Prediction and Optimization of Heavy Clay Products Quality - Advanced Materials for Agriculture, Food and Environmental Safety - page 103

design. h e number of neurons in a hidden layer depends on the com-
plexity of the relationship between inputs and outputs. As this relationship
becomes more complex, more neurons should be added [13].
h e optimum number of hidden neurons was chosen upon mini-
mizing the dif erence between predicted ANN values and desired out-
puts, using SOS during testing as a performance indicator (table 4.1).
Results of CSB , CSC , WAT , WA B , WAC , FS , WLFT , WLFB , WLFC , and
VMC during testing with i ve to thirteen neurons in the hidden layer
are presented. Used MLPs are marked according to StatSot Statistica's
notation; MLP followed by number of inputs, number of neurons in the
hidden layer, and the number of outputs. According to ANN perfor-
mance, from table 4.4 (sum of r 2 and SOSs for all variables in one ANN),
it was noticed that the optimal number of neurons in the hidden layer
is thirteen (network MLP 10-13-10, No 4.), when obtaining high values
of r 2 and also low values of SOS . It was noticed that a greater number of
neurons increases the structure complexity, but does not necessarily sig-
nii cantly improve the network behavior [18], (during testing step MLP
10-13-10, No. 4 gained r 2 = 0.949, SOS = 0.010, while MLP 10-9-10, No.
6 gained r 2 = 0.943 and SOS = 0.011).
h e goodness of i t, between experimental measurements and model-
calculated outputs, represented as ANN performance (sum of r 2 between
measured and calculated CS , WA , FS , WLF , and VMC for each ANN) and
also the SOS between measured and calculated technological parameters,
during training, testing and validation steps, are shown in table 4.4. h e
SOS between the experimental and the network predicted values was used
as the iteration termination criterion, as StatSot Statistica's default. As
soon as the cross-validation SOS starts to increase, the training step is ter-
minated; otherwise, the training step ends at er a i xed number of epochs
or training cycles [13].
Table 4.4 shows ANN performance data, expressed as the sum of r 2 and
SOS , for all variables in one ANN, while table 4.5 presents r 2 for each vari-
able ( CSB , CSC , WAT , WA B , WAC , FS , WLFT , WLFB , WLFC , and VMC )
during training, testing, and validation steps.

4.3.4 Simulation of the ANNs

Process outputs CSB , CSC , WAT , WA B , WAC , FS , WLFT , WLFB , WLFC ,
and VMC can be calculated by the eq. (4.4), using matrices W 1 and B 1 , and
matrices W 2 and B 2 , which represent system, incorporating coei cients
associated with the hidden layer (both weights and biases). Output vari-
ables are calculated by applying transfer functions f 1 and f 2 (from table 4.1)