The data sets used in this study come from an air quality monitoring station from an urban area of Ploiesti, Romania, and each data set contains approximately 4200 samples for PM2.5 concentrations and temperature. From all meteorological parameters the temperature is correlated with PM2.5 evolution. The data from Ploiesti monitoring station referring to PM2.5 concentrations has the maximum of 36.45 μg/m3, and a minimum of 0.19 μg/m3. In the same time, the temperature data set has the maximum of 37.24 °C, and the minimum of −0.2 °C.
The proposed forecasting models use normalized data for both PM2.5 concentrations and temperature. The data were randomly divided with the following percentages: 70 % for training, 15 % for validation and 15 % for testing. We propose two types of forecasting models in this study, based on ANNs. One model has as inputs the four previous PM2.5 hourly concentrations (Fig. 3a) and the other has one more input than the first one, namely the current hourly temperature (Fig. 3b). The output of the models is the same in both cases - short term forecasted value for the next hour PM2.5 concentration.
The structure of the proposed neural network contains four neurons in the input layer, one hidden layer and one neuron in the output layer. In the study there were used two types of neural networks, namely feed forward backpropagation (FFwd) and layer recurrent (LRec). As training algorithm the preferred method is Levenberg-Marquardt, and for the adaptive learning functions there are studied the gradient descent with momentum weight and bias (learngdm) and gradient descent weight and bias (learngd). The simulations were performed modifying also the number of neurons in the hidden layer.
The training and validation errors have values around 0.001 and 0.0007 respectively. The accuracy of the models can be evaluated based on the comparison between the actual value and forecasted value of PM2.5 concentration, with mean error and standard deviation criteria. The performances of the designed ANN models are compared using statistical indices such as RMSE, IA, R2, and R.
The two models are compared using statistical criteria and a selection of the results are presented in Tables 1 and 2, the best configuration for each ANN model being highlighted.
For the first model using only PM concentrations as inputs the best results are obtained in the case of layer recurrent structure with 5 neurons in the hidden layer and the learngdm adaptation learning function. In this case the root mean squared error have the smallest value, and IA, R2 and R indices have the biggest values.
The second model with temperature as additional input has the best results (comparing the same statistical indices) in the case of feed forward structure with 6 neurons in the hidden layer and the learngd adaptation learning function.
The best results from the two models showed that no significant enhancement has been produced when current hourly temperature is included as additional input variable to the second ANN model. The best structure between the two is the one from the first model with PM concentrations as inputs (4 × 5 × 1 – Learngdm – Layer Recurrent) with: RMSE = 1.0908 μg/m3, IA = 0.9905, R2 = 0.9634 and R = 0.9815.
Figure 4 presents a partial view of the comparison between testing and forecasted data for the best ANN structure.