Multifractal Methods Research For PM2.5 Air Pollution Analysis

With the rapid development of economy and society, urban air pollution has become more and more serious. PM2.5 is one of the most important pollutants in the air,which has brought great impact to everyday life, work and health. How to make effective analysis and forecast of these data becomes a key issue. In view of the complex and nonlinear characteristics of the meteorological environment data, the important branch of the nonlinear theory, fractal theory, is introduced into the research of the meteorological environment.The single fractal theory can only describe the macroscopic appearance of the complex system, and it will lose a lot of details. When the local features of complex systems need to be analyzed, we need to use multifractal theoryt. Compared to the traditional single fractal, multifractal theory can more accurately describe the characteristics of data set. After improved and perfected the multifractal theory, In this paper, the correlation analysis of PM2.5, influence factors of PM2.5, the fractal correlation between PM2.5 and influence factors are studied.The research content is as follows.(1) The asymmetric multifractal detrending moving average analysis (A-MFDMA)method is proposed, which can explore the asymmetric correlation in non-stationary time series, that is,the fractal feature of time series with uptrends or downtrends. In this paper, the proposed method is applied to explore the fractal characteristics of PM2.5 daily average concentration with uptrends or downtrends in China. In addition, shuffling and phase randomization procedures are applied to detect the sources of multifractality.The experimental results show that the method is robust and provides a new idea for the study of asymmetric correlation.(2) Considered the influence factors of PM2.5 air pollution problem, a novel feature selection method based on multi-fractal dimension and harmony search algorithm is proposed. The diference of multifractal dimension between the feature subset and the original data-set is taken as the objective function. An improved harmony search algorithm is used as the search strategy. The experiment results on UCI data set verify the feasibility and the effectiveness of the proposed method. Then the proposed method is used to analyze the influence factors of Chinese PM2.5, which provides a new way for the choice of PM2.5 influencing factors.(3) Considered the correlation between PM2.5 and the corresponding influence factor, the calculating method of joint multifractal based on wavelet packet transform modulus maxima (WPTMM) is 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 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.(4) The multifractal detrended cross-correlation analysis (MF-DCCA) is used to analyze the cross-correlations between PM2.5 and the corresponding meteorological factors, and study further the asymmetric characteristics of cross-correlations by multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA). The both methods are used to analysis the correlation between PM2.5 and the corresponding meteorological factors in Beijing and Hong Kong. The experimental results show that the cross-correlations between PM2.5 concentration and meteorological factors are multifractal and anti-persistent. Meanwhile, the cross-correlations between PM2.5 concentration and meteorological factors are asymmetric.