Aircraft System Identification Using Artificial Neural ...

Aircraft System Identification

Using Artificial Neural Networks

Kenton Kirkpatrick

Jim May Jr.

John ValasekJohn Valasek

Aerospace Engineering Department

Texas A&M University

51st AIAA Aerospace Sciences Meeting

January 9, 2013

Compos Volatus

Overview

� Motivation

� System Identification

� Artificial Neural Networks

2

� Artificial Neural Networks

� ANNSID

� Conclusions and Open Challenges

Motivation

3

Motivating Questions

� Is it possible to use artificial neural networks to determine a linear model

for an aircraft based on experimental data?

� Would a linear model determined by an artificial neural network be able to

accurately model behaviors not present in the training data?

4

accurately model behaviors not present in the training data?

� How would an artificial neural network-determined linear model compare

to other accepted methods of aircraft system identification?

Motivation

� System identification

o Some methods are only accurate under strict conditions

o Determining accurate solutions can be time consuming

o Currently accepted accurate solutions require learning parameters

independently or Kalman filtering

5

� Artificial neural networks

o Require minimal user input

o Easily implemented

o Robust to noise

o Fast

System Identification

6

System Identification

� Identification of linear model for aircraft systems

o Requires experimentally determined data, including state response to

control inputs and excitation of modes

o Separate linear models are generally determined for longitudinal and

lateral/directional modes

� Linear models are needed to analyze stability and determine control policies

� Identifying a linear model requires determining:

7

� Identifying a linear model requires determining:

o State matrix, A

o Control matrix, B

o Output matrix, C

o Carry-through matrix, D

1k k k

k kk

x Ax Bu

y C x Du

+ = +

= +

Longitudinal Linear Model

� Longitudinal Motion

o Covers motion that occurs in the pitching plane

o Includes forward velocity, vertical velocity (or angle-of-attack), pitch

angle, and pitch rate

o Controls include elevator deflection and thrust

[ ]T

x u qα θ=

8

Vα

u q

θ

[ ]x u qα θ=

[ ]T

e Tu δ δ=

Lat/D Linear Model

� Lateral/Directional Motion

o Covers motion that occurs in the rolling and yawing planes

o Includes side velocity (or side-slip angle), roll rate, yaw rate, roll angle,

and heading angle

o Controls include aileron and rudder deflections

[ ]T

x p rβ φ ψ=

9

[ ]T

x p rβ φ ψ=

[ ]T

a ru δ δ=

V

βϕ

ψ

r

p

Observer/Kalman filter Identification

-100

0

100

v (

ft/s

ec)

Nonlinear

OKID

-100

0

100

p (

deg/s

ec)

Flight Condition

Altitude: 27,000 ft

Airspeed: 800 ft/sec

UCAV6 LINEAR SYSTEM IDENTIFICATION (LAT/D)

Valasek, John, and Chen, Wei, "Observer/Kalman Filter Identification for On-Line System Identification of Aircraft,"

Journal of Guidance, Control, and Dynamics, Volume 26, Number 2, pp. 347-353, March-April 2003.

10

0 5 10 15 20-100

0 5 10 15 20-100

0 5 10 15 20-20

0

20

40

r (d

eg/s

ec)

0 5 10 15 200

50

100

150

phi (d

eg)

0 5 10 15 20-5

0

5

dr

(deg)

0 5 10 15 20-5

0

5

da (

deg)

OKID eigenvalues

-1.246 ± 4.2727i

-7.013

.02243

linearizer

eigenvalues

-1.4133 ± 4.5775i

-7.3635

.00835

Artificial Neural Networks

11

Networks

Artificial Neural Networks

� Class of machine learning algorithms designed

to mimic the learning behavior of true neural

networks

� Actual neural networks are created by complex

12

� Actual neural networks are created by complex

interactions between neurons that pass

electrochemical signals between each other

� Artificial neural networks are an attempt to

mimic this behavior by creating virtual units that

process and pass numerical information between

members of a network of units

Feedforward Neural Networks

� Most common artificial neural network

� External information enters the input layer

� Individual units process the inputs and pass the new information to the next

layer in the network

InputHidden

13

.

.

. ...

.

.

.

Output

Feedforward Neural Networks

� Individual units are composed of inputs, internal processing, and outputs

� Inputs:

o Consist of weighted outputs from the previous layer

o Can include an extra weighted input of 1to offset learning bias

� Proccessing:

o Weighted Inputs are summed together

Sum is passed through a user-determined threshold function

14

o Sum is passed through a user-determined threshold function

� Outputs:

o Threshold function result is output from the unit

o Outputs of current layer become inputs of next layer

Threshold Functions

� Threshold functions are used in neural network units to bound the summed

inputs of the unit based on the problem to be solved

� Common threshold functions include:

o Linear

15

o Step (Perceptron)

o Sigmoid

( )t x x=

( )( ) sgnt x x=

1( )

1 xt x

e−

=+

Backpropagation

� Training a feedforward neural network requires an algorithm for updating

the weights of the network

� The most common training algorithm is the Backpropagation algorithm

o Uses gradient descent to update weights starting with the output layer

o Propagates errors between network outputs and desired outputs

backward through the network for weight updates

16

backward through the network for weight updates

( )21

( ) ( )2

k k kE w s o w= −

i

i

Ew

wη

∂∆ = −

∂

ANNSID

17

ANNSID

� Artificial Neural Network System Identification (ANNSID) uses

backpropagation to determine A and B matrices

� ANN Requirements:

1. No hidden layers. Only input and output layers.

InputHidden

Input

18

.

