Analysis and Modeling of GTAW Weld Pool Geometry - Intelligent Computing for Sustainable Energy and Environment - page 290

Fig. 6 is the model simulation results based on the BPNN model where and
are selected as auxiliary variables. Table 4 shows the simulation errors, and it was
concluded that the estimation result is acceptable to realize the real-time estimation. It
can be found that the model based on and gives more precise estimation for ,
but can be estimated more accurately with model based on and . The reason
is that the auxiliary variable includes information of and , and auxiliary
variable contains information of and .
In above discussion, 11 auxiliary variables are presented and they are all related to
the primary variables. Hence, all auxiliary variables will be applied to establish the
model in this section. Every auxiliary variable reflects part information of the process
in different degree, but variables are coupled and would provide redundant
information. Principle component analysis (PCA) method can simplify the data matrix
through dimension reduction. PCA make use of unrelated variables to reflect most
information of original correlated auxiliary variables and delete redundant variables,
which can improve calculation speed of model and simplify the data analysis. PCA is
a well-developed statistic method, and has been widely applied in soft-sensing field.

6 0.5

Process value
BP output

Process value
BP output 0.45

5

0.4

4 0.35

0.3

3

0.25

2 0.2

0.15

1

0.1

0 0.05

0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50

(a) ܹ ௕ (b) ܪ ௕

Sample No Sample No

Fig. 5. Simulation results of BPNN model based on and

Table 3. Simulation errors of BPNN model based on and

Training MSE Training ABE Training RE Testing MSE Testing ABE Testing RE

0.4761 0.4819 0.2203 0.7636 0.7121 0.2470

0.0018 0.0296 0.1743 0.0147 0.0925 0.4687

5.5 0.7

Process value
BP output

Process value
BP output

5

0.6

4.5

0.5

4

0.4

3.5

3 0.3

2.5

0.2

2

0.1

1.5

0

1

0.5 -0.1

0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50

(a) ܹ ௕ (b) ୠ

Sample No Sample No

Fig. 6. Simulation results of BPNN model based on and