[PPT] - Nonlinear Aerodynamics Modeling Using Fuzzy Logic Jay Brandon PowerPoint Presentation

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NARI

Nonlinear Aerodynamics Modeling Using Fuzzy Logic

Jay Brandon Eugene Morelli

NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar

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Outline

Background
Innovations
Fuzzy Logic Technical Approach
Flight Test Data
Result Examples
Next Steps
Closing Remarks

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 2

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NARIFlight Dynamics Analysis Process June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 3

Aerodynamic Analysis (Static & Dynamic)

Wind Tunnel
CFD

Sim Model Build Control Law Design Flight Dynamics Analysis

Wind-tunnel < 6 DOF
Wind-tunnel free-flight
Simulation
Flight test

“Learn to Fly”

Open-loop Analysis

Self Modeling Adaptive Control

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Aerodynamic Models

Aerodynamic Models

– Model of physics so that design and analysis can be undertaken – Based on data

CFD, Wind tunnel, Flight, …

– Linear representations

Cx = Cx0 + Cxαα + Cxββ + Cxδδ + …
Cx|(α=x)= Cx0|(α=x) + Cxα|(α=x) Δα + Cxβ|(α=x) Δβ + Cxδ|(α=x) Δδ + …

– Nonlinear representations

Cx = f(α, β, δ, …)
System Identification

– Determination of structure of model

Parameter Identification

– Determination of parameter values within the structure of the model

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 4

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Phase I Innovations

Nonlinear Aerodynamic System Identification

– No model structure specification required – Large flight envelope with single model

Flight Test Techniques for Rich Data Content

– Multi-axes inputs over large range of flight conditions – Piloted adaptation of similar orthogonal input techniques

Blending of Data from Different Sources

– Ship research data acquisition system – iPad internal sensors for inertial data and GPS

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 5

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Fuzzy Logic System ID

Modeling Challenges Due to Nonlinear Effects

– Separated flow – Large amplitude motion of vehicle or control effectors – Interactions – Unsteady, time-dependent aerodynamics

Fuzzy Modeling Characteristics

– No a-priori or interactive model definition required – Fuzzy cells constructed to identify relationships between input data and output data – Single model across wide range of state variable variations

Relatively New Application for Fuzzy Logic

– Widely used in controls applications

Good for use in areas where there is a lack of quantitative data regarding

input-output relations

– Synergistic with other parameter ID technologies

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 6

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Fuzzy Logic Approaches

Fuzzy Sets

– Membership functions – Weighting factors – If-then rules

Similar to human

decision-making process

Predicted outputs tend to

be piece-wise continuous

Used extensively in

controls applications

Fuzzy Internal Functions

– Membership functions – Internal functions – Fuzzy cells

Multiple internal

functions create the “fuzziness”

Predicted outputs are

smooth

7

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Fuzzy System ID Process

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Pre-Processing

Force & Moment
Data Consistency
Corrections

Select Regression Variables

Normalize
Partition

Training Testing

Compute MF’s

Calculate Internal Function Coefficients for All Fuzzy Cells

Evaluate Fit : OK?

Calculate Model (with all data) Stop [α, β, δ, ω, M, …]

k i k i i i

x p x p p P + + + = ...

1 1

( )

2 1

ˆ

∑

=

− =

m j j j

y y SSE

) 2 ( ) 1 (

2 2 2 2 Required min 2

+ > + > > Ns R Ns R R R R

test test test trn

[ ] [ ]

∑ ∑

= =

=

n i j k i k j i j i n i i j k i k j i j i j

x A x A x A P x A x A x A y

1 , , 2 2 , 1 1 1 , , 2 2 , 1 1

) ( )... ( ) ( ) ( )... ( ) ( ˆ

No Yes Membership Functions

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

x A(x)

MF 1 MF 2

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Large flight envelope
Well instrumented
α/β on boom
Inertial and controls
TM real-time data support

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Flight Test Data

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Portable “Data Systems”

Nx, Ny, Nz
p, q, r
Course, Speed, Altitude
Attitude Angle Estimates

10

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Blending Example

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2340 2350 2360 2370 2380 2390 2400

200
100

100 Data Flight #10; Maneuver:Left Spin; Card:5.1 Prate, dps Blend AHARS 2340 2350 2360 2370 2380 2390 2400

20

20 40 60 Qrate, dps 2340 2350 2360 2370 2380 2390 2400

100
50

50 Rrate, dps Time, sec

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Maneuver Design

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 12

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Fuzzy Decel Video (DF9C4)

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Parameter Map Examples

14

10 20 30

20
15
10
5

5 10 15

α β

10 20 30

25
20
15
10
5

5 10

α δe

10

10 20

25
20
15
10
5

5 10 15 20 25

δa δr

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Fuzzy Model Fit

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 15

50 100 150

0.25
0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 Cm Time, sec Flight Model, R2 = 0.9649

10

10 20 30 40

0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 CNormal

α, deg

Flight Model, R2 = 0.9963

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Linearized Model Results

Large envelope

model with one maneuver

Includes post-

stall stability

Correlates well

with traditional maneuver and analysis for static stability

Very test-

efficient

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 16

5

5 10 15 20 25 30 35

0.04
0.02

Cmα, per deg DF9C4

5

5 10 15 20 25 30 35

0.03
0.02
0.01

Cmδe, per deg

5

5 10 15 20 25 30 35 2 4 x 10

3

Cmα-dot, per deg/sec

5

5 10 15 20 25 30 35

20
10

Cmqhat

α, deg

Fuzzy LESQ

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Distribution of Results

Briefings

– RD – FRSD – SFW (Mike Rogers – results kicked off simulation study) – Navy P-8 team – Test Pilot School Briefing

Publications

– Proposed Paper, SETP conference in September, 2012 – AIAA papers and journals and NASA reports as results are analyzed

Research

– Applications in simulation and in wind tunnel testing

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 17

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NARI Next Steps – Phase II Proposal

Refine fuzzy logic system identification algorithms

– Fuzzy cell filtering – Error bounds calculations

Develop real-time maneuver input guidance algorithms and displays

– Guidance for maneuver inputs – Ensure that required data actually obtained over envelope of interest – Ensure that data is of sufficient richness to result in model of desired fidelity

Improved Airplane Instrumentation
Real-time streaming to cockpit
Engine parameters
Repairs and calibrations
Advance the processes to provide results in near real time

– Verify / validate model inflight and obtain more data if needed – Develop preliminary aerodynamic model of envelope of interest before landing

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 18

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Closing Remarks

Results from Phase I

– Potential for substantial savings in test time and cost – Rapidly available and high fidelity models can improve flight safety

Phase II Project Outcomes

– Assurance of data richness and content – Aero models available onboard airplane near realtime – Model validation inflight – Enabler for self-learning and autonomous health monitoring vehicles

June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 19