NEW PRODUCT RESEARCH & DEVELOPMENT 7
Savings can be made by predictive
modelling of fats in chocolates
n chocolate in the EU one area where falls to 4.67 per cent. Simply adding one extra
In these days of rising
food ingredient costs it is
crucial in order to stay
I
cost savings can be made is to replace measurement point has a tremendous effect on
part of the cocoa butter with up to the accuracy of the predictive equation. Putting
5 per cent cocoa butter equivalent all of the data points in Table 1 into a quadratic
competitive to be able to
(CBE). But which CBE is best? At what level is it equation reduces the RMS error further to
make cost savings
wherever and whenever
optimally used? Can the balance between cocoa 3.15 per cent. If, however, we plot the observed
possible. Geoff Talbot,
butter and milk fat also be brought into the data alongside the predictions from the
Imro 't Zand and
whole optimisation process? quadratic equation (using all the data) we see
Kevin W Smith report. How many measurements do we need to that there is still quite a discrepancy between the
make of blends of two fats in order to be able two (Fig. 1) – the blue line shows the observed
make a fairly accurate prediction of other values, the red line the quadratic equation.
À une époque où le
blends? Knowing only the two end-points There is clearly a 'skew' between 20 per cent and
coût des ingrédients
restricts us to a linear interaction and we know 50 per cent cocoa butter which the quadratic
alimentaires est en
augmentation, pour rester
that fats very rarely intermix in a totally linear equation takes no account of. The normal
compétitif, il est essentiel
fashion (Braipson-Danthine and Deroanne, quadratic equation takes the form:
de pouvoir faire des
2006; Gioelli et al, 2003). This means that,
économies lorsque cela est
generally, we need to move to some form of (1) y = a
1
x
1
+ a
2
x
2
+ b
12
x
1
x
2
possible. Un reportage de quadratic equation needing measurements on at
Geoff Talbot, Imro ‘t Zand
least three and preferably more blends. Two fats where x
n
is the proportion of component n
et Kevin W Smith report.
that are commonly mixed together are cocoa and a and b are constants.
butter and milk fat, the basis of milk chocolate. We have found that adding a denominator to
The solid fat contents are shown in Table 1. the quadratic term in this equation puts a ‘skew’
Um konkurrenzfähig
bleiben zu können, ist es
to the equation and predictions made with it.
Table 1. Solid fat content at 20°C of blends of
heutzutage angesichts
The skewed quadratic equation is of the form:
der steigenden Kosten
cocoa butter and milk fat.
für Nahrungsmittel- Per cent cocoa butter N20 b
12
x
1
x
2
bestandteile besonders
100 78.1
(2) y = a
1
x
1
+ a
2
x
2
+ ------------------
wichtig, Kosten wo
1 + c
12
x
2
möglich einzusparen.
95 73.3
Geoff Talbot, Imro ‘t 90 68.5
Not only can we use equations such as the
Zand und Kevin W Smith
85 64.3
berichten.
skewed quadratic equation to predict binary
80 60.4
blend properties we can combine three of these
75 55.7
binary equations into a single equation to be
70 51.6
able to predict a ternary composition. So the
skewed quadratic terms from the binaries of
60 42.4
components 1 and 2, 2 and 3, 3 and 1 can be
50 32.1
combined to give a skewed quadratic equation
35 14.1
for the ternary of components 1, 2 and 3:
20 10.1
0 13.3
(3) b
12
x
1
x
2
b
23
x
2
x
3
b
31
x
3
x
1
y = a
1
x
1
+ a
2
x
2
+ a
3
x
3
+ ------------- + -------------- + -------------
If we were to take a purely linear interaction 1+c
12
x
2
1+c
23
x
3
1+c
31
x
1
between the two end-points then we would
predict the 50:50 blend to have an N20 of 45.7. The improvement in prediction using a
This is clearly much higher than the measured skewed quadratic equation combined with the
value of 32.1 per cent. Indeed the root mean ability to predict ternary blend properties from a
square (RMS) error if a linear interaction is used knowledge of only the binary equations is
is 9.83 per cent. If, however, we add the observed demonstrated in Table 2 in which the observed
value for the 50:50 blend to the two end points N20 of blends of three chocolate fats are
and define a quadratic interaction then the RMS compared with predictions made from normal
error for the predictions of all blends in Table 1 and skewed quadratic equations.
☞
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