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Analyzing the Dynamics of Particulate Matters (PM) using Nonlinear Dynamical Techniques and Predicting the Behavior Based on Robust Regression Models


Sharjil Saeed Adnan Idris, Lal Hussain, Imtiaz Ahmed Awan


Vol. 17  No. 11  pp. 6-19


Particulate matter (PM) concentrations are outcome of combination of complex natural and anthropogenic contributors. Considerable interest among environmental research community has been found to study the dynamics of particulate matter concentration using nonlinear time series analysis techniques. Due to the reconstruction work after the earthquake 8, 2005 and congestion of vehicles because of traffic jam, the indoor environment of houses located along the road sides is badly affected in the suburb of Muzaffarabad. For quantifying the nonlinear dynamics of the particulates (PM2.5 and PM10), time series data was acquired using Haz-Dust EPAM-5000 monitor from the indoor air of the closed rooms located near the main roadsides of Muzaffarabad city. The data was then transferred to computer for analyzing nonlinear behavior using phase space reconstruction and largest Lyapunov exponent (LLE). The average mutual information (AMI) function was used to estimate the time delay. False nearest neighbors (FNN) approach was used to obtain optimum embedding dimension for phase space reconstruction and Wolf'’s algorithm was used to calculate LLE. Moreover, prediction in terms of root means squared error (RMSE), mean square error (MSE), mean absolute error (MAE), observed and estimated functional values and feasible points in terms of regression tree (RT), support vector regression (SVR) and gaussian process regression (GPR) models was made by extracting multifeatured extracted from indoor particulate matters. Based on nonlinearity, non-stationarity and complex temporal dynamics, the time domain, frequency domain, complexity, wavelet based and statistical features are extracted from indoor particulate matters PM10.0 and PM2.5. The results clearly indicated that indoor particulate time series manifested chaotic behavior. Furthermore, to test whether indoor particulates time series data is measure of temporal dynamics or not, sensitivity of Poincar? plot descriptors, Sv (representing short term variability), Lv (representing long term variability) and complex correlation measure (CCM) was quantified. The findings demonstrated that relative changes in CCM are more sensitive to the changes in temporal dynamics as compared to standard descriptors Sv and Lv for both PM2.5 and PM10. The prediction results reveal that Support vector linear regression and Gaussian Process regression models gives minimal differences between observed and predicted values and optimal performance evaluation in terms of RMSE, R2, MSE and MAE


Complex correlation measure, Lyapunov exponent, Particulate matter, Phase space reconstruction, Poincare plot, Gaussian process regression, support vector regression, root mean squared error