Environmental Engineering Reference
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performance of the ANN, due to a high degree of variability of param-
eters. It was accepted that successful training was achieved when learn-
ing and cross-validation curves (SOS vs. training cycles) approached zero.
Testing was carried out with the best weights stored during the training
step. Correlation coei cient r and SOS were used as parameters to check
the performance (i.e., the accuracy) of the obtained ANNs.
At er the best-behaved ANN is chosen, the model is implemented using
an algebraic system of equations to predict CS , WA , FS , WLF , and VMC ,
by substitution of the corresponding weights and coei cients matrices in
eq. (4.4). h is step can be easily achieved in some spreadsheet calculus
(Microsot Oi ce Excel, for instance).
4.2.4.2 Sensitivity Analysis
Sensitivity analysis is a sophisticated technique that is necessary to use
for studying the ef ects of observed input variables and also the uncer-
tainties in obtained models and general network behavior [13, 19]. Neural
networks were tested using sensitivity analysis, to determine whether and
under what circumstances the combination of obtained models and the
expected actual training data might result in an ill-conditioned system
[13]. On the basis of developed ANN models, sensitivity analysis is per-
formed in order to more precisely dei ne the inl uence of major oxides
content on the observed outputs. h e white noise signals were incorpo-
rated by adding or subtracting the Gaussian error of standard deviation
(SD = 5%) and zero mean with 98% probability, i.e., ±2.241·SD to each
input variable [4, 20]. h e white noise was normally distributed with a
constant intensity and frequency. It was used to test the model sensitivity
and measurement errors.
4.2.5
Fuzzy Synthetic Optimization
Optimization procedure was performed using Fuzzy Synthetic Evaluation
(FSE) algorithm implemented in Microsot Excel 2007, in order to deter-
mine the workable optimum conditions for the thermal processing of
heavy clay bricks [3]. FSE method was implemented, using the results
of models proposed to represent CS , WA , FS , WLF , and VMC , using
eq. (4.5). FSE is a commonly used technique to solve problems with
constraints involving nonlinear functions. h e method aims to solve a
sequence of simple problems whose solutions converge to the solution
of the original problem.
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