Environmental Engineering Reference
In-Depth Information
3.3.4. Optimization
In the present study, variables like concentration of jarosite waste, clay
and PCCRs influences the responses compressive strength, water absorption,
shrinkage, density and leachate concentration of toxic elements). In order to
optimize the response parameters to achieve requisite properties, numerical
optimization using desirability functions (Derringer and Suich, 1980) was
done to find the optimum mixture proportions through mathematical and
graphical approach. In the present study, numerical optimization was followed
which involve defining an objective function known as desirability function
that influence the level of each responses varied from minimum to maximum
desirability. The optimum mixture is defined here as that mixture which
provides targeted compressive strength while meeting specified performance
criteria. A desirability function, D(X) must be defined for each response
(property). It reflects the desirable ranges for each response (d
i
). The desirable
ranges are from zero to one (least to most desirable respectively). The
simultaneous objective function is a geometric mean of all transformed
responses:
D= (d
1
d
2
d
n
)
1/n
=
1
/
n
n
d
i
i
1
Where n is the number of responses in the measure. If any of the
responses or factors falls outside their desirability range, the overall function
becomes zero. The desirability function takes on values between 0 and 1. The
desirability function may take different forms such as ‗maximum',
‗minimum', ‗target', or "in range'. For example, the desirably functions for
compressive strength and brick density used in the present study are shown as
follows.
35
1.45
8.15 115.65
Compressive Strength (kg/cm
2
)
8.15
115.65
1.94
Density (g/cm
3
)
The goal was to optimize the brick quality to meet the following
specifications:
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