Probabilistic Pilot Model Approach for Wake Vortex ...wakenet.eu/fileadmin/user_upload/SpecificWorkshop... · Bode Plot of CO PM A ... Possible limitation of parameter values at 2.5

D. Bieniek, R. Luckner – 2 June 2010WakeNet3 - Europe Specific Workshop: Models and Methods for WVE Simulations

Berlin Institute ofTechnology

Probabilistic Pilot Model Approach for Wake Vortex Encounter Simulations

Slide 2D. Bieniek, R. Luckner 2 June 2010

Content

Objective / Motivation

Pilot Model Requirements

Development Process

Model Structure

Types of Simulation Data

Exemplary Results

Conclusions


40 45 50 55 60 65 70-1

0

1Pilot Side-Stick Roll Input [-]

Why is a probabilistic PM needed?Why is a probabilistic PM needed?

Variation observed for:

a) magnitude

b) phase of control inputs

Modelling these variations via a probabilistic pilot model expands worst case simulation capabilities

40 45 50 55 60 65 70-20

0

20Roll Angle [deg]

Scatter in pilot inputs results in scattered A/C response

Severity model approaches are based on parameters of A/C response (e.g. roll angle, roll rate)

Pilot model quality directly affects inputs to severity model

For identical vortex encounters a variation in pilot control inputs can be observed for one single pilot and in-between pilots.

Worst case Worst caseencounter scenario

Worst casepilot reaction

= +

b)a)


Probabilistic pilot model contributes toseverity assessment


WVE Risk AssessmentWVE Risk Assessment


Pilot Model

A/C Simulation Model

PilotInputs

WV Simulation

Model-40-30-20-10010203040

-20

-15

-10

-5

0

5

10

15

20

Lamb-OseenBurnham & HallockProctorWinckelmans

Vortex Disturbance

Time t

0.00

1.000.660.33

crit

Time t

0.00

1.000.660.33

crit

Time t

0.00

1.000.660.33

Time t

0.00

1.000.660.33

crit

Severity CriteriaTime t

0.00

1.000.660.33

crit

Time t

0.00

1.000.660.33

crit

Time t

0.00

1.000.660.33

Time t

0.00

1.000.660.33

crit

Severity Criteria

A/CResponse

„probabilistic“

deterministicdeterministic

orprobabilistic

deterministic

RiskScenario

deterministic

A/C - WVDistance

Pilot Model

Deterministic / Probabilistic

A/C ResponseDeterministic / Probabilistic

Severity RatingDeterministic / Probabilistic

Probabilistic PM contributes to

risk assessment results


The deterministicdeterministic pilot model shall result in pilot control inputs and aircraft reactions that are well-within (< 1σ) the natural, statistical scatter observed in piloted WVE simulations.

Qualitative Requirements

The probabilisticprobabilistic pilot model shall result in pilot control inputs and aircraft reactions with means and variations about the means comparable to the natural, statistical scatter observed in piloted WVE simulation.

time of peak t(x)

peak value x

range around mean valuedefined by standard deviation s[t(x)]

range around mean valuedefined by standard deviation s(x)

(x)t

x

t [sec]

Quantitative RequirementsMeans and standard deviations of first two significant roll axispeaks (magnitude and time of peak) for:

1) Pilot control input2) A/C response

Peaks contribute directly to severity model results

Pilot Model Requirements

25 30 35 40 45 50 55 60 65-2

0

2

SS

RO

[-]

25 30 35 40 45 50 55 60 65-50

0

50

Φ [

°]

25 30 35 40 45 50 55 60 65-50

0

50

p [°

/s]

25 30 35 40 45 50 55 60 65-2

0

2

4x 106

Δ L W

V [

°/s]

time [s]

Peaks contribute directly to severity model results


PilotModel

Criterion

Optimization

PilotPM

OFF

LIN

E

ON

LIN

E

Pilot-in-the-loop Simulator tests

Test evaluation(Time histories &Questionnaires)

Pilot task

Wake vortex

Normal / special procedure

FCOM

Flight Crew Operational Manual

A/C

R

eact

ions

Pilo

tIn

puts

Piloted Model Development

Models of human pilot behaviour (e.g. Crossover Model)

RMSE optimization criteria

Quality assessment via AAM, R, DTW

PMIn

puts

Piloted WVESimulationData Base

e.g.S-WAKECREDOS

Test

/ Va

lidat

ion

(Offl

ine

sim

ulat

ion,

PM

-in-th

e-Lo

op)


Developed by D. McRuer / E. Krendel in 1960ies

Derived from Crossover Law which describes adaptation capabilities of human pilot

Three elements:

Four parameters: KP, TLead, TLag, τe

WVE pilot modelling: generate side-stick roll input (SSRO) from roll angle Φ

Pilot Model Structure

Crossover Pilot ModelCrossover Pilot Model

- Pilot Gain- Lead / Lag Filter- Time Delay

Effects of KP and TLead on Amplitude [1]

Parameters are correlated with respect to their effects on dynamic characteristics of describing function

Parameter correlations may affect numerical optimizations

Correlation of KP and TLead as found in [1]

[1] Source: Airbus

NOTICE!

