Civil Engineering Reference
In-Depth Information
18000
16000
Total 36 Nodes
Total 48 Nodes
Total 60 Nodes
Total 72 Nodes
14000
12000
10000
Iterations
8000
6000
4000
2000
0
0
1
2
3
4
5
6
7
8
Number of Hidden Layers
FIGURE 7.6
Number of iterations required for convergence of various network configurations. The error threshold
e
0
is 0.09 and the correction gain
is 0.1 for all networks.
If the network parameters include the ones having principal roles in controlling the weld pool, the welder
can achieve the required DWP's with minimal experimentations or experience. While the weld is per-
formed, the IWPs may be recorded in the IWP recorder, and similarly, the resulting DWPs can be
determined and stored in the DWP recorder after welding. Once these data are available the neural
network can be refined by additional off-line training with the new data, and thus its characteristics are
continuously updated as future welds are produced.
Andersen used actual GTA weld data to evaluate the accuracy of the neural networks for weld modeling.
The data consisted of values for voltage, current, travel speed, and wire feed speed, and the corresponding
bead width, penetration, reinforcement height, and bead cross-sectional area. In all, 42 such data sets
were used, of which 31 data sets were selected at random and used for training purposes while the
remaining 11 data sets were presented to the trained networks as new application data for evaluation
purposes. Thus the networks were evaluated using data that had not been used for training.
Networks consisting of 36, 48, 60, and 72 nodes using various number of hidden layers were built.
The 31 sets of welding data were used for training each of the networks. Using a learning rate of
0.1, the number of training iterations required to reduce the conversion measurement,
e
0
, down to 0.09
is illustrated in
Fig. 7.6
.
Andersen defined a training iteration as one round of network adaptation to all
sets of training data.
Figure 7.6
clearly indicates that there is an optimum number of hidden layers that
requires the least amount of training iterations for this particular problem. Although the training itera-
tions take place off-line and are therefore irrelevant to on-line modeling, they can be fairly time con-
suming. Thus, it is clear that training time optimization is advantageous for extensive experiments.
Each network configuration resulted in comparable performance.
Figure 7.7
s
ummarizes the perfor-
mances of each of the networks for the four DWPs. The bars show standard deviations of the modeling
errors for the various networks using the 11 tested data sets. Most of the errors are on the order of 5 to
10%, with penetration errors typically in the 20% range. These results agree with other similar experi-
ments reported by Andersen, in that modeling accuracy is typically on the order of 10 to 20%.
An observation relating to the weld modeling experiments should be noted here. The precision of the
bead measurements was 0.1 mm, which corresponds to 2 to 7% precision for the average bead width
and penetration, respectively. Furthermore, inaccuracies in measurements of the data, which were used
to train the neural network model, tend to degrade the general performance of the model. Width
measurements are generally more reliable than penetration measurements, as they are made in several
locations along the top of the bead. A penetration measurement is usually made on a single cross section,
