplitude definition （V0,VM） under the condition of big samples,which indicates that the random signal group has a statistical fractal （selfsimilarity） characteristic.According to the further theoretical results,it is analyzed that function p（l） has a nonlinear scale invariance.Besides,this function shows a geometrical similarity to the power law l-（1-ε） when statistical parameter （lnl-lnl）2 lnl,where ε  1.