Choice of network structure
Feed-forward neural networks have been used in this study. The architecture of a net is established base on the numbers of neurons in the input and the output layers and the number of the hidden layers and/or the number of neurons in each hidden layer depends on the kind of the modeled system. Designing of the network architecture is based on the theory of Kolmogorov (Kolmogorov 1957). According to this theory, a feed-forward neural network, containing at least one hidden layer with (2N + 1) neurons, is able to approximate any continuous function converting the N-dimensional input vector into the M-dimensional output vector. This theory does not describe precisely a net architecture, but it is rather a starting point to optimization procedure.
In order to determine the optimum number of hidden nodes, a series of topology was used. the number of nodes was varied from 21 to 35. The starting point for nodes in this paper was based on Kolmogorov theory.
Each topology was repeated three times to avoid random correlation due to the random initialization of the weight. Figure 3 illustrates the relation between the network error and number of neuron in hidden layer. The root mean square error (RMSE) was used as the error function. The R
2 of each output was calculated by Eq. (7):
$$ {R}^2=\left(\frac{{\displaystyle {\sum}_i\left[\left({x}_i-\overline{x}\right)\left({y}_i-\overline{y}\right)\right]}}{{\left[{\left({\displaystyle {\sum}_i{x}_i-\overline{x}}\right)}^2{\left({\displaystyle {\sum}_i{y}_i-\overline{y}}\right)}^2\right]}^{1/2}}\right) $$
(7)
where x
i
is original target vector, \( \overline{x} \) is the mean of target vector, y
i
is the predicted vector, \( \overline{y} \) is the mean of predicted vector, and j is an index of data (Zupan and Gasteiger 1999).
Neural model development
Particularly, this step is crucial for a robustness and accuracy of the developed neural model. The following procedure was carried out for selection of input variables:
In the first model configuration, meteorological variables are tested as input. So, wind speed, wind direction, precipitation, vapor pressure, air temperature, relative humidity, barometric pressure, and total radiation were used one by one as input of network, and the NO2 and NO
x
concentrations were used for output. Then, a progressive increase of the number of the input variables was carried out, in order to increase the number of model parameters. The criterion for increasing the number of variables was the value of the correlation coefficient R
2 and RMSE. Thus, if the increase of a given input variable resulted in a decrease in the value of RMSE and increase in the value of (R
2), the variable was added in the model. If not, it was increased (RMSE) and decreased (R
2), the procedure was repeated with another variables, because the selection of input variables has significant effect on performance of networks. The network structure was selected 8-30-1. It was found that there is a good agreement between prediction and real data.
In the case of prediction of NO2 and NO
x
concentrations, we added NO (ANN predicted) and O3 concentrations to input variable set. With this modification in input variables set, significance increasing in regression coefficient (R
2) was observed. It can be due to interaction between this species. This interaction can be described by following chemical reaction set Eqs. (8) to (10), (Gürmen and Fogler 2006):
$$ {\mathrm{NO}}_2+hv\to \mathrm{NO}+\mathrm{O} $$
(8)
$$ \mathrm{O}+{\mathrm{O}}_2\to {\mathrm{O}}_3 $$
(9)
$$ {\mathrm{O}}_3+\mathrm{NO}\to {\mathrm{NO}}_2+{\mathrm{O}}_2 $$
(10)
RMSE in the selected network is 0.0046 and 0.0038; R
2 is 0.92 and 0.94 for NO2 and NO
x
, respectively. Table 1 shows the effect of input variable selection on network performance.
Table 1 The effect of different inputs on optimized network performance
Figures 4 and 5 present the comparisons of prediction results on the testing data during October and November 2012, for NO2 and NO
x
concentrations, respectively. It is shown that the prediction results generated by the MLP model are getting closer to the actual data. Multiple linear regression models were developed in this work for result comparison. The best model with the lowest RMSE 3.6 and 2.94 and the highest R
2 is 0.41 and 0.44 for NO2 and NO
x
concentrations, respectively. The results in this work exhibit that the performance of ANNs is generally superior for air pollution modeling in comparison to multiple linear regression (MLR) as a traditional statistical method.
Importance analyses
The Garson method (Garson 1991) is shown by Olden and Jackson (Olden and Jackson 2002) and is based in the partition of the neural weights of the hidden and output layers. This method determines the relative importance (I) of jth input neuron in the output neuron. This relative importance is defined as:
$$ {I}_j=\frac{{\displaystyle {\sum}_{m=1}^{N^h}\left(\frac{\left|{W}_{jm}^{ih}\right|}{{\displaystyle {\sum}_{k=1}^{m={N}^h}\left|{W}_{km}^{jh}\right|}}*\left|{W}_{mn}^{ho}\right|\right)}}{{\displaystyle {\sum}_{k=1}^{k={N}^i}\left\{{\displaystyle {\sum}_{m=1}^{m={n}^h}\left(\frac{\left|{W}_{jm}^{ih}\right|}{{\displaystyle {\sum}_{k=1}^{m={N}^h}\left|{W}_{km}^{jh}\right|}}\right)*\left|{W}_{mn}^{ho}\right|}\right\}}} $$
(11)
where N
h is the number of neuron in hidden layer, N
i is the number of weight for each neuron in hidden layer and W
mn
is the weight of nth neuron in output layer.
The use of Garson method in this work reveals that the NO (ANN predicted) concentration, relative humidity, and air temperature are the best important variables in NO2 and NO
x
concentration prediction (Fig. 6).
Why the air pollution forecasting is important?