.

.

Input

.

.

.

Hidden

.

.

.

OutputOutput

ANNSID



� ANN Requirements:

1. No hidden layers. Only input and output layers.

2. Must use linear threshold function (i.e., no threshold).

3. No bias inputs to nodes.

19

3. No bias inputs to nodes.

OutputΣ

X t(X)

1w0

I1

I2...In

w1

w2

wn

OutputΣ

I1

I2...In

w1

w2

wn

ANNSID



o Uses experimental data to learn state prediction

o A and B matrices are discrete

�

Inputs:1k k kx Ax Bu+ = + 1 1 2 1 3 1 4 1w w w w

w w w w

→ → → →

20

o Inputs:

− xk

− uk

o Outputs:

− xk+1

1 2 2 2 3 2 4 2

1 3 2 3 3 3 4 3

1 4 2 4 3 4 4 4

w w w wA

w w w w

w w w w

→ → → →

→ → → →

→ → → →

=

5 1 6 1

5 2 6 2

5 3 6 3

5 4 6 4

w w

w wB

w w

w w

→ →

→ →

→ →

→ →

=

Longitudinal Example

� ANNSID for identifying longitudinal linear

model

o C700

All initial conditions are 0

Input

Outputuk

αk

q

uk+1

α

21

o All initial conditions are 0

o Experimentally determined response for

training network

� OKID model simulated for comparison

qk

θk

δe,k

δT,k

αk+1

qk+1

θk+1


0.1462 0.3697 0.1647 0.5904

0.0834 0.3808 0.7905 0.0177

0.0285 0.1274 2.1541 0.1341

0.0078 0.0010 0.8567 0.0027

ANNSID

longA

− − − − − − = − −

− −

0.2371 0.3715 0.0517 0.6304− − − −

0.6635 0.1235

0.6236 0.0051

7.8345 0.0006

0.4836 0.0007

ANNSID

longB

− − = − − − −

0.4012 0.1241−

22

0.1394 1.0602 0.9127 0.0230

0.0918 0.2402 2.0719 0.1316

0.0129 0.0450 0.8722 0.0080

OKID

longA

− − − = − −

−

0.6219 0.0001

7.1121 0.0036

0.6369 0.0003

OKID

longB

− − = − − −

ANNSID OKID

λ1,2 = -0.2187 ± 0.1667j λ1,2 = -0.1384 ± 0.1364j

λ3 = -2.1564 λ3 = -2.2396

λ4 = -0.0901 λ4 = -0.8609


23


24


25


26

Lat/D Example

� ANNSID for identifying lateral/directional

linear model

o C700

All initial conditions are 0

Input

Outputβk

pk

r

βk+1

p

27

o All initial conditions are 0

o Experimentally determined response for

training network

� OKID model simulated for comparison

rk

ϕk

δa,k

δr,k

pk+1

rk+1

ϕk+1

Lat/D Example

/

0.1688 0.0102 0.9895 0.1749

1.2807 2.3198 0.1820 0.0042

3.6614 0.5574 0.2284 0.0053

0.0992 0.8402 0.0288 0.0047

ANNSID

lat dA

− − − − − = − − −

−

0.1718 0.0185 0.9994 0.1919− − −

/

0.0037 0.0014

2.2508 0.2005

0.0022 0.6712

0.1341 0.0126

ANNSID

lat dB

− = − − −

0.0021 0.0282−

28

/

1.0393 2.1342 0.1275 0.0018

3.4943 0.5350 0.2464 0.0019

0.0653 0.8935 0.0362 0.0045

OKID

lat dA

− = − − −

/

1.9976 0.2653

0.0794 0.6607

0.1886 0.0231

OKID

lat dB

− = −

−

ANNSID OKID

λ1,2 = -0.2760 ± 1.8554j λ1,2 = -0.2832 ± 1.8300j

λ3 = -2.1790 λ3 = -2.0162

λ4 = 0.0187 λ4 = 0.0311

Lat/D Example

29

Lat/D Example

30

Lat/D Example

31

Lat/D Example

32

Conclusionsand

33

andOpen Challenges

Conclusions

� Accurate aircraft linear models for longitudinal and lateral/directional

motion can be determined using an artificial neural network

o Resulting matrices are comparable to OKID

o Works well on inputs not used in training

� The network must be restricted for network weights to be equivalent to A

34

� The network must be restricted for network weights to be equivalent to A

and B matrices

o No hidden layers

o Linear threshold

o No bias input

o Inputs of current state and control, outputs of next state

� ANNSID is able to learn accurate models quickly (< 8 seconds CPU time

for scenarios tested)

Open Challenges

� Determine full linear model

o Use ANNSID formulation to determine linear models that include

longitudinal and lateral/directional coupling

o Will require flight conditions involving inputs from all controls

� Learn models for aircraft of different types

35

� Learn models for aircraft of different types

o Investigate more aircraft similar to the C700

o Investigate modeling of high-performance aircraft

o Investigate modeling UAVs

� Investigate using ANNSID-determined models for control

o Develop feedback control laws using linear model

o Test control laws using the linear model on real aircraft

Questions?

36

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