Aerospace and Electronic Systems Magazine October 2017 - 18

Measurement of Wing Deflections in Flexible Aircraft
deflections of the plate from 0 inch
(min) to 1 inch (max), in 0.1 inch increments. These black curves constitute a grid whose purpose is to provide
a reference spectrum against which the
dynamic curve is tracked. These black
curves will be referred to as grid curves
in the subsequent discussion.
At time t = 0.7 sec, the dynamic
curve is in alignment with the zero deflection grid curve. It can be seen from
Figure 6 (grey curve) that the direction
of the plate deflection is reversed every
four seconds. The S11 amplitude of the
dynamic (red) curve at each frequency
lies in between the S11 amplitude values of the max (1 inch) and min (0
inch) grid curves at that frequency. As
such, the dynamic curve intersects the
maximum and minimum grid curves at
Figure 7.
the same times when the deflection is
(a) S11 amplitudes of the dynamic SansEC curve (red), and intersection points with the grid curves, as a
maximum and minimum, respectively.
function of time. (b) S11 amplitude difference.
Tracing the red dynamic curve over
time, it intersects with the black grid
curves at several locations.
As the plate's deflection begins increasing from 0 to 1 inch
during the t = [0.7, 4.7] second interval, the dynamic curve begins
intersecting grid curves that correspond to progressively larger
deflections. Once the maximum deflection is reached, the plate's
deflection is decreased from 1 inch to 0 inch, during the t = [4.7,
8.7] second interval. During this interval, as the plate's deflection
decreases back towards zero, the dynamic curve begins intersecting the grid curves that correspond to progressively smaller deflections. At t = 7.7 seconds, the dynamic curve forms a resonant
peak, which lies between the resonant peaks corresponding to the
0.2 inch and 0.3 inch grid curves. At the instant when this resonant
peak occurs, the grid curves indicate a deflection between 0.2 and
0.3 inches, as expected.
The formation of a resonant peak on the dynamic curve defines
Figure 8.
two regions of the curve. Prior to the resonant peak the curve is
Neural network architecture.
decreasing, and immediately after the peak, the curve is increasing.
Hence, when considering the intersection of the dynamic curve
In order to automate the processing of deflection measurements
with the grid curves, it is essential to only consider intersections
from the SansEC sensors, a neural network was created to model the
where the curve shape exhibits the same directional behavior. In
SansEC data. Based on the method described above of estimating
other words, when the dynamic curve is decreasing, its intersecdeflections by finding intersections of the dynamic S11 amplitudes
tions should be determined only with the decreasing part of a grid
with the premeasured S11 amplitudes from the (static) grid curves,
curve while when the dynamic curve is increasing, its intersections
a neural network architecture was created with the following strucshould be determined only with the increasing part of a grid curve.
ture, shown in Figure 8. The network uses three inputs and has one
Figure 7a shows the S11 amplitudes of the grid curves at these
output. Two of the inputs are the measured frequency and amplitude.
Since the above intersection-based method differentiates between
intersection points. The red dynamic curve of Figure 6 is also plotdownward and upward slopes on the static data, the sign of the slope
ted again in Figure 7a. Figure 7a shows that these two curves are
of the amplitude-vs-frequency curve was used as a third input to the
quite close to each other. Figure 7b then shows the amplitude difneural network. The output of the network is the estimated deflecference between the two curves of Figure 7a. It can be seen that
tion. The network was created in NeuralWorks Prof. II software and
this difference is quite small and this demonstrates that one can
has three inputs, two tanh hidden layers of eight neurons each, and
accurately estimate the values of the dynamic deflection from the
one tanh output layer. Each layer is fully connected to the next.
S11 amplitudes of the grid curves.
18

IEEE A&E SYSTEMS MAGAZINE

OCTOBER 2017



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