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the most important stochastic data changes when
friction is removed as a stochastic input variable.
The table also shows that the standard deviation
of the internal energy is in the order of 5-10% of
the nominal value. By comparison, the number of
deformed elements, i.e. elements exceeding a
specified plastic strain, has a standard deviation
exceeding 50% of the nominal value.
The correlation chart is a versatile tool and figure
7 shows the original 10 input variables versus 4
outputs. Marked boxes are regarded to have high
values of correlation. Since the variables Tilt,
Thickness, Impact Angle and Friction have many
marked boxes but only one box is marked for the
material properties, it is concluded that variations
in material properties are of less importance than
variations in the loading case.
Another important result is the correlation
between the outputs. Figure 8 shows that an increase in the
maximum internal energy of the bumper beam leads to a
decrease in the number of deformed elements on the ring
frame.
Table 2: Variation of friction has a significant effect on some of the
stochastic results. It is also clear that the robustness properties can hardly
be ignored when the maximum value in the study exceed the nominal value
by more than 5 times.
The necessity of metamodels
As seen in the robustness study, the scatter of
the results cannot be neglected in an
optimization. Furthermore, the computational
expense makes it most desirable to find a fast
replacement for the FE simulation during the
optimization. In modeFRONTIER there are 7
types of metamodels which aim to replace the
underlying simulation model with a very fast
but approximate function. The evaluation time
is in the order of 0.05 seconds, making it
possible to evaluate thousands of design
candidates in order to solve the robust design
optimization task.
The process of using metamodels is divided into
3 steps:
Training the metamodel
Evaluating the quality of the fit
Using of the metamodel
It was not obvious which metamodel would
deliver the best fit so Kriging, Radial Basis
Newsletter EnginSoft Year 6 n°4 - 23
Figure 6: The main effects plot shows that the most influential parameter on the internal
energy of the bumper beam is the tilt of the barrier followed by the impact angle and friction.
Function and Neural Networks were included and evaluated.
Besides the previously mentioned robustness parameters, 3
new geometry parameters, implemented through mesh
morphing in ANSA, were introduced.
The training set consisted of 1000 FE simulations and
another 170 FE simulations were used to check the quality of
the metamodels. Figure 9 shows the difference between the
Radial Basis Function and the evaluation set for one of the
results. The mean residual values between the three methods
were close and the response looked similar to the same
design IDs. As such, all three methods in this study are
considered to give equally good results. In the end, the
parameters given by the Neural Networks were chosen for
final verification.
Figure 7: Correlation between input and output variables. The variation in crashworthiness due to
scatter in material properties is small if compared to the scatter in the load case variables.