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Table 4 Comparison of MSE values of fatigue life prediction results of the MLP-NARX and
RBFNN-NARX models
Material and angle orientation
MSE of the MLP-NARX
model
MSE of the RBFNN-NARX
model
E-glass/polyester
[90/0/ ± 45/0] S
On-axis
0.27
0.258
E-glass/polyester
[0/(
On-axis
0.32
0.285
±
45) 2 /0] T
45
°
0.07
0.088
The good accuracy of the RBFNN models may be attributed to the use of radial
basis functions having parameters that control the positions of the RBFs among the
data or sample points and also their widths of influence (spread) to the sample
points, namely the parameters of
, contributing further to the RBFNN
models resolution capability, at the expense of evaluating and determining more
parameters suitably.
c
and
w
5.3 Fatigue Life Assessment of Multivariable and Multiaxial
Loadings with MLP-NARX Model
It is noted here that for this fatigue life assessment task, there are 15 and 10 testing
sets to be predicted for E-glass/polyester and E-glass fabrics/epoxy, respectively.
Note also the arrangement of fatigue data as training set and fatigue data as testing
set, in particular those of R and
values, as shown in Table 2 . The NN simulation
results and the related discussion will be referred to what Table 2 described.
In addition, it is important to note again that only one information value of axial
orientation-
ʸ
was utilized in the training set employed, while two values of stress
ratio-R were employed.
Figures 18 and 19 present respectively multivariable and multiaxial fatigue life
predictions of E-glass/polyester and E-glass fabrics/epoxy materials at the testing
sets examined. It can be seen that the present NN model indeed showed its ability to
dynamically predict the fatigue lives from the testing sets examined by sliding over
each stress level in a fashion of spectrum loading and multiaxial orientation, made
up by several R and
ʸ
values.
The accuracy of the NN-NARX model prediction was stated by the produced
mean squared errors (MSE) values of 0.123 and 0.27 for E-glass/polyester and E-
glass fabrics/epoxy, respectively. It is worth to note that the training sets employed
were a very small number of fatigue data.
It is noted here that there are some noticeable discrepancies observed between
fatigue lives predicted by the NN-NARX model and those of experimental data. For
E-glass/polyester, they belong to fatigue lives of R =
ʸ
1:
ʸ
= 0, 60 and 90
°
,
respectively. For E-glass fabrics/epoxy,
the noticeable discrepancies belong to
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