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back-side parameters. The data used for model establishment were got from the 3D
sensing system, the data from 1 to 38 are training data, and other 10 data are test data.
In the welding process, the auxiliary variables can be acquired through the
monitoring system and image processing algorithm. Prior to establishing the model,
the data have to be pretreated. Some apparently wrong data will be cancelled in this
step to improve the accuracy of the acquired data. Because different variables have
different units, a variable may differ from other variables in several orders. It is thus
necessary to normalize all the data in order to map all the data into [0, 1] because the
modeling results can be improved by using normalized data to fit a model with
multiple inputs. Normalizing can be described as follows. If data sample space of a
variable is
,
,…
,
then normalized data is:
/
(1)
Back-propagation neural network (BPNN) model will be established to obtain the
relationships between the welding parameters, characteristic parameters and
estimation parameters in this section. After the model is established, it will be used to
estimate the back-side parameters of the weld pool based on welding parameters and
characteristic parameters in real time.
gives the pool characteristic in
axis,
shapes the pool characteristic in
plane, and
R
holds pool information in horizontal plane. Hence, we select
,
and
,
as auxiliary variables respectively to establish the model. The structure of the
BPNN is 2-5-1. The weights of the BPNN model are shown as follows, and the upper-
right corner of the weights denotes its layer,
,
,
,
,…,
,
,
,
,
,
,
,…,
,
,
,…,
,
,
,
,…,
,
,
,
,
,…,
,
The amount of weights for the BPNN model is
(2)
11
where
is the number of input-layer neuron nodes, and
m
is the number of hidden-
layer neuron nodes.
∑
∑
(3)
11
⁄
(4)
After the structure of BPNN was determined, the data was used to train the BPNN,
and the weights were obtained. Then Eq. (3) can be used to estimate the penetration in
real-time. Here,
and
denote auxiliary variables
,
and
y
denotes dominant
variables. Based on the real-time estimation of penetration, better analysis of GTAW
process will be conducted which will in turn benefit the control system for it to
achieve desired results.
Fig. 5 is the model simulation results based on the BPNN model where
and
are selected as auxiliary variables. As shown in Fig. 5 the data from 1 to 38 are the
training data, and other 10 data are the test data. Table 3 shows the simulation errors,
and it could be concluded that the estimation effect is accurate enough to realize the
real-time estimation.
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