Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 70

Fig. 1.46. State-space modeling of the hydraulic actuator

1.4.10 An Application of Semiphysical Modeling to a
Manufacturing Process

As mentioned above, semi-physical modeling is a modeling methodology that
allows the designer to make use both of prior knowledge resulting from a
physical or chemical analysis of the process, and of available measurements.
It is explained in detail in Chap. 2. In the present section, we describe its
application to an industrial problem: the drying of the adhesive Scotch tape
manufactured by 3M.
An adhesive tape is made of a plastic film—the substrate—coated with a
liquid, which is passed in an oven, in a gas atmosphere in which the partial
pressure of the solvent is much lower than the equilibrium pressure of the
solvent at the oven temperature; therefore, the solvent evaporates, so that the
solvent concentration at the surface becomes lower than the solvent concen-
tration in the bulk. As a consequence, the solvent diffuses to the surface so
as to compensate that concentration gradient, and evaporates at the surface.
The process stops when the film is dried, so that the adhesive polymer alone
stays on the substrate.
In a traditional process, organic solvents are used. However, for safety and
environmental reasons, organic solvents are replaced by water. A very accurate
model of drying in the presence of an organic solvent is available [Price 1997];
it is made of thirteen nonlinear, coupled algebraic and differential equations.
When the organic solvent is replaced by water, some equations of the model
are no longer valid, so that the whole model becomes inaccurate.
Polymers in aqueous solutions are not as well understood as polymers in
organic solvents, so that no satisfactory physical model of the drying of water-
based adhesives is available. However, sequences of measurements of sample
weight as a function of time and oven temperature are available: the design
of a semi-physical model is therefore possible and appropriate.
The equations of the model express the following phenomena:

• mass conservation in the bulk of the solvent: that equation is naturally

still valid in the case of water-based adhesives;

• the diffusion of solvent towards the free surface (Flick's law); the validity

of that equation is not arguable, but it involves a quantity (the diffusion