Air pollution is rapidly increasing due to various human activities, and it is the introduction into the atmosphere of chemicals, particulates, or biological materials that cause discomfort, disease, or death to humans, damage other living organisms such as food crops, or damage the natural environment or built environment. Indeed, air pollution is one of the important environmental problems in metropolitan and industrial cities (Garcia Nieto and Alvarez Antَn 2014). Stoves in homes, vehicles, factories, and fires are different sources of air pollution. Both ambient (outdoor) and household (indoor) pollution exert many harmful effects on either human health or the environment (Bedoui et al. 2016). Increasing air pollution has become a global problem that is triggering both official anxiety and public concern. As reported in an assessment by the World Health Organization (WHO 2014), air pollution has become the largest single environmental health risk in many parts of the world, and around seven million people died from air pollution exposure in 2012, equivalent to one in eight of the total global deaths (Xie et al. 2016).
Air pollution in all major cities of Iran has reached a dangerous and alarming level. Air pollution poses a dire risk to Iranians today. The consequences can be measured in the numbers of pollution-related deaths, the number of school and work days lost to pollution, and additional health challenges experienced by children, the elderly, and people with heart or lung conditions (Khani 2016). These are drastic times for Iran’s big cities such as Tabriz.
The public is informed of air quality index (AQI) calculated from air pollutants concentrations forecasted and associated health risks through government announcements (Zhang et al. 2012). Therefore, an accurate and reliable model for forecasting air pollutant concentrations is important since it can provide advanced air pollution information at an early stage such that guiding the works of air pollution control and public health protection (Bai et al. 2016).
In recent years, many research efforts have been made to develop the air quality prediction models. Atmospheric dispersion models used to predict the ground level concentration of the air pollutants around the sources (Kesarkar et al. 2007; Bhaskar et al. 2008; Singh et al. 2012) require precised knowledge of several source parameters and the meteorological conditions (Collett and Oduyemi 1997; Gardner and Dorling 1998).
Linear and nonlinear methods for air pollution forecasting
In recent decades, air pollution has been considered a serious threat to the environment, the quality of life, and the health of people around the world and forecasting of air quality parameters is the common goal for a great number of researches due to the diseases caused by the different gas pollutants. In recent time, there have been many attempts to analyze the concentration of air pollutants and explore them to build short-term forecast of concentrations. Linear and nonlinear models were developed, however, there was no significance difference noted between nonlinear and linear models (Pires et al. 2008a; Pires et al. 2008b).
The statistical models attempt to determine the underlying relationship between a set of input data and targets. Several linear (multiple linear regression, principal component regression, partial least squares regression) and nonlinear (multivariate polynomial regression, artificial neural networks, support vector machines) regression models are now available, which have the ability to relate the input and output variables (Singh et al. 2012). Although linear regression modeling finds some applications in the air quality prediction (Shi and Harrison 1997), it generally does not permit for consideration of complex and nonlinearity in data (Gardner and Dorling 1998). Partial least squares (PLS) is a multivariate regression method that projects the input–output data down into a latent space, extracting a number of principal factors with an orthogonal structure, while capturing most of the variance in the original data. Multivariate polynomial regression (MPR) captures nonlinearities in data to some extent and is considered a low-order nonlinear method (Singh et al. 2010). ANN, which has the capabilities of nonlinear mapping, self-adaption, and robustness, has proved its superiority and is widely used in forecasting fields. Recently, various structures of the ANN have been developed for improving the forecasting performances of air pollutant concentrations (Bai et al. 2016). Results in this work confirm that the ANN in air pollution forcasting generally gives better results than linear methods.
Tabriz air pollution resource and the role of metrological parameter in pollution exacerbating
Environment pollution is a challenge to the modern society, especially in developing countries for example Iran. In the beginning of the century, industrialization and expansion of the factories became the main concern of Iranian big cities. The city of Tabriz in Iran that could hold a large population in it turned to become as one of the industrial poles in the country. Within the years 1967–1975, Tabriz city was the subject of new changes and developments. But in the process of industrialization and installation of the manufacturing sites and factories, some decision makers and executive managers did not try to take the geographical and topographical conditions of the city into their considerations; therefore, the city of Tabriz became more and more polluted and the people’s social health and hygiene were endangered (Mojtabazadeh 2005). Establishment of high industrial factories in the west and southwest of Tabriz, such as chemical and petrochemical industries, thermal power plant, and oil refinery, and blowing of wind from west and southwest transferred their pollution to the inner city (Sadr Mousavi and Rahimi 2008). In recent decade, changing the patterns of vehicle use, particularly in urban areas, and increasingly use of private cars instead of urban public transport cause that the vehicles are a significant source of emissions into the atmosphere and Tabriz air pollution. So, industrial factories and vehicles are the main air pollution factors in Tabriz now.
The result of the past study in Tabriz air pollution indicates that the metrological parameters and, especially, wind blowing are the main variables in intensification and alteration of Tabriz air pollution (Sadr Mousavi and Rahimi 2008, 2010, Mojtabazadeh 2005). But, the results in this paper show that the relative humidity and temperature are the main metrological variables in the prediction of NO2 and NO
x
concentrations and the wind importance for NO2 and NO
x
modeling approximately is 7%. While in Sadr Mousavi and Rahimi (2008) studies, wind speed and wind direction important in CO concentration modeling are 19.17 and 14.12%, respectively. Also, based on this work results, we cannot conclude like Mojtabazadeh (2005) results that the main metrological variable in Tabriz air pollution is wind blowing.