enabling advanced automation tools to manage trajectory ... · copyright © 2017 boeing. all rights...

Copyright © 2017 Boeing. All rights reserved.

Engineering, Test & TechnologyBoeing Research & Technology

Enabling Advanced Automation Tools to manage Trajectory

Prediction Uncertainty

Enrique Casado 24/10/2017| | 1

ART 12 - AutomationEnrique Casado (BR&T-E)

[email protected]

Frequentis, Vienna, Austria, October 24th, 2017


Boeing Research & Technology | COPTRA


Outline

Introduction

Trajectory Prediction Framework

Uncertainty Quantification

Polynomial Chaos Theory

Case Study

Conclusions & Remarks




Introduction

• Ground-based automation tools rely on the capability of accurately predicting the traffic flow within an airspace such as that prediction enable the provision of expected safety and efficiency.

• Nowadays the trajectory prediction process is set as a deterministic process, although the nature of required inputs is intrinsically stochastic .

• Due to the underestimation of the stochastic behavior of the trajectory prediction inputs, current systems usually do not provide with reliable predictions.

How could advance automation tools manage stochastic prediction in an efficient manner so that prediction reliability

is increased and enhanced features become available?



Trajectory Prediction Framework


Input Stochastic Trajectory Prediction Model

Aircraft Intent Description

Initial Conditions:t0→{x0,v0}

Aircraft Performance Model

Weather Model

Motion Model

Output

Description of Computed Trajectory

{xi,vi,Li,Di,Ti,Wi}for i=0,1, …

Stochastic factors related to the initial conditions used for trajectory prediction, e.g. differences between the actual position, velocity and weight of the aircraft at a given time and the values of those variables used as initial conditions for trajectory prediction from that time onwards.

Stochastic factors related to the modeling of aircraft performance, e.g. random differences between real aircraft performance characteristics such as thrust, drag or fuel consumption and the aircraft performance models used for trajectory prediction.

Environmental stochastic factors, e.g. wind and temperature modeling or forecast errors.

Operational stochastic factors, e.g. differences between the pilot/FMS behavior models used in trajectory prediction and that actual guidance strategy of the pilot/FMS.





Input




Weather Model

Motion Model

Output



0 200 400 600 800 1000 1200 1400150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]

0 200 400 600 800 1000 1200 1400150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]

0 200 400 600 800 1000 1200 1400150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]0 200 400 600 800 1000 1200 1400

150

200

250

300

350

time [sec]

High number of runs are required

High computational effort

Individual MC simulations to assess sensitivity of outputs to considered stochastic inputs

Trajectory Computation Infrastructure





Input

Trajectory Computation Infrastructure




Weather Model

Motion Model

Output



0 200 400 600 800 1000 1200 1400150

200

250

300

350

time [sec]

0 200 400 600 800 1000 1200 1400150

200

250

300

350

time [sec]

0 200 400 600 800 1000 1200 1400150

200

250

300

350

time [sec]

0 200 400 600 800 1000 1200 1400150

200

250

300

350

time [sec]

Limited number of runs are required

Low computational effort

Straightforward sensitivity assessment



E. Casado, 24/10/2017 | 7

Polynomial Chaos Theory (I)

Application of Polynomial Chaos Expansions (PCE) to quantify the propagation of uncertainty indynamic systems.

Technique extensively applied in several fields: aerodynamic design, vehicle dynamics, micro-electromechanical systems, petroleum engineering, nuclear waste disposal, etc.

The system response u can be represented as a function of the variability ξ of the inputs x withthe time t

Two approaches to obtain u:

• Intrusive Method, which requires thestochastic formulation of the original model

• Non-Intrusive Method, which requires a set ofdeterministic solutions of the original model



E. Casado, 24/10/2017 | 8

Polynomial Chaos Theory (II)



Enrique Casado 24/10/2017 | 9

1. aPCE-based uncertainty quantification relies on the capability of describing the input distributions driven by data.

2. It provides the flexibility of studying any type of trajectory with an unrestricted number of uncertain inputs.

3. It provides high accuracy with a low computational effort (orders of magnitude lower than Monte Carlo simulations).

Number of terms of the multivariate PCE m

!! !

Polynomial Chaos Theory (III)

10




One-dimensional PCE Multi-dimensional PCE

Ψ

mean Ψ

std Ψ

Ψ ,… , Φ , … ,

Φ ∏ , … ,

1, … ,

Polynomial Chaos Theory (IV)




Case Study (I)




STOCHASTIC FACTORS TO BE CONSIDERED

Take-off time

Take-off weight

Cruise Mach speed

Cruise Altitude

Capturing bearing

Descent speed

Top of Descent (TOD) Location

Weather

Individual Uncertainties are described by different probability density functions

APM (drag and fuel consumption coefficients)

Case Study (II)




Case Study (III)




Number of runs required to compute the multivariate PCE

m !

! !

10

Case Study (IV)



Conclusions & Remarks


• aPCE-based uncertainty quantification provides the flexibility of studying the influence of an unrestricted number of uncertain inputs.

• It relies on the capability of describing the input distributions driven by data.

• It provides high reliable uncertainty quantification with a low computational effort (orders of magnitude lower than Monte Carlo simulations).

• Applicable to all Trajectory Prediction tools without requiring any modification of the native implementation.

• It could enable enhanced robust ATM capabilities by the provision of analytical descriptions of the trajectory prediction uncertainty.



Polynomial Chaos Theory (III)


-4 -3 -2 -1 0 1 2 3 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

9

f ,(9

)

HistExact5-order PC approx4-order PC approx3-order PC approx



Polynomial Chaos Theory (IV)


-4.5 -4 -3.5 -3 -2.5 -2 -1.50

0.02

0.04

9

F ,( 9

)

Tail at beginning

1.5 2 2.5 3 3.5 4 4.5

0.96

0.98

1

9

F ,( 9

)

Tail at end

-4 -3 -2 -1 0 1 2 3 4

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

9

F ,( 9

)

Exact5-order PC approx



What is different from other algorithms


enabling advanced automation tools to manage trajectory ... · copyright © 2017 boeing. all rights...

Documents