Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 67

• in making a much larger number of welds than necessary, just to be sure

that a su cient number of valid spots are produced.

Both the excessive current and the excessive number of spots result in a fast
degradation of the electrodes, which must be changed or redressed frequently.
For all the above reasons, the modeling of the process, leading to a reliable
on-line prediction of the weld diameter, is an important industrial challenge.
Modeling the dynamics of the welding process from first principles is a very
di cult task, for several reasons, including

• the computation time necessary for the integration of the partial differen-

tial equations of the knowledge-based model is many orders of magnitude
larger than the duration of the process, which precludes real-time predic-
tion of the spot diameter;

• many physical parameters appearing in the equations are not known reli-

ably.

Those arguments lead to considering black-box modeling as an alternative.
Since the process is nonlinear and has several input variables, neural networks
are natural candidates for predicting the spot diameter from measurements
performed during the process, immediately after weld formation, for on-line
quality control [Monari 1999].
The main concerns for the modeling task are the choice of the model
inputs, and the limited amount of examples available in the database, because
gathering data is costly.
In [Monari 1999], the quantities that were candidates for input selection
were mechanical and electrical signals that can be measured during the weld-
ing process. Input selection was performed by the techniques described in
Chap. 2. The experts involved in the knowledge-based modeling of the process
validated that set.
Because no simple nondestructive weld diameter measurement exists, the
database is built by performing a number of welds in well-defined condition,
and subsequently tearing them off; the melted zone, remaining on one of the
two metal sheets, is measured. That is a lengthy and costly process, so that the
initial training set was made of 250 examples only. Using experimental design
through the confidence interval estimates described in Chap. 2, a training set
extension strategy was defined in order to increase the database size. Half
of the resulting data was used for training, and the other half for testing
(the model selection method was virtual leave-one-out which, as explained in
Chap. 2, does not require any validation set).
Figure 1.43 shows typical scatter plots, where each prediction is shown
together with its confidence interval. The estimated generalization error, esti-
mated from the virtual leave-one-out score defined in Chap. 2, was 0.27 mm,
whereas the TMSE was 0.23 mm. Since those quantities are on the order of
the measurement uncertainty, the results are satisfactory.