基于WPTMM的PM2.5与气象条件关系的联合多重分形分析

PM2.5是影响空气质量的主要污染物,PM2.5污染浓度与气象条件关系密切,研究气象条件对PM2.5浓度的影响对改善城市空气质量有着重要意义.鉴于分形和小波在处理复杂非线性系统时的优势,本文提出了基于小波包变换模极大值(wavelet:packet transform modulus maxima,WPTMM)的联合多重分形,首先对变量序列进行小波包分解,使用模极大值进行去噪,然后构造联合配分函数,最后计算联合多重分形谱,分析两个变量之间的分形相关性.该方法将单个变量的多重分形扩展到两个变量的联合多重分形,并且利用WPTMM计算联合多重分形谱降低了计算复杂度,同时去除噪声的影响.用本文方法分析北京、香港PM2.5浓度与各气象要素之间的关系,实验结果表明,该方法能够有效地分析各种气象要素在不同季节中对PM2.5浓度的影响.

Joint multifractal analysis of relationship of PM2.5 and meteorological condition based on WPTMM

PM2.5 is the main pollutant affecting the air quality, the concentration of PM2.5 is closed related to meteorological conditions, studying the influence of meteorological conditions on the concentration of PM2.5 has important significance for improving urban air quality. As fractal and wavelet have lots of advantages when dealing with complex nonlinear system, the calculating method of joint multifractal based on wavelet packet transform modulus maxima (WPTMM) has been proposed, first the variable sequences are decomposed by wavelet packet, this paper uses modulus maxima to denoise, then constructs the joint distribution function, finally calculates the joint multifractal spectrum, and analyzes the fractal correlation between two variables. This proposed method has extended single multifractal to the joint multifractal of two interacting variables, calculating joint multifractal spectra based on WPTMM can reduce computational complexity, meanwhile avoid the effects of noise. The paper has analyzed the relationship between the concentration of PM2.5 and the meteorological factors of Beijing and Hong Kong, experiment results show that this method can effectively analyze each meteorological factor on the impact of PM2.5 concentration in different seasons.