Because the small column size involved few variables, the
ANN architecture adopted here was straightforward. The
input layer for the FFANN estimator had four input
nodes, one for each still temperature, and a single hidden
layer. The RANN estimator included an additional input
node for the last concentration prediction. In both estimators,
the output layer comprised a single output node for
the predicted ethanol concentration. Sigmoid activation
functions were used to compute the output signal of each
neuron.
Back-propagation optimization algorithms from MATLAB
6.5 release 13 (‘‘TRAINLM” Levenberg-Marquardt
for static networks, ‘‘TRAINBFG” BFGS quasi-Newton
for dynamic networks) were used for calibration. Convergence
criteria were assigned RMSE arbitrary low calibration
targets of 0.5% v/v for laboratory and 0.7% v/v for
industrial data. Calibration target values were selected by
trial and error to avoid overfit and to achieve good prediction
accuracy within reasonable calibration times. The
RMSE target for laboratory data was smaller since the
L-dens ethanol sensor was more accurate than the laboratory
hydrometer used with industrial samples.