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Abstract
The air pollution caused by particulate matter (PM) has become a public health issue due to the risks to human life and the environment. The PM concentration in the air causes haze and affects the lungs and the heart, leading to reduced visibility, allergic reactions, pneumonia, asthma, cardiopulmonary diseases, lung cancer, and even death. In this context, the development of systems for monitoring, forecasting, and controlling emissions plays an important role. The literature about forecasting systems based on Artificial Neural Networks (ANNs) ensembles has been highlighted regarding statistical accuracy and efficiency. In this article, trainable and non-trainable combination methods are used for PM10 and PM2.5 (particles with an aerodynamic diameter less than 10 and 2.5 micrometers, respectively) time series forecasting for eight different locations, in Finland and Brazil, for different periods. Trainable ensembles based on ANNs, linear regression, and Copulas are compared with non-trainable combinations (mean and median), single ANNs, and linear statistical approaches. Different models are considered so far, including Autoregressive model (AR), Autoregressive and Moving Average Model (ARMA), Infinite Impulse Response Filters (IIR), Multilayer Perceptron (MLP), Radial Basis Function Networks (RBF), Extreme Learning Machines (ELM), Echo State Networks (ESN), and Adaptive Network Fuzzy Inference System (ANFIS). The use of ANNs ensembles, mainly combined with MLP, leads to a better one step ahead forecasting performance. The use of robust air pollution forecasting tools is prime to assist governments in managing air pollution issues like hospital collapse during adverse air quality situations. In this sense, our study is indirectly related to the following United Nations sustainable development goals: SDG 3 - good health and well-being and SDG 11 - sustainable cities and communities.
Highlights
Air pollution is one of the worst toxic issues worldwide [1]–[3]
As single models we applied the Autoregressive model (AR) [40], Autoregressive and Moving Average model (ARMA) [40], Infinite Impulse Response Filters [41], Multilayer Perceptron (MLP) [20], Radial Basis Function Networks (RBF) [42], Extreme Learning Machines (ELM) [43], Echo State Networks (ESN) [44], and Adaptive Network Fuzzy Inference System (ANFIS) [45]; as non-trainable ensembles, it is considered the mean and median [36]; as trainable ensembles we addressed a linear regression with (LR-Feature Selection (FS)) and without features selection (LR) [46], ELM with and without the coefficient of regularization (CR), MLP [37], and normal Copula-based models [25], [29]
While the AR considers the lags of the series, the ARMA creates the output response addressing the previous residuals presented by the model, at−P−j, which are weighted by θj coefficients, as in Equation 2: xt = φ1xt−P + · · · + φpxt−P−p+1
Summary
Air pollution is one of the worst toxic issues worldwide [1]–[3]. The World Health Organization (WHO) [4] reported that 0.8 million deaths and 7.9 million disability-adjusted life years from respiratory problems, lung diseases, and cancer were attributed to urban air pollution. As single models we applied the Autoregressive model (AR) [40], Autoregressive and Moving Average model (ARMA) [40], Infinite Impulse Response Filters [41], Multilayer Perceptron (MLP) [20], Radial Basis Function Networks (RBF) [42], Extreme Learning Machines (ELM) [43], Echo State Networks (ESN) [44], and Adaptive Network Fuzzy Inference System (ANFIS) [45]; as non-trainable ensembles, it is considered the mean and median [36]; as trainable ensembles we addressed a linear regression with (LR-FS) and without features selection (LR) [46], ELM with and without the coefficient of regularization (CR), MLP [37], and normal Copula-based models [25], [29] These combination methods have emerged among the most promising from the time series forecasting literature [12], [29], [35], [37], [38]. The rest of the work is organized as follows: Section II presents the background regarding the single and combination methods adopted for modeling and forecasting PM; Section III presents computational results, while Section IV brings relevant discussions; Section V shows concluding remarks
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