AI - a Guide to Intelligent Systems.pdf - Member of EEPIS

WILL A HYBRID INTELLIGENT SYSTEM WORK FOR MY PROBLEM?
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Figure 9.39
On-line time-series predication of an aircraft’s trajectory
on-line with the current motion profile, and required to predict the aircraft’s
motion in the next few seconds. A time-series prediction of an aircraft’s
trajectory is shown in Figure 9.39.
To predict an aircraft’s position on-line we will use an ANFIS. It will learn
from time-series data of given landing trajectories in order to determine the
membership function parameters that best allow the system to track these
trajectories.
What do we use as ANFIS inputs?
To predict a future value for a time series, we use values that are already known.
For example, if we want to predict an aircraft’s position 2 seconds ahead, we may
use its current position data as well as data recorded, say, 2, 4 and 6 seconds
before the current position. These four known values represent an input pattern
– a four-dimensional vector of the following form:
x =[x(t 6) x(t 4) x(t 2) x(t)],
where x(t) is the aircraft position recorded at the point in time t.
The ANFIS output corresponds to the trajectory prediction: the aircraft’s
position 2 seconds ahead, x(t + 2).
For this case study, we will use 10 landing trajectories – five for training and
five for testing. Each trajectory is a time series of the aircraft’s position data
points recorded every half a second over a time interval of 60 seconds before
landing. Thus, a data set for each trajectory contains 121 values.
How do we build a data set to train the ANFIS?
Let us consider Figure 9.40; it shows an aircraft trajectory and a 35 training data
set created from the trajectory data points sampled every 2 seconds. Input
variables x 1 , x 2 , x 3 and x 4 correspond to the aircraft’s flight positions at (t 6),
(t 4), (t 2) and t, respectively. The desired output corresponds to the
two-second-ahead prediction, x(t þ 2). The training data set shown in Figure
9.40 is built with t equal to 6.0 s (the first row), 6.5 s (the second row) and 7.0 s
(the third row).
By applying the same procedure to a landing trajectory recorded over a time
interval of 60 seconds, we obtain 105 training samples represented by a 1055