Aerospace and Electronic Systems - August 2018 - 43

Sarego, Zaccariotto, and Galvanetto

Figure 8.

ANN diagram for the reconstruction of the location of the impact.

Four impact locations were reconstructed: Table 5 lists their
original locations.
The results of the ANN are in good agreement with those simulated by Abaqus/CAE. Figure 9 shows the position of the impacts
(blue triangles) and those evaluated by the ANN (red squares).
It should be highlighted that the positions that can be properly
identified by the ANN are those inside the area delimited by the
positions of the impacts used for training the network (the black
squares in Figure 5).
Figure 10 shows the absolute error for every impact in terms of
distance between the simulated and the recovered positions, while
Table 6 reports them.
In addition, it should be noticed that the errors listed in Table
6 are all smaller than the radius of the impactor hemispheric head,
therefore this aspect may affect the accuracy of the algorithm.

META-MODEL VERIFICATION

Figure 9.

Positions of the impacts recovered by the ANN (red squares) compared
to the simulated positions (blue triangles) for the four impacts. The red
stars identify the positions of the sensors on the laminate.

While model validation aims at assessing how accurately the numerical model reproduces the experimental test, model verification
is the assessment of the solution accuracy of the model with respect
to the conceptual model [32]. In this section, the ANN employed
for the recovery of the location of the impact is verified: ANNs
are meta-models and replace FEM simulation models requiring
expensive computational resources. The verification is carried out
by studying the uncertainty distribution of the outputs, needed to
evaluate the influence of input uncertainty on the prediction of the
model. One of the most common techniques is the conventional
sample-based Monte Carlo Simulation (MCS) approach, where
random number generation is used for simulating the values of random inputs [33]. In this way, the uncertainty of the computational
meta-model prediction can be evaluated by providing a representation of the probability density function (PDF) for the outputs,
which can't be obtained analytically. When a sufficient number of
simulations are performed, the MCS is robust in the sense that it
provides good estimates of uncertainty in the predicted parameters,
regardless of whether the model is highly nonlinear or not.
The procedure for this type of analysis, taken from [34], is:
1. To establish the model equation between the analytical outputs
O and the input parameters I.

Table 6.

Figure 10.

Distance error for the four impact positions.

Positions of the Impacts Reconstructed by the ANN
and Absolute Error

Table 5.

Positions of the Impacts to be Reconstructed by the ANN
Impact

X Position (mm)

Impact

Recovered
X Position
(mm)

Y Position (mm)

Recovered
Y Position
(mm)

Position
Error
(mm)

n° 4

−5

−35

n° 4

−2.6

−35.8

2.6

n° 5

−5

n° 5

25.4

−13.7

8.7

n° 6

−40

n° 6

−33.4

31.6

6.8

n° 7

−5

−30

n° 7

−1.6

−27.4

4.3

AUGUST 2018

IEEE A&E SYSTEMS MAGAZINE

Aerospace and Electronic Systems - August 2018

Table of Contents for the Digital Edition of Aerospace and Electronic Systems - August 2018