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

NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar NARI Nonlinear Aerodynamics Modeling Using Fuzzy Logic Jay Brandon Eugene Morelli

Outline NARI • 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

NARI Flight Dynamics Analysis Process Aerodynamic Analysis (Static & Dynamic) • Wind Tunnel • CFD Open-loop Analysis Sim Model Build Control Law Design Flight Dynamics Analysis • Wind-tunnel < 6 DOF “ Learn to Fly ” • Wind-tunnel free-flight • Simulation • Flight test Adaptive Control Self Modeling June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 3

Aerodynamic Models NARI • Aerodynamic Models – Model of physics so that design and analysis can be undertaken – Based on data • CFD, Wind tunnel, Flight, … – Linear representations • C x = C x0 + C x α α + C x β β + C x δ δ + … • C x | ( α= x) = C x0 | ( α= x) + C x α | ( α= x) Δ α + C x β | ( α= x) Δ β + C x δ | ( α= x) Δδ + … – Nonlinear representations • C x = 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

Phase I Innovations NARI • 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

Fuzzy Logic System ID NARI 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

Fuzzy Logic Approaches NARI • Fuzzy Sets • Fuzzy Internal Functions – Membership functions – Membership functions – Weighting factors – Internal functions – If-then rules – Fuzzy cells • Similar to human • Multiple internal decision-making process functions create the • Predicted outputs tend to “ fuzziness ” be piece-wise continuous • Predicted outputs are • Used extensively in smooth controls applications 7

Fuzzy System ID Process NARI Select Regression [ α , β , δ , ω , M, …] Pre-Processing Variables • Force & Moment • Normalize • Data Consistency • Partition Membership Functions Training • Corrections Testing 1 0.8 0.6 A(x) Compute MF ’ s 0.4 MF 1 MF 2 0.2 0 = + + + 0 0.2 0.4 0.6 0.8 1 i i i i Calculate P p p x ... p x x 0 1 1 k k Internal Function ( ) 2 m ∑ Coefficients for = − ˆ SSE y y All Fuzzy Cells [ ] j j n ∑ = i i i i A ( x ) A ( x )... A ( x ) P j 1 1 1 , j 2 2 , j k k , j = = i 1 y ˆ [ ] j n ∑ i i i > A ( x ) A ( x )... A ( x ) 2 2 R R 1 1 , j 2 2 , j k k , j trn min Required = i 1 > + > + 2 2 2 R R ( Ns 1 ) R ( Ns 2 ) test test test Calculate Evaluate Model Stop Fit : OK? Yes No (with all data) 8

Flight Test Data NARI • Large flight envelope • Well instrumented • α / β on boom • Inertial and controls • TM real-time data support 9

Portable “ Data Systems ” NARI Nx, Ny, Nz • • p, q, r • Course, Speed, Altitude • Attitude Angle Estimates 10

Blending Example NARI Data Flight #10; Maneuver:Left Spin; Card:5.1 100 Prate, dps 0 Blend -100 AHARS -200 2340 2350 2360 2370 2380 2390 2400 60 40 Qrate, dps 20 0 -20 2340 2350 2360 2370 2380 2390 2400 50 Rrate, dps 0 -50 -100 2340 2350 2360 2370 2380 2390 2400 11 Time, sec

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

Fuzzy Decel Video (DF9C4) NARI 13

Parameter Map Examples NARI 15 10 25 20 10 5 15 5 0 10 5 0 -5 δ e δ r 0 β -5 -10 -5 -10 -10 -15 -15 -15 -20 -20 -20 -25 -25 0 10 20 30 0 10 20 30 -10 0 10 20 α α δ a 14

Fuzzy Model Fit NARI 0.2 1.4 Flight 0.15 Model, R 2 = 0.9649 1.2 0.1 1 0.05 0.8 0 C Normal C m 0.6 -0.05 0.4 -0.1 0.2 -0.15 0 -0.2 Flight Model, R 2 = 0.9963 -0.25 -0.2 0 50 100 150 -10 0 10 20 30 40 α , deg Time, sec June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 15

Linearized Model Results NARI • Large envelope DF9C4 0 Cm α , per deg model with one Fuzzy LESQ -0.02 maneuver -0.04 • Includes post- -5 0 5 10 15 20 25 30 35 0 stall stability Cm δ e , per deg -0.01 • Correlates well -0.02 -0.03 with traditional -5 0 5 10 15 20 25 30 35 Cm α -dot , per deg/sec -3 4 x 10 maneuver and analysis for static 2 stability 0 -5 0 5 10 15 20 25 30 35 • Very test- 0 efficient Cm qhat -10 -20 -5 0 5 10 15 20 25 30 35 α , deg June 5-7, 2012 NASA Aeronautics Mission Directorate FY11 Seedling Phase I Technical Seminar 16

Distribution of Results NARI • 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

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

Closing Remarks NARI • 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