Paper Technology International 2020 - Journal - Page 77

PAPERTECHNOLOGYINTERNATIONAL
The problem looks somewhat similar from the modelling
point of view for a wide variety of materials and processes.
Nonlinear models combined as shown in Figure 4 make process
development more efficient by reducing expensive experimentation
and by helping achieve better combinations of product properties,
often optimised for cost.
Sometimes the composition variables or feed characteristics
might be constants. In other situations, the process variables may be
constant or dependent variables, and the only degrees of freedom
in materials development may be the composition of the feed, the
amounts of raw materials and possibly dimension variables. This
is often referred to as recipe development. In this case, we have
freedom in both composition as well as process variables.
Figure 4: Composition variables, process variables and dimension
variables determine product properties, production rate and
production economics.
Experimentation
Nonlinear modelling needs either experimental or production
data. A lot of experiments are carried out at the pilot plant in
Järvenpää round the year. From 22 series of such experiments from
2019 to 2021, a total of 970 usable observations were collected. The
equipment allows hard nip sizing as well as film sizing, and the data
contains a small fraction of film sizing results also. These include a
wide variety of papers and boards, particularly liners with modified
starches of different viscosities. These experiments were used for
the model development work.
If nonlinear models are to be developed for a single paper
mill, a small number, probably 25 to 30, would have been sufficient
for developing nonlinear models, if the experiments had been
planned keeping in mind that nonlinear models would be developed
based on that data. Besides SCT index in the cross direction and
burst index, air porosity, thickness and density were also measured
from each of the experiments.
Nonlinear model development
From the raw data set, it was possible to see the effects of
certain variables. For example, the higher the base paper’s basis
weight, the lower is the increase in SCT index and burst index.
Higher nip loads also produce larger increases in SCT index as
well as burst index. The raw experimental data was analysed and
preprocessed, after which nonlinear models were developed and
tested using the NLS 020 software. The experimental data taken into
use was fairly consistent and of good quality, and as a consequence,
good nonlinear models could be developed.
Nonlinear models of SCT CD and burst indices
Nonlinear models in the form of neural networks with a
single hidden layer were attempted and tested to predict SCT CD
index, increase in SCT CD index, burst index as well as the increase
in burst index over unsized paper. The rms error (roughly speaking,
the standard deviation of prediction errors) of SCT CD index was
around 1.2 J/g while the rms error of burst index was 0.13 kN/g
which amount to about 5% in terms of fractional errors for both.
Figure 5 shows the burst index predicted from the nonlinear model
plotted against the 970 measured values from 22 series. The model
predictions look close enough to the measurements. It is natural
that the nonlinear models perform well since the effects are not
very linear, while the linear models will not hesitate to predict even
negative values of the indices.
Figure 5: Burst index predicted from the nonlinear model plotted
against measured values.
Implementation of the models in software
Nonlinear models in the form of neural networks are not
simple equations. The equations are clumsy and unwieldy, and
not easy to work with. Engineers, let aside plant operators, cannot
be expected to be familiar with such mathematics. It is therefore
imperative to implement the models in software which makes
the use of models easy for anyone. LUMET systems are a set
of software components which are assembled depending on the
needs of the users. In all LUMET systems, the central point is the
prediction screen (Figure 6), where the user can feed in the values
of the input variables on the left side, and can predict the outputs
shown on the right side. Besides SCT CD index and burst index,
there are also economic variables like raw material cost. Figure 6
shows a typical prediction calculation. A lot more things can be done
once the models have been developed and implemented in software
like this.
Figure 6: SCT CD index, burst index, raw material cost and
several other consequences of sizing are predicted using the
nonlinear models on the prediction screen.
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