Optimization of neural network performances by means of exogenous input variables for the forecast of ozone pollutant in Rome urban area

Abstract

Air quality problems produced by high levels of ozone affect human health and are related to respiratory problems. Ozone is a reactive gas and presents concentrations which are dependent both from the meteorological conditions and seasonal effects. For Ozone models the most difficult problems is to deal with simulation of chemical reactions, linked to long range transport and to solar radiation and turbulence conditions. Among the complex systems, an important tool in order to forecast air pollution data is the neural network (NN), that can be used in assessing the dynamics of such systems. More, in our simulations we used Support Vector Machine (SVM) for ozone forecasting. Both models have been used to forecast ozone using data at different temporal lags.

In our work, NN and SVM methods have been developed to forecast hourly ozone levels using data from one to ten days in advance (T1-T10). We have analyzed data recorded by monitoring stations for the city of Rome during calendar year 2005.

Our work concerns analysis of the different performances that can be obtained including as input variables to the problem some exogenous variables, as well as the conventional ones, which task is to optimize the training of NN and SVM models. As a consequence, as input variables we considered two sets of simulations, the first using only conventional data as pollutants and meteorological measurements (Conventional Data Set - CDS), and the second including some external data (e.g. time of the day) in addition to the other conventional variables (Extended Data Set - EDS).

The data used in our simulations came from the monitoring stations of the ARPA LAZIO network in the urban center of Rome. The conventional variables used for simulations are:

Monitored pollutants variables:

• Carbon monoxide

• Nitrogen oxide

• Nitrogen dioxide

• Ozone– (Input/Output variable)

Meteorological variables:

• Temperature

• Global Solar Radiation

• Relative Humidity

• Pressure

The additional external variables used for the second simulation set (e.g. time of the day, Julian day, day of the week, month of the year) are to be considered as exogenous variable.

The inclusion of these variables:

a) takes account of hourly and seasonal average conditions

b) takes into consideration a simple periodic mathematical formulation as well as the trend of conventional variables

c) assists the conventional variables during the training of NN and SVM

The Multi Layer Perceptron (MLP) is most commonly used neural network in the field of air quality prediction.

We presented here results obtained using a classical architecture consisting of a single 3-LP with one hidden layer of 20 neurons and an output layer with 1 neuron.

The first layer contains input variables of neural network related to all relevant physical parameters, as well as the exogenous variable in the case of the second set.

The second layer consists of neurons of the hidden layer. The third layer is the output layer, which consists of the target variable to be reproduced, i.e. the hourly Ozone concentration.

In general, the task of NN training is to find the optimum weights of the NN by means of input/output pattern presentation, thus enabling the Neural Network to simulate chemical reactions and turbulence dispersion of the Ozone levels.

Support vector machines (SVM) are a set of related supervised learning methods used for classification and regression. Viewing input data as two sets of vectors in an n-dimensional space, an SVM will construct a separating hyperplane in that space, one which maximizes the margin between the two dataset. To calculate the margin, two parallel hyperplanes are constructed, one on each side of the separating hyperplane, which are “pushed up against” the two datasets.

Intuitively, a good separation is achieved by the hyperplane that has the largest distance to the neighboring datapoints of both classes, since in general the larger the margin the lower the generalization error of the classifier.

We compared the results of NN and SVM for the ozone concentrations, considering the CDS and the EDS separately.

Results and conclusion

For each simulation set, and for each temporal lag within the simulation set, we calculated coefficient of determination R˛ for ozone levels and found good correlations for both simulation sets. Our work was the result of about 108 simulations, where each one is composed of a training and a test phase.

In general, results showed that SVM performed better than NN.

In the table below results coming from the more significant simulations are given.

We calculated the R˛ coefficients for target ozone using the conventional statistical regression model (Regr), the MLP for the CDS (NN(8)), the MLP for the EDS where the additional exogenous variable was the time of the day (NN(9)), the SVM for the EDS with all the exogenous variables (time of the day, day of the week, Julian day, month of the year) (SVM(12)) and the time of the day alone (SVM(9)).

Regr NN(8) NN(9) SVM(9) SVM(12)

T1 0.64 0.71 0.74 0.74 0.80

T2 0.51 0.62 0.68 0.70 0.78

T3 0.45 0.56 0.64 0.66 0.77

T4 0.45 0.57 0.64 0.66 0.77

T5 0.46 0.58 0.66 0.65 0.77

T6 0.46 0.61 0.64 0.66 0.77

T7 0.47 0.59 0.64 0.66 0.75

T8 0.44 0.57 0.64 0.65 0.77

T9 0.42 0.54 0.65 0.65 0.79

T10 0.40 0.54 0.62 0.65 0.78

Table 1: R˛ coefficients for different simulations

As highlighted by the table, NN and SVM perform better (R˛ from 0.54 to 0.80) than the classic statistical linear regression model (R˛ from 0.40 to 0.64).

The most interesting results concern the NN and SVM performances when we add the exogenous variables to the conventional dataset, as we can see from the increasing of the R˛ values.

Observing these values we can appreciate that after an initial decay the coefficient of determination becomes stable and there is not a considerable variation in its value.

In conclusion, our work suggests that using the exogenous variables as input significantly improved the results of simulations and suggested a way of optimizing the environmental simulation using NN and SVM models approach.