1jT1jT

Lag

Lead

+⋅+⋅

ωω

Φ SSROPK eje τω ⋅−


-5 0 5 10 15 20-1

0


-5 0 5 10 15 20-10

0

10

20Roll Angle [deg]

-5 0 5 10 15 20-4

-2

0

2x 106 Vortex Induced Rolling Moment [Nm]

Free / Forced WVE Simulation Data

Simulation Characteristics

Free evolution of vortex induced disturbances in time depending on A/C flight path

Vortex disturbances comply exactly with simulated A/C motion

Pilot inputs before encounter affect vortex disturbance via flight path

Recorded data includes pilot reactions for a large number of different encounter scenariosbutEach encounter is “unique”, no exact reproducibility

Variation in pilot inputs may be a result of factors other than behaviour (e.g. WVE scenario)

Characteristics w.r.t. PM Development

Suited for deterministicdeterministic pilot model tuning

Complete simulation of WVE


40 45 50 55 60 65 70-1

0


40 45 50 55 60 65 70-20

0

20Roll Angle [deg]

40 45 50 55 60 65 70-4

-2

0

2x 106 Vortex Induced Rolling Moment [Nm]

Fixed WVE Simulation Data

Simulation Characteristics

Characteristics w.r.t. PM Development

Vortex induced disturbances are realistic but fixed in time

Vortex disturbances do not comply exactly with simulated A/C motion

Pilot inputs before encounter do not affect vortex disturbance via flight path

Pilot reactions for small number of representative encounter scenarios,butMultiple recordings of pilot inputs for identically reproduced encounters

Pilot inputs only affected by probabilistic behaviour

Suited for probabilisticprobabilistic pilot model tuningSuited for pilot model testing / validation

Pre-recorded time series of vortex disturbances


Parameter Optimizations

Deterministic PM“Multi-Case”: combine all encounters during optimization

Probabilistic PM“Single-Case”: optimization for each recorded encounter

PilotInputs

A/CResponse

PMInputs

Encounter 1 Encounter 2 Encounter n

One set of parameters that gives best overall result for all piloted encounters

Encounter 1 Encounter 2 Encounter n

Distributions of pilot model parameters

KP = 2.63 TLead = 1.73

TLag = 0.04τe = 0.66 sec

KP =TLead =TLag =

τe =

Example :

Pilot Model

Criterion

Optimization WVE Data Base


Deterministic PM Results - Offline

-6 -4 -2 0 2 4 6 8 10 12

-1

-0.5

0

0.5

1

SS

RO

[-]

R

mean = 0.91 P

mean = 0 MRE

mean = 0.627 AAM

mean = 0.663 RMSE

mean = 0.21777 PRE

mean = 0.268

-6 -4 -2 0 2 4 6 8 10 12-30

-20

-10

0

10

20

30

Rig

ht O

uter

Aile

ron

[°]

time [sec] (synchronized, t=0 at large(st) induced rolling moment)

Piloted SimulationsCO Pilot Model

-150-100-50050100150

-40

-20

0

20

40

60

80

wd_

zacv

txm

[m]

wd_yacvtxm [m]

Γ = 565-965 m 2/sec ΔΨWV = 10 ° ΔγWV = -3 °

WVE Start: Square WVE End: Dot

-30 -20 -10 0 10 20 30-3

-2

-1

0

1

2

3x 106

Δ LW

V [N

m]


-4 -2 0 2 4 6 8 10 12

-1

-0.5

0

0.5

1

SS

RO

[-]

R

mean = 0.893 P

mean = 0 MRE

mean = 0.671 AAM

mean = 0.62 RMSE

mean = 0.22878 PRE

mean = 0.319

-4 -2 0 2 4 6 8 10 12-30

-20

-10

0

10

20

30

Rig

ht O

uter

Aile

ron

[°]


Piloted SimulationsCO Pilot Model

-150-100-50050100150200

-20

-10

0

10

20

30

40

50

60

wd_

zacv

txm

[m]

wd_yacvtxm [m]

Γ = 465-865 m 2/sec ΔΨWV = 15 ° ΔγWV = -3 °

WVE Start: Square WVE End: Dot

-30 -20 -10 0 10 20 30-3

-2

-1

0

1

2x 106

ΔL W

V [N

m]



40 45 50 55 60 65-1

-0.5

0

0.5

1

SS

RO

[-]

40 45 50 55 60 65

-20

0

20

Rig

ht In

ner A

il. [d

eg]

40 45 50 55 60 65-20

-10

0

10

20

Φ [d

eg]

40 45 50 55 60 65

-20

-10

0

10

20

p [d

eg/s

ec]

40 45 50 55 60 65-4

-2

0

2x 106

Δ LW

V [N

m]

time [sec]

CO

Deterministic PM Results - Online

Pilot-in-the-loop Simulator tests

PMPM

PM-in-the-loop Simulator tests

PM-in-the-Loop Tests

Test pilot model within dynamic loop (e.g. check for instability problems, offline vs. online behaviour)

Compare pilot model results to piloted simulations (only way to compare results for A/C response)

Validation of pilot model (are requirements fulfilled?)

