ANN models developed
The ANN model parameters were set considering cascading-
training technique of the FANN library to automate the
selection of hidden layer neuron count. Maximum number of
epochs was set to 1000, applying an early stopping criterion to
avoid overfitting setting the validation process at every 10
epochs. A starting learning rate of 0.5 was gradually decreased
by 1% at every epoch during cascading training. Determined
lagged terms were used to feed ANN models to predict 1-dayahead
PM10 level in training and testing. In order to be able
obtain the best ANN structure for seasons, various models were
examined in training and testing phases. The developed ANN
models were: (1) seasonal ANN models for winter and summer
periods coded as NN_W# and NN_S#, respectively, and (2)
singular or nonseasonal models (NSNN#). Table 4 shows the
best structures for seasonal models and also the singular
models for benchmarking, and ANN topologies in the form
of input-hidden-output layer neuron count along with input
vectors. Only the seasonal NN models, named as NN_W1
and NN_S1, were fed with the inputs determined by PCA,
whereas all the others were constructed as benchmark models.
Likewise, the same input vector was used in the singular model
NSNN1, and the other singular ANN models were used as
benchmark based on lagged terms up to 3 days. It can be
noticed that hidden neuron counts increased as larger-sized
input vectors fed to ANN models, which may be a handicap
in this case in terms of increasing complexity and reducing
handling of the models.
Model performance evaluations and error statistics
The seasonal models generally yielded the best scores with
up to 8 hidden neurons in the middle layer, whereas the single
models used up to 9 hidden neurons. Accuracy and error
measures, learning rates, and learning momentums of the
ANN models obtained in training and testing were summarized
in Table 5.
For seasonal ANN models, the overall agreement in training
denoted by IA between modeled and observed values varied in
the range of 0.78–0.83, RMSE values ranged in 0.587–0.655,
FMB values ranged in −0.19–0.10, and R2 values ranged in
0.681–0.727. FMB values obtained from the estimates of ANN
models varied around zero. The ANN models did thus not
show a tendency towards overpredicting or underpredicting
the daily average PM10 levels.
NN_W1 model for winter periods produced the best testing
IA and R2 values of 0.82 and 0.711, with the lowest training
RMSE of 0.587. For summer period, the models NN_S1 and
NN_S3 produced the best testing IA value of 0.79 and R2
values of 0.715 and 0.709; however, the better testing RMSE
value of 0.602 was obtained from NN_S1 model. Among the