Aerospace and Electronic Systems - August 2018 - 45
Sarego, Zaccariotto, and Galvanetto
Figure 11.
PDF of the trained network the inputs of which are perturbed.
Table 8.
Mean Values Recovered by the ANN, Corresponding Standard Deviation, Skewness, and Confidence Interval
Corresponding to a 95% Coverage Probability
Monte-Carlo
Simulation
Expected Values
(mm)
Recovered Mean
Values (mm)
Standard
Deviation (mm)
Skewness (mm)
95% Confidence
Interval
Trained ANN
X
−5
−4.35
16.36
−0.16
[−39 24]
Y
−35
−23.62
62.04
0.18
[−140 90]
CONCLUSIONS
In this study, ANNs are applied to model the complex nonlinear
behavior of a composite laminate subjected to a low-velocity impact. Two ANNs, one for recovering the time history of the impact
force and one for the location of the impact, are built and trained
by the Neural Network Toolbox of Matlab®. Afterwards, impacts
characterized by different positions and different force time histories are simulated by Abaqus/CAE. For three of them, the time histories of the impact force were reconstructed, and the ANN results
are in good agreement with the simulated time histories (the peak
force is recovered with an error smaller than 14%). Finally, the positions were recovered for four of them: their distance errors were
smaller than 9 mm, which is smaller than the radius of the tip of
the impactor. Differently from previous works on the topic, a large
number of spectral components of signals have been employed to
properly reconstruct the force time history and impact location.
AUGUST 2018
Neural Networks have proven to be powerful tools to provide
reasonable results for force and position reconstruction due to impacts causing large deflections. The accuracy of these results is not
likely to be achieved if approaches based on linearity assumptions
are employed.
For the ANN trained with the mean values of inputs and outputs, the accuracy in the recovery of the X component of the impact
position is better than the accuracy for recovery the Y component
of the impact position, while they are comparable when the training of the ANNs itself is carried out with the perturbed data. In
addition, the outputs of both the trained ANN and the set of ANNs
training with the perturbed inputs have slightly asymmetric PDFs,
as it is expected due to the nonlinear nature of the meta-model.
They have, however, different skewness: for the previously trained
ANN, the skewness for the X component is smaller than that for
the Y component, while they are comparable when the perturbed
data are used for the training of the ANNs. These results show that
IEEE A&E SYSTEMS MAGAZINE
45
Aerospace and Electronic Systems - August 2018
Table of Contents for the Digital Edition of Aerospace and Electronic Systems - August 2018
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