Acceptable regions / limits as derived from statistical analysis of peaks

Respective peaks of PM results*

Fixed Encounter Simulation


Probabilistic PM Optimizations

Considerations during OptimizationParameters correlations affect distribution results

Avoid correlation affects by reducing number of tuners

Gain sufficient to describe scatter in magnitude

Time delay sufficient to describe scatter in phase

Lead / Lag filter fixed (based on MC optimization)-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

SS

RO

[-]

b)

a)

1jT1jT

Lag

Lead

+⋅+⋅

ωω

Φ SSROPK eje τω⋅−

a) b)


10-1 100 101-40

-30

-20

-10

0

10Bode Plot of CO PM

A(ω

) [dB

]

10-1 100 101

-150

-100

-50

0

50

ω [rad/s]

φ(ω

) [°]

FXE Multi-Case OptimizationFXE Single-Case Optimizations

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

KP

Pro

babi

lity

Den

sity

Optimization ResultsGamma Estimation

0 0.5 1 1.50

0.5

1

1.5

2

2.5

3

τe

Pro

babi

lity

Den

sity

Optimization ResultsWeibull Estimation

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80.5

1

1.5

2

2.5

3

3.5

4

τe

KP

Results modelled by continuous Gamma

probability distribution

Results modelled by continuous Weibull

probability distribution

Exemplary KP / τe optimization results (A330 Departure)

Optimization Results

Probabilistic parameters result in scatter of dynamic characteristics of pilot model describing function

Describing function behaviour is scattered around mean behaviour resulting from Multi-Case optimizations

No significant correlation between parameters KPand τe

Description of optimization results with continuous probability distributions (e.g. Gamma, Weibull)

Possible limitation of parameter values at 2.5 and 97.5 percentiles of cumulative distribution function


Simulation Results

40 45 50 55

-1

-0.5

0

0.5

1

1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

5

10

15

20

25

30

35

40

45

50

KP

Num

ber o

f Cas

es

Distribution of KP during Simulation

0.4 0.5 0.6 0.7 0.8 0.90

5

10

15

20

25

30

35

40

45

τe [sec]

Num

ber o

f Cas

es

Distribution of τe during Simulation

Deterministic PM

Probabilistic PMPeaks

Pilot Side-Stick Roll Input [-]

Exemplary A330 encounters during ILS approach

Bank angle inputs taken from PM-in-the-Loop simulations of these fixed encounter cases

Examples show 500 simulation runs with parameters generated via identified probability distributions

Side-Stick roll inputs of probabilistic PM are scattered around inputs of deterministic (mean) model

Comparison of statistical scatter of peaks with standard deviations of piloted tests has been difficult because of side-stick saturation

Evaluation of resulting scatter in A/C response should provides a more realistic quality assessment (PM-in-the-loop desktop simulation needed) 40 45 50 55

-1

-0.5

0

0.5

1

ti [ ]

40 45 50 55

-1

-0.5

0

0.5

1

Offline Test

Pilot Model Parameters during Simulation runs

*


Conclusions

Probabilistic pilot models may contribute to worst case analysis

Methodology to set up simple probabilistic roll axis WVE pilot models has been introduced

Fast-time capable (model parameters are determined before simulation, similar to other probabilistic parts of Monte-Carlo simulation)

Testing / validation of approach within dynamic simulation still needed

Application to pitch axis is difficult because scatter in pilot behaviour much higher

Is this approach feasible / should it be revised (e.g. other probability distributions)?

Is this approach useful for future Monte-Carlo simulations?


Open Questions / Discussion

Are pilot model optimization / validation criteria accepted by authorities?

What is the necessary level of required pilot model quality to be accepted by authorities?

Are additional single-event simulator tests (one unexpected encounter vs. sessions of 30-40 encounters) necessary to see more realistic pilot behaviour?

Thank you for your attention!Thank you for your attention!Questions?Questions?


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The statements made herein do not constitute an offer. They are based on the mentioned assumptions and are expressed in good faith. Where the supporting grounds for these statements are not shown, TU Berlin will be pleased to explain the basis thereof.

Documents

Probabilistic Pilot Model Approach for Wake Vortex ...wakenet.eu/fileadmin/user_upload/SpecificWorkshop... · Bode Plot of CO PM A ... Possible limitation of parameter values at 2.5