


Neural Network Technique
Application for
the Identification of
Aircraft Flight Manoeuvres
Boev J., Tagarev T., Stoianov Tz.
Abstract
This paper aims to present a method and a technique which enable
to solve the identification problem of the aircraft space manoeuvres, in
case of an information insufficiency. For this purpose is used the neural
network technique. The backpropagation algorithm application is explained
in details. The validity of the method is proved by accomplishment of a
numerical experiment.
1. INTRODUCTION
One of the main tasks of the express flight data processing is the aircraft flight manoeuvres identification after every flight. Every one of the flight manoeuvres can decompose to separate images (parameters), which characterize them (the change of the altitude, acceleration, speed, roll, pitch, ect., for example). Some of this parameters can be recorded by aircraft flight recorders.
The used methods and algorithms don‘t give a possibility to identify the aircraft flight manoeuvres with high precision and reliability, using only one of this parameters. To identify the separate flight figure this methods need more of one parameter (usually three or four).
In this work is proposed to use the neural network technique for express
aircraft space manoeuvres identification in case of an information insufficiency.
For a neural network learning to identify the flight figure is used the
standard backpropagation learning algorithm (BPLA)for the multilayer perceptron
(MLP).
2. GIST OF THE METHOD
The neural behavior should be determined on the basis of a set of input/output
pairs. Each learning example is composed of n input signals xi (i=1, 2,
... n) and m corresponding desired output signals dj (j=1, 2, ... m). The
input/output pairs are expressed as stable states of neurons which are
usually represented by +1 (ON) and –1 (OFF). Learning of the MLP consists
in adjusting all weights such that the error measure between the desired
output signals djp. and the actual output signals yjp. averaged over all
learning examples p will be minimal (possibly zero). The standard backpropagation
learning algorithm uses the steepestdescent gradient approach to minimize
the meansquare error function.
The local error function for the pth. learning example can be formulated
as
,
and the total error function as
where djp and yjp are desired and actual output signal of the jth output
neuron for the pth pattern, respectively.
To find the minimum of the global error function E we will use the online learning technique in which the training patterns are presented sequentially, usually in random order. The architecture of the used BPLA for a threelayer perceptron is shown on the fig. 1.
For each learning example the synaptic weights
( s=1, 2, 3 ) are changed by an amount
proportional to the respective negative gradient of the local error function
Ep , which can be written mathematically as
, ?>0
It has been proved that, if the learning parameter ? is sufficiently small, this procedure minimizes the global error function E = [ ].
The updating formula (in case of a threelayer perceptron) for the synaptic
weights of the output layer is
Fig.1.
,
where .
The updating formulas for the hidden layers are
,
where ;
where
The chosen sigmoid activation function for all neurons may be an unipolar,
i.e. described by
,
or a hyperbolic tangent function, i.e.
.
The major difference of the learning rule for the output layer and the
hidden layers is the evaluation of the local error
( s=1, 2, 3 ). In the output layer the error is a function of the desired
and the actual output and the derivative of the sigmoid activation function.
For the hidden layers the local errors are evaluated on the basis of the
local errors in the upper layer.
The algorithm can be performed by realizing the following steps [ ]:
Step 1. Initialize all synaptic weights to small random values.
Step 2. Present an input from the class of learning examples and calculate
the actual outputs of all neurons using the present values of .
Step 3. Specify the desired output and evaluate the local errors
for all layers.
Step 4. Adjust the synaptic weights according to the iterative formula
( s=1, 2, 3 ) .
Step 5. Present another input pattern corresponding to the next learning example and go back to Step 2.
An improvement of the algorithm is possible by adding the socalled
momentum term
?>0 ; 0? ?<1
(typically ?=0,9) ; s=1, 2, 3 .
The weights are now updated using the formula
.
3. NUMERICAL RESULTS
The method described in Sec. 2 is imployed to identify the aircraft manoeuvres using data of one of the flight parameters. We use records, made by the flight recorder type SARPP12, of the altitude change for four types of manoeuvres  zoom (hump), take off, combat turn and immelman. The data shown on the fig.2 are normalized in the limits of (0 , 1).
fig.2
To realize the learning of the neuron network (three layer perceptron) to it input are supplied in series 50 random samples for every one of the manoeuvres  total 200 samples. The network realizes the identification, calculates the error and changes the synaptic weights. The learning processes completed when the error reaches the admissible value or after determined number of iterations (epochs).
After training the multilayer perceptron has the ability for proper response to input patterns not presented during the learning process.
The network has tested, first by the same 200 samples, second by 200
new samples, which the network was not “saw”. During the second testing
the initial values of the synaptic weights are the values stabilized during
the training process. In Fig.3 is presented the change of the total error
and in Fig. 4 the learning rate during the learning process.
Fig. 3.
Fig. 4.
The results of the numerical experiment show that if the learning epochs
are more than 4000 the learning examples are identified correctly and the
total error is admissible. No more than four of the testing examples are
identified wrong.
4.CONCLUSIONS
The described backpropagation algorithm can be applied for the aircraft
manoeuvres identification, based on the data recordered by the simple flight
recorder units. These results are encouraging and future work will be devoted
to the improvement of the method. The derived algorithms can be utilized
as a base for developing program systems for an aircraft flight manoeuvres
identification.
REFERENCES
[1] Cichocki A., Unbehauen R. Neural Networks for Optimization and Signal Processing, John Wiley & Sons, Stuttgart, 1993.
[2] Rodin E.Y., Wu Y. Artificial Intelligence Methodologies for Aerospace and Other Control Systems, Washington University, 1993.
[3] Scsvanefeld R.W., Goldsmith T.E. Neural Network Models of Air Combat Maneuvering, Brooks AFB, Texas, 1992.
[4] Tagarev T.D., Ivanova P.I., Moscardini A. Computing Methods for Early Warning of Violent Conflicts , Proceeding of the AFCEA Sofia seminar, 1996, pp 4451.
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