Enabling Advanced Automation Tools to manage Trajectory Prediction Uncertainty

Transcription

1 Engineering, Test & Technology Boeing Research & Technology Enabling Advanced Automation Tools to manage Trajectory Prediction Uncertainty ART 12 - Automation Enrique Casado (BR&T-E) enrique.casado@boeing.com Frequentis, Vienna, Austria, October 24 th, 217 Enrique Casado 24/1/217 1

2 Outline Introduction Trajectory Prediction Framework Uncertainty Quantification Polynomial Chaos Theory Case Study Conclusions & Remarks Enrique Casado 24/1/217 2

3 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? Enrique Casado 24/1/217 3

4 Trajectory Prediction Framework 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 Aircraft Intent Description Stochastic Trajectory Prediction Model Motion Model Output Description of Computed Trajectory Initial Conditions: t {x,v } Aircraft Performance Model Weather Model {x i,v i,l i,d i,t i,w i } for i=,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. Enrique Casado 24/1/217 4

5 Uncertainty Quantification Inpu t Aircraft Intent Description Trajectory Computation Infrastructure Motion Model 4 Output Description of Computed Trajectory t {x,v} Aircraft Performan ce Model Weather Model Initial Conditions: {xi,vi,li,di,ti, Wi} for i=,1, High number of runs are required High computational effort Individual MC simulations to assess sensitivity of outputs to considered stochastic inputs Enrique Casado 24/1/217 5

6 Uncertainty Quantification Inpu t Aircraft Intent Description Trajectory Computation Infrastructure Motion Model Output Description of Computed Trajectory Initial Conditions: t {x,v } Aircraft Performan ce Model Weather Model {x i,v i,l i,d i,t i, W i } for i=,1, Limited number of runs are required Low computational effort Straightforward sensitivity assessment Enrique Casado 24/1/217 6

7 Polynomial Chaos Theory (I) Application of Polynomial Chaos Expansions (PCE) to quantify the propagation of uncertainty in dynamic systems. Technique extensively applied in several fields: aerodynamic design, vehicle dynamics, microelectromechanical 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 with the time t Two approaches to obtain u: Intrusive Method, which requires the stochastic formulation of the original model Non-Intrusive Method, which requires a set of deterministic solutions of the original model E. Casado, 24/1/217 7

8 Polynomial Chaos Theory (II) E. Casado, 24/1/217 8

9 Polynomial Chaos Theory (III) 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!!! 1 Enrique Casado 24/1/217 9

10 Polynomial Chaos Theory (IV) One-dimensional PCE Multi-dimensional PCE Ψ Ψ,, Φ,, mean Ψ std Ψ Φ,, 1,, Enrique Casado 24/1/217 1

11 Case Study (I) Enrique Casado 24/1/217 11

12 Case Study (II) 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 APM (drag and fuel consumption coefficients) Individual Uncertainties are described by different probability density functions Enrique Casado 24/1/217 12

13 Case Study (III) Enrique Casado 24/1/217 13

14 Case Study (IV) Number of runs required to compute the multivariate PCE m!!! 1 Enrique Casado 24/1/217 14

15 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. Enrique Casado 24/1/217 15

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17 Polynomial Chaos Theory (III) Hist Exact 5-order PC approx 4-order PC approx 3-order PC approx.25 f, (9) Enrique Casado 24/1/217 17

18 Polynomial Chaos Theory (IV) F, (9).4.2 Tail at beginning F, (9) Tail at end F, (9) Exact 5-order PC approx Enrique Casado 24/1/217 18

19 What is different from other algorithms Enrique Casado 9/1/217 19

20 What is different from other algorithms Enrique Casado 9/1/217 2

21 What is different from other algorithms Enrique Casado 9/1/217 21

22 What is different from other algorithms Enrique Casado 9/1/217 22