A Novel Phase Space Reconstruction- (PSR-) Based Predictive Algorithm to Forecast Atmospheric Particulate Matter Concentration

Abstract

e prediction of atmospheric particulate matter (APM) concentration is essential to reduce adverse effects on human health and to enforce emission restrictions. e dynamics of APM are inherently nonlinear and chaotic. Phase space reconstruction (PSR) is one of the widely used methods for chaotic time series analysis. e APM mass concentrations are an outcome of complex anthropogenic contributors evolving with time, which may operate on multiple time scales. us, the traditional single-variable PSR-based prediction algorithm in which data points of last embedding dimension are used as a target set may fail to account for multiple time scales inherent in APM concentrations. To address this issue, we propose a novel PSR-based scientific solution that accounts for the information contained at multiple time scales. Different machine learning algorithms are used to evaluate the performance of the proposed and traditional PSR techniques for predicting mass concentrations of particulate matter up to 2.5 micron (PM 2.5 ), up to 10 micron (PM 10.0 ), and ratio of PM 2.5 /PM 10.0 . Hourly time series data of PM 2.5 and PM 10.0 mass concentrations are collected from January 2014 to September 2015 at the Masfalah air quality monitoring station (couple of kilometers from the Holy Mosque in Makkah, Saudi Arabia). e performances of various learning algorithms are evaluated using RMSE and MAE. e results demonstrated that prediction error of all the machine learning techniques is smaller for the proposed PSR approach compared to traditional approach. For PM 2.5 , FFNN leads to best results (both RMSE and MAE 0.04 μgm −3 ), followed by SVR-L (RMSE 0.01 μgm −3 and MAE 0.09 μgm −3 ) and RF (RMSE 1.27 μgm −3 and MAE 0.86 μgm −3 ). For PM 10.0 , SVR-L leads to best results (both RMSE and MAE 0.06 μgm −3 ), followed by FFNN (RMSE 0.13 μgm −3 and MAE 0.09 μgm −3 ) and RF (RMSE 1.60 μgm −3 and MAE 1.16 μgm −3 ). For PM 2.5 /PM 10.0 , FFNN is the best and accurate method for prediction (0.001 for both RMSE and MAE), followed by RF (0.02 for both RMSE and MAE) and SVR-L (RMSE 0.05 μgm −3 and MAE 0.04).

Characterization of daily rainfall variability in Hong Kong: A nonlinear dynamic perspective

“…As addressed in numerous previous studies (Rodriguez‐Iturbe et al ., 1989; Sivakumar et al ., 1999; 2006; 2014; Kyoung et al ., 2011; Mocenni et al ., 2011; Feng et al ., 2020), the time‐dependent behaviour of rainfall is chaotic, which can be analysed in the framework of nonlinear dynamic system (Mocenni et al ., 2011). The analysis of a nonlinear dynamic system generally consists reconstructing the phase space, in which the complete system dynamics can be reconstructed by a single time series (Bradley and Kantz, 2015; Ali Shah et al ., 2019). Essentially, the phase space is a graphic representation of the variables necessary to describe the state of the system at any time (Sivakumar et al ., 2014).…”

Machine learning algorithms to forecast air quality: a survey

“…Ali Shah et al. ( 2019 ) compare a phase-space reconstruction algorithm combined with an RF, with an SVM and with an MLP neural network to forecast air quality in Masfalah, Saudi Arabia. The combination with the MLP network obtains the best results.…”

Dynamic analysis of meteorological time series in Hong Kong: A nonlinear perspective

“…Phase space reconstruction is a common method in nonlinear dynamic analysis, which allows the time series to be mapped into a phase space, such that the temporal process can be analysed in spatial dimension (Sivakumar et al ., 2002). Fundamentally, phase space reconstruction is graphic representation of the variables needed to describe the state of the system at any moment, in which the entire system dynamics is represented by a single time series (Bradley and Kantz, 2015; Ali Shah et al ., 2019). The trajectories in the phase space diagram represent the system evolution from certain initial conditions (Packard et al ., 1980), and the region of attraction of these trajectories provides useful qualitative information of the nature of the system dynamics, such as the degree of complexity or variability (Sivakumar et al ., 2007).…”